Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology New Series / Editor in Chief: W. Martienssen
Group VIII: Advanced Materials and Technologies Volume 1
Laser Physics and Applications Subvolume B: Laser Systems Part 1
Editors: G. Herziger, H. Weber, R. Poprawe Authors: J. Beránek, M. Hugenschmidt, U. Keller, G. Marowsky, K. Rohlena, W. Schulz, W. Seelig, P. Simon, U. Sowada, S. Szatmári, J. Uhlenbusch, W. Viöl, R. Wester
ISSN 1619-4802 (Advanced Materials and Technologies) ISBN 978-3-540-26033-2 Springer Berlin Heidelberg New York Library of Congress Cataloging in Publication Data: Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology, New Series. Editor in Chief: W. Martienssen. Group VIII, Volume 1: Laser Physics and Applications. Subvolume B: Laser Systems. Part 1. Edited by G. Herziger, H. Weber, R. Poprawe. Springer-Verlag, Berlin, Heidelberg, New York 2007. Includes bibliographies. 1. Physics - Tables. 2. Chemistry - Tables. 3. Engineering - Tables. I. Börnstein, Richard (1852-1913). II. Landolt, Hans (1831-1910). QC 61.23 502'.12 62-53136 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution act under German Copyright Law. Springer is a part of Springer Science+Business Media. springeronline.com © Springer-Verlag Berlin Heidelberg 2007 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Product Liability: The data and other information in this handbook have been carefully extracted and evaluated by experts from the original literature. Furthermore, they have been checked for correctness by authors and the editorial staff before printing. Nevertheless, the publisher can give no guarantee for the correctness of the data and information provided. In any individual case of application, the respective user must check the correctness by consulting other relevant sources of information. Cover layout: Erich Kirchner, Heidelberg Typesetting: Authors and Redaktion Landolt-Börnstein, Darmstadt Printing and Binding: AZ Druck, Kempten (Allgäu) SPIN: 1087 7750
63/3020 - 5 4 3 2 1 0 – Printed on acid-free paper
Editors Herziger, Gerd Rheinisch-Westf¨alische Technische Hochschule, Aachen, Germany Weber, Horst Technische Universit¨at Berlin, Optisches Institut, Berlin, Germany Poprawe, Reinhart Fraunhofer-Institut f¨ ur Lasertechnik (ILT), Aachen, Germany
Authors Ber´ anek, Jaroslav Academy of Sciences of the Czech Republic, Institute of Physics, Prague, Czech Republic Hugenschmidt, Manfred German-French Research Institute of Saint-Louis, Saint-Louis Cedex, France / University of Karlsruhe, Faculty of Electrical Engineering and Information Technique, Karlsruhe, Germany Keller, Ursula ETH Zurich, Physics Department, Institute of Quantum Electronics, Z¨ urich, Switzerland Marowsky, Gerd Laser-Laboratorium G¨ ottingen, G¨ ottingen, Germany Rohlena, Karel Academy of Sciences of the Czech Republic, Institute of Physics, Prague, Czech Republic Schulz, Wolfgang Fraunhofer-Institut f¨ ur Lasertechnik (ILT), Aachen, Germany Seelig, Wolfgang Technische Universit¨at Darmstadt, Institut f¨ ur angewandte Physik, Darmstadt, Germany Simon, Peter Laser-Laboratorium G¨ ottingen, G¨ ottingen, Germany Sowada, Ulrich Fachhochschule Kiel, Institut f¨ ur Mechatronik, Kiel, Germany Szatm´ ari, S´ andor University of Szeged, Department of Experimental Physics, Szeged, Hungary Uhlenbusch, J¨ urgen Heinrich-Heine-Universit¨ at D¨ usseldorf, Institut f¨ ur Laser- und Plasmaphysik, D¨ usseldorf, Germany Vi¨ ol, Wolfgang Hochschule f¨ ur angewandte Wissenschaft und Kunst Fachhochschule Hildesheim/Holzminden/ G¨ ottingen, Fakult¨ at Naturwissenschaften und Technik, G¨ ottingen, Germany Wester, Rolf Fraunhofer-Institut f¨ ur Lasertechnik (ILT), Aachen, Germany
VI
Authors
Landolt-B¨ ornstein Editorial Office Gagernstraße 8 D-64283 Darmstadt, Germany fax: +49 (6151) 171760 e-mail:
[email protected] Internet www.landolt-boernstein.com
Preface
The three volumes VIII/1A, B, C document the state of the art of “Laser Physics and Applications”. Scientific trends and related technological aspects are considered by compiling results and conclusions from phenomenology, observation and experiments. Reliable data, physical fundamentals and detailed references are presented. In the recent decades the laser source matured to an universal tool common to scientific research as well as to industrial use. Today the technical goal is the generation of optical power towards shorter wavelengths, shorter pulses, higher efficiency and higher power for applications in science and industry. Tailoring the optical energy in wavelength, space and time is a requirement for the investigation of laser-induced processes, i.e. excitation, non-linear amplification, storage of optical energy, etc. According to the actual trends in laser research and development, Vol. VIII/1 is split into three parts: Vol. VIII/1A with its two subvolumes 1A1 and 1A2 covers laser fundamentals, Vol. VIII/1B with its two subvolumes 1B1 and 1B2 deals with laser systems and Vol. VIII/1C gives an overview on laser applications. In Vol. VIII/1B1 the following topics are treated in detail: Part 1: Survey of laser systems The laser principle is presented as a collection of fundamental phenomena as there are nonlinear regenerative amplification and stimulated emission by the active laser medium, as well as selection of optical modes and feedback by the resonator. The challenge is to reveal the mutual interactions of the coupled phenomena underlying the laser action, and, finally, realizing the technical optimum while approaching the physical limit. Tailoring the laser performance means to balance the fundamental phenomena involved in the laser action and actually the task is to take full advantage of the diode laser as excitation source for the laser crystal. The mechanisms of excitation, amplification and saturation in the crystal depending on spectral and spatial matching of diode pump volume to the volume of the desired laser mode dominate efficiency and beam quality. Part 2: Short and ultrashort pulse generation An updated review of the progress in ultrafast solid-state lasers since 1990 is given when modelocking became a scientific topic again and the era of ultrafast dye lasers has come to its end. The advent of high-average-power diode lasers stimulated the development of femtosecond pulses in the near infrared by reaching a band width large enough to only support one to two optical cycles underneath the pulse envelope. The essential steps in scientific progress ranging from Kerr-Lens Mode-locking (KLM), self-starting passive mode-locking by Semiconductor Saturable Absorber Mirrors (SESAM) to stabilization of the Carrier-Envelope Offset (CEO) in laser oscillators with attosecond accuracy are explained, such that the expert gains a comprehensive reference and the non-expert can get an efficient starting position to enter into this field.
VIII
Preface
Part 3: Gas lasers In seven sections, the physical and engineering aspects of different gas lasers are presented. The first gas laser was realized in 1961 half a year after T.H. Maiman had achieved the solid-state ruby laser. Solid-state crystal and liquid lasers can only be pumped by photons. Excitation by free electrons e.g. in gas discharges, fast cooling by gas dynamical effects or excitation by chemical processes is the domain of gas lasers. The different types of gases, their specific advantages and technical solutions are compiled.
September 2007
The Editors
Contents
Part 1 Survey of laser systems 1.1
Survey of laser systems W. Schulz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.1.2 1.1.2.1 1.1.2.2 1.1.2.3
Principles and experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selection of optical modes or directional selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . Feedback resonator and regenerative amplification . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 4 6 7
1.1.3 1.1.3.1 1.1.3.1.1 1.1.3.1.2 1.1.3.1.3 1.1.3.1.4 1.1.3.2 1.1.3.2.1
Technical implementation, performance and applications . . . . . . . . . . . . . . . . . . . . . Gas laser systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CO2 laser systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Excimer laser systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Argon-ion laser systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Helium-neon laser systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solid-state laser systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diode-pumped solid-state laser systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 9 9 10 10 10 11 12
1.1.4 1.1.4.1 1.1.4.1.1 1.1.4.1.1.1 1.1.4.1.1.2 1.1.4.1.1.3 1.1.4.1.1.4 1.1.4.1.1.5 1.1.4.2 1.1.4.3 1.1.4.4 1.1.4.5
Advanced design and short-pulse solid-state laser systems . . . . . . . . . . . . . . . . . . . . Fundamentals of laser performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resonator design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rod end-pumped design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rod side-pumped design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slab side-pumped design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Innoslab” end-pumped design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Disc end-pumped design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Advances in laser performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resonator design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slitting with pulsed solid-state laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Processing with higher harmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13 14 14 14 14 15 15 15 15 16 17 18
1.1.5 1.1.5.1 1.1.5.2 1.1.5.3 1.1.5.4 1.1.5.5
High-power diode laser (HPDL) systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Packaging technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiplexing the emission of single bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coherent coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Direct applications with low beam intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cutting and welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20 21 22 23 24 24
References for 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
X
Contents
Part 2 Short and ultrashort pulse generation 2.1
Ultrafast solid-state lasers U. Keller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.1.2 2.1.2.1 2.1.2.2
Definition of Q-switching and mode-locking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Q-switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Mode-locking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.1.3 2.1.3.1 2.1.3.1.1 2.1.3.1.2 2.1.3.1.3 2.1.3.1.4 2.1.3.1.5 2.1.3.1.6 2.1.3.2 2.1.3.3 2.1.3.3.1 2.1.3.3.2 2.1.3.3.3
Overview of ultrafast solid-state lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview for different solid-state laser materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solid-state laser materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mode-locked rare-earth-doped solid-state lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mode-locked transition-metal-doped solid-state laser . . . . . . . . . . . . . . . . . . . . . . . . . Q-switched ion-doped solid-state microchip lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ultrafast semiconductor lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ultrafast fiber lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design guidelines of diode-pumped solid-state lasers . . . . . . . . . . . . . . . . . . . . . . . . . Laser cavity designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical picosecond lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical femtosecond lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High-power thin-disk laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39 39 40 66 67 68 69 73 73 76 76 77 78
2.1.4 2.1.4.1 2.1.4.2 2.1.4.2.1 2.1.4.2.2 2.1.4.3 2.1.4.3.1 2.1.4.3.2
79 79 79 82 82 83 83
2.1.4.3.3 2.1.4.3.3.1 2.1.4.3.3.2 2.1.4.3.3.3 2.1.4.3.3.4 2.1.4.3.3.5 2.1.4.3.3.6 2.1.4.3.4 2.1.4.4 2.1.4.4.1 2.1.4.4.2 2.1.4.4.3 2.1.4.4.4 2.1.4.5
Loss modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical modulators: acousto-optic and electro-optic modulators . . . . . . . . . . . . . . . Saturable absorber: self-amplitude modulation (SAM) . . . . . . . . . . . . . . . . . . . . . . . . Slow saturable absorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fast saturable absorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Semiconductor saturable absorbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Semiconductor dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical self-amplitude modulation (SAM) from semiconductor saturable absorbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Semiconductor saturable absorber materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . InGaAs/GaAs/AlGaAs semiconductor material system . . . . . . . . . . . . . . . . . . . . . . . GaInAsP/InP semiconductor material system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GaInNAs semiconductor material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AlGaAsSb semiconductor material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GaAs wafer for ≈ 1 μm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Semiconductor-doped dielectric films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Historical perspective and SESAM structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effective saturable absorbers using the Kerr effect . . . . . . . . . . . . . . . . . . . . . . . . . . . Transverse and longitudinal Kerr effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear coupled cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kerr lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear polarization rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear mirror based on second-harmonic generation . . . . . . . . . . . . . . . . . . . . . . .
2.1.5 2.1.5.1 2.1.5.2 2.1.5.2.1 2.1.5.2.2
Pulse propagation in dispersive media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dispersive pulse broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dispersion compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gires–Tournois interferometer (GTI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grating pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92 92 94 96 96
85 86 86 86 87 87 87 87 88 90 90 90 91 92 92
Contents
XI
2.1.5.2.3 2.1.5.2.4
Prism pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Chirped mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.1.6 2.1.6.1 2.1.6.2 2.1.6.2.1 2.1.6.2.2 2.1.6.2.3 2.1.6.2.4 2.1.6.2.5 2.1.6.3 2.1.6.4
2.1.6.7 2.1.6.8 2.1.6.9
Mode-locking techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Haus’s master equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Loss modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Fast saturable absorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Group velocity dispersion (GVD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Self-phase modulation (SPM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Active mode-locking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Passive mode-locking with a slow saturable absorber and dynamic gain saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Passive mode-locking with a fast saturable absorber . . . . . . . . . . . . . . . . . . . . . . . . . 112 Passive mode-locking with a slow saturable absorber without gain saturation and soliton formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Soliton mode-locking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Design guidelines to prevent Q-switching instabilities . . . . . . . . . . . . . . . . . . . . . . . . 119 External pulse compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
2.1.7 2.1.7.1 2.1.7.2 2.1.7.3 2.1.7.3.1 2.1.7.3.2 2.1.7.3.3
Pulse characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Electronic techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Optical autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 New techniques: FROG, FROG-CRAB, SPIDER, . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 FROG, SHG-FROG, FROG-CRAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 SPIDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Comparison between FROG and SPIDER techniques . . . . . . . . . . . . . . . . . . . . . . . . 125
2.1.8
Carrier envelope offset (CEO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
2.1.9
Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
2.1.10
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
2.1.6.5 2.1.6.6
References for 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Part 3 Gas lasers 3.1
Gas laser systems R. Wester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
3.1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
3.1.2 3.1.2.1 3.1.2.1.1 3.1.2.1.2 3.1.2.1.3
Threshold pump power density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Line Broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Natural line broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Doppler broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Pressure broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
3.1.3 3.1.3.1 3.1.3.2 3.1.3.3 3.1.3.4
Excitation mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 Gas discharge excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 Electron-beam excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Gas-dynamic excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Chemical excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
3.1.4 3.1.4.1
Gas discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Elementary processes in gas discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
XII 3.1.4.2 3.1.4.2.1 3.1.4.2.2 3.1.4.2.3 3.1.4.2.4 3.1.4.2.5 3.1.4.2.6 3.1.4.3 3.1.4.4 3.1.4.5 3.1.4.5.1 3.1.4.6 3.1.4.6.1 3.1.4.6.1.1 3.1.4.6.2 3.1.4.6.3 3.1.4.6.3.1 3.1.4.6.4 3.1.4.6.5
Contents Electron distribution function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Similarity laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Characteristic frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Rate coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Approximate solutions of the Boltzmann equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Charged-particle densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Ambipolar diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 Electromagnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Neutral gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 Discharge instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Thermal instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Discharge types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Glow discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Secondary processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 High-pressure glow discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 High-frequency glow discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Boundary layers in high-frequency discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Microwave discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 Arc discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 References for 3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
3.2
CO2 laser and CO laser ¨ l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 J. Uhlenbusch, W. Vio
3.2.1 3.2.1.1 3.2.1.2 3.2.1.2.1 3.2.1.2.2 3.2.1.2.3 3.2.1.2.4 3.2.1.2.5 3.2.1.3 3.2.1.3.1 3.2.1.3.2
CO2 laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Fundamentals of CO2 laser discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Practical design of cw CO2 lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 Sealed-off lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Lasers with slow axial flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Lasers with fast axial flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Transverse-flow lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 Gas-dynamic lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 Practical design of pulsed CO2 lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 Transversely excited atmospheric-pressure lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 Q-switched low-pressure lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
3.2.2 3.2.2.1 3.2.2.2 3.2.2.2.1 3.2.2.2.2 3.2.2.2.3
CO laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Fundamentals of CO laser process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Practical design of cw CO lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 Sealed-off lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Lasers with axial and transversal flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Pulsed CO lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 References for 3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
3.3
Femtosecond excimer lasers and their applications ´ri, G. Marowsky, P. Simon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 S. Szatma
3.3.1 3.3.1.1 3.3.1.2 3.3.1.3 3.3.1.4
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Advantages and difficulties associated with short-wavelength lasers . . . . . . . . . . . . 215 General features of dual-wavelength laser systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Comparison of high-power solid-state and excimer lasers . . . . . . . . . . . . . . . . . . . . . . 217 Seed pulse generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Contents
XIII
3.3.1.4.1 3.3.1.4.2
General features of hybrid dye/excimer lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Hybrid solid-state/excimer lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
3.3.2
Short-pulse amplification properties of excimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
3.3.3 3.3.3.1 3.3.3.2 3.3.3.2.1 3.3.3.2.2 3.3.3.2.3 3.3.3.2.4 3.3.3.3 3.3.3.3.1 3.3.3.3.2 3.3.3.3.3 3.3.3.4 3.3.3.4.1 3.3.3.4.2 3.3.3.4.3 3.3.3.4.4 3.3.3.4.5 3.3.3.4.6 3.3.3.4.7
Critical issues for a high-power excimer amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Nonlinear effects, attainment of minimum pulse duration (spatially evolving chirped-pulse amplification) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Amplification in media having nonsaturable absorption . . . . . . . . . . . . . . . . . . . . . . . 225 ASE content, nonsaturable absorption, limitations on the cross-section . . . . . . . . . 225 Off-axis amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 Multiple-pass off-axis amplification schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Requirements for the discharge geometries of off-axis amplifiers . . . . . . . . . . . . . . . . 230 Limited energy storage time (interferometric multiplexing) . . . . . . . . . . . . . . . . . . . . 230 Limitations on multiple-pass amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Optical multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Interferometric multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 Focusability of short-wavelength high-intensity lasers . . . . . . . . . . . . . . . . . . . . . . . . . 233 Pulse front distortion, spatially dependent temporal broadening . . . . . . . . . . . . . . . 233 Origin of phase-front distortions in dual-wavelength laser systems . . . . . . . . . . . . . 234 Active spatial filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 Spectral filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Optimization of off-axis amplifiers for minimum phase-front distortion . . . . . . . . . 238 Beam homogenization method for short-pulse excimers . . . . . . . . . . . . . . . . . . . . . . . 238 Focusability measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
3.3.4 3.3.4.1 3.3.4.2
Application of short laser pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 Application of short laser pulses for plasma generation . . . . . . . . . . . . . . . . . . . . . . . 242 Micromachining of materials with subpicosecond UV pulses . . . . . . . . . . . . . . . . . . . 244 References for 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
3.4
Ion lasers and metal vapor lasers W. Seelig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
3.4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
3.4.2
Properties of gas discharge laser media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
3.4.3 3.4.3.1 3.4.3.2 3.4.3.2.1 3.4.3.2.2 3.4.3.2.3 3.4.3.2.4 3.4.3.2.5
Noble gas ion lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Excitation mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Operating characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Neutral gas depletion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Axial gas pumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 Transition regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 Magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Summary of operation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
3.4.4 3.4.4.1 3.4.4.2
Helium metal ion lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Excitation mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Operating characteristic of the continuous He–Cd laser . . . . . . . . . . . . . . . . . . . . . . . 266
3.4.5 3.4.5.1 3.4.5.2
Self-terminating metal vapor lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 Excitation mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 Operating characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 References for 3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
XIV
Contents
3.5
Excimer lasers U. Sowada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
3.5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
3.5.2 3.5.2.1 3.5.2.1.1 3.5.2.1.2 3.5.2.2 3.5.2.3
Wavelengths and stimulated emission cross sections . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Rare-gas halogen excimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Rare-gas monohalides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Polyatomic rare-gas halogen excimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Rare-gas excimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 Halogen excimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
3.5.3
Chemical reactions in the discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
3.5.4 3.5.4.1 3.5.4.2
Beam properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 Pulse energy and pulse duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 Output power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 References for 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
3.6
Gasdynamical lasers, chemical lasers M. Hugenschmidt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
3.6.1
Introduction, historical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
3.6.2 3.6.2.1 3.6.2.1.1 3.6.2.1.2 3.6.2.1.3 3.6.2.1.4 3.6.2.1.5 3.6.2.1.6 3.6.2.1.7 3.6.2.1.8 3.6.2.2 3.6.2.3
Gasdynamic lasers (GDLs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 Conventional combustion-driven GDLs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 Population inversion due to gasdynamic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 GDL fuels and energy requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 Numerical modeling and simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 Population densities and small-signal gain achieved in gasdynamic lasers . . . . . . . 295 Power extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 Simplified calculation of small-signal gain, analytical approximations . . . . . . . . . . . 297 Specific experimental investigations, realization of pulsed laser systems . . . . . . . . . 299 Optical cavity design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Downstream mixing GDLs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 Gasdynamic CO2 laser by detonation of solid explosives . . . . . . . . . . . . . . . . . . . . . . 301
3.6.3 3.6.3.1 3.6.3.2 3.6.3.3
Fast-flow electric discharge lasers (EDL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 Electrically excited fast-flow or gasdynamic CO lasers . . . . . . . . . . . . . . . . . . . . . . . . 301 Electrical discharge excited gasdynamic CO2 lasers . . . . . . . . . . . . . . . . . . . . . . . . . . 304 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
3.6.4 3.6.4.1 3.6.4.2 3.6.4.3 3.6.4.3.1 3.6.4.3.1.1 3.6.4.3.1.2 3.6.4.3.2 3.6.4.3.2.1 3.6.4.3.2.2 3.6.4.3.2.3 3.6.4.3.3 3.6.4.3.3.1 3.6.4.3.3.2 3.6.4.3.4
Chemical lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 Fundamental processes, vibrational, rotational and translational temperatures . . . 306 Specific reactions and operation principles of chemical lasers . . . . . . . . . . . . . . . . . . 307 Discussion and evaluation of chemical laser systems . . . . . . . . . . . . . . . . . . . . . . . . . . 308 Iodine lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 Pulsed systems, photolytically initiated iodine lasers (PIL) . . . . . . . . . . . . . . . . . . . 308 Continuous-wave iodine lasers (COIL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 HCl and HBr lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 Pulsed HCl lasers and HBr laser studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 Continuous-wave laser excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Numerical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 CO lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Pulsed CO lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 Continuous-wave CO lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 HF, DF lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
Contents 3.6.4.3.4.1 3.6.4.3.4.2 3.6.4.3.5 3.6.4.3.5.1 3.6.4.3.5.2 3.6.4.3.6 3.6.4.3.6.1 3.6.5
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Pulsed HF, DF lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 Continuous-wave HF or DF lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 Transfer chemical lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Pulsed transfer chemical (TCL) CO2 lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 Continuous-wave DF–CO2 transfer chemical lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Pulsed NO laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 References for 3.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
3.7
Iodine lasers ´nek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 K. Rohlena, J. Bera
3.7.1
Principles of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
3.7.2
Laser transition cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
3.7.3 3.7.3.1
Iodine photodissociation lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 Pumping kinetics of the iodine photodissociation laser . . . . . . . . . . . . . . . . . . . . . . . 344
3.7.4 3.7.4.1 3.7.4.2 3.7.4.3
Chemical oxygen iodine laser (COIL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Generators of the excited oxygen (SOG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 Pumping kinetics of the chemical oxygen-iodine laser . . . . . . . . . . . . . . . . . . . . . . . . 348 All-gas chemical oxygen-iodine lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
3.7.5
Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 References for 3.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
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1.1 Survey of laser systems W. Schulz
1.1.1 Introduction Based on a fascinating physical principle and the technical development laser systems matured to be a widespread tool common to scientific research as well as industrial use. During the final pre-laser days (1950–1960) the prediction and discovery [95Bro] of laser-related optical and optoelectronic phenomena – such as holography [51Gab, 52Rog, 56Loh], population inversion [83Web], optical information processing [52Eli, 56ONe], Fourier imaging theory [53Mar, 53Hop, 88Web], electron multiplication in semiconductors [53McK, 54McK], light pipes and fiber optics [54Hee], intensity interferometry [54Han], confocal optical microscopy [61Min, 88Min, 97She] – prepared the invention of the laser. The first working laser was indisputably achieved, demonstrated and manufactured by Maiman, using a chromium-doped crystal of ruby as a three-level lasing medium [60Mai]. In the early nineteensixties (1960–1965) almost monthly some new lasing material were added to the actually long list [97Web] and Schawlow noted later that “nearly anything can be made to lase, even jello (jelly in english)” [95Bro]. Finally, laser systems had to be evaluated by their experimental and technical benefits and as a consequence only a few laser systems are singled out and survive until today. Frequently, the early experiments were conducted on a low effect level, the new nonlinear phenomena became observable under carefully prepared experimental conditions only for some narrow parameter window and did not appear in their fully developed state. Suffering from the poor performance of the first laser systems a huge amount of the early knowledge found its scientific and technical implementation much later and a lot of the potentials are not fully exploited until today. Establishing a “vertical structure” between science and technology – merging basic and engineering sciences for a common goal – enables both the introduction of physical principles into improved rugged systems reliably working in the industrial environment as well as the usage of tailored high-performance laser systems to probe deeper into the underlying physics and their technological potentials. The technical challenge is to reveal the mutually coupled additional effects which might become dominant outside such narrow parameter windows and as a consequence can obscure the appearance and observability of the underlying physical principle. Pure technical tasks – such as the thermal management in semiconductor and solid-state laser systems – strongly influence the chances of success for pioneering physical experiments. Until today in diode laser systems [01Bou] heat dissipation, optical damage and brightness limit diode laser power, but the actual diode laser systems are not near the physical limit yet. The fundamental features of such diode laser devices – like threshold current, thermal coupling between single emitters, degradation by thermal migration, etc. – strongly depend on temperature and therefore on the performance of the cooling devices for the diode laser action. As example, investigating new epitaxial structures for improved active media in diode lasers the number of working single emitters from every wafer and consequently the number of well working emitters enabling successful and meaningful experimental evaluations is of importance. Ubiquitous low-power devices found in CD players, laser printers, bar-code readers and optical communication systems span one part of the applications [98Kap]. The main factors driving the
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actual development of high-power laser systems are beam quality and output power – improved simultaneously at high efficiency – as well as improved economical features such as reduction of costs and maintenance. During the past decade considerable progress has been achieved for CO2 gas laser and solid-state laser systems in the multi-kW power range. The maintenance as well as the beam quality have been improved, while the power per volume and the absolute volume of laser systems have been drastically reduced. Early systems emitting 20 kW of CO2 radiation used a volume larger than 6 × 3 × 3 m3 . A few years ago the first 12 kW CO2 -system having a volume of about 2 × 2 × 2 m3 was commercialized and such systems delivering an output power up to 6 kW became really manageable in any lab. Especially with the advent of High-Power Diode Lasers (HPDL) the perspective of high beam quality compact fiber compatible all solidstate lasers with electrical-to-optical efficiency around 0.5 have significant impact on modern laser systems and production technology. In addition to high electrical-to-optical efficiency, compactness (< 1 cm3 /W), maintenance interval (> 104 h) and low system cost (< 102 $/W) introduce new scales for laser systems. In the past few years the first generation of diode-laser-based new laser sources – where the lamps are substituted by laser diodes in rod laser systems – has been introduced into industrial production. Actually first prototypes of the second generation – characterized by advanced resonator design by slab and disc laser systems – of diode-pumped solid-state lasers are ready for use. Beside improvements in efficiency and beam quality these laser sources provide short (ns) and ultrashort (ps and fs) pulses with very high pulse powers, leading to improved process efficiencies and new fields of laser application. Advances in the design of crystal shapes and crystal types as well as their cooling adapted to excitation by diode lasers have enabled the second generation of solid-state lasers which have become very efficient and compact tools for a wider range of laser parameters. Actual development of reliable short-pulse laser systems and efficient generation of higher harmonics enables new applications like marking on the inside of “transparent” materials as well as polishing of metal parts, micro-machining of materials transparent in the infrared region with higher form accuracy and also generation of EUV radiation at 13 nm wavelength for next-generation lithography. Beyond metals and ceramics also materials like diamond and semiconductors as well as very weak materials like silicon and rubber can be processed. Theoretical aspects of actual approaches leading to new laser sources and their applications are presented.
1.1.2 Principles and experiments The most important phenomena involved in the laser principle and their technical implementation will be summarized. The laser principle is a collection of fundamental phenomena as there are nonlinear amplification, selection of optical modes without resonator (gain-guided modes) and with resonator (resonator modes) as well as regenerative amplification. For the technical implementation the challenge is to reveal the mutual interactions of the coupled phenomena underlying the laser action, and, finally, realizing the technical optimum while approaching the physical limit.
1.1.2.1 Nonlinear amplification The laser medium is considered as a collection of N randomly distributed atoms within a volume L3 having the length scale L. Initially, the atoms are excited to the upper energy level. Photons of energy hν and wavelength λ are emitted while the atoms undergo transitions to the lower level. For a small scale L λ the spatial extent of the emitted photons has to be taken into account
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as the second length scale, which is in the order of the wavelength λ. The photons do not escape completely from the small volume L3 during the time interval Δ t = λ/c, which can be considerably larger than L/c. As result, collective light emission takes place from the collection of atoms within the small scale L λ and turns out to be coherent. The resulting collective emission is referred to as superradiance1 . The key for understanding coherent emission is nonlinear amplification which forces all the energy stored in the excited medium to appear in the light field on a time scale Δ t = tA /N much smaller than the time tA taken for spontaneous emission of an excited single atom. The temporal behavior of the photon number Q is quite similar to the first spike (Fig. 1.1.2) well-known from the relaxation oscillation without regenerative excitation. The corresponding scales can be estimated from the rate equations – balancing the number of inverted atoms and the emitted photons – for N0 four-level atoms. The lower energy level of the laser transition remains empty by rapid decay into the ground level. As a consequence the population N of the upper level gives the inversion. If the pump rate – after populating all upper levels of the atoms – is switched off, then the rate equations for the time interval Δ t = λ/c and the volume L3 read: ¯ dN ¯ (1 + Q) ¯ , N ¯ (τ = 0) = N¯0 , = −N dτ ¯ dQ ¯ (1 + Q) ¯ , Q ¯ (τ = 0) = 0 , = N dτ where the generalized Einstein coefficients A, B (tA = A−1 ) are used for scaling the time τ = A t, ¯ = (B/A) Q as well as the inversion N ¯ = (B/A) N . Considering the temporal the photon number Q evolution the inversion and the photon number takes, then for the initial stages τ ≈ 0 the photon ¯ (τ = 0) = 0 and the minimum values for the rates are established, which number is small Q are proportional to the number of inverted atoms. Until the intermediate time Δ τ defined by ¯ (τ = Δ τ ) = N ¯0 /2 and becomes ¯ (τ = Δ τ ) = N ¯0 /2 the photon number is increased up to Q N comparable to the number of inverted atoms: ¯ ¯ dN dQ τ ≈0: =− = −N¯0 , dτ dτ ¯ ¯ 2 ¯ ¯ ¯ N0 N0 dN dQ N0 1+ ≈− τ ≈ Δτ : . (1.1.1) =− =− dτ dτ 2 2 2 The maximum rates and hence the maximum amplification are established and will decay further on since there is no further excitation. The spiking time Δ τ ≈ 2/N¯0 is a direct consequence of ¯ (1.1.1) since dQ/dτ ≈ (N¯0 /2)/Δ τ . For a large number of collectively emitting atoms the spike appears on a time scale Δ τ ≈ 2/N¯0 1 much shorter than the time needed for spontaneous emission to initiate the transition of a single atom. The number of emitted photons Δ Q = N0 /2 – each carrying the energy hν – collected during the time Δ t ∝ 2/N0 from the volume L3 is directly related to the intensity I = hν (L/Δ t) (Δ Q/L3 ) which turns out to be proportional to Δ Q/Δ t ∝ (N0 /2)2 , the square of the number of emitting atoms. The most interesting technical potential is the generation of intense and coherent radiation without mirrors, for example, in the Extreme UltraViolet (EUV) or X-ray spectral range. The two drawbacks of superradiance from a spherical volume are the microscopically small volume (L λ) and the isotropic emission of radiation which result in small values for the emitted power and the intensity, respectively. 1
See Benedict, M.G., Trifonov, E.D.: Superradiance, Chap. 6.2, in: Landolt-B¨ornstein Vol. VIII/1 “Laser Physics and Applications”, Subvol. A2 “Laser Fundamentals, Part 2”, 2006, pp. 67–81.
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1.1.2.2 Selection of optical modes or directional selectivity The principle of nonlinear amplification can be applied to a macroscopic volume. Introducing a pencil-shaped volume for the excited atoms – having a cross section a2 and a now macroscopic length L = LΩ – the wave field turns out to be concentrated around the long axis. This behavior can be well understood assuming the spike forms a “plane wave” traveling along the axis. Then the atoms – randomly distributed along and around the axis – will collide in phase with the wave front of the developing spike and will interfere constructively with all the previous emissions from other atoms (Fig. 1.1.1). In the direction perpendicular to the axis – this is along the wave front – the spatial distance of the randomly distributed atoms will introduce a random phase difference between each two emissions and the coherent superposition leads to destructive interference. By interference the total emission has got a directional selectivity and is directed dominantly along the axis2 . Incident plane wave front
Destructive interference
Constructive interference
Fig. 1.1.1. Six atom sites are singled out and indicated by dots. The identical atoms are emitting a wave field and emission starts instantaneously when the incident plane wave front passes the atom. The corresponding circular phase fronts characteristic for dipole emission are plotted for a fixed time when the plane wave passed all the atom sites. The path lengths c Δ t of the circular wave fronts from dipole emission and the plane wave front measured from any of the atom sites are equal within the direction of propagation of the plane wave. Constructive interference takes place only within the direction of propagation of the incident plane wave.
This strong effect due to nonlinear amplification and interference generates a directional selectivity FΩ = Δ Ω/(4 π) which can be measured by the solid angle Δ Ω ≈ π θ2 , where θ 1 is the far-field diffraction angle of a laterally bounded light-emitting area. The lateral extent of the diffraction pattern is characterized by θ=c
λ , a
(1.1.2)
where c is a factor of order one depending on the lateral field amplitude pattern (c = 1.22 rectangular, c = 2/π Gaussian), λ is the wavelength and a is the typical lateral length of the field pattern. The product θa/2 is referred to as Beam Parameter Product BP P , where the radius of the beam waist w0 = a/2 is related to the lateral extent a of the diffracting aperture. The ratio BP P/BP P0 ≡ 1/M 2 [00Sie] of the actual beam parameter product BP P = θa/2 and its diffraction-limited value BP P0 = λ/π is a measure of beam quality in laser systems. Emission from such a pencil-shaped area redirects the radiation from the full solid angle Δ Ω = 4 π of the randomly oriented single emitters (dipole emission) into a diffraction-limited cone, which develops on a diffraction length scale given by LΩ = (1/θ)a corresponding to a Fresnel number Nf = a2 /(λLΩ ) = 1. Consequently, collecting the emission of N atoms happens on a larger length scale LΩ λ until the spike evolves and during a prolongated time Δ τΩ = (2/N¯0 ) FΩ−1 . Coherent emission takes place as long as Δ τΩ 1 remains shorter than the time needed for spontaneous emission of the single atom. 2
See Martienssen, W., Paul, H.: Coherence, Chap. 6.1, in: Landolt-B¨ornstein Vol. VIII/1 “Laser Physics and Applications”, Subvol. A2 “Laser Fundamentals, Part 2”, 2006, pp. 49–65. Landolt-B¨ ornstein New Series VIII/1B1
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In quantum mechanics the effect of directional selectivity is referred to as forbidden final states for the system of interacting atoms and photons. Any emitted photon corresponds to an increased population number of an optical mode. Optical modes can be labeled by their wave vector k, where the atomic transition energy Δ E = ω selects the optical modes with given absolute value | k | for the wave vector as final states such that Δ E = c | k |, the photon is in resonance with the atomic transition. Having a spherical spatial volume with excited atoms all the optical modes on the sphere Δ E = c | k | in k-space act as possible final states and the emission is isotropic. For a pencil-shaped volume of excited atoms a small sector ΔΩ 4 π of the sphere in k-space is cut out and the number of final states is reduced. Only the photon states having directions of propagation within this sector are possible final states, whereas the others do not appear in the wave field (forbidden final states). The action of excimer lasers [00Ewi] as systems with very high gain per roundtrip is a technical realization of the physical principle related to directional selectivity FΩ . Excimer laser systems generate pulsed laser radiation at high repetition rates which are profitably used in lithographic processing of electronic chips (writing with mask techniques). Using such a pencil-like shape of the active medium the generation of intense and coherent radiation without mirrors, especially in the Extreme UltraViolet (EUV) or X-ray spectral range, is demonstrated. The simultaneous emission of intense ion beams and the lack of repeatability or stability of the spiking process intrigued scientists during the past decades. The main drawback is related to the restriction introduced by the statistics of the rise time elapsed until the spike of duration Δ τΩ = (2/N¯0 ) FΩ−1 evolves. The rise time just before the dominant spike can differ within the statistics of the first emission of a single atom. Additionally, the corresponding length L < c Δ τΩ restricts the extent of the coherently emitting volume and the rest of atoms not within the length L build up independently emitting segments.
1.1.2.3 Feedback resonator and regenerative amplification The transient behavior of an inverted medium, the effects of the rise time of the first spike and the breakdown of the active medium into independently emitting segments can be avoided by adding two resonator mirrors. Introducing a resonator folding of the wave field and feedback into the length of the active medium takes place. A lot of additional phenomena can take place, for example, supporting the pulse mode operation by Q-switching [62McC] and mode locking [00Hau]. The feedback increases the number of passes or roundtrips the photon makes until it leaves the active medium and the cavity through the partially transmitting mirror. An equilibrium of fluxes ¯ or rates between the external excitation rate P¯ (pump rate) of atoms, the transmission rate β¯ Q ¯ ¯ through the partially reflecting mirror and the transition rate (1+Q) N of the atoms each generating ¯, N ¯Q ¯ – either going into the full solid angle, where the part FΩ N ¯ into the the photon rates FΩ N ¯ ¯Q ¯ into solid angle Δ Ω remains in the laser beam and is counted for Q or is emitted with the rate N the resonator mode directly. As before, using the generalized Einstein coefficients A, B a convenient scaling is introduced: ¯ dN ¯ (1 + Q) ¯ ¯ (τ = 0) = 0 , = P¯ − N , N dτ ¯ dQ ¯ +N ¯Q ¯ − β¯Q ¯, Q ¯ (τ = 0) = 0 . = FΩ N dτ The stationary solution ¯ = (1 + Q) ¯ −1 β¯ P¯ ¯ = 1 (P¯ − 1) ± (P¯ − 1)2 + 4FΩ P¯ , N (1.1.3) Q 2
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N 1
1
Q/10
0
0
Time τ
Inversion N
¯ ), N ¯(τ )} (left) and the temporal evolution of Q, ¯ N ¯ (right) of the Fig. 1.1.2. The phase portrait {Q(τ relaxational oscillation for P¯ = 2, β¯ = 1. The generalized Einstein coefficients A, B are used for scaling the ¯ = (B/A) Q, the inversion N ¯ = (B/A) N time τ = A t, the pump rate P¯ = (B/A2 ) P , the photon number Q ¯ as well as the rate coefficient β = β/A for transmission losses (β = (c/L) T , 0 < T < 1).
reveals the essential difference introduced by the resonator and regenerative amplification. The energy of the system can be stored either in the inversion as a consequence of external excitation (pump rate P¯ ) or as photons captured by the resonator as prescribed by the rate coefficient β¯ for transmission through the mirrors. Depending on the pump rate P¯ and for small values of FΩ 1 there is a sharp phase transition of the second kind – the laser threshold – for the stationary solution (1.1.3) at P¯ = 1 ¯ = FΩ P¯ , N ¯ = (1 + FΩ P¯ )−1 β¯P¯ P¯ 1 : Q ¯ = P¯ − 1 , N ¯ = β¯ P¯ 1 : Q
(amplifier) , (oscillator) .
Below the laser threshold, P¯ < 1, the photon number remains small since FΩ 1 and the energy is stored as the inversion of the atoms, which increases linearly with the pump rate β¯P¯ . For an external photon signal the laser acts as amplifier. Above the threshold the energy is stored in the photon system, which increases linearly with the pump rate P¯ − 1 and the inversion is determined ¯ Above threshold the laser acts as oscillator, which cannot be disturbed by external signals. by β. The laser oscillator emits the laser light highly directional into one single mode and with constant amplitude. As a consequence of the nonlinear coupling between atoms and photons and during the transition from amplifier to oscillator pronounced spiking (Fig. 1.1.2) can appear (β¯ 1) as far as the photons do not escape from the resonator and the medium. In this case the resonator is referred to as high-quality resonator and fast changes of the resonator quality are used to generate short laser pulses, called Q-switching. This phenomenon was first proposed by Hellwarth [61Hel] and demonstrated by McClung and Hellwarth [62McC] in 1962.
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1.1.3 Technical implementation, performance and applications Today the gas laser systems are well developed and the advances in laser system design are related to improvement of reliability and increase of maintenance intervals. In solid-state and semiconductor laser systems the thermal management and coherent coupling of different single emitters, new epitaxial structures with extended gain areas emitting coherently are the key features. The technical tasks in laser design are related to the external excitation (laser pump module) of the laser medium, the active medium itself (gas supply in gas laser systems and cooling), the resonator design and construction as well as the beam-guiding system. Instructive and easy readings [92Hue, 00Pop], overviews [71Len, 63Dit, 86Sie, 98Sve] and data collections about laser lines [97Web] and laser systems [75Tra] are available.
1.1.3.1 Gas laser systems Although most of the gases – in atomic, ionized (ion laser) and molecular state – are suitable for laser action, the most prominent laser systems are the CO2 and excimer laser applied for processing as well as the helium-neon (HeNe) and the argon-ion laser for metrology. Properties of gas lasers are determined by gas mixtures itself, the thermodynamical parameters in the laser gas (temperature, density, pressure and electric field), the gas discharge as excitation process (DC, AC-HF). The main degrees of freedom for technical design are related to the resonator design (linear, folded, rod- or slab-shape), the gas-flow type (axial, transverse (also called radial)) and cooling of the laser gas (diffusion or convection cooling). Specific properties in comparison with liquid, solid-state and semiconductor lasers are: – the relatively small density of the active medium, which results in a large discharge length (low gas pressure 10–104 Pa), – the fast gas exchange for efficient cooling, which allows to realize high-power laser performance, – the high homogeneity of the active medium to achieve highest beam quality at largest power levels. To address the most common gas laser systems (CO2 , excimer, HeNe, argon ion), their specific features and some of the actual achievements are summarized.
1.1.3.1.1 CO2 laser systems In the four-level system the gas mixture CO2 : N2 : He is HF-excited (N2 ) at a gas pressure of 103 – 104 Pa and collisions of second kind transfer the energy to the asymmetric stretching vibration of the laser active CO2 -molecule. Emitting 1–105 W (commercially 7 · 102 –2 · 104 W) of laser power at a wavelength of 9–11 nm with highest efficiency of about η = 0.05–0.30 which can actually be achieved also by highly sophisticated diode-pumped solid-state laser systems. To reach highest power levels also excitation in transversal direction with respect to the gas flow is used. Especially giant pulse systems, called Transversely Excited Atmospheric pressure lasers (CO-TEA), generate 1–103 Joule per pulse of 5 · 10−4 s duration at a repetition rate of 2 · 103 Hz. The technical challenges are “hidden” in the gas supply and maintenance of the laser system. During gas discharge the CO2 -molecule can dissociate into C, O, and CO which is a reactive gas mixture and consequently the laser gas is consumed. Two different kinds of resonator shape and corresponding cooling system are implemented in commercially available CO2 laser systems: tube Landolt-B¨ ornstein New Series VIII/1B1
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1.1.3 Technical implementation, performance and applications
[Ref. p. 27
resonators with axial gas flow systems and external heat exchanger as well as slab resonators with diffusion cooling via the plane electrodes. Diffusion-cooled systems operate in the multi-kW level for approximately 12 months until the gas mixture has to be renewed. The slab resonator is unstable and additional beam forming is performed outside the cavity. Well developed standard CO2 laser systems are working with fast axial gas flow and external cooling using water as coolant. Commercial CO2 laser systems are available with power levels ranging from 700 W up to 12 kW (20 kW) at beam quality M 2 = 1.3 up to 3.8, respectively. The actual achievements in CO2 fast axial flow systems are related to nearly maintenance-free roots blower and turbines (oil-free magnetic bearings, etc.), thermal stability of the mirror mountings, improved surveillance of the laser modules, tele-diagnose systems and easy-to-use interfaces.
1.1.3.1.2 Excimer laser systems Excitation by gas discharge at 105 Pa generates an instable dimer molecule KrF∗ with 9 ns lifetime in the excited state. This mechanism caused the name EXCIted DiMER (excimer) for this kind of active media. The molecule exists only for 10−12 s after emission of a photon at a wavelength of 248 nm and hence the lower energy level of the laser transition remains always empty and high-efficiency laser action is possible. The laser performance singles out the KrF∗ as excimer laser medium which gives high energy per pulse (0.1–75 J) at a wide range of pulse durations (15–500 ns) and with high repetition rates (10–103 Hz). Relatively large values for the efficiency (0.01 < η < 0.1) are achieved. Very high gain per roundtrip is characteristic for excimer lasers such that the properties of the radiation are close to that from a superradiant medium (Sect. 1.1.2.1).
1.1.3.1.3 Argon-ion laser systems In argon-ion lasers the whole argon gas has to be ionized by the gas discharge at a pressure of about 130 Pa prior to inverting the active medium. Emitting relatively large powers of 0.5–20 W cw power (100 W demonstrated) at λ = 454–528 nm (10 transitions) an efficiency of η = 10−3 can be achieved. The ion lasers add a huge amount of laser lines to the available spectrum but additional tasks like handling the plasma system and large electrical currents typically in the range of a few hundred ampere have to be managed.
1.1.3.1.4 Helium-neon laser systems The helium-neon laser system is a typical four-level cw laser system like the CO2 system, where the active medium is a gas mixture of He : Ne (6 : 1) and excitation of He is performed by a DC gas discharge at a gas pressure of 270 Pa. Collisions of the second kind excite the Ne atoms in which the laser transition (λ = 632 nm, 3 transitions) takes place. The light is linear-polarized due to Brewster windows at both ends of the laser tube having no reflection for p-polarized waves at power levels up to P = 0.1 W at low efficiency η = 10−3 . A single mode – axial and lateral – can be selected by reducing the length of the laser tube (≈ 120 mm). Frequency stabilization can be done down to Δ ν/ν < 10−10 by a piezo-electric mirror driven by the amplitude modulation taken from an extra-cavity Zeeman cell [75Tra]. The magnetically shifted laser frequency is absorbed in the Zeeman cell depending on the shift amplitude. Switching the direction of the magnetic field the amplitude of the laser light passing the Zeeman cell is changed and the modulation amplitude is used for control of the mirror.
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 27]
1.1 Survey of laser systems
11
1.1.3.2 Solid-state laser systems The active medium of solid-state lasers is a doped isolator crystal. Ions of the rare earth or transition metals are doped into dielectric crystals. Optical excitation is carried out with broadband noble gases- or halogen lamps (200–1000 nm) or narrow-band diode lasers (806 nm, (GaAl)As). The diode laser emission matches the strong absorption band of the Nd:YAG crystal. The mechanical design is characterized by a water-cooled laser rod, slab or disc, elliptical reflectors (excitation by lamps), diode laser stacks and fiber coupling. Specific properties in comparison to gaseous-, liquidand semiconductor lasers are high power (cw multi-kW range), short pulses (ns–ps) and efficient frequency conversion to higher harmonics. Efficient generation of higher harmonics is crucial for applications like processing of materials transparent in the infrared spectral region. The main advantage of solid-state lasers is the fiber compatibility which allows flexible beam guidance by fiber optics. The technical challenges are matching of the excited volume to the optical mode volume as well as the thermal management to avoid the thermal lensing effect of the heated laser crystal. The resonator design – especially the crystal shape – dominantly influences the thermal load in the crystal. Comparing the maximum temperatures in the rod (1.1.4) and the slab design (1.1.5) clearly reveals the advantages of the slab due to the additional scaling length, the slab thickness d, which enters the expression for the maximum temperature. Radial heat conduction takes place in the rod of radius R and length L: λ d dT + Q = 0 , T = T (r) , r ∈ [0, R] , r dr r dr P T (r = R) = 0 , Q = , 4 π R2 L where the rod is heated homogeneously by the power density Q and the temperature at the rod surface r = R is kept constant by the action of the coolant. P is the total power liberated in the volume 4 π R2 L of the rod. The solution T (r) =
Q 2 R − r2 , 4λ
Tmax,rod =
P 4 π λL
(1.1.4)
for the maximum temperature Tmax,rod does not depend on the radius R of the rod. In the slab volume a d L of length L, the front face a d of width a and slab thickness d has to be compared with the front face 4 π R2 of the rod. Now the surfaces separated by the slab thickness d are kept at the constant temperature of the coolant: d2 T d d λ 2 + Q = 0 , T = T (y) , y ∈ − , , dy 2 2 d P T y=± =0, Q= . 2 Lad The solution Q T (y) = 2λ
2 d − y2 , 2
Tmax,slab =
P d/2 · 4 π λL a
(1.1.5)
shows the dependance of the maximum temperature on the slab thickness d which can be significantly smaller than the width a. Although lamp-pumped solid-state laser systems are on a high level of their technical development actually the diode-pumped rod lasers entered the industrial use in the power range up to 6 kW for precision cutting and welding. “The Laser-Roadmap” shows the advent of disk and slab lasers for cw and pulsed mode operation. New processes enabled by Diode-Pumped Solid-State Laser (DPSSL) systems are Selective Laser Melting (SLM), cleaning and polishing (Fig. 1.1.6). Joining of polymers is a direct application of high-power diode lasers, Landolt-B¨ ornstein New Series VIII/1B1
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1.1.3 Technical implementation, performance and applications
[Ref. p. 27
especially scanning-mode and single-shot simultaneous welding of complete contours. High-power diode lasers are also used for surface treatment, not yet deep-penetration welding. First deeppenetration welds are demonstrated in the lab (Sect. 1.1.5).
1.1.3.2.1 Diode-pumped solid-state laser systems Diode-pumped solid-state laser systems of the first generation commercially available are based on rod-laser operation and have improved beam quality in comparison with lamp-pumped systems (Fig. 1.1.3). They represent a simple, compact and robust tool for industrial manufacturing. Also special applications like “next-generation EUV-lithography” rely on power amplifiers with sidepumped rods. Further improvement with respect to beam quality is possible but limited by thermal lensing. The slab as well as the disc laser are seen to be the most promising concepts for diode-pumped lasers of the second generation, where the resonator design and new dopants as well as host crystals are used to take full advantage of the excitation by diode lasers. Tailoring the optical energy density with respect to the desired spatial features and dynamical processing domain gets a broader sense due to the extended range of accessible parameters for the laser performance and its control. Requirements of micro-machining and demands on form accuracy can be approached by diode-pumped lasers of the second generation.
Innoslab
Disc
Rod
Beam parameter product BPP [mm mrad]
1000
100 Diode laser (1998) 10
C O 2- laser 1
0.1 1
Lamp - pumped Nd:YAG laser 10
100 Average power P [W]
1000
10000
Fig. 1.1.3. High beam quality is achieved by high-power laser systems in the multi-kW range measured by the beam parameter product BP P = BP P0 /M 2 , where BP P0 is the diffraction-limited minimum value BP P0 = λ/π of the beam parameter product realized by the ideal Gaussian mode. For highest beam quality the shape of the laser beam is diffraction-limited, i.e. BP P takes its minimum value BP P0 = λ/π. Open circles indicate diode laser systems and black symbols mark the actual values for diode-pumped solid-state laser systems in slab, disc and rod design.
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 27]
1.1 Survey of laser systems
13
1.1.4 Advanced design and short-pulse solid-state laser systems A variety of tools including high-precision turning [93Wec], electric discharge [98Kru], electron and laser beams are used for micro-machining. Each has a different mechanism for energy coupling, such as mechanical heating of the cut edge as well as Joule heating of the current density (volume source and homogeneous Neumann-type boundary condition) and scattering and absorption of electrons and photons within a few tenths of an ˚ Angstr¨ om (Neumann-type boundary conditions) up to a few centimeters (volume source and homogeneous Neumann-type boundary condition) depending on material and photon energy. Lasers are well established industrial production tools for cutting, welding, soldering, marking and transformation hardening. Two types of lasers – excimer lasers and solid-state lasers – are widely used in industrial production for generating a structure size in the range of 130 nm (for example Pentium 4 lithography) and for laser ablation by melting and vaporization of material with structure sizes of 0.1 mm and form accuracy of 1–10 μm. Excimer lasers with light generation based on gas discharge and operating in the UV wavelength range as well as solid-state lasers based on lamp-pumped crystals and first-generation diode-pumped lasers are competing. For diode-pumped lasers of the first generation the lamp is substituted by diode lasers while the resonator design remains almost unchanged. Today the domain of excimer lasers are applications which need high average output powers (up to several 100 W) and large pulse energies in the UV wavelength regime. Excimer lasers offer large pulse energies (10 mJ to 1 J) at pulse durations around 30 ns and discrete UV wavelengths between 157 and 355 nm. Typical applications are: UV lithography, annealing of LCD displays, eye surgery and surface treatment by mask imaging techniques. Solid-state lasers with a wavelength of 1.06 μm based on Nd:YAG and Nd:vanadate crystals are widely used for marking and micro-structuring processes in industry. With the option of nonlinear frequency conversion to 532 nm, 355 nm and 266 nm laser characteristics and material properties like wavelength-dependent absorption can be matched. Diode-pumped solid-state lasers compared to excimer lasers are more compact and offer better beam quality which enables direct processing and a wider range of wavelengths, pulse durations and pulse frequencies. Different types of solid-state lasers are used, which can be labeled by pulse energy Ep , average power P and pulse duration tp . Conventional lamp-pumped, acousto-optic Qswitched lasers (Ep > 10 mJ, P = 10–200 W, tp = 60 ns to several 100 ns) are widely used low-cost systems for marking applications. Electro-optic Q-switched lasers offer shorter pulse durations and higher pulse powers (Ep < 1 mJ, P = 1–30 W, tp > 5–20 ns) used for structuring and drilling. Higher output powers (up to the kW-level) are gained by amplification of the oscillator pulses. The key properties are beam quality and output power – improved simultaneously at high efficiency – as well as compact design. The combination of both, enhanced capabilities for tailoring the optical energy density with new laser systems and improved processing strategies using the advanced ps-lasers as well as lasers with only a few ns pulse duration [99Kli] leads to further improvement. Actual development (Fig. 1.1.4) enables new applications like marking on the inside of “transparent” materials as well as polishing of metal parts (Fig. 1.1.6), micro-machining of transparent material (Fig. 1.1.7) with higher form accuracy and also generation of EUV radiation at 13 nm wavelength for next-generation lithography. Beyond metals and ceramics also materials like diamond and semiconductors as well as very weak materials like silicon and rubber can be processed. Theoretical aspects of actual approaches leading to new laser sources and their applications are presented.
Landolt-B¨ ornstein New Series VIII/1B1
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1.1.4 Advanced design and short-pulse solid-state laser systems
Industrial laser systems
rod, side−pumped, >10 mJ, 5-50 kHz, >100 ns, M2=10-50
Industrial applications
drilling, structuring, cleaning
10-12
10-9 Pulse duration tp [s]
[Ref. p. 27
10-6
New laser systems slab, end−pumped, 4 mJ, 5 kHz, 5 ns, M2=1.5 MOPA, 76 mJ, 2 kHz, 14 ns, M2=1.5 Prospective applications generation of EUV−radiation, 13 nm lithography marking on the inside, polishing
Fig. 1.1.4. Solid-state laser systems are introduced to industrial applications like drilling, structuring, and cleaning. Advances in tailoring of the optical energy density will enable prospective applications. The most valuable parameters of the achievable laser performance are given (pulse energy Ep [mJ], repetition rate νrep [kHz], pulse duration tp [s], and beam quality M 2 [–]). For highest beam quality M 2 = 1 the shape of the laser beam is diffractionlimited.
1.1.4.1 Fundamentals of laser performance Tailoring the laser performance means to balance the fundamental phenomena involved in the laser action and especially to take full advantage of the diode laser as excitation source for the laser crystal. The mechanisms of excitation, amplification and saturation in the crystal depending on spectral and spatial matching of diode pump volume to the volume of the desired laser mode influence efficiency and beam quality. In conventional side-pumped laser designs for example dominantly thermo-optical effects introduce thermal lensing and birefringence which reduce beam quality and stable laser operation. As a consequence of thermal-induced birefringence the state of polarization is changed and additional optical losses are introduced.
1.1.4.1.1 Resonator design Successful resonator design depends on detailed knowledge about the most important physical phenomena today limiting the laser performance. Actually the disc and the “Innoslab” are the most promising concepts for the resonator design and their potentials are not fully discovered. Suitable matching of diode laser characteristics and resonator design is the challenge of actual development and enables the advanced laser performance of so-called diode-pumped solid-state lasers of the second generation.
1.1.4.1.1.1 Rod end-pumped design The output power is limited by thermomechanical damage of the crystal even for high-strength YAG-material and the beam quality and scalability of output power is limited by thermal lensing.
1.1.4.1.1.2 Rod side-pumped design The beam quality is limited by birefringence, since the thermal lens becomes polarizationdependent. In spite of these limitations actual development of industrial solutions for robust and economical power amplifiers for “next-generation EUV-lithography” is based on rod side-pumped modules.
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 27]
1.1 Survey of laser systems
15
1.1.4.1.1.3 Slab side-pumped design In conventional slabs almost the whole slab volume is excited. The amplifier gain is limited by parasitic modes. The laser emission is not gain-guided and therefore additional, parasitic modes are amplified outside the fundamental mode volume. The output power is limited by thermomechanical damage of the crystal. In particular excitation and heating at the corners and edges of the crystal are critical.
1.1.4.1.1.4 “Innoslab” end-pumped design For the principle setup see Fig. 1.1.5. The scalability of the laser power at high beam quality is limited by the spatial homogeneity of the pump radiation in the scaling direction (Fig. 1.1.5, x-direction). Shaping of the diode laser beam by optical integrators is the challenge.
1.1.4.1.1.5 Disc end-pumped design The thin (100 μm) disc concept [00Ste] relies on multi-pass excitation and high regenerative amplification in order to compensate the small crystal volume. Optical arrangement of multi-pass excitation instead of thermal management becomes crucial for the beam quality. In comparison to the end-pumped slab (“Innoslab”) both heat exchange and reflection of the laser light take place at the mounted surface of the disc. One challenge is to handle both demands – thermo-mechanical robustness for reliable heat exchange and high optical quality – simultaneously.
1.1.4.2 Advances in laser performance New laser sources like diode-pumped solid-state lasers and diode lasers lead to improved beam quality, efficiency and compactness compared to conventional CO2 - and lamp-pumped lasers. In the past four years the first generation of diode-laser-based new laser sources has been introduced into industrial production. Actually first prototypes of the second generation of diode-pumped solid-state lasers are ready for use. Beside improvements in efficiency and beam quality these laser sources provide short (ns) and ultrashort (ps and fs) pulses with very high pulse powers, leading to improved process efficiencies and new fields of laser application. Advances in the design of crystal cooling and excitation by diode lasers enable the secondgeneration solid-state lasers to become very efficient and compact tools for a wider range of pulse parameters. Additionally new types of laser crystals like Yb:YAG [00Ste] or Yb:KGW [00Bru] can be used. The simple two-level electronic structure of the Yb ion avoids undesired loss processes such as upconversion, excited-state absorption, and concentration quenching. Compared with the commonly used Nd:YAG crystal the Yb:KGW crystal has a much larger absorption bandwidth and a 3 or 4 times longer emission lifetime in similar hosts with enhanced storage capacity. Disc lasers and end-pumped slab lasers allow average powers up to the kW regime and beam qualities comparable to a CO2 -laser. While disk lasers have been proven to provide good cw performance, pulse performance is limited by comparable low pulse energy and low gain, leading to 100 ns pulses in Q-switched operation. Modelocked oscillators generating ps pulses at more than 100 W average output power have been demonstrated. Slab lasers provide highest beam quality at kW output level and the ability of short-pulse generation (5 to 10 ns) in Q-switch mode. Compact diode-pumped fs-laser are ready for use with 30 fs pulse duration and 90 MHz repetition rate emitting 135 W of averaged output power at 880± 25 nm wavelength (M 2 < 1.3). Also ps-slab-amplifier on laboratory scale emitting 48 W of averaged Landolt-B¨ ornstein New Series VIII/1B1
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1.1.4 Advanced design and short-pulse solid-state laser systems
[Ref. p. 27
output power with 8 ps pulse duration and 80 to 120 MHz repetition rate are demonstrated. High gain leads to efficient single-pass amplification for example amplification of a 4 W signal at 7 ps pulse duration and 100 MHz repetition rate to about 50 W average power with a single amplifier stage. Most ps-systems are also build up in Master Oscillator Power Amplifier (MOPA) configurations, ps pulses with average output power of several W are generated by modelocked solid-state lasers and amplified by regenerative and/or high-gain single- or multipass amplifiers. These lasers are mostly on a laboratory level. Material processing by means of ultrashort pulses (Ep < 100 mJ, P = 1 mW to 100 W, tp > 10– 150 fs) is actually under investigation. Since fs-lasers are still very expensive and not as robust as industrial ns-lasers there are actually only few fs-systems used for production. Next-generation fs-lasers are direct-diode-pumped in order to reduce system size and costs. First laser sources based on crystals like Cr:LiSAF and Cr:LiSGAF have been demonstrated, amplifier prototypes will be available soon.
1.1.4.3 Resonator design
10
Excited volume
Beam shaping
Contact cooling
Slab crystal
x
Resonator mirror (unstable x / stable y)
Pulse width [ns]
y Diode laser
15 kHz
9 8 7 6
10 kHz
Intensity I [arb.units]
The core issue by scaling the output power at high beam quality is the thermal management to maintain high beam quality simultaneously. An effective design is given by the diode end-pumped slab laser [98Du]. The design is characterized by a slab-shaped crystal having two polished end faces only for passing the pumping beam and the laser beam. The waste heat in the crystal is effectively removed by its two large faces thermally contacted to heat sinks (Fig. 1.1.5, contact cooling). Matching the emission and absorption spectra as well as the spatial volume of pump and laser mode the slab crystal is pumped by a diode-laser stack. The excitation and amplification is gain-guided inside the slab having a line-shaped cross section, which underfills the cross section of the slab. A hybrid resonator – stable in the plane of small gain dimension (high beam quality) and off-axis unstable (high power) in the plane of large gain dimension – is used for getting high efficiency at diffraction-limited beam quality. The resonator has a length of some cm since the time for one round trip in the resonator limits the achievable pulse length and repetition rate. The slab design (Fig. 1.1.5) takes – spatial and spectral – advantage of the diode lasers, in particular the lineshaped diode laser beam is diffraction-limited in the “fast direction” (Fig. 1.1.5, y-direction) where it matches the requirements of gain guiding. Simultaneously, the line-shaped diode laser beam with low beam quality in the “slow direction” (Fig. 1.1.5, x-direction) matches the slab shape. In combination with the cooling design the end-pumped slab laser has a compact size, efficient cooling
0
10 Time t [ns]
20
5 kHz
5 40
50 Diode current [A]
60
Fig. 1.1.5. “Innoslab” concept takes advantage of gain-guided generation of laser radiation and homogeneous excitation by beam shaping of the diode laser is a key feature. With the “Innoslab” concept shortest pulse durations of about 5 ns at 5 kHz repetition rate are demonstrated emitting a nearly diffraction-limited laser beam (M 2 = 1.5) of high quality and an energy of 5 mJ per pulse.
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 27]
1.1 Survey of laser systems
17
in one spatial direction (low thermal lensing), proper overlap of the excited and laser mode volumes (high efficiency and beam quality). Short pulses in Q-switch operation are achieved and the power is expected to be scalable at diffraction-limited beam quality by increasing the extent of the slab the length of the line-shaped diode-laser beam (Fig. 1.1.5, x-direction). Based on the end-pumped slab laser concept an electro-optically Q-switched laser system is developed. The laser delivers an output power as high as 50 W at a repetition rate of 45 kHz. Figure 1.1.5 shows a typical pulse shape. The pulse length is about 5 ns at 5 kHz. The pulse energy reaches 5 mJ at 5 kHz. The pulse peak power is as high as 800 kW, which is of interest for efficient frequency conversion. The beam quality (M 2 = 1.5) is close to the diffraction limit (M 2 = 1.0). The high peak power and high beam quality can be used for engraving on the inside of transparent materials (Fig. 1.1.6). In this case the laser beam is focused into the transparent material. At the focus the extremely high intensity of about 400 GW cm−2 leads to localized absorption and optical breakdown in the volume of the material. The absorbed laser energy generates a microdeformation which scatters the light (Fig. 1.1.6, inlet). By moving the focus with for example of a scanner, three-dimensional pictures can be generated. The applications of such a process are mainly permanent coding of glass products, anti-counterfeiting and quality control. The generation of tools for moulding is done mostly manual and very time-consuming. A new application under development is laser polishing, where preprocessing is done by remelting with cw lasers and for finishing short-pulse lasers are used (Fig. 1.1.6).
Fig. 1.1.6. Engraving on the inside generates a micro-deformation which scatters the light. Laser polishing means remelting with cw lasers and finishing by short-pulse lasers.
1.1.4.4 Slitting with pulsed solid-state laser Slitting of metal foils (< 0.5 mm) with large processing speed up to 2 m/s using CO2 laser systems (laser power < 2 kW, focused beam diameter 2w ≈ 60 μm) is introduced into industry. The performance, especially the achievable cut quality using commercial lamp-pumped Nd:YAG laser systems (laser power < 2 kW) is not sufficient for this application. The minimum value for the achievable beam diameter of lamp-pumped systems is about 120 μm at Rayleigh lengths (≈ 300 μm) suitable for slitting. By experimental evidence increasing the beam diameter quality degradation by melt recast sets in. Conditions comparable to the high-quality CO2 laser performance require a beam parameter product smaller than 10 mm · mmrad, which becomes feasible with the diode-pumped solid-state laser systems (Fig. 1.1.3). This potential for solid-state laser systems is demonstrated using pulsed mode operation of systems with low averaged power (50 W). With such pulsed systems a focus diameter of 60 μm at a Rayleigh length of 300 μm is achieved. The minimum value of the timedependent power (500–2000 W) during each pulse is much larger than the averaged power and Landolt-B¨ ornstein New Series VIII/1B1
18
1.1.4 Advanced design and short-pulse solid-state laser systems
[Ref. p. 27
slitting becomes possible. The differences between CO2 and Nd:YAG laser performance in slitting are due to the different wavelength and the state of polarization. Both properties of the radiation change the degree of absorption. Absorption of the Nd:YAG wavelength at perpendicular incidence is larger, but the statistically linear-polarized Nd:YAG beam (averaged value of linear p- and spolarized parts) is less absorbed than the linear-polarized radiation. As result, using the same laser power and beam parameters – in spite of the less suitable statistical polarization – the Nd:YAG laser beam cuts faster than the linear-polarized CO2 beam.
1.1.4.5 Processing with higher harmonics Generally, laser processing of dielectric materials requires ultraviolet radiation due to the low absorption of the infrared laser wavelength. Nonlinear optical effects like frequency conversion need high beam quality and high pulse peak power to be efficient. Currently laser sources for precision ceramic processing are Q-switch Diode-Pumped Solid-State Lasers (DPSSL) with extra-cavity frequency doubling and tripling [98Koc]. The beam profile can be approximated as a Gaussian mode which results in a near-diffraction-limited beam quality (M 2 ≤ 1.5). Beam quality and stability of modern laser sources is prerequisite for applications. The pulse repetition rate is typically in the range of 1 to 5 kHz and will be increased by actual laser developments. With different beam guiding and shaping devices the focus diameter can be varied between 3 and 20 μm. Illuminating a nonlinear crystal (LBO) with the “Innoslab” (Fig. 1.1.5) a second harmonic conversion efficiency of 65 % is achieved. The pulse length at the doubled frequency remains below 6 ns at a repetition rate as high as 15 kHz. There is a pronounced dependence of absorption on wavelength in the interesting spectral range from 200 to 1200 nm for different ceramic materials (Fig. 1.1.7). The values for the absorption are calculated from the measured reflection and transmission at low intensities with a white-light lamp. At low-intensity illumination the optical properties of the bulk material at low temperatures are detected. The temperature dependence of the optical properties as well as phase transitions and decomposition are not encountered, so that the results cannot give an exact value for the energy deposition during laser processing but they figure out the general course. For example, also materials transparent at low intensities like sapphire can be machined at high intensities or with a rough surface. The absorption increases rapidly in the UV-range for
6
Hard metal (WC) 60
ZrO2 (Tz3Y)
30
ZrO2 (Tz8Y) Al2O3 (96%)
Al2O3 (99%) Sapphire
0 400
800 Wavelength λ [nm]
1200
Ra,x
500 μm
Si3N4
5 Roughness R [μm]
Absorption α [%]
90
Ra,y
4 3
Rz,x
2
Rz,y
1 40
50
70 60 Overlap dx, dy [%]
80
90
Fig. 1.1.7. The absorption of ceramics depends on wavelength. With the option of efficient nonlinear frequency conversion to 532 nm, 355 nm and 266 nm laser characteristics and material properties like wavelength-dependent absorption can be matched. Surface roughness of WC after laser micro-structuring (λ = 355 nm, fp = 5 kHz, Ep = 0.26 mJ). Surface of WC-embossing tool (λ = 355 nm, fp = 5 kHz, Ep = 0.3 mJ, inlet).
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 27]
1.1 Survey of laser systems
19
Al2 O3 and ZrO2 . For Si3 N4 and hard metals like WolframCarbide (WC), tungsten carbide, there is no significant change over the whole spectrum, sapphire is nearly transparent as well. Based on the absorption characteristics excimer lasers and frequency-tripled Nd:YAG lasers are used yielding low optical absorption lengths and high ablation efficiency. Short-pulse lasers, especially frequency-tripled, diode-pumped Nd:YAG lasers with a high beam quality, offer the possibility to ablate these materials with high quality. With a spot size of about 10 μm, high fluence (> 100 J cm−2 ) can be achieved, so that the materials are vaporized with a small amount of molten material. This technique is applicable for drilling small holes with diameters ≥ 5 μm (aspect ratio up to 60) and cutting of thin ceramic substrates (thickness < 0.5 mm). The edges are rectangular and the surface roughness can be reduced to Ra ≤ 0.1 μm. Low ablation rates (0.05 μg per pulse) are in favor of controlled micro-machining and high precision. As known from ablation or removal using excimer laser radiation, the achieved removal depth per pulse is maximum at a material-specific energy density and decreases for higher values. The best quality is achieved at lowered intensity to avoid thermomechanical damage of the surrounding material. Furthermore, the thickness of the recast layer can be reduced down to < 5 μm depending on energy per pulse and pulse length. High quality of the ablation process results for example in Si3 N4 and diamond. The parameter ranges to produce cut edges in Si3 N4 (λ = 355 nm, fp = 5 kHz, Ep = 0.34 mJ) and in polycrystalline diamond (λ = 355 nm, fp = 5 kHz, Ep = 0.34 mJ) are reachable. It is possible that due to the thermal shock behavior of ceramics a small layer of damaged material could exist under the recast layer. Investigations with shorter pulse length show no significant advantage [92Toe]. At higher energy densities also laser pulses in the fs-range can cause a material damage. The machining quality is dependent on the maximum pressure of the vaporized material. The pulse length dominantly influences the amount of molten material. To produce three-dimensional microstructures with direct writing the laser beam moves – in most cases scans – along the workpiece. To get a three-dimensional microstructure the geometry is sliced into several layers comparable to a milling process. Precise microstructures are produced at an overlap of 30–50 % and out of this range the roughness increases steeply [97Hel]. Furthermore the energy density influences the depth of a single layer and the roughness. The surface roughness increases at higher aspect ratios of a single pulse mould (removal depth of a single laser pulse in comparison to the effective working diameter). A periodic wavy surface is the result, where the period of these waves is not a function of the grid of the laser pulses. As example, the roughness of WC surface processed at a spatial distance between two laser pulses of 10 μm, then period of the waves is around 40 μm. An improved surface roughness can be achieved with flat removed areas, that means a low aspect ratio of the single pulse mould. Especially the pyramid made of WC as part of an embossing tool has a very good surface roughness, which is in the range of erosion technique (Fig. 1.1.7). The height of the single ablation steps is around 1 μm . Due to the low energy densities damage caused by removed grains could not be detected. The debris is very low and the removed material has only a very weak adhesion to the basic material, so that the structures can be cleaned in an ultrasonic bath. Compared to the combined mask and direct writing process with an excimer laser, the direct writing process with a Q-switch Nd:YAG laser offers a higher flexibility concerning the possible shapes, because curved lines can be generated by the CAD/CAD-system. The main restrictions are caused by the accuracy of the moving system. With this technique three-dimensional structures can be produced. The final structures can be used as tools for the production of embossed metal micro-parts.
Landolt-B¨ ornstein New Series VIII/1B1
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1.1.5 High-power diode laser (HPDL) systems
[Ref. p. 27
1.1.5 High-power diode laser (HPDL) systems To increase the applicability of High-Power Diode Laser (HPDL) systems requires high-precision manufacturing of the laser system, packaging and cooling of the laser bars and subsequent beam forming, namely incoherent superposition by multiplexing as well as coherent coupling. In order to specify the actual abilities and future needs in power and quality of HPDL beams the basic mechanisms for radiation superposition of single bars have to be identified, investigated and optimized. The optical output power and the beam quality of diode lasers are limited by four main mechanisms: The Catastrophic Optical Damage (COD) of the output facet limits the maximum value for the intra-cavity intensity, the possible heat exchange with the environment limits the power density, while self-absorption within the device limits the total length of the active semiconductor medium, and the degradation of the beam quality by electro-optical filamentation limits the acceptable electric current for excitation. These phenomena inherent in laser diodes result in the demand for multiple combination of single diode lasers to one HPDL system. The heat exchange is well implemented by copper micro-channel heat sinks, having nice electrical and thermal material properties. The coolant is fed through 5–10 copper layers of 0.3–0.5 μm thickness, which are structured by laser fusion cutting and joined by diffusion welding. The coolant flow rate of about 500 ml min−1 evolves at a pressure drop of 0.6 bar and a fairly high cooling performance (< 0.29 W K−1 ) is established. In spite of the reachable output power demonstrated up to the kW range (Fig. 1.1.3) the beam quality suffers from the superposition of incoherently emitting single laser beams. Incoherent superposition of N single laser beams leads to a linear increase of the intensity I ∼ N only, and simultaneously the beam parameter product BP P/BP P0 = M 2 goes down: BP P ∼ 1/N . BP P0 = λ/π is the diffraction-limited minimum value of the beam parameter product BP P = wθ (w: beam waist radius, θ: far-field divergence angle). At low power almost all the laser systems approach their diffraction limit, which is BP P0 = 0.3 mm mrad for Nd:YAG lasers and slightly smaller values are achieved for GaAs diode lasers at 780–900 nm wavelength (Fig. 1.1.8). The square-root dependence of the BP P with respect to the laser power results from stacking, collimation and geometric-optical folding of the light emission from the diode laser bars. Stacking is a vertical configuration of diode laser bars, where each beam is collimated separately in the fast axis by a cylindrical micro-lens [97Stu]. For fiber coupling beam shaping, lateral alignment can be applied in order to match the highly asymmetric beam to the circular cross section of the fiber. Applying a micro-step mirror having N steps the rectangular beam of the laser bar is subdivided into N parts and folded. The emission patterns of the single emitters are sufficiently separated for tolerable diffraction losses (Fig. 1.1.9, bottom right). Finally the spatial extent w of the laser beam is changed (index r) differently with respect to the slow axis wslow,r and fast axis wfast,r such that the new values for the radii wslow,r = wslow /N and wfast,r = wfast N decrease and increase, respectively. The resulting cross section of the reflected beam becomes equally sized in the fast and slow direction if the number of steps is chosen according to the relation w
θ M2 θfast slow 2 = slow = Mfast N = (wfast N ) . N BP P0 N BP P0 slow
2 2 /Mfast ≈ 1700 are quite different the required number N ≈ 40 of Although the beam qualities Mslow steps of the mirror remains reasonably low and feasible for practical system solutions [97Du]. Up to 100 W cw output power coupled to 150 μm fiber diameter are realized and 500 W cw output power coupled into a 200 μm fiber at BP P = 20 mm mrad−1 seems technically reasonable, which would enable fusion cutting and advanced welding operation (Fig. 1.1.8). In principle, this technique can be scaled to higher output power by bundling several fibers, however, actually in the kW-range it is more cost-efficient to set up diode laser systems employing multiplexing and stacking techniques.
Landolt-B¨ ornstein New Series VIII/1B1
1.1 Survey of laser systems
Plastic welding
10 2 Soldering
101
100
HPDL 4 F= 1.5 F=
Remelting
Brazing
Welding metal foils
F
F=
10 3
=4
Metal sheet welding (27.7%)
1.5
Metal sheet cutting (44.8%)
10
Marking (13.5%)
10 2 Laser power P [W ]
10 3
267 W @ 332 A
0.5
10 4
1
300 250
0.4
10 2
10-1 10 1
21
200 0.3 150 0.2
Power [W]
Transformation hardening
Efficiency
103
Beam parameter product BPP [mm mrad] F = 1.5 (NA 0.12)
Beam parameter product BPP [mm mrad] F = 4 (NA 0.12)
Ref. p. 27]
100 0.1
50
0
0 0
100 200 Diode current [A]
300
Fig. 1.1.8. Beam performance of HPDL in terms of laser power and beam parameter product is related to the required process intensity depending on application. The leading percentage (86 %, 2001) of the present West-European laser market for industrial applications in materials processing is indicated. The laser performance for two different F -numbers (F = 4 – solid line, F = 1.5 – dashed line) is given. A reasonable F -number (F = 1.5) allows for welding applications with commercial HPDLs. Commercial bars at 40 W, laboratory bars at 267 W.
The characteristic values – beam parameter product BP P and power P – of the laser can be related to the intensity range specified by the different processes (Fig. 1.1.8). The total power P = cIw2 depends quadratically on the beam radius w, where c is a shape factor of the lateral intensity distribution (c = π/2 : Gaussian, c = π : top-hat) and I is the maximum value of the spatial intensity distribution. Fixed focusing conditions (F = const., θ = const.) lead to the squareroot dependence BP P ∼ P 1/2 , indicated as straight lines in Fig. 1.1.8, since the beam radius w depends linearly on the BP P = wθ. In particular, considering the focused beam and inserting the far-field divergence θF = 1/(2F ) yields the relation P = cI(2F · BP P )2 between the laser power and the beam parameter product BP P . Consequently, the characteristic values of the laser performance {BP P, P } can be related to the intensity range specified by the different processes. These relations are given in Fig. 1.1.8 for two different F -numbers (F = 4 – solid line, F = 1.5 – dashed line). Using a small F -number (F = 1.5) commercial HPDL systems already allow for welding applications. Promising increase of the cw output power of laser bars from 80 W in 1994 to actually 267 W in 1999 was possible by combining and adapting [98Bra] the skills in epitaxial manufacturing [98Mik], packaging and multiplexing of the bars.
1.1.5.1 Packaging technology To achieve high power and quality for fiber coupling of HPDLs today means to collimate the beam by micro-lens arrays, geometric-optical folding, e.g. by micro-step mirrors, to collect the radiation of the single emitters of one laser bar and stacking several bars. The quality of the collected light emission strongly depends on the skills [99Jan] to package the laser bar (front facet dimensions 100 μm × 10 mm, overhang 10 μm, Fig. 1.1.9), the heat sink (p-contact) and the top cover (n-contact). The overhang of about 10 μm is introduced to match Landolt-B¨ ornstein New Series VIII/1B1
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1.1.5 High-power diode laser (HPDL) systems
[Ref. p. 27
Fig. 1.1.9. Packaging and characterization of laser bars. Spatial scales of the front facet 100 μm × 10 mm (front view) and the overhang 10 μm (side view) of the laser bar differ by several orders of magnitude. The required accuracy is prescribed to be smaller than the collimated beam spot dimension 1 μm of one single emitter (smile).
the competing constraints to maintain efficient cooling performance while wetting of the front facet by the solder has to be avoided. A detrimental increase of the folded beam spot sets in with spatial deviations (“smile”, Fig. 1.1.9, bottom right) of the front facet from a straight line. The challenge is to maintain a spatial accuracy below the inherent collimated spot dimension (< 1 μm), i.e. to position and solder the laser bar with minimized strain, while the solder material (In/InSn), the heat sink (Cu) and the bar (GaAs) with their different coefficients of thermal expansion are strained during resolidification cooling by 200 K. Combining ultra-large-working-distance microscopes together with DC-positioning motors and image processing allows for the required repetition accuracy in the sub-micrometer range.
1.1.5.2 Multiplexing the emission of single bars High-efficiency superposition is demonstrated [99Gil] to combine eight laser bars into one emission profile maintaining the beam quality of one single bar. The actually achieved rise of the band-edge of oxide-coated interference filters allows to select four different wavelengths in the range from 780 to 900 nm at a degree of transmission and reflection of about 0.95 and 0.02, respectively. Two directions of polarization with four wavelength emission each are combined by zero-order phase shift (Fig. 1.1.10). The simultaneous phase shift of the four different wavelengths requires 120 nm band width whereas practically about 200 nm are feasible. At the maximum, incoherent superposition of N HPDLs will result in the N -fold intensity of the single application.
Fig. 1.1.10. 8 bars emitting as 1 bar at an multiplexing efficiency of about 90 %. Superposition of 4 different wavelengths in the range between 730 nm and 970 nm are demonstrated (BE: BandEdge interference filter, AR: Anti-Reflection coating, HR: High-Reflective coating).
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 27]
1.1 Survey of laser systems
23
1.1.5.3 Coherent coupling In the case of coherent coupling of N emitters in one bar, theoretically the N 2 -fold intensity can be achieved [94San] at the diffraction-limited beam quality BP P = BP P0 of the single emitter. Methods like Distributed FeedBack (DFB) structures [98Lan] inclined by an angle α with respect to the direction of emission, for example the so-called α-DFB laser, and general concepts such as optical periodicity in Talbot-cavities [98Apo] are investigated to achieve coupling between the single emitters of the diode laser bar by the exchange of radiation. Although, these more or less straightforward concepts seem to be technically not promising, there are possible arrangements under investigation like the so-called Z-laser, where the ideas behind structured broad-area emitters and phase coupling of single emitters might be successfully combined. In general, coupling is achieved by the exchange of radiation between the spatially separated single emitters of the diode laser bar. The coupling scheme has to be designed to achieve phasematched coupling strong enough to overcome the single laser’s noise and thermal drift effects. In most experimental investigations the external feedback has been realized by the Talbot effect [94Leg]. Although some experiments demonstrated a coherent coupling [98Apo], the results are not yet satisfying: In the high-power region the coupling strength is too low and the inhomogeneity of the single emitter properties is too large, leading to pronounced phase distortions in the coupled state, and therefore to a low beam quality. Also the output power of these setups is limited, due to the restriction to low array fill factor, which is defined by the ratio of active-emitting and dark space at the front facet. Alternative coupling schemes, based on specially designed spherical resonators, can be used to increase the coupling strength between the single emitters and the achievable output power of the array [99Bou1]. Actually, the achievable coupling strength suffers from a frequency deviation δωn of the individual laser eigenfrequency ωn , which unfortunately is not small but comparable to the frequency spacing Δ ω = ωn+1 − ωn ≈ δωn between two adjacent modes. Consequently, the drawbacks in efficiency so far exceed the advantages, so that this technology is not feasible yet. Since the frequency deviation of spatially separated single emitters seems to hinder coherent coupling it is evident to try broad-area emitters and to suppress the free-running higher-order lateral modes in order to decrease the far-field divergence. Consequently, a Z-shaped [99Bou2] lateral structure (Fig. 1.1.11) of the index of refraction is under investigation. The spatial profile (reflecting barrier) for the index of refraction can be chosen such that nearly total reflection takes up to an angle of incidence of about α = 5◦ with respect to the normal direction of the High-Reflection (HR) coating of the broad-area emitter. Calculation of the optical resonator mode inserting reasonable layout parameters yields large amplifying areas contributing to the emission with nearly plane phase front at the Anti-Reflective AR
HR
A' A Reflecting barrier
Cut A - A'
Fig. 1.1.11. Z-shaped high-power diode laser concept promising high-power and high-quality beam. For reasonable layout parameters α = 5◦ , diode length: 1200 μm, b1 = 60 μm, calculation of the optical resonator mode yields a lateral extent of the emitting area of about 60 μm and a low far-field divergence angle θ = 3◦ corresponding to M 2 = 4.
Landolt-B¨ ornstein New Series VIII/1B1
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1.1.5 High-power diode laser (HPDL) systems
[Ref. p. 27
(AR) output window. Further investigation of the Z-laser concept with respect to efficiency and total power remains exciting.
1.1.5.4 Direct applications with low beam intensity One of the intrinsic HPDL properties is the rectangular beam shape which can be profitably used in welding of large polymer parts. Polymer welding with a single moving HPDL beam was one of the earliest applications. Welding operations can be performed simultaneously when a single scannable beam is replaced by several larger rectangular beams. The rectangular beams are aligned along the whole weld track. For polymer-based windows the length of the weld track is favorable for simultaneous weld processing as there are no moving parts. Beyond reduced handling costs the residual mechanical properties of the weld governed by the thermal cycle can be controlled by the pulse shape and is no longer constrained by the welding speed. With increased pulse duration also a larger lateral extent of the molten zone evolves and experimental experience showed improved adaptive gap-bridging performance. In general, the additional degree of freedom for the processing parameters enables a more flexible process, and, therefore, investigation of new processes should be fruitful. Experimental results on metal working with higher intensities up to 105 W cm−2 were obtained using industrial HPDLs at proper focusing conditions with an output power of 1.3 and 2.5 kW, respectively. While these HPDLs are built on the basis of commercial diode laser bars with 40 W output power each, in the meantime a record cw output power of 267 W (Fig. 1.1.8) per bar has been demonstrated in the laboratory. Already, industrial HPDL systems with an output power of 1.3 and 2.5 kW are at the threshold of being applicable for direct use in cutting and welding. Depending on the focusing optics, even deep-penetration welding can be achieved (Fig. 1.1.8). Promising increase of the cw output power of laser bars from 80 W in 1994 to actually 267 W in 1999 favors further performance enhancements using the aforementioned packaging and multiplexing methods [99Gil].
1.1.5.5 Cutting and welding In particular, the extent of the preheated area in the advance of the melting front is of interest in laser-supported oxygen cutting [93Fra], where the acethylene flame is substituted by a preheating diode laser. As known from literature [94Fra], the main action of the gas flame during the oxyacethylene flame cutting process can be substituted by laser radiation. Cutting performance up to 120 mm sheet thickness was achieved with 2.5 kW CO2 laser power. Oxygen cutting performed in rolling mills makes use of the circumstance that the cutting process can be self-sustained by the heat of the exothermal reaction, only, at elevated temperatures of about 700 ◦ C. Power balance considerations indicate that a reaction of 68 % of the iron is sufficient to supply the total cutting power at normal conditions. In this case the combustion process can proceed only if in the advance of the cutting front, where the oxygen jet hits the metal surface, the ignition temperature necessary for the reaction is maintained. The diameter of this hot spot is larger than the width of the evolving cut kerf. In flame cutting the torch flame just generates a hot spot. The combustion of the iron in the kerf cannot establish the ignition temperature, because locally a higher power than in the kerf is necessary. At normal conditions preheating of the metal surface is the main action of the gas flame. The typical flame power of about 2000 to 3000 W used for flame cutting of 30 mm thick steel plates is of the same order of magnitude as the required laser power used for preheating the cutting front. Having approximately 0.5 m3 h−1 acetylene flow and a flame power of 2–3 kW then Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 27]
1.1 Survey of laser systems
25
Fig. 1.1.12. Laser-supported oxygen cutting (left). Oxygen cutting of mild steel at 10 mm thickness using a commercial 2.5 kW HPDL system together with a Laval-nozzle supplying the oxygen. The laser head is protected by an additional gas jet. High quality of the cut is achieved by laser irradiation for 1 kW laser power at 0.5 m min−1 and 2 kW power at 0.8 m min−1 . Circular-symmetric arrangement of the laser diodes is under investigation (HPDL cutting torch). Deep-penetration welding (right) with commercial high-power diode laser: simulation and experimental demonstration.
the heat transfer of a flame to the workpiece reaches a maximum value of about 0.5 times the flame power [98Rad], namely 1.0–1.5 kW. This value for the absorbed power can be realized by commercial diode laser systems used with 2.5 kW output power and the degree of absorption for the diode laser radiation of about 0.4. However, the usage of CO2 and Nd:YAG lasers is rather expensive compared with a gas flame. With the advent of efficient and high-power diodes the laser beam oxygen cutting process comes into consideration. First experiments using HPDLs demonstrated that the ignition temperature [98Rad] can be maintained at the top of the cut and thus cuts of thickness up to 10 mm were demonstrated. It is straight forward to align the HPDLs to the evolving cut (Fig. 1.1.12). Recently [99Gil], deep-penetration welding up to 6 mm thickness in stainless steel using HPDLs was achieved. The crucial step was to settle the beam parameters necessary for the onset of evaporation at the melt pool surface. For this purpose a reliable, fast and handy software tool giving the solution of the heat-conduction equation was created (Fig. 1.1.12) to estimate suitable beam parameters. The software settles on the Rosenthal-solution taking into account the finite material thickness. The experimentally accessible power distributions can be easily inserted. The halfanalytical solution is complemented by a numerical solution in order to check out the additional effects of phase transitions for selected interesting parameter settings. In heat-conduction welding the penetration depth of a given isotherm is limited by heat diffusion and as a general rule its shape is restricted to a maximum value for the aspect ratio equal to unity (Fig. 1.1.12, circular line). This maximum value is reachable in the limiting case of a point source at rest acting at the material surface. Significant increase of the penetration depth evolves owing to the finite extent of the material thickness. If the thermal energy released by the laser approaches the bottom of the workpiece any isothermal surface starts to increase its penetration depth. Additionally, melt flow induced by Marangoni-type convection [77Ant] slightly changes the appearance. For increased intensity the surface temperature reaches the evaporation point TV and the recoil pressure of the evaporated metal accelerates molten material out of the evaporating zone and the so-called capillary evolves. However, the onset of evaporation can be calculated as solution of the corresponding free-boundary value problem for the movement of the melting front, where an arbitrary spatial distribution for the values of the inhomogeneous Neumann condition, the energy consumption of the melt transition and the finite extent of the material thickness can be easily covered. The wellLandolt-B¨ ornstein New Series VIII/1B1
26
1.1.5 High-power diode laser (HPDL) systems
[Ref. p. 27
known Marangoni-type melt convection due to temperature gradients is regarded as an additional effect, which slightly affects the results of energy balance considerations in the advance of the moving laser beam, but can significantly change the shape of the melt pool in the wake. The properties of heat conduction will remain observable and often dominant while considering the additional effects of melt flow. These findings are revealed looking for global aspects like the onset of melting and evaporation which are closely connected to energetics of the process [00Sch]. The advantage of considering the basic process of heat conduction separately can be realized by investigating more precisely the spatially one-dimensional properties of the solution. The model predicts that the transition from heat-conduction welding to deep-penetration welding takes place for a laser power of 1.5 kW in stainless steel of 2 mm thickness. At a welding speed of about 500 mm min−1 the evaporation temperature TV is reached. Deep penetration is characterized by a cross-sectional width of the welded zone which is small compared to the penetration depth. The recrystallization shows characteristic dendrite formation perpendicular to the weld center line. The maximum value of the laser intensity of about 2 · 105 W cm−2 can lead to the onset of an intense metal vapor jet during welding. Successful entering this new process domain will open up a wide range for cost-effective laser welding applications.
Landolt-B¨ ornstein New Series VIII/1B1
References for 1.1
27
References for 1.1 51Gab
Gabor, D.: Proc. R. Soc. London B 64 (1951) 449.
52Eli 52Rog
Elias, P., Grey, D.S., Robinson, D.Z.: J. Opt. Soc. Am. 43 (1952) 229. Rogers, G.L.: Proc. R. Soc. Edinburgh Sect. A 63 (1952) 193.
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Hopkins, H.H.: Proc. R. Soc. London A 217 (1953) 408. Marechal, A., Croce, P.: C. R. Acad. Sci. Paris 237 (1953) 706. McKay, K.G., McAffee, K.B.: Phys. Rev. 91 (1953) 1079.
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Maiman, T.H.: Nature (London) 187 (1960) 493.
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Hellwarth, R.W., in: Advances in Quantum Electronics, Singer, R.J. (ed.), New York: Columbia University Press, 1961, p. 334. Minsky, M.: US Patent No. 3,013,467 (1961), filed 1957.
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McClung, F.J., Hellwarth, R.W.: J. Appl. Phys. 33 (1962) 828.
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Ditchburn, R.W.: Light, Glasgow: Blackie & Son Ltd., 1963.
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Anthony, T.R., Cline, H.E.: J. Appl. Phys. 48 (1977) 3888.
83Web
Weber, R.L., in: Bertolotti, M. (ed.), Masers and Lasers, Bristol: Hilger, 1983, p. 74.
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92Hue 92Toe
H¨ ugel, H.: Strahlwerkzeug Laser, Stuttgart: B.G. Teubner Verlag, 1992. T¨onshoff, H.K., Mommsen, J.: G¨ ottingen: Proc. Eur. Conf. Laser Treatment of Materials (ECLAT92), 1992.
93Fra
Franke, J., Schulz, W., Herziger, G.: Schweißen & Schneiden 45 (1993) 490 & 45 (1993) E161. Weck, M., Schr¨ oder, H.B.: Proc. 8th ASPE Ann. Meet., Seattle, Washington, USA, 1993, p. 170.
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Franke, J.: Modellierung und Optimierung des Laserstrahlbrennschneidens niedriglegierter St¨ ahle, PhD Thesis RWTH-Aachen, DVS-Berichte 161 (1994) 122.
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94Leg 94San
Leger, J.R., Mowry, G., Chen, D.: Appl. Phys. Lett. 64 (1994) 2397. Sanders, S.: Appl. Phys. Lett. 64 (1994) 1478.
95Bro
Brown, R.W.G., Pike, E.R.: A history of optical and optoelectronic physics in the twentieth century, Brown, L.M., Pais, A., Pippard, B., (eds.), in: Twentieth Century Physics, Vol. III, Bristol, Philadelphia: IOP Publishing, and New York: AIP Press, 1995, p. 1385.
97Du 97Hel 97She
Du, K., Liao, J., Loosen, P.: Opt. Commun. 140 (1997) 53. Hellrung, D., Gillner, A., Poprawe, R.: Proc. SPIE 3097 (1997) 267. Sheppard, C.J.R., Hotton, D.M., Shotton, D.: Confocal Laser Scanning Microscopy, Oxford: BIOS Scientific Publishers, 1997. Sturm, V., Treusch, H.-G., Loosen, P.: Proc. SPIE 3097 (1997) 717. Weber, M.J.: Handbook of Laser Wavelengths, Boca Raton: CRC Press, 1997.
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00Ewi 00Hau
Apollonov, V.V.: IEEE J. Quantum Electron. 28 (1998) 344. Braunstein, J., Mikulla, M., Kiefer, R., Walther, M., Jandeleit, J., Brandenburg, W., Loosen, P., Poprawe, R., Weimann, G.: Proc. Photonics West 98 (1998). Du, K., Wu, L., Xu, J., Giesekus, J., Loosen, P., Poprawe, R.: Opt. Lett. 23 (1998) 370. Kapon, E.: Semiconductor Lasers I: Fundamentals, San Diego: Academic Press, 1998. Koch, R., Schr¨ oder, T., Stamm, U., Zschocke, W., Basting, D.: Proc. Cleo/Europe 98, 1998, paper CWJ5. Kruth, J.-P., T¨ onshoff, H.K., Klocke, F.: Int. Symp. Electromachining ISEM XII 1998, Aachen, Germany, in: Klocke, F., Kruth, J.-P. (eds.), VDI Berichte 1405 (1998) 33. Lang, R.J., Dzurko, K., Hardy, A.A., Demars, S., Schoenfelder, A., Welch, D.F.: IEEE J. Quantum Electron. 34 (1998) 2196. Mikulla, M., Schmit, A., Chazan, P., Wetzel, A., Walther, M., Walther, R., Kiefer, R., Pletschen, W., Braunstein, J., Weimann, G., in: In-Plane Semiconductor Lasers: from Ultraviolet to Mid-Infrared II, Choi, H.K., Zory, P.S. (eds.), Proc. SPIE 3284 (1998) 72. Radaj, D.: W¨ armewirkungen des Schweißens, Berlin: Springer-Verlag, 1998, p. 65. Svelto, O., Hanna, D.C.: Principles of Lasers, New York: Plenum Publishing Corporation, 1998. Boucke, K.: Phasengekoppelte Arrays f¨ ur Hochleistungsdiodenlaser, PhD Thesis RWTH-Aachen, Aachen: Shaker Verlag, 1999. Boucke, K., Du, K., Loosen, P., Poprawe, R.: FhG-Patent Pending, Fraunhofer Institut Lasertechnik Aachen, 1999. Gillner, A., Loosen, P., Petring, D., Wissenbach, K., Poprawe, R.: Proc. ICALEO’99, San Diego, USA, 1999. Jandeleit, J., Wiedmann, N., Ostlender, A., Brandenburg, W., Loosen, P., Poprawe, R.: Proc. ISPA, SPIE 3896 (1999) 65. Klimentov, S.M., Garnov, S.V., Kononenko, T.V., Konov, V.I., Pivovarov, P.A., Dausinger, F.: Appl. Phys. A 69 (1999) 633. Schmidt, G., Hoffmann, H.D., Bonati, G., Wester, R., Loosen, P., Poprawe, R.: Proc. Photonics West 99 (1999). Brunner, F., Sp¨ uhler, G.J., Aus der Au, J., Krainer, L., Morier-Genoud, F., Paschotta, R., Weiss, S., Harder, C., Lagatsky, A.A., Abdolvand, A., Kuleshov, N.V., Keller, U.: Opt. Lett. 25 (2000) 1119. Ewing, J.J.: IEEE J. Selected Topics Quantum Electron. 6 (2000) 1061. Haus, H.A.: IEEE J. Selected Topics Quantum Electron. 6 (2000) 1173.
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01Bou
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Poprawe, R.: Lasertechnik, CD-ROM zur Vorlesung Lasertechnik, Lehrstuhl f¨ ur Lasertechnik der RWTH Aachen, http://www.ilt.fhg.de, 2000. Schulz, W., Poprawe, R.: IEEE J. Selected Topics Quantum Electron. 6 (2000) 696. Siegmann, A.E.: IEEE J. Selected Topics Quantum Electron. 6 (2000) 1389. Stewen, C., Contag, K., Larionov, M., Giesen, A., H¨ ugel, H.: IEEE J. Selected Topics Quantum Electron. 6 (2000) 650. Boucke, K.: Photonics Spectra 35 (2001) 122.
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2.1 Ultrafast solid-state lasers U. Keller
2.1.1 Introduction Since 1990 we have observed a tremendous progress in ultrashort pulse generation using solid-state lasers (Fig. 2.1.1). Until the end of the 1980’s, ultrashort pulse generation was dominated by dye lasers which produced pulses as short as 27 fs with a typical average output power of about 20 mW [85Val]. Shorter pulse durations, down to 6 fs, were only achieved through additional amplification and fiber-grating pulse compression at much lower repetition rates [87For]. The tremendous success of ultrashort dye lasers in the 1970’s and 1980’s diverted the research interest away from solid-state lasers. In 1974 the first sub-picosecond passively mode-locked dye lasers [74Sha, 76Rud, 78Die] and in 1981 the first sub-100-femtosecond Colliding Pulse Mode-locked (CPM) dye lasers [81For] have been demonstrated. The CPM dye laser was the “work horse” all through the 1980’s for ultrafast laser spectroscopy in physics and chemistry. The development of higher average-power diode lasers in the 1980’s stimulated again a strong interest in solid-state lasers. Diode laser pumping provides dramatic improvements in efficiency, lifetime, size and other important laser characteristics. For example, actively mode-locked diodepumped Nd:YAG [89Mak1] and Nd:YLF [89Mak2, 90Kel1, 90Wei, 90Juh] lasers generated 7–12 ps pulse durations for the first time. In comparison, flashlamp-pumped Nd:YAG and Nd:YLF lasers typically produced pulse durations of ≈ 100 ps and ≈ 30 ps, respectively. Before 1990, all attempts to passively mode-lock solid-state lasers with long upper-state lifetimes (i.e. > 100 μs) resulted however in Q-switching instabilities which at best produced stable mode-locked pulses within longer Q-switched macropulses (i.e. Q-switched mode-locking) (Fig. 2.1.2). In Q-switched mode-locking, the mode-locked pico- or femtosecond pulses are inside much longer Q-switched pulse envelopes 10 4
10 3
-15
FWHM pulse width [10 s]
Ti :sapphire laser 5-6 fs with > 100 mW
10 2
Dye laser 27 fs with » 10 mW
10 compressed 1
1960
1970
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1990
2000
Fig. 2.1.1. Development of shortest reported pulse duration over the last three decades. Circles refer to dye-laser technology, triangles refer to Ti:sapphire laser systems. Filled symbols indicate results directly obtained from an oscillator, open symbols indicate results achieved with additional external pulse compression.
34
2.1.1 Introduction cw Q -switching
Power
Power
cw running Single mode
[Ref. p. 134
Time
Time
Self -starting modelocking cw modelocking
Power
Multimode
Power
Q - switched modelocking
Time
Time
Fig. 2.1.2. Different modes of operation of a laser. cw: continuous-wave; single- and multi-mode refers to longitudinal modes.
(typically in the μs-regime) at much lower repetition rates (typically in the kHz-regime). The strong interest in an all-solid-state ultrafast laser technology was the driving force and formed the basis for many new inventions and discoveries. Today, reliable self-starting passive mode-locking for all types of solid-state lasers is obtained with semiconductor saturable absorbers, first demonstrated in 1992 [92Kel2]. Since then, more than a decade later, the performance of compact ultrafast solid-state lasers has been improved by several orders of magnitude in pulse durations, average powers, pulse energies and pulse repetition rates, based on semiconductor saturable absorbers that are integrated into a cavity laser mirror (i.e. generally referred to as SEmiconductor Saturable Absorber Mirrors – SESAMs) [96Kel, 99Kel, 03Kel]. Diode-pumped SESAM-mode-locked solid-state lasers offer very reliable and compact ultrafast lasers with unsurpassed performance [03Pas, 04Kel]. Currently, pulse duration can range from nanosecond to a few femtoseconds depending on the different laser materials and saturable absorber parameters (Table 2.1.1 to Table 2.1.3). The average power has been increased to 60 W and 80 W directly from a mode-locked diode-pumped laser with pulse energies larger than 1 μJ [03Inn, 06Inn] and most recently even more than 10 μJ [07Maa]. The pulse repetition rate has been increased to more than 100 GHz [02Kra2]. The breakthrough of femtosecond solid-state lasers happened with the discovery of the Ti:sapphire laser [86Mou], which was the first laser that was able to support sub-10-femtosecond pulses. The existing passive mode-locking techniques, primarily developed for dye lasers, were inadequate because of the much smaller gain cross-section (i.e. in the 10−19 cm2 regime) of Ti:sapphire compared to dyes (i.e. in the ns and 10−16 cm2 regime). Therefore, passive pulse generation techniques had to be re-evaluated with new laser material properties in mind. Kerr-Lens Mode-locking (KLM) [91Spe] of Ti:sapphire lasers was discovered in 1991 and is still the only successful technique to push the frontier in ultrashort pulse duration into the fewfemtosecond regime with a pulse duration that only contains 1 to 2 optical cycles. For the first time in 1999 the long-lasting world record with pulse-compressed dye lasers resulting in 6-fs pulses in 1987 [87For] was passed by with KLM mode-locked Ti:sapphire lasers without any external pulse compression [99Sut, 99Mor1, 99Mor2, 00Mat]. Novel dispersion compensation methods based on chirped [94Szi] and double-chirped mirrors [97Kae] had to be developed for this result. Today, only slightly shorter pulses close to 5 fs has been obtained [01Ell]. However, the measurement of such pulses has become rather challenging and new complete pulse characterization methods (e.g. FROG [93Kan] and SPIDER [98Iac]) have been developed. KLM however has serious limitations because the mode-locking process is generally not self-starting and critical cavity alignment is required to obtain stable pulse generation. Thus, the laser cavity has to be optimized for best KLM and not necessarily for best efficiency and output power – this sets serious constraints on the cavity design, which becomes even more severe at higher average output powers and more compact monolithic cavities. Thus, passively mode-locked solid-state lasers using intracavity SESAMs have become a very attractive alternative to KLM and are more widely used today (Table 2.1.2). Landolt-B¨ ornstein New Series VIII/1B1
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Shorter pulses are only obtained with external pulse compression. Sub-4-femtosecond pulses have been demonstrated with external pulse compression [03Sch] for the first time using cascaded hollow fiber pulse compression. External pulse compression into the few optical cycle regime [99Ste] is either based on optical parametric amplification [99Shi], compression of cavity-dumped pulses in a silica fiber [97Bal], hollow fiber pulse compression [97Nis] or more recently through filamentation [04Hau1, 05Hau]. Especially the latter two allow for pulse energies of more than 100 μJ with only a few optical cycles which fulfill a central task in the generation of attosecond eXtreme UltraViolet (XUV) pulses [01Dre]. For such applications using intense few-cycle pulses in the near infrared driving extreme nonlinear processes the electric field amplitude rather than the intensity envelope becomes the important factor. Femtosecond pulses in the near infrared reached a bandwidth large enough to only support one to two optical cycles underneath the pulse envelope. Therefore, the position of the electric field underneath the pulse envelope becomes important. This Carrier-Envelope Offset (CEO) [99Tel] can be stabilized in laser oscillators with attosecond accuracy [03Hel]. At the beginning this was a challenging task as it was not obvious how to obtain this because normally only the pulse intensity and not the electric field is detected. Also mode-locking theory fully confirms that the position of the peak electric field underneath the pulse envelope can have very large fluctuations by much more than one optical cycle. The stabilization is done in the frequency domain using the extremely stable and broadband frequency comb generated with femtosecond solid-state lasers [99Tel]. The simplest approach is based on a f -to-2f -interferometer [99Tel] which was first realized with a spectrally broadened Ti:sapphire laser pulse using photonic crystal fibers [00Jon, 00Apo]. The emphasis of this chapter is to give an updated review of the progress in ultrafast solid-state lasers since 1990 when mode-locking became a hot topic again and the era of ultrafast dye lasers has come to its end. The topics mentioned above will be discussed in more details. The goal is to give also to the non-expert an efficient starting position to enter into this field without providing all the detailed derivations. Relevant and useful references for further information are provided and a brief historic perspective is given throughout this chapter. A basic knowledge in lasers is required. The emphasis is on solid-state lasers because they will dominate the field in the future. More extended reviews and books have summarized the dye laser era [88Sha, 90Die]. Here, no emphasis is put on fiber and semiconductor lasers, but some useful references to recent review articles and book chapters will be provided.
2.1.2 Definition of Q-switching and mode-locking 2.1.2.1 Q-switching The history of Q-switching goes back to 1961, when Hellwarth [61Hel] predicted that a laser could emit short pulses if the loss of an optical resonator was rapidly switched from a high to a low value. The experimental proof was produced a year later [62McC, 62Col]. The technique of Q-switching allows the generation of laser pulses of short duration (from the nanosecond to the picosecond range) and high peak power. The principle of the technique is as follows: Suppose a shutter is introduced into the laser cavity. If the shutter is closed, laser action cannot occur and the population inversion can reach a value far in excess of the threshold population that would have occurred if the shutter were not present. If the shutter is now opened suddenly, the laser will have a gain that greatly exceeds the losses, and the stored energy will be released in the form of a short and intense light pulse. Since this technique involves switching the cavity Q-factor from a low to a high value, it is known as Q-switching. Ideally Q-switched lasers operate with only one axial mode because strong intensity noise is observed in a multi-mode Q-switched laser. Landolt-B¨ ornstein New Series VIII/1B1
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2.1.2 Definition of Q-switching and mode-locking
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In passive Q-switching the shutter is replaced by an intracavity saturable absorber. The saturable absorber starts to bleach as the intensity inside the laser continues to grow from noise due to spontaneous emission. Thus the laser intensity continues to increase which in turn results in stronger bleaching of the absorber, and so on. If the saturation intensity is comparatively small, the inversion still left in the laser medium after the absorber is bleached is essentially the same as the initial inversion. Therefore, after bleaching of the saturable absorber the laser will have a gain well in excess of the losses and if the gain cannot saturate fast enough, the intensity will continue to grow and stable Q-switching can occur. A large modulation depth of the saturable absorber then results in a high Q-switched pulse energy. Typically the pulse repetition rate in Q-switched solid-state lasers is in the hertz to few megahertz regime, always much lower than the cavity round-trip frequency. Picosecond pulse durations can be obtained with Q-switched diode-pumped microchip lasers [89Zay, 97Zay] with pulses as short as 115 ps for active Q-switching using electro-optic light modulators [95Zay] and 37 ps for passive Q-switching using SESAMs [99Spu1, 01Spu3]. For LIDAR applications passively Q-switched Er:Yb:glass microchip lasers around 1.5 μm are particularly interesting [98Flu, 01Hae1]. The performance of Q-switched microchip lasers bridge the gap between Q-switching and mode-locking both in terms of pulse duration (nanoseconds to a few tens of picoseconds) and pulse repetition rates (kilohertz to a few tens of megahertz) (Table 2.1.3).
2.1.2.2 Mode-locking Mode-locking is a technique to generate ultrashort pulses from lasers. In cw mode-locking the pulses are typically much shorter than the cavity round trip and the pulse repetition rate (from few tens of megahertz to a few hundreds of gigahertz) is determined by the cavity round-trip time. Typically an intracavity loss modulator (i.e. a loss modulator inside a laser cavity) is used to collect the laser light in short pulses around the minimum of the loss modulation with a period given by the cavity round-trip time TR = 2L/vg , where L is the laser cavity length and vg the group velocity (i.e. the propagation velocity of the peak of the pulse intensity). Under certain conditions, the pulse repetition rate can be some integer multiple of the fundamental repetition rate (i.e. harmonic mode-locking) [72Bec]. We distinguish between active and passive mode-locking. For active mode-locking (Fig. 2.1.3), an external signal is applied to an optical loss modulator typically using the acousto-optic or electro-optic effect. Such an electronically driven loss modulation produces a sinusoidal loss modulation with a period given by the cavity round-trip time TR . The saturated gain at steady state then only supports net gain around the minimum of the loss modulation and therefore only supports pulses that are significantly shorter than the cavity round-trip time. For passive mode-locking (Fig. 2.1.3), a saturable absorber is used to obtain a Self-Amplitude Modulation (SAM) of the light inside the laser cavity. Such an absorber introduces some loss to the intracavity laser radiation, which is relatively large for low intensities but significantly smaller for a short pulse with high intensity. Thus, a short pulse then produces a loss modulation because the high intensity at the peak of the pulse saturates the absorber more strongly than its low intensity wings. This results in a loss modulation with a fast initial loss saturation (i.e. reduction of the loss) determined by the pulse duration and typically a somewhat slower recovery which depends on the detailed mechanism of the absorption process in the saturable absorber. In effect, the circulating pulse saturates the laser gain to a level which is just sufficient to compensate the losses for the pulse itself, while any other circulating low-intensity light experiences more loss than gain, and thus dies out during the following cavity round trips. The obvious remaining question is – how does passive mode-locking start? Ideally from normal noise fluctuations in the laser. One noise spike is strong enough to significantly reduce its loss in the saturable absorber and thus will be more strongly amplified during the following cavity round trips, so that the stronger noise spike Landolt-B¨ ornstein New Series VIII/1B1
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Laser resonator Loss
Gain
L Cavity length
Output coupler
High reflector
Active modelocking Loss Saturated gain Pulse intensity l (t)
Time t
TR Passive modelocking
Loss Saturated gain
Pulse intensity l (t)
Time t
TR Fig. 2.1.3. Schematic laser cavity setup for active and passive mode-locking.
continues to further reduce its loss and continues its growth until reaching steady state where a stable pulse train has been formed. Generally, we can obtain much shorter pulses with passive mode-locking using a saturable absorber, because the recovery time of the saturable absorber can be very fast, resulting in a fast loss modulation. Mode-locked pulses are much shorter than the cavity round-trip time and therefore can produce an ideal fast loss modulation inversely proportional to the pulse envelope. In comparison, any electronically driven loss modulation is significantly slower due to its sinusoidal loss modulation. In the time domain (Fig. 2.1.4), this means that a mode-locked laser produces an equidistant pulse train, with a period defined by the round-trip time of a pulse inside the laser cavity TR and a pulse duration τp . In the frequency domain (Fig. 2.1.4), this results in a phase-locked frequency comb with a constant mode spacing that is equal to the pulse repetition rate νR = 1/TR . The spectral width of the envelope of this frequency comb is inversely proportional to the pulse duration. Mode-locking in the frequency domain can be easily understood by the fact that a homogeneously broadened laser normally lases at one axial mode at the peak of the gain. However, the periodic loss modulation transfers additional energy phase-locked to adjacent modes separated by the modulation frequency. This modulation frequency is normally adapted to the cavity round-trip frequency. The resulting frequency comb with equidistant axial modes locked together in phase forms a short pulse in the time domain. Mode-locking was first demonstrated in the mid-1960s using a HeNe-laser [64Har], ruby laser [65Moc] and Nd:glass laser [66DeM]. The passively mode-locked lasers were also Q-switched, which means that the mode-locked pulse train was strongly modulated (Fig. 2.1.2). This continued to be a problem for passively mode-locked solid-state lasers until the first intracavity saturable absorber was designed correctly to prevent self-Q-switching instabilities in solid-state lasers with microsecond or even millisecond upper-state lifetimes [92Kel2].
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...
¦rep
...
1 tp ~ Dnp
Envelope
~ Intensity I (n)
Intensity I (t)
TR = 1 ¦rep
[Ref. p. 134
Dnp
Frequency n
Phase shift f (t)
~ Phase shift f (t)
Time t
Time t Time domain
Frequency n Frequency domain
Fig. 2.1.4. Mode-locked pulses in the time and frequency domain.
Loss
Loss
Loss
Gain
Gain
Pulse
Pulse
Gain
Pulse Time t
a
Time t
b
Time t
c
Fig. 2.1.5. Passive mode-locking mechanisms explained by three fundamental models: (a) slow saturable absorber mode-locking with dynamic gain saturation, (b) fast saturable absorber mode-locking and (c) slow saturable absorber mode-locking without dynamic gain saturation, which in the femtosecond regime is described by soliton mode-locking.
Q-switching instabilities are a serious issue with passively mode-locked solid-state lasers. The parameters of the saturable absorber have to be chosen such that the mode-locking is self-starting (i.e. starting from normal intensity noise of the laser) and stable, i.e. without any Q-switching instabilities (Sect. 2.1.6.8). For example, if the loss modulation becomes too large it can drive the laser unstable: The loss saturation increases the intensity inside the laser cavity. The gain then needs to saturate more strongly to compensate for the reduced loss and to keep the intensity inside the laser cavity constant. If the gain cannot respond fast enough, the intensity continues to increase as the absorber is bleached which leads to self-Q-switching instabilities or in the best case to stable Q-switched mode-locking. In the latter case, the mode-locked pulse train is strongly modulated at close to the relaxation oscillation frequency of the laser (typically in the kHz rate) (Fig. 2.1.2). A large modulation depth of the saturable absorber results in shorter pulses but an upper limit is set by the onset of Q-switching instabilities. Passive mode-locking mechanisms are well-explained by three fundamental models: slow saturable absorber mode-locking with dynamic gain saturation [72New, 74New] (Fig. 2.1.5a), fast saturable absorber mode-locking [75Hau1, 92Hau] (Fig. 2.1.5b) and slow saturable absorber modelocking without dynamic gain saturation in the picosecond [01Pas1] and femtosecond domain described by soliton mode-locking [95Kae1, 96Kae] (Fig. 2.1.5c). In the first two cases, a short net-gain window forms and stabilizes an ultrashort pulse. In Fig. 2.1.5a, an ultrashort net-gain window can be formed by the combined saturation of absorber and gain for which the absorber has to saturate
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and recover faster than the gain, while the recovery time of the saturable absorber can be much longer than the pulse duration. Dynamic gain saturation means that the gain experiences a fast, pulse-induced saturation that then recovers again between consecutive pulses (Fig. 2.1.5a). For solid-state lasers we cannot apply slow saturable absorber mode-locking as shown in Fig. 2.1.5a, because no significant dynamic gain saturation is taking place due to the small gain cross-section of the laser. The upper state lifetime of solid-state lasers is typically in the μs to ms regime, much longer than the pulse repetition period, which is typically in the nanosecond regime. In addition, the gain cross-section is 1000 or even more times smaller than for dye lasers. We therefore do not observe any significant dynamic gain saturation and the gain is only saturated to a constant level by the average intracavity intensity. This is not the case for dye, semiconductor and color-center lasers for which Fig. 2.1.5a describes most mode-locking processes. Therefore it was assumed that without other pulse-forming mechanisms (such as soliton pulse shaping) a fast saturable absorber is required for solid-state lasers. Kerr-lens mode-locking is nearly an ideal example for fast saturable absorber mode-locking. However, SESAM mode-locking results revealed that even a slow saturable absorber can support significantly shorter pulses even though a net gain window remains open after the short pulse (Fig. 2.1.5c). At first this seems surprising, because on the trailing edge of the pulse there is no shaping action of the absorber and even worse one would expect that the net gain after the pulse would destabilize the pulse. However, we have shown that in the picosecond regime without soliton formation, a more strongly saturated slow saturable absorber can stabilize a shorter pulse because the pulse is constantly delayed by the absorber and therefore swallows any noise growing behind himself [01Pas1]. This means that even with solid-state lasers we can work with relatively slow saturable absorbers that have approximately a recovery time in the range of 10 to 30 times the absorber recovery time. In the femtosecond regime soliton formation is actually the dominant pulse-forming mechanism and the slow saturable absorber needs only to be fast enough to stabilize this soliton – which is referred to as soliton mode-locking [95Kae1, 95Jun2, 96Kae].
2.1.3 Overview of ultrafast solid-state lasers 2.1.3.1 Overview for different solid-state laser materials Table 2.1.1 to Table 2.1.3 give a full overview of the different results that have been achieved using different solid-state lasers. The long list as shown in Table 2.1.2 demonstrates how active the field of cw mode-locked lasers has been. The shortest pulses in the two optical cycle regime are being generated by the Ti:sapphire laser using Kerr-Lens Mode-locking (KLM). Otherwise, more recent results clearly demonstrate that the emphasis has shifted towards SESAM mode-locking because more stable and self-starting mode-locking can be achieved and the saturable absorber can be optimized independently from the cavity design. This allowed us to push the frontier in terms of pulse repetition rate and pulse energy by several orders of magnitude. Today, we can obtain a pulse repetition rate of about 160 GHz as compared to around 1 GHz in 1990. In addition, we have increased the pulse energy from the nJ-regime to more than 10 μJ from a passively mode-locked diode-pumped solid-state laser at 10–50 MHz pulse repetition rates during the last decade which is an increase of more than four orders of magnitude. More results are summarized in Table 2.1.2 and discussed below in Sect. 2.1.3.1.1 to Sect. 2.1.3.1.3. Q-switching results are restricted to microchip lasers because the pulse duration scales with the photon cavity lifetime. Thus, the shorter the laser cavity, the shorter the pulses that can be generated as discussed in Sect. 2.1.3.1.4. In the past few years, a novel type of laser has bridged the gap between semiconductor lasers and solid-state lasers. The Vertical-External-Cavity Surface-Emitting Laser (VECSEL) [99Kuz] Landolt-B¨ ornstein New Series VIII/1B1
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[Ref. p. 134
combines the best of both worlds: the semiconductor gain medium allows for flexible choice of emission wavelength via bandgap engineering and offers a wealth of possibilities from the semiconductor processing world. SESAM mode-locked optically pumped VECSELs have already pulled even with solid-state lasers in the GHz pulse repetition rate regime and will be briefly reviewed in Sect. 2.1.3.1.5. For a more detailed recent review we refer to [06Kel]. Semiconductor lasers have the advantage that the SESAM can be integrated into the gain structure. This holds promise for high-volume wafer-scale fabrication of compact, ultrafast lasers. Recently, this vertical integration of ultrafast semiconductor lasers has been demonstrated for the first time and is referred to as a Mode-locked Integrated External-cavity Surface Emitting Laser (MIXSEL) [07Bel]. Ultrafast fiber lasers also demonstrate very good performances and are being briefly reviewed in Sect. 2.1.3.1.6.
2.1.3.1.1 Solid-state laser materials Solid-state lasers can be grouped in two types: transition-metal-doped (Cr2+ , Cr3+ , Cr4+ , Ti3+ , Ni2+ , Co2+ ) and rare-earth-doped (Nd3+ , Tm3+ , Ho3+ , Er3+ , Yb3+ ) solid-state lasers (Table 2.1.1). Color-center lasers have also supported ultrashort pulse durations, but they require cryogenic cooling [87Mit, 89Isl]. A similar wavelength range can be covered with Cr:YAG lasers, for example. Table 2.1.1 to Table 2.1.3 summarize the laser parameters of these solid-state lasers and the performance that has been demonstrated with these lasers up to date with mode-locking (Table 2.1.2) and Q-switching (Table 2.1.3). Q-switching in Table 2.1.3 is restricted to microchip lasers because of the very short laser cavity that can support even picosecond pulses with Qswitching. Several factors are important to achieve a good power efficiency: a small quantum defect, the absence of parasitic losses, and a high gain (σL τL product, where σL is the gain cross section and τL the upper-state lifetime of the gain medium) are desirable. The latter allows for the use of an output coupler with relatively high transmission, which makes the laser less sensitive to intracavity losses. For high-power operation, we prefer media with good thermal conductivity, a weak (or even negative) temperature dependence of the refractive index (to reduce thermal lensing), and a weak tendency for thermally induced stress fracture. For ultrafast lasers, in addition we require a broad emission bandwidth because of large bandwidths of ultrashort pulses. More precisely, we need a large range of wavelengths in which a smoothly shaped gain spectrum is obtained for a fixed inversion level. The latter restrictions explain why the achievable mode-locked bandwidth is in some cases (e.g., some Yb3+ -doped media [99Hoe2]) considerably smaller than the tuning range achieved with tunable cw lasers, particularly for quasi-three-level gain media. A less obvious requirement is that the laser cross sections should be high enough. While the requirement of a reasonably small pump threshold can be satisfied even with low laser cross sections if the fluorescence lifetime is large enough, it can be very difficult to overcome Q-switching instabilities (see Sect. 2.1.6.8) in a passively mode-locked laser based on a gain material with low laser cross sections. Unfortunately, many broad-band gain media tend to have low laser cross sections, which can significantly limit their usefulness for passive mode-locking, particularly at high pulse repetition rates and in cases where a poor pump beam quality or poor thermal properties necessitate a large mode area in the gain medium. Finally, a short pump absorption length is desirable because it permits the use of a small path length in the medium, which allows for operation with a small mode area in the gain medium and also limits the effects of dispersion and Kerr nonlinearity. The latter is particularly important for very short pulses. In addition, short pump absorption length is required for the thin-disk laser concept [94Gie] which so far supports the highest pulse energies in the 10 μJ-regime directly generated from a passively mode-locked laser [06Mar, 07Mar].
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σL [10−20 cm2 ]
[86Mou, 96Koe] [89Pay, 91Sch1, 96Koe] [88Pay] [92Smi] [92Cha] [79Wal, 89Sam, 96Koe] [88Pet, 93Car, 96Koe] [88Ang, 95Kue] [97Pag, 03Dru] [97Pag, 03Dru]
790 850 758 835 ≈ 800 750 1240 1378 2500 2350
[91Kut, 94Mey] [94Jen] [03Qin] [99Sch]
[87Fan, 88Ris, 98For] [97Zay]
Nd:YVO4
Nd:YAlO3 Nd:LSB (10 at.%) Nd:GdVO4 Nd:(Gd,Y)VO4 Nd:phosphate glass (LG-760)
[64Geu, 97Zay] [69Har, 97Zay, 96Koe]
Nd:YAG Nd:YLF
1064 1047 1314 914 1064 1342 930 1064 1064 1064 1054
Rare-earth-doped solid-state lasers (Nd3+ , Yb3+ , Er3+ )
Ti3+ :sapphire Cr3+ :LiSAF Cr3+ :LiCAF Cr3+ :LiSGAF Cr3+ :LiSCAF Cr3+ :alexandrite Cr4+ :forsterite Cr4+ :YAG Cr2+ :ZnSe Cr2+ :ZnS
100 100 160 118 90 323
4.5
230 480 480
3.2 67 175 88 80 260 2.7 4.1 7 4.5
τL [μs]
4 300 60 4.1 13 76
33 18
0.76 14.4 33 90 140
41 5 1.23 3.3
Transition-metal-doped solid-state lasers (Cr2+ , Cr3+ , Cr4+ , Ti3+ )
Laser material
24.3
2.5 4
0.8
0.6 1.2
≈ 230 180 115 190 ≈ 155 ≈ 100 170 ≈ 250 600 (≈ 11 fs) 500
Δλg [nm]
4.5 ps 1.5 ps 5.7 ps 3 ps 2.7 ps 4.6 ps 1.9 ps 1.6 ps 4.4 ps 2.6 ps 150 fs
5–6 fs 9.9 fs 9 fs 14 fs 90 fs 3 ps 14 fs 20 fs 83 fs
τp,min
(continued)
[00Lar] [90Mal] [96Flu2] [05Sch1] [00Kra2, 05Lec1] [96Flu2] [98Kel] [96Bra2] [05Agn] [05Wan] [95Kop1]
[99Sut, 01Ell] [03Uem] [02Wag] [97Sor] [94Wan] [84Pes] [01Chu] [02Rip1] [07Sor]
τp,min Ref.
Table 2.1.1. Relevant laser materials for short and ultrashort pulse generation. λ0 : center lasing wavelength. σL : gain cross-section. τL : upper-state lifetime. Δλg : FWHM gain bandwidth. τp,min : minimal pulse duration that has been demonstrated so far (coupled-cavity mode-locking schemes are not considered because of their complexity, for further information with regards to coupled-cavity mode-locking results see Table 2.1.2).
Ref. p. 134] 2.1 Ultrafast solid-state lasers 41
1088 1030 1034 1041 1040 1047 1043 1025–1060 1025–1060 1025–1060 1535
1000–1010 1110 820 1170 600–1200 680 1260 1100 1300 1100 1300 7900
380 309 285 2600 1100 820
≈ 2.0 3 3.5 0.36 0.2 0.44
0.42 1.0 1.3 0.28 0.8 7.3 5.9 0.049 0.093 0.158 0.8
≈ 250 ≈ 250
250 256
950
495
361
τL [μs]
1.25 0.2–1.0 0.75 2.8 3.0
2.0
2.6
2.54
σL [10−20 cm2 ]
25 4 4.1 62 77 81 55
24
70
44 60 73
≈ 25 ≈ 25
6.3
26.1
35.9
Δλg [nm]
[97Aus]
[97Aus]
τp,min Ref.
[00Dru] [02Dru1] [04Dru] [04Luc] [06Thi] [06Thi] [07Li] [04Gri]
58 fs 61 fs 60 fs 255 fs
[98Hoe, 99Hoe2] [98Hoe, 99Hoe2] [98Hoe] [05Spu1]
72 fs (58 fs) [07Riv] 198 fs [02Led]
90 fs 69 fs 70 fs 150 fs 122 fs 198 fs 343 fs 220 fs
38 fs [02Han] 340 fs [96Kel, 99Hoe2] 136 fs [05Uem] 120 fs [05Kis] 58 fs [06Riv] 110 fs (47 fs) [06Zao] 100 fs [04Pau] 71 fs [01Liu] 114 fs [05Riv] 120 fs [06Cas] 67 fs (53 fs) [07Gar]
60 fs
68 fs
τp,min
2.1.3 Overview of ultrafast solid-state lasers
[91Lap, 96Kig, 99Lap]
[06Cas] [07Gar] [05Man] [99Mou] [02Dru1] [03Dru] [04Pet] [04Jac, 95Jac] [95Jac] [06Xue] [04Gri] [96Sch] [05Rom] [00Wan] [94DeL] [94DeL]
1014–1079 ≈ 1030 1000 1045 1062 1040
1064 1030 1050 1037 1020–1055 1016–1050 1026 1025
Nd:fluorophosphate & silicate [93Fan]
[04Kis, 04Kra1] [05Liu, 06Riv] [05Pet] [97Kul1, 97Kul2, 03Kul] [97Kul1, 97Kul2, 02Puj, 00Dem]
1054
[78Sch]
Yb:YVO4 Yb:LuVO4 Yb:CAlGO Yb:KGW Yb:KYW Yb:KLuW Yb:NGW Yb:NaYW Yb:NLM Yb:GdCOB Yb:BOYS Yb:SIS Yb:CaF2 Yb:YSO Yb:LSO Yb:GSO Yb:Lu2 O3 Yb:BCBF Yb:LSB Yb:YAB Yb:S-FAP Yb:FAB Yb:phosphate glass Yb:silicate glass Yb:fluoride phosphate Er,Yb:glass
1059.7
[99Sch]
Nd:silicate glass (LG-680) Nd:fluorophosphate glass (LG-812) Dual glass gain laser Yb:YAG
λ0 [nm]
Ref.
Laser material
Table 2.1.1 continued.
42 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
Ti3+ :Al2 O3
Ti:sapphire
Laser material
600 mW
240 mW
110 mW
60 fs 73 fs
47 fs
880 nm 852 nm
KLM
813 nm 33 fs
39 fs 32 fs
820 nm
140 fs
750 nm
dye sat. absorber
320 mW
1.5 W
300 mW
90 mW
2 ps
860 nm
300 mW
2W
CCM-RPM
1.3 ps
Pav,out
1.4 ps
150 fs
780 nm
τp
814 nm
λ0
CCM-APM
active-AOM
ML technique
≈ 100 MHz
82 MHz
134 MHz
250 MHz
82 MHz
80.5 MHz
frep
[92Kaf]
[91Cur]
Ref.
2.1 Ultrafast solid-state lasers (continued)
Schott F2 prisms, 8 mm [92Kra1] Ti:sapphire crystal thickness
LaFN28-glass prisms, 2 cm [92Hua1] Ti:sapphire crystal thickness
[92Kaf]
[92Riz1]
KLM, a Gaussian approxima- [91Sal1] tion
first experimental evidence [91Kel] for KLM, self-starting due to RPM
first demonstration of KLM [91Spe] (but KLM not understood)
KLM started with dye sat- [91Sar] urable absorber (not understood – assumed to have a CPM Ti:sapphire laser)
[90Kel2]
highly chirped 1.4 ps output [89Goo] pulses externally compressed down to 200 fs
Remarks
Table 2.1.2. CW mode-locked solid-state lasers using different mode-locking techniques. “Best” means in terms of pulse duration, highest average output power, highest pulse repetition rate etc. – the result for which “best” applies is in bold letters. The lasers are assumed to be diode-pumped, if not stated otherwise (except Ti:sapphire laser). ML: Mode-Locking. CCM: Coupled-Cavity Mode-locking. APM: Additive Pulse Mode-locking. RPM: Resonant Passive Mode-locking. KLM: Kerr-Lens Mode-locking. SESAM: passive mode-locking using SEmiconductor Saturable Absorber Mirrors (SESAMs). Soliton-SESAM: Soliton mode-locking with a SESAM. AOM: Acousto-Optic Modulator. EOM: Electro-Optic phase Modulator. λ0 : center lasing wavelength. τp : measured pulse duration. Pav,out : average output power. frep : pulse repetition rate.
Ref. p. 134] 43
Laser material
Table 2.1.2 continued.
ML technique
6.5 fs
5.8 fs
≈ 5 fs
≈ 5 fs
800 nm
≈ 800 nm
≈ 800 nm
≈ 800 nm
9.5 fs
7.5 fs
800 nm
180 mW
120 mW
200 mW
300 mW
200 mW
150 mW
100 mW
≈ 1 mW
500 mW
85 MHz
65 MHz
90 MHz
85 MHz
86 MHz
80 MHz
100 MHz
80 MHz
100 MHz
frep Ref.
[94Sti]
[96Xu2]
[95Sti]
(continued)
KLM self-starting with novel [02Sch2] broadband fluoride SESAM
similar to [99Mor1] but with [01Ell] double-Z cavity with second focus in a glass plate for additional SPM
CaF2 prisms, double-chirped [99Mor1, mirrors, pulse duration mea- 99Mor2] sured with fit to IAC (not very accurate)
fused silica prisms and [99Sut, double-chirped mirrors, KLM 00Mat] is self-starting with SESAM, pulse duration measured with SPIDER [00Mat]
fused silica prisms and [97Jun3] double-chirped mirrors, KLM is self-starting with SESAM
chirped mirrors, ring cavity
chirped mirrors only
metal mirrors and fused silica [94Zho] prisms
chirped mirrors, no prisms
fused silica prisms, 4.5 mm [93Asa] Ti:sapphire crystal thickness
fused silica prisms, 4 mm [93Cur] Ti:sapphire crystal thickness
Schott LaKL21 prisms, 9 mm [92Hua2] Ti:sapphire crystal thickness
Schott LaK31 prisms, 2 cm [92Lem] Ti:sapphire crystal thickness
Remarks
2.1.3 Overview of ultrafast solid-state lasers
≈ 800 nm
8.2 fs
11 fs
800 nm
300 mW
11 fs
780 nm
8.5 fs
12.3 fs
775 nm
850 nm
500 mW
17 fs
817 nm
950 mW
22 fs
804 nm
Pav,out
τp
λ0
44 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Laser material
Table 2.1.2 continued.
Landolt-B¨ ornstein New Series VIII/1B1
KLM and dumped
soliton-SESAM
ML technique
23 fs
≈ 800 nm 782 nm
780 nm
800 nm
[02Bar]
special [95Tsu]
2.1 Ultrafast solid-state lasers (continued)
[97Bal] [06Zho]
2 MW peak power 0.45 μJ pulse energy 0.8 MHz
≤ 1 MHz
60 fs
4.6 fs
[94Psh] [96Gib]
212 nJ pulse energy
1 kHz
17 fs
62 nJ, 5 MW peak power
80 kHz
13 fs
[93Ram2]
[06Dew]
[03Sto]
shortest pulse with soliton [96Kae] mode-locking and no KLM
new acronym for SESAM design: SBR
first SESAM design with a sin- [95Bro2] gle quantum-well absorber in a Bragg reflector
five-element ring laser
100 nJ pulse energy
0.36 W
[05Nau]
ring laser, ML is self-starting [99Bar] due to feedback from external mirror
0.5 μJ 50 nJ
130 nJ par 280 nJ, > 5 MW [04Fer] peak
[03Kow]
[99Cho]
150 nJ, 3.5 MW peak
[99Bed]
1 MW peak, 13 nJ out 0.7 MW peak, 0.011 μJ
0.56 μs pulse energy
3.5 W
Ref.
1.5 MW peak, focused intensity [98Xu] 5 × 1013 W/cm2
Remarks
≤ 950 kHz
2.3 GHz
85 MHz
98.9 MHz
1 GHz
2 GHz
2 MHz 50 MHz
11 MHz 11 MHz
5.85 MHz
15 MHz
110 MHz
75 MHz
frep
6.23 MHz
54 fs
800 nm
10 mW
80 mW
140 mW
300 mW
1W 2.5 W
≈ 1.5 W ≈2W
170 mW
1.5 W
1W
Pav,out
50 fs
240 fs
840 nm cavity-835 nm
13 fs
90 fs 810 nm
840 nm
34 fs
50 fs
≈ 800 nm
560–1150 nm @ −50 dBc
43 fs 26 fs 30 fs
788 nm
13 fs 16.5 fs
800 nm
8.5 fs
780 nm 850 nm
τp
λ0
Ref. p. 134] 45
Cr3+ :LiSrAlF6
Cr:LiSAF
Laser material
Table 2.1.2 continued.
KLM
ML technique
KLM started by SESAM
pumped by a SHG diode- [94Lin1] pumped actively mode-locked Nd:YLF laser, prism modelocker to start KLM
≈ 1 mW
≈ 10 mW < 20 mW
300 ps
220 fs
55 fs
880 nm 850 nm
2.7 mW
70 mW (≈ 1 mW)
10 mW
42 mW
80 MHz
80 MHz
90 MHz
KLM self-starting
KLM started by regen. AOM
KLM started by regen. AOM
(continued)
[95Mel]
[95Fal]
[95Dym]
[94Dym]
[94Mel]
Ar-ion pumped, intracavity [92Riz3] dye absorber for starting KLM
Ar-ion pumped, regenerative [92Eva] AOM for starting KLM
2.1.3 Overview of ultrafast solid-state lasers
40 fs (24 fs)
97 fs 34 fs
860 nm
90 fs
first diode-pumped mode- [93Fre] locked Cr:LiSAF laser, AOM or RPM for starting KLM
5 mW
93 fs
870 nm
Ar-ion pumped, KLM started [93Riz] with intracavity SESAM
25 mW
33 fs
85 MHz
Ar-ion pumped, intracavity [92Riz2] dye absorber for starting KLM
150 mW
135 mW
50 fs
fem- [92Mil] laser,
Ref.
880–920 nm
first mode-locked tosecond Cr:LiSAF Kr-pumped
Remarks
50 fs
82 MHz
frep
≈ 840 nm
50 mW
Pav,out
150 fs
τp
800–880 nm
λ0
46 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Laser material
Table 2.1.2 continued.
Landolt-B¨ ornstein New Series VIII/1B1
soliton-SESAM
ML technique
110 fs 57 fs 94 fs
875 nm 855 nm 848 nm
146 fs 113 fs 39 fs 43 fs
857 nm 844 nm 867 nm 856 nm
80 fs
60 fs 50 fs
70 fs
868 nm
875 nm
160 fs
842 nm
860 nm
100 fs
865 nm
9.9 fs
≈ 850 nm
45 fs
12 fs
850 nm
850 nm
14.8 fs
880 nm
98 fs
18 fs
875 nm
840 nm
τp
λ0
5.5 mW
6.5 mW
20 mW
3 mW
110 mW
8.4 MHz
8.6 MHz
407 MHz
1 GHz
100 MHz
130 MHz
150 MHz
150 MHz
500 mW 6.5 mW
150 MHz
176 MHz
178 MHz
176 MHz
120 MHz
200 MHz
70 MHz
frep
340 mW
125 mW
100 mW
25 mW
11 mW
105 mW
50 mW
23 mW
70 mW
≈ 1 mW
Pav,out
[03Uem]
[99Uem]
[97Sor]
[97Dym]
Ref.
[97Kop2]
[96Tsu]
[99Rob]
[01Kem] [02Hop] 0.66 nJ, DCM with prisms
(continued)
[03Pra]
0.75 nJ, DCM without prisms [03Pra]
less than 110 mW pump
20 fs (25 mHz . . . 10 kHz) [99Tsu] rms timing jitter
only one GTI mirror
only 72 mW pump power with [98Hop] 1.5 V AA batteries
low-brightness 0.9 cm wide, [97Kop3] 15 W diode laser array
low-brightness 0.9 cm wide, [97Kop3] 15 W diode laser array
0.5 W diffraction-limited MOPA pump
compact cavity design with no [96Kop2] prisms for dispersion compensation (dispersive SESAM)
[95Tsu]
[95Kop2, 97Kop2]
first soliton mode-locking, no [94Kop1] KLM required
strong wings in IAC
ML not self-starting
Kr-ion-laser pumped
Remarks
Ref. p. 134] 2.1 Ultrafast solid-state lasers 47
Cr4+ :Mg2 SiO4
Cr:forsterite
Cr3+ :LiSr0.8 Ca0.2 AlF6
Cr:LiSCAF
Cr3+ :LiSrGaIF6
Cr:LiSGaF
Cr3+ :LiCaAlF6
Cr:LiCAF
Laser material
Table 2.1.2 continued.
KLM
KLM
soliton-SESAM
KLM
KLM
ML technique
48 fs 50 fs 25 fs 20 fs
1.24–1.27 μm 1.27 μm 1.28 μm
90 fs
80 MHz
82 MHz
81 MHz
140 MHz
90 MHz
119 MHz
70 MHz
80 MHz
71 MHz
110 MHz
97 MHz
[98Gab]
[98Gab]
[92LiK]
Ref.
[96Sor2]
[96Sor1]
[95Yan]
[03Wag]
[94Wan]
[93Yan]
[93Sea]
(continued)
Nd:YVO4 laser pumped, not [97Zha2] self-starting
Nd:YAG laser pumped
Nd:YAG laser pumped
Nd:YAG laser pumped, KLM [93Sen] self-starting with AOM
Kr-ion-laser pumped
[01Dai]
[97Loe]
Kr-ion-laser pumped, chirped [97Sor, mirror 98Sor]
Kr-ion-laser pumped, GTI
Kr-ion-laser pumped
DCM and prisms, SPIDER
Ti:sapphire laser pumped, only [02Wag] fit to IAC measurement
Kr-pumped
Remarks
2.1.3 Overview of ultrafast solid-state lasers
300 mW
45 mW
380 mW
100 mW
20 mW
38 fs
1.23 μm (1.21–1.27 μm)
860 nm
78 mW
61 fs
100 mW
14 fs
895 nm 839 nm
200 mW
44 fs
842 nm
35 mW
40 mW
64 fs
≈ 850 nm
220 mW
100 fs (50 fs)
10 fs
≈ 850 nm
95 MHz 95 MHz
75 mW 13 mW
835 nm
9 fs
820 nm
90 MHz
frep
100 mW
Pav,out
830 nm
52 fs 20 fs
793 nm
170 fs
τp
800 nm
λ0
48 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
Cr4+ :Y3 Al5 O12
Cr:YAG
Laser material
Table 2.1.2 continued.
KLM
soliton-SESAM
ML technique
43 fs 75 fs 55 fs 115 fs 20 fs 68 fs 26 fs 55 fs 65 fs
1.52 μm 1.54 μm 1.45 μm 1.52 μm 1.5 μm 1.569 μm
53 fs
1.54 μm 1.54 μm
60 fs
1.55 μm
1.52 μm
70 fs
1.51 μm
78 fs
1.26 μm
120 fs
80 fs
1.27 μm
1.52 μm
40 fs 36 fs
25 fs
1.3 μm
1.29 μm
14 fs
1.3 μm
1.29 μm
τp
λ0
30 mW
250 mW 600 mW
138 mW
400 mW
150 mW
280 mW
200 mW
250 mW
50 mW
50 mW
360 mW
800 mW
68 mW
60 mW
60 mW
80 mW
Pav,out
100 MHz
100 MHz 65 MHz
2.33 GHz
110 MHz
2.64 GHz
1.2 GHz
1 GHz
70 MHz
235 MHz
81 MHz
83 MHz
90 MHz
100 MHz
frep [01Chu]
Ref.
[98Pet]
[98Liu]
[97Zha2]
[97Zha1]
[97Ton]
[96Ton]
[94Ish]
[94Con]
[02Rip1]
[01Tom]
[00Tom]
directly diode-pumped
Yb-fiber laser pumped
(continued)
[04Nau]
[03Nau]
optimized three-element cav- [03Tom] ity
Nd:YVO4 laser pumped
Nd:YVO4 laser pumped
Nd:YVO4 laser pumped
Nd:YVO4 laser or Yb:fiber [98Mel] laser pumped
Nd:YVO4 laser pumped
Nd:YAG laser pumped
Nd:YAG laser pumped
Nd:YAG laser pumped
Nd:YAG laser pumped, regen. [94Sen] AOM for starting KLM
Nd:YAG laser pumped
double-clad fiber pumped
Nd:YVO4 laser pumped
Nd:YVO4 laser pumped
KLM self-starting due to [02Pra] InAs-doped silica films [04Pra]
double-chirped mirrors
Remarks
Ref. p. 134] 2.1 Ultrafast solid-state lasers 49
Nd3+ :Y3 Al5 O12
Nd:YAG
Cr2+ :ZnSe
Laser material
Table 2.1.2 continued.
25 ps 12 ps 8 ps 53 ps
1.064 μm 1.064 μm 1.32 μm 1.32 μm
active FM
active EOM
active AOM
83 fs
2.4 μm
active AOM
4.4 ps
2.5 μm
soliton-SESAM
10 ps
57 fs
1.510 nm
≈ 1.5 μm
active AOM
semiconductor-doped glass
36 fs 120 fs
1.528 μm
44 fs
1.52 μm 1.5 μm
75 fs 400 fs
1.46 μm
200 fs
1.52 μm
1.52 μm
110 fs 114 fs
1.5 μm
soliton-SESAM
1.541 μm
τp
λ0
ML technique
200 MHz
1 GHz
350 MHz
180 MHz
81 MHz
235 MHz
205 MHz
152 MHz
1 GHz
0.9, 2.7 GHz
185 MHz
frep [97Spa]
[96Col]
Ref.
[98Mel]
[07Sor]
[00Car]
[04Lag2]
[03Nau]
[03Lag2]
[02Rip2]
[99Zha]
(continued)
lamp-pumped and harmonic [88Kel] mode-locked
[91Zho]
[89Mak1]
lamp-pumped: pulse shorten- [86Ros] ing due to intracavity etalon
10 optical cycles
PbS-doped glass as sat. abs.
Yb:fiber laser pumped
Yb:fiber laser pumped
oxidized GaAs/AlAs SESAM
Nd:YVO4 laser pumped
Nd:YAG laser pumped, single [98Cha] prism for dispersion comp.
Nd:YVO4 laser pumped
1.8,Nd:YVO4 laser pumped, [97Col] 0.9 GHz fundamental, then double and triple harmonics
Nd:YVO4 laser pumped
Nd:YVO4 laser pumped
Remarks
2.1.3 Overview of ultrafast solid-state lasers
1.5 W
240 mW
65 mW
80 mW
82 mW
35 mW
200 mW
95 mW
300 mW
65 mW
230 mW
280 mW
82 mW
94 mW
70 mW
Pav,out
50 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
Nd3+ :LiYF4
Nd:YLF
Laser material
Table 2.1.2 continued.
active EOM
1.3 μm
1.053 μm
1.047 μm
1.053 μm
1.064 μm
polarization switching in nonlinear crystal
active AOM
800 mW
4.5 ps 1.064 μm
SESAM
19 ps 8.3 ps
400 mW
4.5 ps
240 mW
400 mW
8 ps
350 mW
4 ps
6.2 ps 13 ps
135 mW 20 mW
7 ps
12 mW 150 mW
18 ps 9 ps
6.5 W
37 ps
4W
27 W 1.59 W
16 ps
23 ps
400 mW 10.7 W
6.8 ps
100 mW
675 mW
6.7 ps 8.7 ps
1W
8.5 ps
1.064 μm
KLM
2.4 W 700 mW
6 ps 10 ps
1.32 μm
25 mW 110 mW
2 ps
1.064 μm
CCM-APM
Pav,out
1.7 ps
τp
λ0
ML technique
1 GHz
2.85 GHz
237.5 MHz
5.4 GHz
1 GHz
2 GHz
500 MHz
230 MHz
100 MHz
150 MHz
130 MHz
55 MHz
88 MHz
217 MHz
100 MHz
101.5 MHz
106 MHz
100 MHz
100 MHz
100 MHz
125 MHz
136 MHz
frep
[92Liu]
[90Liu1]
[90Liu1]
[91McC]
[90Goo]
Ref.
Ti:sapphire laser pumped
Ti:sapphire laser pumped
lamp-pumped
2.1 Ultrafast solid-state lasers (continued)
[91Zho]
[92Wei]
[92Wei]
[91Sch2]
[90Wal]
[90Wei]
[90Kel1]
[89Mak2]
[87Bad]
[99Kub]
[05Guo] lamp-pumped, KTP crystal
[00Spu]
multiple laser heads
[99Spu3]
[94Kel]
[93Wei]
[00Lar]
[97Hen]
ceramic Nd:YAG
Ti:sapphire laser pumped
lamp-pumped, severe insta- [95Chu1] bilities
lamp-pumped
lamp-pumped
Remarks
Ref. p. 134] 51
Laser material
Table 2.1.2 continued.
2.3 ps 1.047 μm
SESAM
CCM-RPM
CCM-APM
800 mW
3 ps
1.047 μm
KLM
550 mW
4 ps 3.7 ps
20 mW 1W
1.5 ps
7W
250 MHz
120 MHz
123 MHz
103 MHz
Ti:sapphire laser pumped
pump laser for PPLN OPO
lamp-pumped
low-loss buried resonant GaInNAs SESAM
1.4 GHz
76 MHz
detailed studies about ML stability above the Q-switched mode-locking threshold
GaInNAs-SESAM
GaInNAs-SESAM but only quasi-cw mode-locking demonstrated
Ti:sapphire laser pumped
lamp-pumped, microdot mirror
semiconductor MultipleQuantum-Well (MQW) modulator
Remarks
119 MHz
117 MHz
98 MHz
220 MHz
100 MHz
220 MHz
82 MHz
160 MHz
100 MHz
frep
(continued)
[92Kel1]
[99Lef]
[90Mal]
[99Jeo]
[90Liu2]
[02Rot]
[06Zel]
[04Sch1]
[04Liv]
[02Sun]
[96Flu2]
[94Kel]
[93Wei]
[92Kel2]
[93Ram1]
[94Lin2]
[90Juh]
[95Bro3]
Ref.
2.1.3 Overview of ultrafast solid-state lasers
1.047 μm
1.047 μm
1.7 ps
3.7 ps
127 mW
21 ps
1.053 μm
630 mW
48 ps
< 680 mW
580 mW
6.7 ps
70 ps . . . 4 ns
< 20 W on-time
> 22 ps
460 mW
2.8 ps 130 mW
225 mW
5.7 ps
700 mW
5.1 ps
160 mW
3.3 ps
1.053 μm
1.3 μm
250 mW
7 ps
1.047 μm
active piezoelectric diffraction modulator
27 mW
200 ps
1.047 μm
active MQW
Pav,out
τp
λ0
ML technique
52 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Nd:YVO4
Laser material
Table 2.1.2 continued.
SESAM
ML technique
1.064 μm
λ0
Landolt-B¨ ornstein New Series VIII/1B1
90 MHz 147 MHz
198 mW 81 mW 4.4 W 20 W 23.5 W 80 mW 288 mW
6.8 ps 33 ps 21 ps 21.5 ps 4.8 ps 2.7 ps
10 GHz
2.1 W < 220 mW
1.5 W
13.7 ps 9–23 ps
31 ps
[04Lec]
4.1 W 3.9 W 3.5 W
13 ps
4.1 MHz 2.6 MHz 1.5 MHz
2.1 Ultrafast solid-state lasers (continued)
[03Kol]
[05Fan] output coupling (OC) SESAM, more OC-SESAM [01Spu1] and [96Sha]
1.28 W
2.1 ps
96.5 MHz
detailed studies about [04Sch1] ML stability above the Q-switched mode-locking threshold
400 mW
[02She] [03Sei]
10.6 ps
coated GaAs wafer for ML all-optical synchronization
100 MHz
[00Kra2] [02Kra2]
6 ps
154 MHz
Ti:sapphire laser pumped
157 GHz
[05Lec1]
[00Kra1]
[01Che1]
[00Bur]
[99Gra]
[99Kra2]
[99Kra1]
[97Ruf]
Ref.
[01Led] ion-implanted InGaAs SESAM, also see [99Led] for SESAM details
Ti:sapphire laser pumped
77 GHz
65 mW 45 mW
2.7 ps
Ti:sapphire laser pumped
Ti:sapphire laser pumped
Remarks
2.7 ps
40 GHz
39, 49, 59 GHz
235 & 440 MHz
29 GHz
13 GHz
4.5 W
84 MHz
frep
8.3 ps
Pav,out
7 ps
τp
Ref. p. 134] 53
Nd:La2 Be2 O5
Nd:BEL
Nd:LnM3 (BO3 )4
Nd:LSB
Laser material
Table 2.1.2 continued.
30 mW 30 mW
7.5 ps 2.9 ps 3.9 ps
1.070 μm 1.070 μm
active-AOM
230 mW
210 mW 400 mW
670 mW
2.8 ps
2.8 ps
1.064 μm
3.25 W
1.35 W
1.6 ps
29 ps
1.062 μm
7.9 ps
1.064 μm
850 mW
26 ps
1.064 μm
40 mW
7.3 ps
42 mW
45 mW
7 ps
3 ps
50 mW
4.6 ps
20 GHz
238 MHz
250 MHz
177 MHz
240 MHz
130 MHz
170 MHz
150 MHz
234 MHz
152 MHz
10 GHz
5 GHz
93 MHz
harmonic mode-locking
harmonic mode-locking
Ti:sapphire laser pumped
two LBO crystals used
Ti:sapphire laser pumped
InAs/GaAs quantum dot SESAM
4 pJ @ 10 GHz
GaInNAs SESAM
2.6,with additional amplifier 50 W
24 kW peak
3.5, 3.9, 4.1 W 1.5, 4.1 MHz
13 ps
1.2 MHz
470 mW
16.3 ps
Remarks
frep
Pav,out
τp
914 nm
1.34 μm
λ0
active-FM
SESAM
intensity-dependent polarization rotation
nonlinear mirror ML
ML technique
2.1.3 Overview of ultrafast solid-state lasers (continued)
[91God]
[91God]
[91Li]
[96Bra2]
[96Bra2]
[99Cou]
[05Dat]
[97Agn]
[05Sch1]
[05Su]
[05Spu2]
[05Spu2]
[96Flu2]
[04Lut]
[03Pap]
Ref.
54 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
Nd:GdVO4
Nd3+ :KGd(WO4 )2
Nd:KGW
Nd:YAlO3
Nd:YAP
Laser material
Table 2.1.2 continued.
24 ps
50 ps 15 ps 31 ps
1.34 μm
1.08 μm 1.34 μm 1.08 μm
1W
600 mW 4.9 W 3.46 W 500 mW
8 ps 11.5 ps 18.9 ps 12 ps
5.4 W
6.3 ps
1.067 μm
SESAM
850 mW
7 W on-time
410 mW
220 mW
Pav,out
9.2 ps
2.3 ps
1.067 μm
CCM-APM
1.064 μm
1.7 ps
1.067 μm
KLM
SESAM
12 ps
1.067 μm
active-FM
nonlinear mirror ML
1.9 ps
930 nm
SESAM
10 ps
τp
1.08 μm
λ0
active AOM
ML technique
9.66 GHz
0.37–3.4 GHz
140 MHz
154 MHz
119 MHz
64.5 MHz
76.5 MHz
200 MHz
178 MHz
frep
GaAs wafer SESAM
pure passive ML unstable, thus used additionally AOM
LiIO3 frequency doubler
GaInNAs-SESAM but only quasi-cw mode-locking demonstrated
Remarks
(continued)
[04Kra2]
[04Kon]
[04Zha1]
[03Zha]
[03He]
[02Maj2]
[02Maj1]
[96Let]
[95Flo]
[99Agn]
[91Sta]
[02Sun]
[98Kel]
[96Guy]
Ref.
Ref. p. 134] 2.1 Ultrafast solid-state lasers 55
active-AOM
active-FM
CCM-APM
soliton-SESAM
Nd:phosphate
Nd:phosphate
Nd:phosphate
≈ 60 mW
4.4 ps
9 ps 122 fs 150 fs 120 fs
1.054 μm 1.054 μm 1.054 μm 1.054 μm
275 fs
310 fs
1.063 μm
175 fs
9 ps
1.054 μm
1.054 μm
≈ 10 ps
1.057 μm
7 ps
74 MHz
117 MHz
150 MHz
180 MHz
235 MHz
240 MHz
240 MHz
96.4 MHz
112 MHz
121 MHz
2.5-2.7 GHz
146 MHz
frep
single-prism for dispersion compensation
Kr-ion laser pumped
Ti:sapphire laser pumped, regeneratively actively mode-locked
Ar-ion laser pumped
output coupling (OC) SESAM, more OC-SESAM [01Spu1] and [96Sha]
Remarks
(continued)
[00Pas1]
[98Aus]
[96Kop1]
[95Kop1]
[91Spi]
[91Hug]
[94Kop2]
[92Hug]
[88Bas]
[86Yan]
[05Wan]
[04He]
[05Lin1]
[05Agn]
[05Zha1]
Ref.
2.1.3 Overview of ultrafast solid-state lasers
1.4 W
1W
30 mW
110 mW
200 mW
14 mW
70 mW
30 mW
30 mW
20 mW
2.15 W
2.6 ps
1.054 μm
3.9 W
3.8 ps
2.65 W
120 mW
16 ps
38 ps
Pav,out
τp
1.054 μm
1.064 μm
1.064 μm
NL mirror ML
SESAM
λ0
ML technique
Nd:phosphate
Nd:glass
Nd:GdYVO4
Laser material
Table 2.1.2 continued.
56 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
Yb3+ :Y3 Al5 O12
Yb:YAG
Nd: fluorophosphate and Nd:silicate
CCM-APM
soliton-SESAM
40 mW
1.9 ps (4.7 ps)
45 W
791 fs
1.03 μm
63 W
796 fs
2.5 W (2.7 W)
3.1 mW
80 W
705 fs
136 fs
57 MHz
60 W
810 fs
≈ 1.05 μm
34.3 MHz
12 W
3.3–89 ps 0.83–1.57 ps
115 MHz
4 MHz
12.3 MHz
28 MHz
35 MHz
16.2 W
730 fs
63 MHz
170 mW 8.1 W
2.2 ps
81 MHz
180 MHz
114 MHz
frep
340 fs
100 mW
38 fs
1.064 μm
soliton-SESAM
30 mW
80 mW
84 mW
Pav,out
540 fs
64 fs
≈ 1.07 μm
KLM
1.03 μm
130 fs
1.064 μm
soliton-SESAM
Nd:silicate
60 fs
1.065 μm
soliton-SESAM
Nd:fluorophosphate
τp
λ0
ML technique
Laser material
Table 2.1.2 continued.
[01Lu]
[95Kop1]
[97Aus]
Ref.
[01Bru]
2.1 Ultrafast solid-state lasers (continued)
[03Maj]
shorter pulses only with extra [05Uem] spectral filtering
thin-disk laser with multi- [07Mar] pass cavity [64Her], 11 μJ pulse energy
thin-disk laser, 5.1 μJ pulse [06Mar] energy, 5.6 MW peak power
thin-disk laser, 1.4 μJ pulse [04Bru] energy
thin-disk laser, 1.75 μJ pulse [03Inn] energy, 1.9 MW peak power
tunable pulse duration
first passively mode-locked [00Aus] thin-disk laser, 0.47 μJ pulse energy
[99Aus]
[99Hoe2]
first passively mode-locked [95Hoe] Yb:YAG laser
dual gain medium both at [02Han] Brewster’s angle
spectral shaping required
Remarks
Ref. p. 134] 57
Yb3+ :KGd(WO4 )2
Yb:KGW
Yb3+ :CaGdAlO4
Yb:CAlGO
Yb:LuVO4
Yb:YVO4
Laser material
Table 2.1.2 continued.
soliton-SESAM
soliton-SESAM
soliton-SESAM
soliton-SESAM
ML technique
169 fs 100 fs
296 fs 433 fs
1.028 μm 1.037 μm
1.031 μm 1.040 μm 134 fs
112 fs
1.046 μm
5.3 W
10 W
3.7 W
126 mW
18 mW
200 mW
1.1 W
38 mW
47 fs
176 fs
48 mW
85 mW
300 mW
Pav,out
110 fs
58 fs
120 fs
τp
1.037 μm
1.050 μm
1.036 μm
1.021 μm
λ0
45 MHz
45 MHz
61 MHz
100 MHz
86 MHz
86 MHz
109 MHz
109 MHz
94 MHz
150 MHz
frep
[02Maj3]
[00Bru]
[00Bru]
[06Zao]
[06Zao]
[06Riv]
[05Kis]
Ref.
[06Maj]
(continued)
[06Hol]
[06Hol]
2.1.3 Overview of ultrafast solid-state lasers
0.12 μJ pulse energy
0.22 μJ pulse energy
Yb:KGW and Y:KYW tested [04Pau] with the same cavity and SESAM
plus external prism pulse compressor
strongly chirped output pulses
Remarks
58 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
Yb3+ :NaY(WO4 )2
Yb:NaYW
Yb3+ :NaGd(WO4 )2
Yb:NGW
Yb:KLuW Yb3+ :KLu(WO4 )2
Yb3+ :KY(WO4 )2
Yb:KYW
Laser material
Table 2.1.2 continued.
soliton-SESAM
soliton-SESAM
soliton-SESAM
SESAM and cavity-dumping
KLM
soliton-SESAM
ML technique
1.030 μm
1.038 μm
1.030 μm
96 MHz 96 MHz
97 MHz
101 MHz
1.06 MHz
1 MHz
294 MHz
110 MHz
105 MHz
114 MHz
25 MHz
95 MHz
frep
53 fs
91 mW
360 mW
31 mW
3.21 W
1.35 W
126 mW
120 mW
90 mW
92 mW
107 mW
22 W
100 mW
Pav,out
67 fs
120 fs
114 fs
680 fs
71 fs
1.057 μm
1.024 μm
6.8 ps
1.029 μm
107 fs
106.5 fs
1.039 μm
380 fs
123 fs
1.047 μm
1.056 μm
240 fs
1.040 μm
101 fs
1.028 μm
τp
1.046 μm
λ0
[02Klo]
Ref.
tunable 1042–1075 nm
[04Lag1]
[07Gar]
[06Cas]
[05Riv]
[07Pal]
[05Kil1]
2.1 Ultrafast solid-state lasers (continued)
plus external cavity SF10- [07Gar] prism compressor
Ti:sapphire laser pumped
potential for shorter pulses
3 μJ pulse energy
1.35 μJ pulse energy
[01Liu]
quantum dot SESAM under [05Lag] reverse bias
Yb:KGW and Y:KYW tested [04Pau] with the same cavity and SESAM
[03Lag1]
thin-disk laser, 0.9 μJ pulse [02Bru] energy, 3.3 MW peak power
Remarks
Ref. p. 134] 59
soliton-SESAM
soliton-SESAM
Yb:Lu2 O3
soliton-SESAM
soliton-SESAM
soliton-SESAM
soliton-SESAM
ML technique
Yb3+ :LnM3 (BO3 )4
Yb:LSB
Yb:CaF2
Yb3+ :SrY4 (SiO4 )3 O
Yb:SIS
Yb3+ :Sr3 Y(BO3 )3
Yb:BOYS
Yb3+ :Ca4 GdO(BO3 )3
Yb:GdCOB
Laser material
Table 2.1.2 continued.
1.034 μm
1.053 μm
266 mW
73 mW
58 fs 220 fs
79 mW
880 mW 1.74 W
156 mW
110 mW
80 mW
40 mW
Pav,out
72 fs
150 fs 230 fs
70 fs
1.066 μm
1.049 μm
94 fs
69 fs
90 fs
τp
1.068 μm
1.062 μm
1.045 μm
λ0
97 MHz
90 MHz
90 MHz
98 MHz
108 MHz
113 MHz
100 MHz
frep
Ti:sapphire laser pumped
plus external cavity SF10prism compressor
Ti:sapphire laser pumped
Remarks
2.1.3 Overview of ultrafast solid-state lasers (continued)
[04Gri]
[07Riv]
[07Riv]
[04Luc]
[04Dru]
[02Dru1]
[02Dru1]
[00Dru, 02Dru2]
Ref.
60 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
Er:Yb:glass
Yb:silicate glass
Yb:phosphate glass
Yb:glass
Yb3+ :Gd2 SiO5
Yb:GSO
Yb3+ :Lu2 SiO5
Yb:LSO
Yb3+ :Y2 SiO5
Yb:YSO
Laser material
Table 2.1.2 continued.
90 ps 9.6 ps 9.6–30 ps 48 ps
≈ 1.53 μm
≈ 1.5 μm 1.533 μm
250 fs 470 fs
1.04 μm
1.53 μm
61 fs
1.03–1.082 μm
active FM
58 fs
1.3 ps 343 fs
198 fs 260 fs
122 fs
τp
1.025–1.065 μm
1.031 μm 1.030 μm
1.044 μm 1.059 μm
1.041 μm
λ0
active AOM
SESAM and cavity-dumped
soliton-SESAM
soliton-SESAM
soliton-SESAM
soliton-SESAM
ML technique
1 mW
3 mW
3 mW
7 mW
0.33 W 0.375 W
53 mW
65 mW
586 mW 396 mW
2.61 W 2.6 W
410 mW
Pav,out
5 GHz
2.5 and 5 GHz
2.5 GHz
100 MHz
1.1 MHz 0.5 MHz
112 MHz
112 MHz
101 MHz
75 MHz 75 MHz
75 MHz
frep
dual wavelength with 165 GHz separation
3rd -order harmonic modelocking
3rd -order harmonic modelocking
0.3 μJ pulse energy 0.75 μJ pulse energy
Remarks
2.1 Ultrafast solid-state lasers (continued)
[98Lon]
[95Lap]
[94Lon]
[94Cer]
[05Kil2]
[98Hoe]
[98Hoe]
[07Li]
[06Thi]
[06Thi]
Ref.
Ref. p. 134] 61
Laser material
Table 2.1.2 continued.
40 GHz MUX
> 5 dBm
2.5 ps 2.5 ps
1.535 μm
soliton-SESAM
10 GHz
50 mW
3.8 ps
9 mW
2 ps 3 ps
20 ps 5 ps 4.7 ps 380 fs 255 fs
1.533 μm 1.536 μm
1.535 μm 1.534 μm 1.535 μm 1.535 μm 1536 μm 1.54 μm
70 mW
1.7–1.9 ps
1.534 μm
58 mW
4 mW
80 mW
10.7 mW
7.5 mW
> 20 mW
18 mW
4.3 ps
1.534 μm
25 mW
1.9 ps
1.528–1.561 μm
12 mW
169 MHz
50 MHz
100 MHz
10 GHz
61 MHz
61 MHz
77 GHz
50 GHz
8.8–13.3 GHz
40 GHz
25 GHz
10 GHz
114 MHz
1.534 μm
68 mW
2.5 ps
1.534 μm
frep
SESAM
Pav,out
τp
λ0
ML technique [99Spu2]
Ref.
[02Spu]
220 fs with external pulse compression, first Si/Ge-SESAM
AlGaAsSb-SESAM
first GaInNAs-SESAM at 1.5 μm
first AlGaAsSb-SESAM
(continued)
[05Gra1]
[05Spu1]
[01Was]
[06Gra]
[05Rut]
[04Gra]
optical frequency comb with [07Zel] > 56 dB OSNR (Optical Signal-to-Noise Ratio)
10 discrete channels locked to [04Zel] 50 GHz ITU grid
pulse repetition rate is contin- [04Ern] uously tunable
[03Zel]
gain equalized frequency [03Spu] comb with 36 discrete channels, tunable over C-band
40 GHz multiplexed (MUX)
[02Spu]
nearly quantum-noise-limited [02Kra1] timing jitter [05Sch2]
Remarks
62 2.1.3 Overview of ultrafast solid-state lasers [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
Laser material
Table 2.1.2 continued. λ0
soliton-CNT (Carbon 1.56 μm NanoTube saturable absorber)
ML technique
85 MHz 74.5 MHz
63 mW
90–200 MHz
frep
261 fs
10 mW
Pav,out
68 fs
100 fs
τp
[05Sch3]
[05Sch3]
Ref.
single-all CNT, nonlinear [07Fon] reflectivity measurements: ΔRns = 1.1 %, ΔR = 0.5 %, Fsat,A = 57 μJ/cm2
Remarks
Ref. p. 134] 2.1 Ultrafast solid-state lasers 63
Nd:YVO4
Nd:YAG
Laser material
440 kHz 7.8 MHz
0.16 μJ 0.28 μJ 45 nJ
117 ps 181 ps 2.64 ns
53 kHz
510 kHz
53 nJ
37 ps
230 ps
17 W peak, 350 mW average
160 kHz
48 nJ
143 ps
1.34 μm
1.6 kW peak, 120 mW average
160 kHz
0.37 μJ
68 ps
450 kW peak
1.4 kW peak, 82 mW average
1.4 kW peak, 8.5 mW average
Output Coupling (OC) SESAM
5.4 kW peak, 58 mW average
85 kHz
62 nJ
56 ps
1.1 kW peak, 5.3 mW average
optimization for max. energy [04Bur]
pulse width increases with increased frep for 5–500 kHz: 13.3 ns at 500 kHz
pumped by Q-switched intracavity SHG Nd:YAG laser
Remarks
1.064 μm
1 kHz
4 kHz
6 kHz
5 kHz
4 kHz
frep
SESAM
12 μJ
11 μJ
6.8 μJ
Ep
115 ps
148 ps
337 ps
270 ps
760 ps
τp
1.064 μm
1.064 μm
λ0
active-EOM
Cr4+ :YAG
active-EOM
ML technique
(continued)
2.1.3 Overview of ultrafast solid-state lasers
[97Flu]
[99Spu1, 01Spu3]
[99Spu1, 01Spu3]
[99Spu1, 01Spu3]
[99Spu1, 01Spu3]
[01Spu1]
[97Bra]
[97Bra]
[95Zay]
[03Zay]
[94Zay]
[92Zay]
[89Zay]
Ref.
Table 2.1.3. Q-switched microchip lasers using different techniques. First microchip laser introduced by Zayhowski and Mooradian [89Zay]. “Best” means in terms of pulse duration, highest average output power, highest pulse repetition rate etc. – the result for which “best” applies is in bold letters. The lasers are assumed to be diode-pumped, if not stated otherwise. SESAM: passive Q-switching using SEmiconductor Saturable Absorber Mirrors (SESAMs). EOM: Electro-Optic phase Modulator. λ0 : center lasing wavelength. τp : measured pulse duration. Ep : pulse energy. frep : pulse repetition rate.
64 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
Cr:YAG
Er:Yb:glass
Yb:YAG
Nd:LSB
Laser material
:YAG
p-i-n modulator
SESAM
SESAM
Cr
4+
SESAM
ML technique
Table 2.1.3 continued.
56 ns
1.553 μm
42 ns
840 ps
≈ 1.5 μm
1.2 ns
≈ 1.5 μm
530 ps
650 ps
180 ps
τp
1.535 μm
1.03 μm
1.063 μm
1.062 μm
λ0
470 nJ
11.2 μJ
45 nJ
1.1 μJ
3–4 μJ
0.1 μJ
Ep
1 MHz
10 kHz
1.4 kHz
47 kHz
12 kHz
110 kHz
frep
diode-pumped Nd:YVO4 pumped, Q-switched ML
previously p-i-n modulator for ML [95Bro3]
16 mW average, 10.6 kW peak
2.1 mW average
1.9 kW peak
Remarks
[01Sch]
[01Han]
[01Hae1]
[98Flu]
[01Spu2]
[05Voi]
[96Bra1]
Ref.
Ref. p. 134] 2.1 Ultrafast solid-state lasers 65
66
2.1.3 Overview of ultrafast solid-state lasers
[Ref. p. 134
2.1.3.1.2 Mode-locked rare-earth-doped solid-state lasers The rare-earth-doped (e.g. Nd3+ , Tm3+ , Ho3+ , Er3+ , Yb3+ ) solid-state lasers have favorable properties for diode-pumped high-power operation, but cannot be used in the high-power regime for femtosecond pulse generation because of their relatively small amplification bandwidth. These lasers have 4f-electrons responsible for the laser transition, which are shielded from the crystal host. Thus the gain bandwidth is normally not very large and pulse durations are limited to a few 100 fs (Table 2.1.1 and Table 2.1.2). Shorter pulses can only be obtained in inhomogeneously broadened rare-earth-doped lasers in glass hosts for example but at the expense of lower power due to the limited thermal conductivity of glasses (Table 2.1.1 and Table 2.1.2). Typical examples are Nd3+ :YAG and Nd3+ :YVO4 . With high-power laser diodes, one or several conventional end-pumped or side-pumped laser rods and a SESAM for mode-locking, up to 27 W of average power in 19-ps pulses has been achieved with Nd3+ :YAG [00Spu], or 23.5 W in 22-ps pulses with Nd3+ :YVO4 [01Che1]. Significantly shorter pulse durations have been achieved with Nd:YAG at lower output powers, down to 1.7 ps with 25 mW [90Goo] using the technique of Additive Pulse Mode-locking (APM). For all these Nd3+ -doped crystals, the relatively large laser cross sections usually make it relatively easy to achieve stable mode-locked operation without Q-switching instabilities, if the laser mode area in the gain medium is not made too large. Phosphate or silicate glasses doped with rare-earth ions such as Nd3+ or Yb3+ have been used for pulse durations down to ≈ 60 fs [97Aus, 98Hoe] and output powers of a few hundred milliwatts. The relatively poor thermal properties make high-power operation challenging. Up to 1.4 W of average power in 275-fs pulses [00Pas1], or 1 W in 175-fs pulses [97Aus], have been obtained from Nd3+ :glass by using a specially adapted elliptical mode pumping geometry [00Pas2] initially developed for diode-pumped Cr:LiSAF lasers [97Kop1, 95Kop3]. Here, a strongly elliptical pump beam and laser mode allow the use of a fairly thin gain medium which can be efficiently cooled from both flat sides. The resulting nearly one-dimensional heat flow reduces the thermal lensing compared to cylindrical rod geometries, if the aspect ratio is large enough. A totally different route toward high peak powers is to use a cavity-dumped laser; with such a device, based on Yb3+ :glass, 400-nJ pulses with more than 1 MW peak power have been generated [04Kil]. Yb3+ :YAG has similar thermal properties as Nd3+ :YAG and at the same time a much larger amplification bandwidth. Another favorable property is the small quantum defect. However, challenges arise from the quasi-three-level nature of this medium and from the small laser cross sections, which favor Q-switching instabilities. High pump intensities help in both respects. An end-pumped laser based on a Yb3+ :YAG rod has generated 340-fs pulses with 170 mW [95Hoe]. As much as 8.1 W in 2.2-ps pulses was obtained from an elliptical-mode Yb3+ :YAG laser. In 2000, the first Yb3+ :YAG thin-disk laser has been passively mode-locked, generating 700-fs pulses with 16.2 W average power [99Aus]. The concept of the passively mode-locked thin-disk laser has been demonstrated to be power scalable, which so far lead up to 80 W in 0.7-ps pulses [06Inn]. In recent years, a few Yb3+ -doped crystalline gain materials have been developed which combine a relatively broad amplification bandwidth (sufficient for pulse durations of a few hundred femtoseconds) with thermal properties which are better than those of other broad-band materials, although not as good as e.g. those of YAG or sapphire. Examples are shown in Table 2.1.1 and Table 2.1.2. With an end-pumped Yb3+ :KGW rod, 1.1 W of average power have been achieved in 176-fs pulses [00Bru]. A Kerr-lens mode-locked Yb3+ :KYW laser produced pulses as short as 71 fs [01Liu], while a SESAM mode-locked Yb3+ :KYW produced pulses as short as 107 fs [04Pau]. Around 70-fs pulses have been obtain with SESAM mode-locked Yb3+ :NGW laser with 23 mW average power [06Riv], Yb3+ :BOYS laser with 80 mW [02Dru1], Yb3+ :SYS laser with 156 mW [04Dru]. However, so far the shortest pulses are still obtained with Yb:glass lasers [98Hoe]. Note that some of these media exhibit rather low emission cross sections and therefore make stable passive mode-locking difficult, while they might be very useful e.g. in regenerative amplifiers. Tungstate crystals (Yb3+ :KGW, Yb3+ :KYW) have been rather useful for passive mode-locking since they have relatively high cross sections. Yb3+ :KYW has been applied in a thin-disk laser, generating Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 134]
2.1 Ultrafast solid-state lasers
67
22 W in 240-fs pulses [02Bru]. With improved crystal quality, significant performance enhancements appear to be feasible. Another new class of materials with particular importance are the Yb3+ -doped sesquioxides such as Y2 O3 , Sc2 O3 and Lu2 O3 , which appear to be very suitable for high-power operation with short pulses. Up to a few years ago, the repetition rate of passively mode-locked solid-state lasers was limited to a few gigahertz. Q-switching instabilities have limited the highest pulse repetition rates (Sect. 2.1.6.8). In recent years, the consequent exploitation of the flexibility of SESAMs supported passively mode-locked lasers with multi-GHz pulse repetition rates, very good pulse quality, comparatively high output powers, and wavelength tunability in the areas of interest (for example the ITU-specified C-band from approximately 1525 nm to 1565 nm, ITU stands for International Telecommunication Union). Passive mode-locking means that the pulses are achieved without using any expensive multi-gigahertz electronics. In addition, the pulses originate from fundamental mode-locking. Thus, every output pulse is a copy of the same single pulse, which travels back and forth in the cavity. Therefore, pulse-to-pulse variations are minimized and the phase of the pulses is constant. For the first time, pulse repetition rates above 10 GHz from passively mode-locked iondoped solid-state lasers have been generated with Nd:YVO4 lasers at a center wavelength around 1 μm [99Kra1]. This laser has a large gain cross section and therefore Q-switching instabilities are more strongly suppressed. Shortly afterwards the frontier was pushed up to 77 GHz [00Kra2] and 160 GHz [02Kra2]. The average power has been optimized at a 10 GHz pulse repetition rate to as high as 2.1 W [04Lec]. The peak power was sufficient for efficient nonlinear frequency conversion. For example, a synchronously pumped Optical Parametric Oscillator (OPO) was demonstrated producing picosecond pulses broadly tunable around 1.55 μm with up to 350 mW average output power [04Lec, 02Lec]. Such all-solid-state synch-pumped OPOs can reach the S-, C- and L-band in telecommunication. With an additional Yb-doped fiber amplifier the repetition rate was pushed up to 80 GHz [05Lec2]. Particularly in the telecom wavelength ranges (around 1.3 μm and 1.55 μm), where only few solid-state gain media are available, multi-GHz pulse repetition rates initially were not directly possible [97Col, 95Lap]. However, with improved SESAM designs [05Spu3] and an improved understanding of the Q-switching instabilities [04Sch1, 05Gra2] full C-band tuning [03Spu] and up to 77 GHz pulse repetition rate [07Zel] has been demonstrated with a diode-pumped Er:Yb:glass laser. At 1.3 μm both Nd:YLF [06Zel] and Nd:YVO4 [05Spu2] have been passively mode-locked at GHz repetition rates. In addition, the timing jitter of diode-pumped solid-state lasers is very close to the quantum noise limit [05Sch2].
2.1.3.1.3 Mode-locked transition-metal-doped solid-state laser Transition-metal-doped (e.g. Cr2+ , Cr3+ , Cr4+ , Ti3+ , Ni2+ , Co2+ ) solid-state lasers are characterized by a much broader amplification bandwidth, typically allowing for pulse durations well below 0.5 ps, but also usually by significantly poorer thermal properties and lower laser cross sections. Ti3+ :sapphire is a notable exception, combining nearly all desired properties for powerful ultrafast lasers, except that the short pump wavelength excludes the use of high-power diode pump lasers, and that the quantum defect is large. These lasers have 3d-electrons responsible for the laser transition, which are not very well shielded from the host material. Thus these lasers are strongly phonon-broadened and can support much shorter pulses than the rare-earth-doped crystal. Presently, the shortest pulses generated from a laser are based on Ti:sapphire using KLM (Table 2.1.1). Using a frequency-doubled solid-state laser as a pump source, Ti3+ :sapphire lasers have been demonstrated to generate pulses with durations below 6 fs and a few hundred milliwatts of average power [99Sut, 01Ell]. For these pulse durations, KLM is required, and self-starting may be achieved with a SESAM in addition [99Sut, 00Sut]. With a SESAM alone, 13-fs pulses with 80 mW have been demonstrated [96Kae]. If significantly longer pulse durations are acceptable, several watts of average power can be generated with a commercially available Ti3+ :sapphire laser, usually pumped Landolt-B¨ ornstein New Series VIII/1B1
68
2.1.3 Overview of ultrafast solid-state lasers
[Ref. p. 134
with a frequency-doubled diode-pumped solid-state laser at ≈ 1 μm. Another option is to achieve rather high pulse energies and peak powers by using a very long laser cavity and limiting the peak intensities by the use of longer and chirped pulses in the cavity, which may be compressed externally. Such a laser has been demonstrated to produce 130-nJ pulses with < 30 fs pulse duration and > 5 MW peak power [04Fer]. And more recently with a 2-MHz cavity pulse energies as high as 0.5 μJ have been demonstrated still maintaining < 40-fs pulses [05Nau]. Diode-pumped femtosecond lasers can be build with crystals like Cr3+ :LiSAF, Cr3+ :LiSGaF, 3+ Cr :LiSCAF etc. (see Table 2.1.2) which can be pumped at longer wavelengths than Ti3+ :sapphire. However, these media have much poorer thermal properties and thus can not compete with Ti3+ :sapphire in terms of output power; the achievable optical bandwidth is also lower. Cr3+ :LiSAF lasers have generated pulses as short as 12 fs [99Uem], but only with 23 mW of output power, using KLM without self-starting ability. This has been more recently further reduced to 9.9 fs [03Uem]. The highest achieved mode-locked power was 0.5 W in 110-fs pulses [97Kop3] using SESAM modelocking. More recently, compact Cr3+ :LiSAF lasers with very low pump threshold have been developed, delivering e.g. 136-fs pulses with 20 mW average power for < 100 mW optical pump power using again SESAM mode-locking in order to optimize the laser cavity design independently of the saturable absorber [02Aga]. Cr4+ :forsterite emits around 1.3 μm and is suitable for pulse durations down to 14 fs with 80 mW using KLM [01Chu], or for 800 mW in 78-fs pulses using SESAM [98Pet]. Normally, a Nd3+ -doped laser (which may be diode-pumped) is used for pumping of Cr4+ :forsterite. The same holds for Cr4+ :YAG, which emits around 1.4–1.5 μm and has allowed to generate pulses with 20 fs, 400 mW [02Rip1]. Cr2+ -doped II–VI materials have become interesting for ultrafast solid-state lasers in the midinfrared regime [04Sor, 05Sor]. In recent years, Cr2+ :ZnSe has been identified as another very interesting gain material which is in various ways similar to Ti3+ :sapphire, but emits at mid-infrared wavelengths around 2.2–2.8 μm. This very broad bandwidth should allow for pulse durations below 20 fs, although until recently the shortest achieved pulse duration is much longer, ≈ 4 ps [00Car]. The large Kerr nonlinearity of this medium is causing significant problems for shortpulse generation. However, the main obstruction for femtosecond pulses turned out to be the water absorption lines in the resonator around 2.5 μm [07Sor]. Water absorption lines have been identified as a problem for SESAM mode-locking before [96Flu2]. Removing the water absorption in the Cr:ZnSe laser resulted in 80 fs pulses at a center wavelength of 2.5 μm. These are only about 10 optical cycles [07Sor]. 2.1.3.1.4 Q-switched ion-doped solid-state microchip lasers Q-switching results are restricted to microchip lasers because the pulse duration scales with the photon cavity lifetime. Thus, the shorter the laser cavity, the shorter the pulses that can be generated. Microchip lasers [89Zay] are single axial frequency lasers using a miniature, monolithic, flat-flat, solid-state cavity whose mode spacing is greater than the medium-gain bandwidth. They rely on gain guiding, temperature effects and/or other nonlinear optical effects to define the transverse dimension of the lasing mode. The microchip lasers are longitudinal-pumped with a diode laser. Table 2.1.3 summarizes the results obtained with actively and passively Q-switched microchip lasers. The shortest pulses of only 37 ps were obtained with Nd:YVO4 passively Q-switched with a SESAM attached to the microchip laser (Fig. 2.1.6) [99Spu1, 01Spu3]. Using different laser crystal thicknesses ranging from 185 μm to 440 μm the pulse duration could be changed from 37 ps to 2.6 ns and the pulse repetition rate from 160 kHz to 7.8 MHz. Such a laser therefore can be easily adapted to different application requirements. Active Q-switched microchip lasers generated pulses as short as 115 ps [95Zay]. These results also demonstrate that passively Q-switched microchip lasers can bridge the gap in terms of pulse durations between mode-locking and Q-switching. Generally the pulse energies in actively Q-switched microchip lasers tend to be higher (e.g. 12 μJ in [95Zay]), Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 134]
2.1 Ultrafast solid-state lasers
69
SESAM
10 % Output coupler
Output @ 1064 nm
Diode pump laser @ 808 nm
Copper SESAM holder
Sampling oscilloscope
Nd:YVO4 microchip laser (3% doped, 185 μm thick)
37 ps
Dichroic beamsplitter HT @ 808 nm HR @ 1062 nm -100
0
100 Delay [ps]
200
Fig. 2.1.6. Passively Q-switched Nd:YVO4 microchip laser producing pulses as short as 37 ps with 53 nJ pulse energy, 160 kHz pulse repetition rate, and an average power of 8.5 mW. The SESAM design is based on an A-FPSA with 35 InGaAs/GaAs multiple-quantum-well saturable absorbers and a 50 % top reflector resulting in a modulation depth of 13 %.
however a passively Q-switched Yb:YAG microchip laser using a SESAM resulted in 1.1 μJ pulse energy [01Spu2]. More results are summarized in Table 2.1.3.
2.1.3.1.5 Ultrafast semiconductor lasers Diode-pumped Vertical-External-Cavity Surface-Emitting Lasers (VECSELs) [99Kuz] combine the world of diode-pumped solid-state lasers and semiconductor lasers: The semiconductor gain medium allows for flexible choice of emission wavelength via bandgap engineering. The combination of the mature optical pumping technology extensively used for diode-pumped solid-state lasers with efficient heat removal of solid-state thin-disk lasers resulted in performance of VECSELs that surpasses anything possible to date with conventional semiconductor lasers. Continuous-wave output powers of up to 30 W with an M 2 of 3 have been reported from such optically pumped VECSELs [04Chi], and electrically pumped devices have reached 0.5 W single-mode output power [03McI]. A more detailed review of passively mode-locked VECSELs has been given recently [06Kel]. Concerning high-performance passive mode-locking, a domain where diode-pumped solid-state lasers have been dominant for years using SEmiconductor Saturable Absorber Mirrors (SESAMs) (Table 2.1.2), the VECSEL possesses the advantage of a large gain cross-section which suppresses Q-switching instabilities. Thus, VECSELs are ideally suited for high-repetition-rate mode-locking in combination with high average output powers. After the first demonstration of a passively modelocked VECSEL in 2000 [00Hoo], pulse width and output power have improved continuously to 486-fs pulses at 10 GHz with 30 mW [05Hoo] and 4.7-ps pulses at 4 GHz with 2.1 W average output power [05Asc1]. More results are summarized in Table 2.1.4. Novel SESAMs based on Quantum-Dot SEmiconductor Saturable Absorber Mirrors (QDSESAMs) were developed to move towards an even more ambitious goal: the integration of the absorber into the VECSEL gain structure [04Lor]. In a first step passive mode-locking with the same mode area in the gain and the absorber had to be demonstrated for the full wafer-scale integration. We refer to this as “1:1 mode-locking” which was successfully demonstrated using these new QD-SESAMs and therefore the viability of the integrated-absorber VECSEL concept
Landolt-B¨ ornstein New Series VIII/1B1
30 mW
486 fs
6.1 ps 3 ps
960 nm 960 nm 975 nm 489 nm
4.7 ps
957 nm
13 InGaAs/AlGaAsP + intracavity LBO
9.7 ps 4.7 ps
980 nm 960 nm
7 InGaAs/GaAsP QWs
3.8 ps 3.9 ps
15 ps 3.9 ps
950 nm
5 InGaAs/GaAs QWs
[06Lor]
83 mW 6 mW
1.88 GHz 1.88 GHz
[05Asc2]
10 GHz 50 GHz
1.4 W 100 mW
2.1.3 Overview of ultrafast solid-state lasers (continued)
[05Cas]
[05Asc1]
4 GHz
[04Lor]
[02Hae]
[05Hoo]
[02Gar]
2.1 W
low saturation QD-SESAM 1:1 ML for the first time towards wafer scale integration
soliton-like pulse shaping in the positive GVD regime [02Pas]
strain-balanced InGaAs QW
[01Gar]
[07Saa]
[01Hae2]
[00Hoo]
[99Hol]
Ref.
21 GHz 30 GHz
6 GHz
10 GHz
1.21 GHz
harmonic mode-locking
first passively ML VECSEL
acousto-optic modulator
Remarks
55 mW 25 mW
950 mW 530 mW
100 mW
477 fs
1040 nm 1034 nm
6 InGaAs/GaAs QWs
2.1 GHz 328 MHz
< 100 mW 16 mW
15 ps 13.2 ps
1040 nm 1030 nm
2 GHz
4.4 GHz
frep
213 mW
20 mW
Pav,out
6 InGaAs/GaAsP QWs
3.2 ps
22 ps
100 ps
τp
7 InGaAs/GaAs QWs
1030 nm
850 nm
λ0
950 nm
SESAM
active
ML
9 InGaAs/GaAs QWs
12 InGaAs/GaAs QWs
InGaAs-based
GaAs/AlGaAs QWs
GaAs-based
ML OP-VECSEL
Laser material
Table 2.1.4. Passively mode-locked Vertical External Cavity Surface Emitting semiconductor Lasers (VECSELs) using different mode-locking techniques. “Best” means in terms of pulse duration, highest average output power, highest pulse repetition rate etc. – the result for which “best” applies is in bold letters. The VECSELs are either electrically pumped (EP-VECSELs) or optically pumped using diode lasers (OP-VECSELs). ML: Mode-Locking. QW: Quantum Well. λ0 : center lasing wavelength. τp : measured pulse duration. Pav,out : average output power. frep : pulse repetition rate.
70 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
active
SESAM
GaAs/AlGaAs QWs
7 InGaAs/GaAs QWs
InGaAs-based
ML EP-VECSEL
980 nm
830 nm
15 GHz
≈ 10 mW 30 mW
14.8 ps 50 ps
6 GHz
1.1 GHz
960 MHz
2.97 GHz
1.34 GHz
frep
40 mW
4 mW
120 mW
13.5 mW
Pav,out
57 ps
81 ps
3.2 ps
1.554 μm
20 InGaAsP/InGaAsP QWs
τp
6.5 ps
λ0
1.5 μm
ML
7 InGaAsP QWs
InGaAsP-based
Laser material
Table 2.1.4 continued.
SA dynamics [05Zha2]
novel compact linear cavity
first electrically pumped passively ML VECSEL
quasi-cw, liquid N2 cryostat cooling
Remarks
[04Zha2]
[04Jas]
[03Jas]
[93Jia]
[05Lin2]
[03Hoo]
Ref.
Ref. p. 134] 2.1 Ultrafast solid-state lasers 71
72
2.1.3 Overview of ultrafast solid-state lasers
[Ref. p. 134
has been demonstrated [04Lor]. With the QD-SESAM we can resolve the saturation issue for higher pulse repetition rates (i.e. shorter cavities) with nearly equal laser beam sizes in the gain and the absorber to obtain a stable cavity design. This requires a lower saturation fluence. With QD-SESAMs we can obtain both a low saturation fluence and a sufficiently low modulation depth with the optimization of the dot density and the design of the structure (i.e. moving from a antiresonant to a resonant design) [07Maa]. This is not possible with quantum-well absorbers. With an optimized QD-SESAM consisting of only one single self-assembled InAs quantum-dot layer at low growth temperatures we succeeded to push the repetition rate of passively modelocked VECSELs up to 50 GHz [06Lor]. In addition, these QD-SESAMs allowed for the first demonstration of passively modelocked VECSEL with an integrated saturable absorber layer in the gain structure [07Bel, 07Maa]. This will ultimately offer the potential for wafer-scale fabrication and operation at even higher repetition rates. We refer to this device as the Modelocked Integrated eXternal-cavity Surface Emitting Laser (MIXSEL). Such lasers could become an enabling technology basis for ultra-compact high-repetition-rate laser devices suitable for cost-efficient high-volume fabrication. The ultimate goal is to extend the excellent results with optically pumped VECSELs to electrical pumping. However, this is not just a simple extension even though very promising results have been achieved in the cw regime with 500 mW average output power [03McI]. Initial mode-locking results reported however only very moderate average output power well below 100 mW [04Zha2]. For comparison, it is also instructive to consider briefly the performance of pulsed edge-emitting semiconductor diode lasers, which can exhibit the highest pulse repetition rates of any optical source. The obvious advantages of compactness, efficiency of pumping, and ease of manufacture and integration make these sources primary candidates for applications such as optical time-domain multiplexing, microwave carrier generation and optical clock recovery. The efficiency of direct modulation of the diode current falls off exponentially with increasing frequency above the diode relaxation resonance, which lies typically in the range 1–10 GHz: Thus the highest repetition frequencies are achieved using mode-locking of monolithic diode lasers, with gain, saturable absorption and/or external modulation all built into a single chip. Mode-locked edge-emitting diodes are immensely versatile in repetition frequency, from individual gain-switched pulses, through the microwave region of the spectrum and up to THz. The various schemes developed to realize lasers of this type have been reviewed by Avrutin et al. [00Avr]. Passive mode-locking, with a reverse-biased saturable absorber section included in the monolithic cavity, is particularly well-adapted to the generation of ultrashort pulses at high repetition rate because it does not require electrical modulation, which imposes a bandwidth limitation on repetition rate, and also impresses phase structure on the pulses. The first demonstration of such a monolithic device was reported by Vasil’ev et al. [89Vas], who reported a 100-GHz train of 2.5-ps pulses from an AlGaAs/GaAs injection laser, corresponding to fundamental mode-locking of the 380-μm long cavity. The highest output power to date is 250 mW at 4.3 GHz [06Pla]. Unfortunately, such high average power cannot be extended to pulse repetition rates well above 10 GHz because gain guiding at higher current densities gives rise to higher-order transverse modes. In addition, edge-emitting semiconductor lasers have strongly asymmetric beam profiles, which often need to be corrected with precisely mounted lenses. Typically, the same epitaxial layer forms both the gain (with a forward-biased section) and the saturable absorber (with a reverse-biased section) – and can therefore not be optimized independently. The long interaction length in the device introduces significant dispersion and nonlinearities. It is also challenging to fabricate an edge-emitting laser cavity length with a very precise pulse repetition rate and have this laser synchronized to an external reference clock. A more extensive recent review of ultrashort pulse generation with edge-emitting semiconductor lasers is given in [95Jia, 95Vai, 03Del, 00Avr]. Higher output power can be achieved from Semiconductor Optical Amplifiers (SOAs) [92Del, 95Del]; it is outside the scope of this review. However, mode-locking of SOAs in external cavities currently attracts considerable interest. It involves extreme pulse chirping, so that the amplifier is re-pumped during the passage of the pulse. Stretching and external recompression of these pulses is accomplished using chirped fiber Bragg gratings, with dispersion > 1600 ps nm−1 . A system of
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 134]
2.1 Ultrafast solid-state lasers
73
this type has recently been reported by the Delfyett group achieving 590-fs pulses with 1.4 kW of peak power [05Kim].
2.1.3.1.6 Ultrafast fiber lasers Mode-locked and Q-switched ion-doped fiber lasers also showed a lot of progress during the last ten years. More recent reviews on mode-locked fiber lasers are given in book chapters and review articles by I.N. Duling et al. [95Dul], by M.E. Fermann [94Fer, 95Fer, 97Fer, 03Fer] and by H.A. Haus [95Hau1, 95Hau2]. Generally, mode-locked fiber lasers generate significantly lower pulse energies and longer pulse durations than bulk lasers. However, recent progress in mode-locked fiber lasers resulted in Er/Yb-doped fiber lasers that generate 2.7-nJ pulses at 32 MHz with 100 fs pulse duration [96Nel]. Much shorter pulses but also at much lower pulse energies have been obtained in Nd-doped fiber lasers with pulse durations as short as 38 fs [92Hof] and in erbium fiber lasers with pulses as short as 84 fs [93Fer] and 63 fs [95Tam]. Fiber lasers require somewhat different saturable absorber parameters than bulk lasers. However, as has been demonstrated early on, the SESAM parameters can be adjusted for stable cw mode-locking of fiber lasers [91Zir, 93Obe]. Thus, the interested readers are referred to the review articles given above. Impressive results have been obtained with fiber amplifiers and we refer interested readers to a more recent review given by A. Galvanauskas [03Gal]. A. T¨ unnermann’s group achieved new world record results with 400-fs pulses at 75 MHz and an average power of 76 W based on Yb-doped double-clad fiber-based Chirped Pulse Amplification (CPA) system [03Lim]. This system is based on a SESAM mode-locked Nd:glass laser, a fiber stretcher, one Yb-doped preamplifier, one Ybdoped power amplifier and a transmission grating pulse compressor. This result has been further improved using an Yb-doped photonic-crystal-fiber-based CPA system producing 220-fs pulses at 73 MHz and an average power of 131 W [05Ros]. This corresponds to a pulse energy of 1.8 μJ and a peak power as high as 8.2 MW. In this case the seed laser is a SESAM mode-locked Yb:KGW laser followed by a bulk grating stretcher.
2.1.3.2 Design guidelines of diode-pumped solid-state lasers An all-solid-state ultrafast laser technology is based on diode-pumped solid-state lasers. These lasers have to be optimized to support stable pulse generation. The discussion in the following sections will show that a small saturation energy of the laser medium results in a lower tendency of self-Q-switching instabilities. The saturation fluence of a four-level laser system is Fsat,L =
hν mσL
(2.1.1)
and for a three-level system Fsat,L =
hν , m σL + σLabs
(2.1.2)
where hν is the lasing photon energy, σL is the gain cross section, σLabs is the absorption cross section of the three-level gain medium and m is the number of passes through the gain medium per cavity round trip. In case of a standing-wave laser cavity this factor is m = 2, in a unidirectional ring laser cavity it is m = 1. A small saturation energy, low pump threshold and good beam quality is obtained with a small pump and cavity mode volume while maintaining good spatial overlap of the pump laser and laser mode. This can be easily obtained when a diffraction-limited pump laser is used, as for example in a Ti:sapphire laser. The lower limit of the pump volume is then set Landolt-B¨ ornstein New Series VIII/1B1
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2.1.3 Overview of ultrafast solid-state lasers
[Ref. p. 134
by diffraction, and ultimately pump-induced damage to the crystal. However, diode laser arrays or bars do not generate diffraction-limited pump beams, which makes the situation a bit more complicated and is therefore explained next. The propagation of diffraction-limited Gaussian laser beams is extensively described in many text books, as for example in [91Sal2] and [86Sie]. A beam quality factor M 2 was introduced to describe the propagation of non-diffraction-limited beams [89Sas]. The objective was to provide propagation equations for non-diffraction-limited beams that retain the simplicity of the fundamental Gaussian mode beam equations. The M 2 -factor is given by M2 ≡
θ θG
with θG ≡
λ , π W0,G
(2.1.3)
where θ is the actual far-field divergence angle of any beam with any mixtures of modes, θG the far-field Gaussian beam divergence angle, W0,G the beam waist of a Gaussian beam which is set equal to the beam waist of the non-diffraction-limited beam. The quantity M 2 is then a numerical expression of (inverse) beam quality with 1 being a perfect Gaussian beam and higher values indicating “poorer” quality. This is entirely equivalent to the “number of times diffraction limit” quantity introduced by Siegman [86Sie]. The beam quality does not give any information about the details of higher-order mode content in the beam. The propagation of laser beams with M 2 larger than 1, can be reduced to standard Gaussian beam propagation after substituting the wavelength λn with a new “effective wavelength” λeff given by λeff = M 2 · λn ,
(2.1.4)
where λn is the wavelength in the dispersive medium (i.e. λn = λ/n) in which the beam is propagating. Physically, this means that non-diffraction-limited beams propagate like an ideal diffractionlimited Gaussian beam but with the new, longer “effective wavelength”. Beams with larger M 2 have larger “effective wavelengths”, and therefore a smaller depth of focus for a given beam waist. The output beam of a laser diode array or broad-stripe diode suffers from poor beam quality. In the so-called “fast” axis, perpendicular to the pn-junction of the diode laser, the light diverges with a large angle (25 ◦ to 40 ◦ typically) from a narrow aperture of ≈ 1 μm. However, in this 2 direction the light is nearly diffraction-limited with Mfast ≈ 1. Thus, even though the light in the fast axis is highly divergent, it can be efficiently collected with a “fast” high-numerical aperture lens and tightly focused due to its diffraction-limited nature. In the “slow” axis, parallel to the pnjunction of the diode laser, the beam typically has a divergence of ≈ 10 ◦ . For single-stripe diodes, the emitting aperture is ≈ 3 μm, resulting in a beam close to diffraction-limited. For higher-power “arrays” of such apertures, the divergence is also ≈ 10 ◦ , but the total aperture has increased to typically 50 μm to more than 200 μm, or in case of “arrays of arrays” (i.e. bars) to a width of approximately 1 cm. The diode laser light in the slow axis is therefore many times worse than diffraction-limited. High-brightness diode arrays with ≈ 1 W output power and ≈ 100 μm stripe 2 width typically have Mslow ≈ 10, whereas low brightness bars with ≈ 20 W and ≈ 1 cm stripe 2 width have Mslow > 1000. The slow axis ultimately limits the spot size of focused pump due to the requirements of mode matching to the laser mode. With such pump lasers, the lowest pump threshold can be achieved with the following Optimized-Mode-Matching (OMM) design guidelines applied to both fast and slow axis of the diode pump laser [90Fan, 97Kop3]: 1. Determine M 2 for the pump beam (2.1.3) where 2W0,G is set equal to the width of the pump source Dp . The width of the pump source is approximately given by the stripe width of a diode array or bar or more accurately by the second-order intensity moment. 2. Determine the “effective wavelength” λeff (2.1.4). 3. Set the depth of focus or confocal parameter b of the pump beam approximately equal to the absorption length La of the pump beam in the laser medium, i.e. b ≈ La . Landolt-B¨ ornstein New Series VIII/1B1
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4. Determine the smallest pump beam waist W0,opt for which a good mode overlap over the absorption length of the pump and the cavity mode can be obtained. This is the minimum pump spot size in the gain medium that still guarantees good laser beam quality and therefore determines the lowest pump threshold: Calculate optimum beam waist radius W0,opt using Rayleigh range formula for an ideal Gaussian beam (i.e. b = 2z0 , where z0 is the Rayleigh range of a Gaussian beam) with the “effective wavelength” given in (2.1.4) and a confocal parameter b given in 3. of this enumeration: λeff b M 2 λn La W0,opt = = . (2.1.5) 2π 2π From (2.1.5) it becomes clear that for a small spot size the absorption length La in the gain medium should be as short as possible. The absorption length, however, limits the maximum pump power at which some thermal effects will start to degrade the laser’s performance. This will be more severe for “thermally challenged” lasers which exhibit a low thermal heat conductivity and/or upper-state lifetime quenching. Low thermal conductivity results in large thermal lenses and distortions, which limit the maximum pump power. Such a thermally challenged laser material is Cr:LiSAF which is interesting for an all-solid-state femtosecond laser. Upper-state lifetime quenching as observed in Cr:LiSAF results in the following: As the temperature in the laser medium increases, the upperstate lifetime of the laser drops, and the pump threshold increases. Beyond a critical temperature, the laser actually switches off. If the absorption length is too short for these materials, this critical temperature occurs at relatively low pump powers. There is an optimum doping level for best mode matching to the available pump diodes and for minimizing pump-induced upper-state lifetime quenching. In standard diode pumping, we use high-brightness diode arrays (i.e. brightness as high as possible) and apply OMM, (2.1.1)–(2.1.5), only in the slow axis of the diodes and weaker focusing in the fast axis. This results in an approximately circular pump beam that becomes slightly elliptical when the laser crystal is pumped at a Brewster angle. The standard diode pumping is explained in more detail by the example of a diode-pumped Cr:LiSAF laser [94Kop1]. With this standard pumping approach, the average output power was limited by the mentioned thermal problems to 230 mW cw and 125 mW mode-locked with 60-fs pulses [97Kop2]. Standard diode pumping has also been successfully used with most other solid-state lasers such as Nd:YAG. Such lasers are not “thermally challenged”, and much higher average output power has been achieved with this approach. Significantly more output power can be obtained with a diode-pumped Cr:LiSAF laser for which OMM, (2.1.1)–(2.1.5), is applied in both axes in combination with a long absorption length and efficient cooling [97Kop1, 95Kop3]. Optimized mode matching in both axes results in a highly elliptical laser mode in the crystal, because the pump beam can be focused to a much smaller beam radius in the diffraction-limited fast axis compared to the slow axis. Additionally, we can extract the heat very efficiently with a thin crystal of ≈ 1 mm height and obtain approximately a onedimensional heat flow. With cylindrical cavity mirror we still obtained nearly ideal TEM00 output 2 2 beams. Using a 15 W, 0.9 cm wide diode pump array with Mslow = 1200 and Mfast = 1 [95Ski], the average output power of such a diode-pumped Cr:LiSAF laser was 1.4 W cw, 500 mW modelocked with 110-fs pulses, and 340 mW mode-locked with 50-fs pulses [97Kop2]. Combined with a relatively long absorption length, we pumped a thin sheet volume with a width of approximately 1 mm, a length of La ≈ 4 mm and a thickness of ≈ 80 μm in the laser crystal. This approach has been also applied to a diode-pumped Nd:glass laser, resulting in an average output power of about 2 W cw and 1 W mode-locked with pulses as short as 175 fs [98Aus] and more recently 1.4 W with pulses as short as 275 fs [00Pas1]. In addition, a diode-pumped Yb:YAG laser with the same approach produced 3.5 W average power with 1-ps pulses and 8.1 W with 2.2-ps pulses [99Aus].
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2.1.3 Overview of ultrafast solid-state lasers
[Ref. p. 134
2.1.3.3 Laser cavity designs 2.1.3.3.1 Typical picosecond lasers The setups of picosecond lasers typically do not differ very much from those of lasers for continuouswave operation. Some mode-locker is installed, which might be either an Acousto-Optic Modulator (AOM) for active mode-locking (Sect. 2.1.4.1) or e.g. a SESAM (Sect. 2.1.4.2 and Sect. 2.1.4.3) for passive mode-locking. Also, the cavity design needs to fulfill a few additional demands. As an example, we refer to Fig. 2.1.7a, which shows the setup of a high-power Nd3+ :YAG laser [00Spu], passively mode-locked with a SESAM. The cavity design must provide appropriate beam radii both in the laser head (where the fundamental Gaussian mode should just fill the usable area) and on the SESAM to obtain an appropriate degree of saturation. This depends on a number of factors: the output power, the output coupler transmission, the cavity length, and the saturation fluence of the SESAM. Obviously the cavity length must be chosen to obtain the desired repetition rate. The equations given in Sect. 2.1.6.8 can be used to ensure that the chosen design will not suffer from Q-switching instabilities. The laser head is side-pumped in the mentioned example, but end-pumped laser heads can also be used, where the pump light is typically injected through a folding mirror which is highly reflective for the laser light. The SESAM should typically be used as an end mirror, not as a folding mirror. Otherwise a tendency for the generation of multiple pulses, which would meet on the SESAM, might be induced. Similar setups can be used for actively mode-locked lasers, where the SESAM is replaced by an AOM. The AOM should be placed close to an end mirror, for similar reasons as discussed above for the SESAM. Brewster plate
SESAM
Dichroic mirror Pump DCP laser head
Output coupler
Nd:YVO4
Output
SESAM
Output coupler coating
b
a
M3 SESAM Laser diode OC
M1 Gain medium
M2 Pump optics
c Fig. 2.1.7. (a) Setup of a passively mode-locked high-power Nd3+ :YAG laser, containing a Direct-Coupled Pump (DCP) laser head, two curved mirrors, a SESAM, and an Output Coupler mirror (OC) with 7 % transmission. (b) Quasi-monolithic setup as used for passively mode-locked Nd3+ :YVO4 lasers with repetition rates above 20 GHz. (c) Typical setup of a femtosecond laser. The gain medium is pumped with a laser diode. A prism pair is used for dispersion compensation, and a SESAM as mode-locker.
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For high pulse repetition rate an even simpler cavity design has been used. In the 1-μm spectral region, Nd:YVO4 has been found to be a particularly suitable gain medium for very high repetition rates, as already discussed in Sect. 2.1.3.1. For repetition rates of 40 GHz and above, a quasimonolithic design [99Kra2] is useful, where the output-coupler mirror is a dielectric coating directly fabricated on a curved and polished side of the laser crystal, while the SESAM is attached to the other side of the crystal (see Fig. 2.1.7b). The crystal may be anti-reflection-coated on the flat side, or just uncoated. Note that with a reflecting coating on this side, there is a cavity effect: Depending on the exact size of the air gap between crystal and SESAM, the optical field can more or less penetrate the SESAM structure, and accordingly the effective modulation depth and saturation fluence of the SESAM are modified. In this case for optimum performance, one has to manipulate the width of the air gap. A quasi-monolithic cavity design has also been used for Q-switched microchip lasers (Fig. 2.1.6) and described in more detail in Sect. 2.1.3.1. Counterpropagating waves overlap in the crystal, leading to the phenomenon of spatial hole burning, which can have significant influence on the mode-locking behavior [95Bra2, 95Kae3, 01Pas2]. In particular, it allows for shorter pulses, although often with some amount of chirp, because gain narrowing is effectively eliminated: even without a mode-locker, such lasers tend to run with a significant emission bandwidth, and the mode-locker more or less only has to lock the phases of the running cavity modes.
2.1.3.3.2 Typical femtosecond lasers Most femtosecond lasers are based on an end-pumped laser setup, with a broad-band laser medium such as Ti3+ :sapphire, Cr3+ :LiSAF, Nd:glass or Yb3+ :glass (see Sect. 2.1.3.1 for an overview). In the case of Ti3+ :sapphire, the pump source can be either an Ar ion laser or a frequency-doubled solid-state laser. In any case, one typically uses a few watts of pump power in a beam with good transverse beam quality, because the mode radius in the Ti3+ :sapphire rod is usually rather small. Other gain media like Cr3+ :LiSAF, Nd:glass or Yb3+ :glass are typically pumped with highbrightness diode lasers, delivering a few watts with beam-quality factor M 2 in the order of 10 in one direction and < 5 in the other direction, which allows for diffraction-limited laser output with typically a few hundred milliwatts. The typical laser cavities (see Fig. 2.1.7c as an example) contain two curved mirrors in a distance of a few centimeters on both sides of the gain medium. The pump power is usually injected through one or both of these mirrors, which also focus the intracavity laser beam to an appropriate beam waist. One of the two “arms” of the cavity ends with the output coupler mirror, while the other one may be used for a SESAM as a passive mode-locker. One arm typically contains a prism pair (Sect. 2.1.5.2.3), GTI (Sect. 2.1.5.2.1) or chirped mirrors (Sect. 2.1.5.2.4) for dispersion compensation, which is necessary for femtosecond pulse generation. In most cases, femtosecond lasers operate in the regime of negative overall intracavity dispersion so that soliton-like pulses are formed. Instead of a SESAM, or in addition to it, the Kerr lens in the gain medium can be used for mode-locking (Sect. 2.1.4.4). In most cases, soft-aperture KLM is used. Here, the cavity design is made so that the Kerr lens reduces the mode area for high intensities and thus improves the overlap with the (strongly focused) pump beam. This is achieved by operating the laser cavity near one of the stability limits of the cavity, which are found by varying the distance between the above mentioned curved folding mirrors, or some other distance in the cavity. For the shortest pulse durations around 5–6 fs, the strong action of KLM as an effective fast saturable absorber is definitely required. Also double-chirped mirrors (Sect. 2.1.5.2.4) are required for precise dispersion compensation over a very broad bandwidth. Typically, several dispersive mirrors are used in the laser cavity, and additional mirrors may be used for further external compression. A broadband SESAM allows for self-starting mode-locking.
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[Ref. p. 134
Higher pulse energies and peak powers have been generated by using laser setups with reduced repetition rates of only a few MHz. The long cavity length required for such repetition rates is achieved by inserting a multi-pass cell [64Her]. However, the limiting factor to the pulse energy is ultimately not the practically achievable cavity length but rather the nonlinearity of the gain crystal – at least in the sub-30-femtosecond domain: If self-phase modulation becomes too strong, this destabilizes the mode-locking process.
2.1.3.3.3 High-power thin-disk laser The by far highest average powers in the sub-picosecond domain can be obtained from thin-disk Yb3+ :YAG lasers, passively mode-locked with a SESAM. The first result, with 16.2 W in 700-fs pulses [00Aus], received a lot of attention for its unusually high output power. More importantly, this new approach introduced the first power-scalable technology for sub-picosecond lasers. For this reason, further big improvements became possible, first to 60 W average power [03Inn] and later even to 80 W [04Bru], in both cases with pulse durations near 700 fs. Recently, pulse energies well above 1 μs have been generated directly from the passively mode-locked thin-disk laser first with 5.1 μs [06Mar] and then even with 11 μs [07Mar] pulse energies. These lasers are operated in the soliton mode-locked regime (Sect. 2.1.6.7). For thermal reasons negative dispersion was obtained with GTI dispersive mirrors (Sect. 2.1.5.2.1), which however also have to be carefully optimized. The power scalability of the passively mode-locked thin-disk laser is important. First of all, the thin-disk laser head [94Gie] itself is power-scalable because of the nearly one-dimensional heat flow in the beam direction: Thermal effects (like thermal lensing) do not become more severe if the mode area is scaled up proportional to the power level. A possible problem is only the effect of stress, which has to be limited with refined techniques for mounting the crystal on the heat sink. The SESAM also has the geometry of a thin disk and thus does not limit the power: More power on an accordingly larger area does not significantly increase the temperature excursion, nor the optical intensities in the device. Finally, the tendency for Q-switching instabilities does not become stronger if e.g. the pump power and the mode areas in the disk and the absorber are all doubled while leaving pump intensity and cavity length unchanged. Thus the whole concept of the passively mode-locked thin-disk laser is power-scalable in the sense that the output power can be increased without making the following key challenges more severe: heating in the disk, heating or nonthermal damage of the SESAM, and Q-switching instabilities. Of course, further power increases can introduce other challenges which are no issue at lower powers, such as the difficulty to do dispersion compensation with optical elements that can stand the very high intracavity powers. For a longer period the maximum pulse energy obtained directly from a passively mode-locked thin-disk laser had been 1.75 μJ [03Inn]. A further increase of the pulse energy was limited by strong nonlinearities of initially unknown origin. We then discovered that the Kerr nonlinearity of the air inside the cavity was large enough to add a significant amount of nonlinear phase shift per cavity roundtrip. Numerical estimations using the nonlinear refractive index of air show good agreement with the missing nonlinearity in [03Inn]. To avoid contributions of the air to the nonlinear phase shift, we thus covered the laser cavity with a box that was then flooded with helium, which has a negligible nonlinearity compared to air. This resulted in pulse energies of 5.1 μJ and then even 11 μJ with transform-limited soliton pulses of about 790 fs duration. These are the highest pulse energies ever obtained directly from a cw modelocked laser without any further amplification. We believe that in the near future we can scale cw mode-locked thin-disk lasers to average powers of around 500 W and to pulse energies well above 100 μJ. In comparison low-repetitionrate Ti:sapphire lasers will not scale as well and are currently limited to the sub-1- μJ regime, even with cavity dumping (Table 2.1.2) Simple pulse compression of the high-energy ultrafast Yb:YAG thin-disk laser resulted in 33-fs pulses with a peak power of 12 MW [03Sue]. Further improvements resulted in pulses as short as 24 fs and peak intensity around 1014 W/cm2 . Such a source even makes high-field physics experiments possible but at a much higher pulse repetition rate than the Landolt-B¨ ornstein New Series VIII/1B1
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typical 1-kHz rate. This greatly increases the signal-to-noise ratio in measurements [07Mar] and reduces space-charge effects that tend to hide the underlying interesting physical processes with current sources at 1 kHz.
2.1.4 Loss modulation 2.1.4.1 Optical modulators: acousto-optic and electro-optic modulators Many textbooks, for example [86Sie, 84Yar, 98Sve], have reviewed optical modulators for pulse generation. Today the most important optical modulators for short pulse generation are the acoustooptic and electro-optic modulators. The acousto-optic modulators have the advantage of low optical insertion loss and can readily be driven at high repetition rates. They are typically used for cw mode-locking. However, for Q-switching their loss modulation is limited and the switching time is rather slow. Therefore, acousto-optic modulators are primarily used for repetitive Q-switching of cw-pumped lasers (e.g. Nd:YAG) and electro-optic modulators are used for Q-switching in general. For mode-locking the acousto-optic modulator typically consists of an acousto-optic substrate (typically fused quartz) and a transducer that launches an acoustic wave into the substrate. An acoustic resonator is formed when opposite to the transducer the crystal substrate is air backed. Then the acoustic wave is reflected and an acoustic standing wave is formed which produces a light modulator at twice the microwave drive frequency. At higher frequencies (a few hundreds of megahertz to a few gigahertz) the loss modulation is strongly reduced by the acoustic attenuation in the substrate. Thus, at higher modulation frequencies a sapphire [90Kel1, 90Wei] or a GaP [90Wal] substrate has been used successfully.
2.1.4.2 Saturable absorber: self-amplitude modulation (SAM) Saturable absorbers have been used to passively Q-switch and mode-lock many lasers. Different saturable absorbers, such as organic dyes, color filter glasses, dye-doped solids, ion-doped crystals and semiconductors have been used. Independent of the specific saturable absorber material, we can define a few macroscopic absorber parameters that will determine the pulse generation process. The relevant macroscopic properties of a saturable absorber are the modulation depth, the nonsaturable loss, the saturation fluence, the saturation intensity and the impulse response or recovery times (Table 2.1.5). These parameters determine the operation of a passively mode-locked or Q-switched laser. In our notation we assume that the saturable absorber is integrated within a mirror structure thus we are interested in the nonlinear reflectivity change R (t) as a function of time and R (Fp,A ) as a function of the incident pulse energy fluence on the saturable absorber. If the saturable absorber is used in transmission, we simply characterize the absorber by nonlinear transmission measurements, i.e. T (t) and T (Fp,A ). Both the saturation fluence Fsat,A and the absorber recovery time τA are determined experimentally without any needs to determine the microscopic properties of the nonlinearities. The saturation fluence of the absorber does not only depend on material properties but also on the specific device structure in which the absorber is integrated, which gives significantly more design freedom. Standard pump-probe techniques determine the impulse response R (t) and therefore τA . In the picosecond regime we typically only have to consider one picosecond recovery time, because much faster femtosecond nonlinearities in the saturable absorber give negligible modulation depth. This is shown with a semiconductor saturable absorber in Fig. 2.1.8, where the differential impulse Landolt-B¨ ornstein New Series VIII/1B1
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Table 2.1.5. Saturable absorber quantities, their defining equations and units. Symbol
Defining equation or measurement
Unit
Saturation fluence
Fsat,A
measurement R (Fp,A ) or T (Fp,A ), (Fig. 2.1.9)
J/cm2
Recovery time
τA
measurement R (t) or T (t), (Fig. 2.1.8)
s
Incident beam area
AA
measurement
cm2
Saturation energy
Esat,A
Esat,A = AA Fsat,A
J
Saturation intensity
Isat,A
Isat,A = Fsat,A /τA
W/cm2
Modulation depth
ΔR or ΔT
measurement R (Fp,A ) or T (Fp,A ), (Fig. 2.1.9)
Nonsaturable loss
ΔRns or ΔTns
measurement R (Fp,A ) or T (Fp,A ), (Fig. 2.1.9)
Incident pulse energy
Ep
measurement
J
Incident pulse fluence
Fp,A
J/cm2
Incident intensity
IA (t)
Fp,A = Ep /AA Fp,A = IA (t) dt
Reflectivity pump − probe signal
Quantity
-10
W/cm2
100 fs excitation pulse
4 ps excitation pulse
-5
0
5 15 20 10 Pump − probe delay [ps]
25
30
Fig. 2.1.8. Typical measured impulse response of a SESAM measured with standard degenerate pumpprobe measurements using two different excitation pulse durations. The saturable was grown at low temperature, which reduced the recovery time to about 20 ps. The short intraband thermalization recovery time results in negligible modulation depth with a 4 ps excitation pulse. Thus, only the slower recovery time due to carrier trapping is important in the picosecond regime.
response DR (t) was measured for two different excitation pulse durations using a semiconductor saturable absorber. For excitation with a picosecond pulse the pump-probe trace clearly shows no significant modulation depth with a fast time constant. In the femtosecond pulse regime we normally have to consider more than one absorber recovery time. In this case the slow component normally helps to start the initial pulse formation process. The modulation depth of the fast component then determines the pulse duration at steady state. Further improvements of the saturable absorber normally require some better understanding of the underlying physics of the nonlinearities which can be very interesting and rather complex. A more detailed review about the microscopic properties of ultrafast semiconductor nonlinearities for saturable absorber applications is given in a recent book chapter [00Sie]. Ultrafast semiconductor dynamics in general are discussed in much more detail by [99Sha]. However, the basic knowledge of the macroscopic properties of the absorber and how to measure [04Hai] and adjust them to a certain value is normally sufficient for stable pulse generation. The saturation fluence Fsat,A is determined and defined by the measurement of the nonlinear change in reflectivity R (Fp,A ) as a function of increased incident pulse fluence (Fig. 2.1.9). The traveling-wave rate equations [89Agr] in the slow absorber approximation give normally a very Landolt-B¨ ornstein New Series VIII/1B1
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100 F
Reflectivity R [%]
sat,A
= 18 m J/cm 2
D R ns = 3.7%
R ns 95 D R = 4.9%
R 0 R ns 90 0
50
100 150 200 250 Incident pulse fluence F p,A [ m J/cm 2 ]
300
Fig. 2.1.9. Measured nonlinear reflectivity as a function of incident pulse fluence on a typical SESAM. Theoretical fit determines the macroscopic saturable absorber parameters: saturation fluence Fsat,A , modulation depth ΔR and nonsaturable loss ΔRns .
good fit and determine the saturation fluence Fsat,A , modulation depth ΔR and nonsaturable losses ΔRns of the absorber [95Bro1, 04Hai]. The modulation depth is typically small (i.e. a few percent to a fraction of a percent!) to prevent Q-switching instabilities in passively mode-locked solid-state lasers [99Hoe1]. Thus it is reasonable to make the following approximation: ΔR = 1 − e−2q0 ≈ 2q0 ,
q0 1 ,
(2.1.6)
where q0 is the unsaturated amplitude loss coefficient. The saturation of an absorber can be described with the following differential equation [89Agr]: q (t) − q0 q (t) P (t) dq (t) =− − , dt τA Esat,A
(2.1.7)
where q (t) is the saturable amplitude loss coefficient that does not include any nonsaturable losses and P (t) is the time-dependent power incident on the absorber. Note that (2.1.7) may not be precise for high excitations where inverse saturable absorption can start to become important: For example, high excitation many times above the saturation fluence can result in additional effects such as two-photon absorptions, free carrier absorption, thermal and even various damage effects [99Tho], [05Gra2]. Two-photon absorption only starts to become significant in the femtosecond pulse width regime and results in an earlier roll-off of the nonlinear reflectivity at high incident pulse fluences. This is a well-known effect and has been used in power-limiting devices before [86Wal]. In this regime, however, the absorber is operated more closely to the damage threshold which needs to be evaluated separately. Our experience is that damage in semiconductor saturable absorbers typically occurs at around 100 times the saturation fluence of the absorber with longterm degradation observed close to below this damage threshold. Therefore, we normally operate the device a least an order of magnitude below this damage threshold, ideally at an incident pulse fluence of 3 to 5 times the saturation fluence of the absorber. We therefore neglect these very high-fluence effects in the following discussion. They, however, will become important again for suppressing Q-switching instabilities and will be discussed in more detail in Sect. 2.1.6.8. At any time t the reflected (or transmitted) intensity Iout (t) from the saturable absorber is given by Iout (t) = R (t) Iin (t) = e−2q(t) Iin (t) for a given input pulse Iin (t). Then the total net reflectivity is given by Landolt-B¨ ornstein New Series VIII/1B1
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2.1.4 Loss modulation
Rtot
[Ref. p. 134
Iout (t) dt 2 Fout =1− q (t) Iin (t) dt . = = Fin Fin Iin (t) dt
(2.1.9)
This determines the total absorber loss coefficient qp , which results from the fact that part of the excitation pulse needs to be absorbed to saturate the absorber: Rtot = e−2qp ≈ 1 − 2qp .
(2.1.10)
From (2.1.9) and (2.1.10) it then follows 1 qp = q (t) Iin (t) dt = q (t) f (t) dt , Fin
(2.1.11)
where f (t) ≡
Iin (t) Pin (t) = Fin Ep,in
with
f (t) dt =
1 Fin
Iin (t) dt = 1 .
(2.1.12)
We then distinguish between two typical cases: a slow and a fast saturable absorber.
2.1.4.2.1 Slow saturable absorber In the case of a slow saturable absorber, we assume that the excitation pulse duration is much shorter than the recovery time of the absorber (i.e. τp τA ). Thus, we can neglect the recovery of the absorber during pulse excitation and (2.1.7) reduces to: dq (t) q (t) P (t) . ≈− dt Esat,A
(2.1.13)
This differential equation can be solved and we obtain for the Self-Amplitude Modulation (SAM): ⎤ ⎡ t E p (2.1.14) f (t ) dt ⎦ . q (t) = q0 exp ⎣− Esat,A 0
Equation (2.1.11) then determines the total absorber loss coefficient for a given incident pulse fluence Fp,A : Fsat,A qp (Fp,A ) = q (t) f (t) dt = q0 1 − e−Fp,A /Fsat,A . (2.1.15) Fp,A It is not surprising that qp does not depend on any specific pulse form because τp τA . It is useful to introduce a saturation parameter S ≡ Fp,A /Fsat,A . For strong saturation (S > 3), we have qp (Fp,A ) ≈ q0 /S (2.1.15) and the absorbed pulse fluence is about Fsat,A ΔR. 2.1.4.2.2 Fast saturable absorber In the case of a fast saturable absorber, the absorber recovery time is much faster than the pulse duration (i.e. τp τA ). Thus, we can assume that the absorption instantaneously follows the absorption of a certain power P (t) and (2.1.7) reduces to 0=−
q (t) − q0 q (t) P (t) − . τA Esat,A
(2.1.16)
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The saturation of the fast absorber then follows directly from (2.1.16): q (t) =
q0 , IA (t) 1+ Isat,A
(2.1.17)
where we used the fact that Psat,A = Esat,A /τA and P (t) /Psat,A = IA (t) /Isat,A . In the linear regime we can make the following approximation in (2.1.17): q (t) ≈ q0 − γA P (t)
with γA ≡
q0 Isat,A AA
.
(2.1.18)
The total absorber loss coefficient qp , (2.1.10)–(2.1.11), now depends on the pulse form and for a sech2 -pulse shape we obtain for an incident pulse fluence Fp,A and the linear approximation of q (t) for weak absorber saturation (2.1.18):
1 Fp,A 1 q (t) IA (t) dt = q0 1 − qp (Fp,A ) = . (2.1.19) Fp,A 3 τ Isat,A We will later see that we only obtain an analytic solution for fast saturable absorber mode-locking, if we assume an ideal fast absorber that saturates linearly with pulse intensity (2.1.18) – which in principle only applies for weak absorber saturation in a real absorber. For a maximum modulation depth, we then can assume that q0 = γA P0 (assuming an ideal fast absorber over the full modulation depth). We then obtain with (2.1.19) a residual saturable absorber loss of q0 /3, which the pulse experiences to fully saturate the ideal fast saturable absorber.
2.1.4.3 Semiconductor saturable absorbers 2.1.4.3.1 Semiconductor dynamics Semiconductors are well suited absorber materials for ultrashort pulse generation. In contrast to saturable absorber mechanisms based on the Kerr effect, ultrafast semiconductor nonlinearities can be independently optimized from the laser cavity design. In addition, ultrafast semiconductor spectroscopy techniques [99Sha] provide the basis for many improvements of ultrashort pulse generation with semiconductor saturable absorbers. The semiconductor electronic structure gives rise to strong interaction among optical excitations on ultrafast time scales and very complex dynamics. Despite the complexity of the dynamics, different time regimes can be distinguished in the evolution of optical excitations in semiconductors. These different time regimes are schematically illustrated in Fig. 2.1.10, which shows the energy dispersion diagram of a 2-band bulk semiconductor which is typical for a III–V semiconductor material. Optical excitation with an ultrafast laser pulse prepares the semiconductor in the coherent regime (time regime I in Fig. 2.1.10). In this regime, a well-defined phase relation exists between the optical excitations and the electric field of the laser pulse and among the optical excitations themselves. The coherence among the excitations in the semiconductor gives rise to a macroscopic polarization (dipole moment density). Since the macroscopic polarization enters as a source term in Maxwell’s equations, it leads to an electric field which is experimentally accessible. The magnitude and decay of the polarization provide information on the properties of the semiconductor in the coherent regime. The irreversible decay of the polarization is due to scattering processes (i.e. electron–electron and electron–phonon scattering) and is usually described by the so-called dephasing or transversal relaxation time. For a mathematical definition of this time constant the reader is referred to [99Sha, 90Goe, 75All].
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Energy E
III
e-e
e - phonon
II
IV
I
Wave vector k
Fig. 2.1.10. Schematic dispersion diagram of a 2-band bulk semiconductor showing the time regimes I–IV after optical excitation, see text for more details. e–e: electron–electron scattering. e–phonon: electron–phonon scattering.
After the loss of coherence, ultrafast spectroscopy of semiconductors is solely concerned with the dynamics of the population, i.e., electron and hole distributions. In this incoherent regime, the time regimes II–IV in Fig. 2.1.10 can be distinguished, as described as follows. The initial electron and hole distributions are non-thermal in most cases, i.e., they cannot be described by Fermi–Dirac statistics with a well-defined temperature [85Oud, 86Kno, 87Sch]. Scattering among charge carriers is mainly responsible for the redistribution of energy within the carrier distributions and for the formation of thermal distributions. This thermalization is shown as time regime II in Fig. 2.1.10, for the example of a thermalizing electron distribution where thermalization occurs through scattering among the electrons. For excitation of the continuum, thermalization usually occurs on a time scale of 100 fs under most experimental conditions. The exact thermalization time strongly depends on the carrier density, the excess photon energy with respect to the band edge and the type of carrier [99Sha]. In general, the carriers have a temperature different from the lattice temperature after thermalization has been completed. In Fig. 2.1.10 it is assumed that the carriers have a higher temperature than the lattice. For this case, Fig. 2.1.10 schematically shows the cooling of carriers by the emission of phonons, i.e., energy transfer to the lattice. Cooling defines the time regime III. Typical time constants are in the picosecond and tens of picosecond range. Finally, the optically excited semiconductor returns to thermodynamic equilibrium by the recombination of electron–hole pairs. Recombination is shown as time regime IV in Fig. 2.1.10. In a perfect semiconductor crystal, recombination proceeds via the emission of photons or Auger processes at high carrier densities. These recombination processes in a good quality semiconductor (i.e. with a low level of defect states) take place on time scales of hundreds of picoseconds and longer. Another ultrafast process is encountered if large densities of deep-level traps are incorporated in a semiconductor. Trapping of carriers into deep levels can proceed on sub-picosecond time scales (not shown in Fig. 2.1.10). Since carrier trapping is important in many saturable absorber applications, it is discussed in more details in Sect. 2.1.4.3.2. We note that the different time regimes temporally overlap. For example, a scattering process may destroy the coherence and contribute to thermalization. Nevertheless, it is very useful to distinguish between the different time regimes because they are a convenient means for the description of the complex semiconductor dynamics. The schematic picture of the different time regimes also demonstrates that two or more time constants are usually required to describe the temporal response of a semiconductor absorber. For example, we recall that thermalization typically takes place on the 100-fs time scale while carrier trapping proceeds on time scales from a few hundreds Landolt-B¨ ornstein New Series VIII/1B1
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Energy E
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Energy E
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Interband recombination ≈ ns
Conduction band
Density of states D
Conduction band
Density of states D
Mid−gap traps for electrons ≈ ps −ns
Valence band
Intraband thermalization ≈ 100 fs Valence band
Fig. 2.1.11. Typical Self-Amplitude Modulation (SAM) observed in a semiconductor saturable absorber: A semiconductor can absorb light if the photon energy is sufficient to excite carriers from the valence band to the conduction band. Under conditions of strong excitation, the absorption is saturated because possible initial states of the pump transition are depleted while the final states are partially occupied. Within typically 60–300 fs after the excitation, the carriers in each band thermalize, and this already leads to a partial recovery of the absorption. On a longer time scale – typically between a few ps and a few ns depending on defect engineering – they will be removed by recombination and trapping. Both processes can be used for mode-locking of lasers.
of femtoseconds to tens of picoseconds. This results in the measured Self-Amplitude Modulation (SAM) of a semiconductor saturable absorber as shown in Fig. 2.1.11. This corresponds to the loss modulation used for passive mode-locking in Fig. 2.1.3.
2.1.4.3.2 Typical self-amplitude modulation (SAM) from semiconductor saturable absorbers Figure 2.1.11 shows a typical Self-Amplitude Modulation (SAM) observed in semiconductor saturable absorbers and their different relaxation processes as discussed in Sect. 2.1.4.3.1. Semiconductor saturable absorber applications in ultrashort pulse generation often require picosecond or sub-picosecond absorber recovery times [01Pas1]. The simplest way to obtain such short absorber recovery times would be to remove the optically excited carriers from the bands a few hundreds of femtoseconds to a few tens of picosecond after they have been created. However, intrinsic recombination processes are usually too slow to deplete the band states of a semiconductor on picosecond or sub-picosecond time scales. Therefore, one generates defect states in the band gap which give rise to fast carrier trapping to deplete the bands. The trapping time is determined by the density and the type of the traps. Higher trap densities give rise to faster trapping. Standard methods for the controlled incorporation of defect and trap states are ion implantation [89Zie] and Low-Temperature (LT) molecular beam epitaxy [88Smi]. More uncontrolled incorporation of defects occurs close to surfaces. In ion-implanted semiconductors, the trap density and the type of defect are determined by the implantation dose. The growth temperature controls the defect density in LT semiconductors where larger defect densities are incorporated at lower temperatures [94Liu, 93Wit]. Semiconductor saturable absorbers can be produced either with Molecular
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Beam Epitaxy (MBE) or with Metal-Organic chemical Vapor deposition (MOVPE). MBE gives us the additional flexibility to grow semiconductors at lower temperatures, down to ≈ 200 ◦ C, while MOVPE usually requires growth temperatures of ≈ 600 ◦ C to break up the incident molecules on the wafer surface during the growth. Lower growth temperatures lead to microscopic structural defects which act as traps for excited carriers and thus reduce the recovery time, which is beneficial for the use in ultrafast lasers. Optimized materials combine an ultrafast recovery time with low saturation fluence, high modulation and small nonsaturable losses. This material optimization issue has been addressed for ion-implanted [99Led] and LT-grown [96Sie, 99Hai1, 99Hai2] semiconductor saturable absorbers.
2.1.4.3.3 Semiconductor saturable absorber materials Semiconductor materials offer a wide flexibility in choosing the emission wavelength of the lasers. It ranges from ≈ 400 nm in the UV using GaN-based materials to ≈ 2.5 μm in the mid-infrared using GaInAsSb-based materials. More standard high-performance semiconductor material systems which can be grown today cover the infrared wavelength range from 800 nm up to 1.5 μm. Semiconductor compounds used for these wavelengths are AlGaAs (800 nm to 870 nm), InGaAs (870 nm to about 1150 nm), GaInNAs (1.1 μm to 1.5 μm), or InGaAsP (1.5-μm range). A larger wavelength range for a given material composition may only be obtained at the expense of increased defect concentrations because of an increased lattice mismatch to a given substrate material. Generally, bulk quantum-well and quantum-dot semiconductor saturable absorbers have been used. Especially, the quantum-dot saturable absorbers turned out to be advantageous for the integration into the VECSEL structure [04Lor, 07Maa].
2.1.4.3.3.1 InGaAs/GaAs/AlGaAs semiconductor material system This material is best-suited for the 800 nm–1.1 μm wavelength range because of the near-perfect lattice match between GaAs and AlGaAs. InGaAs saturable absorbers have been grown on AlAs/GaAs Bragg mirrors and have been the material of choice for SESAMs at an operation wavelength of ≈ 1 μm. However, thicker InGaAs saturable absorbers above the critical thickness had surface striations that introduced too much scattering losses to be used inside a laser [94Kel]. Low-temperature MBE growth (see more details in Sect. 2.1.4.3.2) resulted in strain-relaxed structures with surfaces that were optically flat, but with strongly increased defect densities. For SESAM applications this is actually advantageous, and has been exploited to optimize the dynamic response of the SESAM. InGaAs saturable absorbers on AlAs/GaAs Bragg mirrors have even been used at an operation wavelength of 1.3 μm [96Flu2, 97Flu] and 1.55 μm [03Spu, 04Zel]. However, these highly strained layers with high indium content exceed the critical thickness, and show significant nonsaturable losses due to strain and defect formation. Optimized low-temperature MBE growth, however, (Sect. 2.1.4.3.2) allowed improved InGaAs SESAMs to support stable mode-locking and Q-switching in diode-pumped solid-state lasers.
2.1.4.3.3.2 GaInAsP/InP semiconductor material system This material system can be lattice-matched on the InP substrate but suffers from low refractiveindex contrast and poor temperature characteristics. Due to the low refractive-index contrast, a high number of InP/GaInAsP mirror pairs are required to form Distributed Bragg Reflectors (DBRs). This demands very precise control of the growth to achieve DBRs with uniform and accurate layer thickness.
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2.1.4.3.3.3 GaInNAs semiconductor material Recently, dilute nitrides (i.e. GaInNAs) have attracted strong attention for laser devices in the telecommunication wavelength range between 1.3 μm and 1.55 μm that can use high-contrast GaAs/AlGaAs DBR mirrors [02Har, 02Rie]. Adding a few percent of nitrogen to InGaAs has two advantages: a redshift of the absorption wavelength and a reduction of the lattice mismatch to GaAs. The drawback is that the nitrogen incorporation decreases the crystalline quality, which is a big challenge for the fabrication of active devices. However, SESAMs are passive devices relying on fast defect-induced nonradiative carrier recombination to allow for short-pulse generation. GaInNAs saturable absorber on GaAs/AlsAs Bragg mirrors operating at 1.3 μm have been demonstrated for solid-state laser mode-locking. The first GaInNAs SESAM was reported to mode-lock a quasi-cw pumped Nd:YLF and Nd:YALO laser at 1.3 μm [02Sun]. Self-starting stable passive cw modelocking of a solid-state laser with a GaInNAs SESAM was demonstrated more recently [04Liv]. A detailed study of the absorber properties and the mode-locking behavior revealed that GaInNAs SESAMs provide low saturation fluences and possess extremely low losses [04Liv, 04Sch2, 05Gra3]. These SESAMs supported mode-locking at repetition rates of 5 GHz and 10 GHz [05Spu2]. In 2003, GaInNAs SESAMs at 1.5 μm were shown to mode-lock Er-doped fiber lasers but had too much loss for solid-state lasers [03Okh]. Just recently for the first time successful mode-locking of a solid-state laser at 1.54 μm using a GaInNAs SESAM has been demonstrated [05Rut].
2.1.4.3.3.4 AlGaAsSb semiconductor material Another interesting long-wavelength semiconductor saturable absorber material is based on antimonide. The quaternary alloy AlGaAsSb has a wide band-gap tunability (1.55 μm to 0.54 μm) and intrinsically low modulation depth [03Saa, 04Ost]. Similar to InGaAsP, AlGaAsSb is latticematched to InP, but its absorption edge is not as steep as the one of InGaAsP [87Ada]. Therefore, operating the absorber in the bandtail results in a sufficiently small modulation depth (i.e. usually below 0.5 %) suitable for high-repetition-rate lasers. An Sb-based SESAM can be grown by MOVPE with AlGaAsSb/InP DBRs [06Ost]. Compared to InGaAsP, AlGaAsSb forms a high refractive-index contrast with InP (0.4) allowing for a lower number of Bragg periods. The first antimonide SESAM self-started and mode-locked a 61-MHz Er:Yb:glass laser [04Gra]. More recently, this was extended to an Er:Yb:glass laser at 10 GHz, 1535 nm and with 4.7 ps pulse duration [06Gra]. 2.1.4.3.3.5 GaAs wafer for ≈ 1 μm Simple GaAs wafers have been used as saturable absorbers to mode-lock [04Kon] and Q-switch [00Li, 01Che1] solid-state lasers at a wavelength of ≈ 1 μm. Photo electrons in the conduction band are generated from mid-gap defect states (i.e. EL2) present in GaAs wafers. These EL2-defects have similar properties as the arsenic antiside point defects in LT-grown materials (Sect. 2.1.4.3.2). This transition, however, has a very high saturation fluence in the range of 1 mJ/cm2 [06Li] which is typically about 100 times higher than the standard valence-to-conduction band transition generally used for SESAMs. This strongly increases the tendency for Q-switching instabilities (Sect. 2.1.6.8).
2.1.4.3.3.6 Semiconductor-doped dielectric films Saturable absorbers based on semiconductor-doped dielectric films have been demonstrated [99Bil]. In this case, InAs-doped thin-film rf-sputtering technology was used which offers similar advantages as SESAMs, i.e. the integration of the absorber into a mirror structure. At this point, however, Landolt-B¨ ornstein New Series VIII/1B1
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the saturation fluence of ≈ 10 mJ/cm2 is still rather high for stable solid-state laser mode-locking. In comparison, epitaxially grown SESAMs typically have a saturation fluence in the range of 10 μJ/cm2 depending on the specific device structure.
2.1.4.3.4 Historical perspective and SESAM structure Semiconductor saturable absorbers have been used as early as 1974 in CO2 lasers [74Gib] and 1980 for semiconductor diode lasers [80Ipp]. A color-center laser was the first solid-state laser that was cw mode-locked with an intracavity semiconductor saturable absorber [89Isl]. However, for both the diode and color-center laser, dynamic gain saturation supported pulse formation and the recovery time of the slow saturable absorber was not relevant for pulse generation (Fig. 2.1.5a). In addition, because of the large gain cross section (i.e. approximately 10−14 cm2 for diode lasers and 10−16 cm2 for color-center lasers) Q-switching instabilities were not a problem. This is not the case for most other solid-state lasers, such as ion-doped solid-state lasers, which have typically 1000 or even more times smaller gain cross sections. Thus, the semiconductor saturable absorber parameters (Fig. 2.1.8 and Fig. 2.1.9) have to be chosen much more carefully for stable cw mode-locking. We typically integrate the semiconductor saturable absorber into a mirror structure, which results in a device whose reflectivity increases as the incident optical intensity increases. This general class of devices is called SEmiconductor Saturable Absorber Mirrors (SESAMs) [92Kel2, 96Kel, 03Kel]. A detailed description and guideline how to design a SESAM for either passive modelocking or Q-switching for different laser parameters is given in recent book chapters [99Kel, 03Pas]. SESAMs are well-established as a useful device for passive mode-locking and Q-switching of many kinds of solid-state lasers. The main reason for this device’s utility is that both the linear and nonlinear optical properties can be engineered over a wide range, allowing for more freedom in the specific laser cavity design. In addition, semiconductor saturable absorbers are ideally suited for passive mode-locking solid-state lasers because the large absorber cross section (in the range of 10−14 cm2 ) and therefore small saturation fluence is ideally suited for suppressing Q-switching instabilities [99Hoe1]. Initially, SESAMs for solid-state lasers were used in coupled cavities [90Kel2, 92Kel1], because these early SESAM designs introduced too much loss for the laser cavity (Fig. 2.1.12b). In 1992, this work resulted in a new type of intracavity saturable absorber mirror, the Antiresonant Fabry–Perot Saturable Absorber (A-FPSA) [92Kel2, 94Kel] where the absorber was integrated inside a Fabry–Perot structure of which the bottom reflector was a high reflector (i.e. approximately 100 %) (Fig. 2.1.12c). This was the first intracavity saturable absorber design that allowed for passive mode-locking of diode-pumped solid-state lasers without Q-switching instabilities. The Fabry–Perot was operated at antiresonance to obtain broad bandwidth and low loss. The A-FPSA mirror was mainly based on absorber layers sandwiched between the lower semiconductor and the higher SiO2 /TiO2 dielectric Bragg mirrors. The top reflector of the A-FPSA provides an adjustable parameter that determines the intensity entering the semiconductor saturable absorber and therefore the saturation fluence of the saturable absorber device. Therefore, this design allowed for a large variation of absorber parameters by simply changing absorber thickness and top reflectors [95Bro1, 95Jun1]. This resulted in an even simpler SESAM design with a single quantum well absorber layer integrated into a Bragg mirror [95Bro2] (Fig. 2.1.12d) – this was later referred to as Saturable Bragg Reflectors (SBRs) [95Tsu]. In the 10-fs regime with Ti:sapphire lasers we have typically replaced the lower semiconductor Bragg mirror with a metal mirror to support the required large reflection bandwidth [96Flu1, 97Jun1]. No post-growth processing is required with an ultrabroadband monolithically grown fluoride semiconductor saturable absorber mirror that covers nearly the entire gain spectrum of the Ti:sapphire laser. Using this SESAM inside a Ti:sapphire laser resulted in 9.5-fs pulses [02Sch2]. The reflection bandwidth was achieved with a AlGaAs/CaF2 semiconductor Bragg mirror [00Sch]. More recently a broadband SESAM was fabricated by increasing the reflection bandwidth Landolt-B¨ ornstein New Series VIII/1B1
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Output coupler Laser gain Mirror cw laser
a
Coupled cavity RPM − Dec 1,1990 Saturable Mirror absorber R bottom A − FPSA− April 1,1992
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c
d
e
Rtop Rbottom Rtop
Scaling A − FPSA − Feb.15,1995 Single quantum well absorber 0 (SBR June 15,1995) SESAM − May 19,1995 Absorber embedded inside an arbitrary mirror
Fig. 2.1.12. Historical evolution of different SESAM designs: (a) Ordinary cw laser. (b) Initially the semiconductor saturable absorber was used inside a nonlinear coupled cavity, termed Resonant Passive Mode-locking (RPM) [90Kel2]. (c) First intracavity saturable absorber to passively mode-lock diodepumped solid-state lasers without Q-switching instabilities: Antiresonant Fabry–Perot Saturable Absorber (A-FPSA) [92Kel2]. (d) Scaling of the A-FPSA resulted in a single quantum well saturable absorber integrated into a Bragg mirror [95Bro2] – later also referred to as Saturable Bragg Reflector (SBR) [95Tsu]. (e) General concept of SEmiconductor Saturable Absorber Mirror (SESAM) without any restrictions on the mirror design [95Kel, 96Kel].
of an AlGaAs/AlAs or InGaAlP/AlAs Bragg mirror using wet oxidation of AlAs which creates low-index Alx Oy layers [04Tan]. In 1995 [95Kel] it was further realized that the intracavity saturable absorber can be integrated in a more general mirror structure that allows for both saturable absorption and negative dispersion control, which is now generally referred to as a SEmiconductor Saturable Absorber Mirror (SESAM) (Fig. 2.1.12e). In a general sense we then can reduce the design problem of a SESAM to the analysis of multilayered interference filters for a given desired nonlinear reflectivity response for both the amplitude and phase. The A-FPSA [92Kel2], the Saturable Bragg Reflector (SBR) [95Bro2, 95Tsu, 95Kno] and the Dispersive Saturable Absorber Mirror (D-SAM) [96Kop2] are then special examples of SESAM designs. In this more general class of design we do not restrict ourselves to Bragg mirror structures, which are defined by a stack of quarter-wave layers with alternating high and low refractive indices (e.g. [95Kno]). For example, we have demonstrated with many examples that non-quarter-wave layers in mirrors give more design freedom for integrating the absorber layers into the mirror structure. Furthermore, double-chirped semiconductor mirror structures can provide very broadband negative dispersion [99Pas1]. One important parameter of a SESAM device is its saturation fluence, which has typical values in the range of 10–100 μJ/cm2 . Lower saturation fluence is particularly relevant for fundamentally mode-locked solid-state lasers with GHz pulse repetition rates and high average power [05Spu3]. Novel design structures allowed to substantially lower the saturation fluence of SESAMs into the 1 μJ/cm2 regime [05Spu3]. New terms “LOw-Field-Enhancement Resonant-like SESAM device” (LOFERS) [03Wei1] and “Enhanced SESAM device” (E-SESAM) [03Wei2] were introduced. A LOFERS can be used to further reduce saturation fluence without the detrimental effects of strongly resonant structures such as bistability and narrow bandwidth. Such a design has a low-finesse resonant structure such that the field strength is substantially higher in the spacer layer containing the absorber and therefore reducing the saturation fluence further. So far the SESAM is mostly used as an end mirror of a standing-wave cavity. Very compact cavity designs have been achieved for example in passively Q-switched microchip lasers (Fig. 2.1.6) Landolt-B¨ ornstein New Series VIII/1B1
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and passively mode-locked miniature lasers (Fig. 2.1.7b) where a short laser crystal defines a simple monolithic cavity. The SESAM attached directly to the laser crystal then formed one end-mirror of this laser cavity. As the laser cannot be pumped through the SESAM, the laser output needs to be separated from the collinear pump by a dichroic mirror. These examples suggest that there is need for a device that combines the nonlinear properties of the SESAM with an output coupler. This has been demonstrated before for a passively mode-locked fiber laser [96Sha] and later also for solid-state lasers [01Spu1].
2.1.4.4 Effective saturable absorbers using the Kerr effect 2.1.4.4.1 Transverse and longitudinal Kerr effect The extremely rapid response and the broad bandwidth of the Kerr nonlinearity are very attractive for a mode-locking process. For high intensities, the polarization inside a dielectric medium does not proportionally follow the electric field anymore. This gives rise to an index change proportional to intensity. Off-resonance, this nonlinear optical effect is extremely fast, with estimated response times in the few-femtosecond range. The transverse and longitudinal effects resulting from the intensity dependence are shown schematically in Fig. 2.1.13. The transverse Kerr effect retards the central and most intense part of a plane wave front and thus acts as a focusing lens, referred to as the Kerr lens. Along the axis of propagation, the longitudinal Kerr effect retards the center of an optical pulse, producing a red shift of the leading part of the pulse, and a blue shift in the trailing part. Consequently, the longitudinal Kerr effect has been named Self-Phase Modulation (SPM). Longitudinal Kerr effect: self - phase modulation (SPM) Dn ( z )= n2 I ( z )
Transverse Kerr effect: Kerr lens Dn (x,y) = n2 I ( x,y )
Fig. 2.1.13. The Kerr effect gives rise to an increase of the refractive index with intensity, causing a retardation of the most intense parts of a pulse (i.e. for n2 > 0). In its longitudinal form, the Kerr effect causes Self-Phase Modulation (SPM) and in its transverse form, a nonlinear lens is formed in the central part of the beam profiles (i.e. Kerr lens).
2.1.4.4.2 Nonlinear coupled cavity The longitudinal Kerr effect can also be used to produce the same effect as a fast saturable absorber. To do this, the phase nonlinearity provided by the longitudinal Kerr effect has to be converted into an effective amplitude nonlinearity. The earliest mode-locking schemes based only on SPM used a coupled cavity to convert SPM into SAM. In the soliton laser [84Mol], pulses compressed by SPM and anomalous dispersion in the coupled cavity are directly coupled back into the main laser cavity. This provides more gain for the center of the pulse. Pulses as short as 19 fs have been Landolt-B¨ ornstein New Series VIII/1B1
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demonstrated with color-center lasers [87Mit]. Later, the SPM-to-SAM conversion with a coupled cavity was demonstrated even when the pulses inside the coupled cavity were broadened due to positive group velocity dispersion [89Kea]. In this case, no compressed pulse was fed back into the main cavity. An effective SAM was obtained because SPM inside the coupled cavity generates a phase modulation on the pulse that adds constructively at the peak of the pulse in the main cavity and destructively in the wings, thus shortening the pulse duration inside the main cavity. This was also later referred to as Additive Pulse Mode-locking (APM) [89Ipp]. Although very powerful in principle, these coupled-cavity schemes have the severe disadvantage that the auxiliary cavity has to be stabilized interferometrically. An alternative method for converting the reactive Kerr nonlinearity into an effective saturable absorber was discovered in 1991: Kerr-Lens Mode-locking (KLM) [91Spe].
2.1.4.4.3 Kerr lens The discovery of Kerr-lens mode-locking has been a breakthrough in ultrashort pulse generation [91Spe]. Initially the mode-locking mechanism was not understood and was somewhat of a mystery. But within a short time after the initial discovery it became clear that the transverse Kerr effect provides a fast saturable absorber. In KLM, the transverse Kerr effect produces a Kerr lens (Fig. 2.1.13) that focuses the high-intensity part of the beam more strongly than the low-intensity part. Thus, combined with an intracavity aperture the Kerr lens produces less loss for high intensity and forms an effective fast saturable absorber [91Kel, 91Sal1, 91Neg] (Fig. 2.1.14). A similar modelocking effect can be obtained without a hard aperture when the Kerr lens produces an increased Δ n = n 2 I (r,t ) Nonlinear medium Kerr lens
Incident beam
Aperture
Intense pulse Low−intensity light
Loss Saturated gain Pulse Time t Fig. 2.1.14. Kerr-Lens Mode-locking (KLM) is obtained due to the Kerr lens at an intracavity focus in the gain medium or in another material, where the refractive index is increased with increased intensity Δn = n2 I(r, t), where n2 is the nonlinear refractive index and I(r, t) the radial- and time-dependent intensity of a short-pulsed laser beam. In combination with a hard aperture inside the cavity, the cavity design is made such that the Kerr lens reduces the laser mode area for high intensities at the aperture and therefore forms an effective fast saturable absorber. In most cases, however, soft-aperture KLM is used where the reduced mode area in the gain medium improves for a short time the overlap with the (strongly focused) pump beam and therefore the effective gain. A significant change in mode size is only achieved by operating the laser cavity near one of the stability limits of the cavity.
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overlap of the laser mode with the pump profile in the gain medium [93Pic]. The Kerr lens provides the strongest advantage for the pulsed operation when the cavity is operated close to the stability limit. Optimization guidelines for SAM produced by the Kerr lens in different cavities can be found in [95Mag]. Unfortunately, the transverse Kerr effect couples the mode-locking process with the laser cavity mode. In contrast, the use of only the longitudinal Kerr effect in mode-locking totally decouples the mode-locking process from the laser mode. This allows optimum cavity design for scaling the laser to higher powers and to higher pulse repetition rates without being constrained by the Kerr lens.
2.1.4.4.4 Nonlinear polarization rotation In fiber lasers a different Kerr-effect-based effective saturable absorber has been used to generate pulses as short as 38 fs [92Hof] – the shortest pulses generated directly from a fiber laser so far. An effective fast saturable absorber is obtained with a Kerr-induced nonlinear polarization rotation in a weakly birefringent fiber combined with a polarization-dependent loss. Previously, a similar idea has been used to “clean up” high-intensity pulses by reducing the low-intensity pulse pedestals [92Tap, 92Bea].
2.1.4.5 Nonlinear mirror based on second-harmonic generation The second-order nonlinear susceptibility χ(2) nonlinearities can also be used to construct effective saturable absorbers [88Sta]. A nonlinear mirror based on this principle consists of a frequencydoubling crystal and a dichroic mirror. For short pulses, a part of the incident laser light is converted to the second harmonic, for which the mirror is highly reflective, and converted back to the fundamental wave, if an appropriate relative phase shift for fundamental and second-harmonic light is applied. On the other hand, unconverted fundamental light experiences a significant loss at the mirror. Thus the device has a higher reflectivity at higher intensities. This has been used for mode-locking e.g. with up to 1.35 W of average output power in 7.9-ps pulses from a Nd3+ :YVO4 laser [97Agn]. The achievable pulse duration is often limited by group-velocity mismatch between fundamental and second-harmonic light.
2.1.5 Pulse propagation in dispersive media 2.1.5.1 Dispersive pulse broadening Dispersion compensation is important in ultrashort pulse generation. When a pulse travels through a medium, it acquires a frequency-dependent phase shift φ(ω) = k n(ω)L, where k is the wave number, n(ω) the refractive index and L the medium length. A phase shift which varies linearly with the frequency corresponds to a time delay, without any change of the temporal shape of the pulse. Higher-order phase shifts, however, tend to modify the pulse shape and are thus of relevance for the formation of short pulses. The phase shift can be expanded in a Taylor series around the center angular frequency ω0 of the pulse: φ (ω) = φ0 +
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Table 2.1.6. Sellmeier equations for different materials. The wavelength λ is given in units of μm. Material
Defining Sellmeier equation
2
2
Constants
2
Aλ Bλ Cλ + 2 + 2 λ2 − λ21 λ − λ22 λ − λ23
Fused quartz
n2 = 1 +
SF10 glass
a2 a3 a4 a5 n2 = a0 + a1 λ2 + 2 + 4 + 6 + 8 λ λ λ λ
Sapphire
n2 = 1 +
2
2
2
a1 λ a2 λ a3 λ + 2 + 2 λ2 − b1 λ − b2 λ − b3
A = 0.6961663 λ1 = 0.0684043 B = 0.4079426 λ2 = 0.1162414 C = 0.8974794 λ3 = 9.896161 a0 a1 a2 a3 a4 a5
= 2.8784725 = −0.010565453 = 3.327942 × 10−2 = 2.0551378 × 10−3 = −1.1396226 × 10−4 = 1.6340021 × 10−5
a1 = 1.023798 a2 = 1.058264 a3 = 5.280792 b1 = 0.00377588 b2 = 0.0122544 b3 = 321.3616
Here, the derivatives are evaluated at ω0 . ∂φ/∂ω is the group delay Tg , ∂ 2 φ/∂ω 2 the Group Delay Dispersion (GDD), ∂ 3 φ/∂ω 3 the Third-Order Dispersion (TOD). The GDD describes a linear frequency dependence of the group delay and thus tends to separate the frequency components of a pulse: For positive GDD, e.g., the components with higher frequencies are delayed with respect to those with lower frequencies, which results in a positive “chirp” (“up-chirp”) of the pulse. Higher orders of dispersion generate more complicated distortions. Material dispersion is normally described with Sellmeier equations for the refractive index as a function of the wavelength, i.e. n (λ). With the Sellmeier equations (Table 2.1.6) all the necessary dispersive quantities can be calculated (Table 2.1.7). An example is given in Table 2.1.8. The broader the bandwidth of the pulse (i.e., the shorter the pulse duration), the more terms of this expansion are significant. GDD which acts on an initially unchirped Gaussian pulse with Full-Width-at-Half-Maximum (FWHM) pulse duration τ0 , increases the pulse duration according to [86Sie] 2
4 ln 2 d2 φ/d ω 2 τp (z) = 1+ , (2.1.20) τ0 τ02 where it is assumed that the incident pulse is transform-limited, i.e. the time–bandwidth product of the Gaussian pulse is τ0 Δ νp = 0.4413, where Δ νp is the Full-Width-at-Half-Maximum (FWHM) spectral width of the pulse intensity (Fig. 2.1.15). Only second-order dispersion (i.e. ∂ 2 φ/∂ ω 2 ) and higher orders are broadening the pulse. The first-order dispersion gives the group delay, i.e. the delay of the peak of the pulse envelope. It is apparent that the effect of GDD becomes strong if GDD > τ02 . Similarly, TOD becomes important if TOD > τ03 . It is important to note that for dispersive pulse broadening (which is in the linear pulse propagation regime) the spectrum of the pulse remains unchanged, only the spectral content of the pulse is redistributed in time. With positive dispersion the long-wavelength part of the spectrum is in the leading edge of the pulse and the short-wavelength part in the trailing edge of the pulse, i.e. “red is faster than blue” (Fig. 2.1.15). In the regime of strong pulse broadening, i.e. d2 φ/d ω 2 τ02 , we can reduce (2.1.20) Landolt-B¨ ornstein New Series VIII/1B1
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Table 2.1.7. Dispersion quantities, their defining equations and units. kn : wave vector in the dispersive media, i.e. kn = k n = n 2 π/λ, where λ is the vacuum wavelength. z: a certain propagation distance. c: vacuum light velocity. ω: frequency in radians/second. Quantity
Symbol
Defining equation
Defining equation using n (λ)
Phase velocity
υp
ω kn
c n
Group velocity
υg
dω dkn
c n
Group delay
Tg
Tg =
z dφ = , φ ≡ kn z υg dω
1 dn λ 1− dλ n nz dn λ 1− c dλ n dn λ 1− dλ n
Dispersion: 1st order
dφ dω
nz c
Dispersion: 2nd order
d2 φ dω 2
λ3 z d2 n 2 π c2 dλ2
Dispersion: 3rd order
d3 φ dω 3
−λ4 z 4 π2 c3
2 d3 n d n 3 2 +λ 3 dλ dλ
Dispersive medium
τ0
φ ( ω) = k . n ( ω ). L
τ
n ( ω) L
Fig. 2.1.15. Dispersive pulse broadening through a material with positive dispersion.
to τp (z) ≈
d2 φ Δ ωp , d ω2
(2.1.21)
where Δ ωp = 2π Δ νp is the FWHM spectral width (in radians/second) of the pulse intensity.
2.1.5.2 Dispersion compensation Without any dispersion compensation the net GDD for one cavity round trip is usually positive, mainly because of the dispersion in the gain medium. Other components like mirrors may also contribute to this. However, in lasers with > 10 ps pulse duration the dispersion effects can often be ignored, as the total GDD in the laser cavity is typically at most a few thousand fs2 , much less than the pulse duration squared (2.1.20). For shorter pulse durations, the GDD has to be considered, and pulse durations well below 30 fs usually require the compensation of Third-Order Dispersion (TOD) or even higher orders of dispersion depending on the thickness of the gain material. In most cases, the desired total GDD is not zero but negative, so that soliton formation
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Table 2.1.8. Examples of material dispersions calculated from the Sellmeier equations given in Table 2.1.6 and the equations given in Table 2.1.7. Material
Refractive index n at a center wavelength of 800 nm
Fused quartz
n (0.8 μm) = 1.45332 ∂n 1 = −0.017 ∂λ 800 nm μm ∂ 2 n 1 = 0.04 ∂λ2 800 nm μm2 ∂ 3 n 1 = −0.24 ∂λ3 μm3
∂kn s ns = 4.84 × 10−9 = 4.84 ∂ω 800 nm m m 2 ∂ 2 kn s fs2 −26 = 3.61 × 10 = 36.1 ∂ω 2 800 nm m mm 3 3 ∂ kn s fs3 = 2.74 × 10−41 = 27.4 3 ∂ω 800 nm m mm
n (0.8 μm) = 1.71125 1 ∂n = −0.0496 ∂λ 800 nm μm ∂ 2 n 1 = 0.176 ∂λ2 800 nm μm2 ∂ 3 n 1 = −0.997 ∂λ3 μm3
∂kn s ns = 5.70 × 10−9 = 5.70 ∂ω 800 nm m m 2 2 ∂ kn s fs2 = 1.59 × 10−25 = 159 2 ∂ω 800 nm m mm 3 3 ∂ kn s fs3 = 1.04 × 10−40 = 104 3 ∂ω 800 nm m mm
n (0.8 μm) = 1.76019 1 ∂n = −0.0268 ∂λ 800 nm μm ∂ 2 n 1 = 0.064 ∂λ2 800 nm μm2 ∂ 3 n 1 = −0.377 ∂λ3 800 nm μm3
∂kn s ns = 5.87 × 10−9 = 5.87 ∂ω 800 nm m m 2 2 ∂ kn s fs2 = 5.80 × 10−26 = 58 2 ∂ω 800 nm m mm 3 3 ∂ kn s fs3 = 4.21 × 10−41 = 42.1 3 ∂ω 800 nm m mm
800 nm
SF10 glass
800 nm
Sapphire
Propagation constant kn at a center wavelength of 800 nm
can be exploited. Usually, one requires sources of negative GDD, and in addition appropriate higherorder dispersion for shorter pulses. The most important techniques for dispersion compensation are discussed in the following subsections. Different optical elements that introduce wavelengthdependent refraction (i.e. prism pairs, Sect. 2.1.5.2.3) or wavelength-dependent diffraction (i.e. grating pairs, Sect. 2.1.5.2.2) can be used to introduce an additional wavelength dependence to the round-trip phase and thus contribute to the overall dispersion. A wavelength-dependent round-trip phase can also be introduced with GTIs (Sect. 2.1.5.2.1) and chirped mirrors (Sect. 2.1.5.2.4). The challenge in ultrashort pulse generation is dispersion compensation over a large bandwidth to compensate for the dispersive pulse broadening that is occurring in the gain material and other elements inside the laser cavity. Dispersion compensation is important because for example, a 10-fs (1-fs) Gaussian pulse at the center wavelength of 800 nm is broadened to 100 fs (1 ps) after only 1 cm of fused quartz due to second-order dispersion. This follows from (2.1.21) for the regime of strong pulse broadening and Tables 2.1.6–2.1.8. In addition, in femtosecond lasers the pulses are ideally soliton pulses for which a constant negative dispersion over the full spectral width of the pulse balances the chirp of the self-phase modulation. The necessary negative dispersion required for a certain pulse duration follows from (2.1.74). It is required that all higher-order dispersion terms are negligibly small. Landolt-B¨ ornstein New Series VIII/1B1
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For optimum soliton formation of a sub-10-fs pulse inside the laser, only a very small amount of a constant negative total intracavity dispersion is necessary to form a stable soliton pulse (2.1.74). For example, we estimated the necessary dispersion to be only −10 fs2 for a Ti:sapphire laser producing 6.5-fs pulses [97Jun3, 98Sut]. Here we assumed an estimated self-phase modulation coefficient of about 0.07/MW, an average output power of 200 mW using a 3 % output coupler and a pulse repetition rate of 86 MHz. This results in an intracavity pulse energy of 77.5 nJ. With (2.1.74) then follows an estimated negative group delay dispersion of −10 fs2 in a cavity round trip. There are different methods for dispersion compensation, such as the Gires–Tournois Interferometer (GTI), grating pairs, prism pairs and chirped mirrors. The dispersion compensation is summarized in Table 2.1.9 with the symbols defined in Fig. 2.1.16.
2.1.5.2.1 Gires–Tournois interferometer (GTI) A Gires–Tournois Interferometer (GTI) [64Gir, 92Kaf] is a very compact dispersion-compensation element, which basically replaces one flat laser cavity mirror. The negative dispersion is obtained due to the Fabry–Perot interferometer, operated in reflection (Fig. 2.1.16a). Normally, in a GTI the rear mirror is highly reflective over the whole wavelength range (i.e. ideally 100 %) whereas the front mirror has a relatively low reflectivity, typically a few percent. The spacer layer in the Fabry–Perot should contain a non-absorbing material and is very often air, such that the thickness can be easily changed. The phase shift varies nonlinearly by 2 π for each free spectral range, calculated as Δ ν = c/2nd, where n and d are the refractive index and the thickness of the spacer material, respectively. Within each free spectral range, the GDD oscillates between two extremes the magnitude of which is proportional to d2 and also depends on the front-mirror reflectivity. Ideally, the GTI is operated near a minimum of the GDD, and the usable bandwidth is some fraction (e.g. one tenth) of the free spectral range, which is proportional to d−1 : d2 φ 1 d2 φ 2 (2.1.22) ∝ . ∝d , Bandwidth of 2 2 dω dω d In Table 2.1.9 the material dispersion in the GTI spacer layer was neglected. The bandwidth compared to the other techniques is limited, thus a GTI is typically used for pulse durations above 100 fs. There is a trade-off: A broader bandwidth is obtained with a smaller Fabry–Perot thickness but then the amount of negative dispersion is strongly reduced. For example, an air-spaced GTI with 80 μm thickness and a top reflectivity of 4 % produces a negative dispersion of about −0.13 ps2 at a wavelength of 799 nm. In comparison a 2.25 μm thick air space results in about −100 fs2 at a wavelength of 870 nm. Tunable GDD can be achieved if the spacer material is a variable air gap, which however must be carefully stabilized to avoid unwanted drifts. More stable but not tunable GDD can be generated with monolithic designs, based e.g. on thin films of dielectric media like TiO2 and SiO2 , particularly for the use in femtosecond lasers. The main drawbacks of GTI are the fundamentally limited bandwidth (for a given amount of GDD) and the limited amount of control of higher-order dispersion.
2.1.5.2.2 Grating pairs Grating pairs [69Tre] produce negative dispersion due to the wavelength-dependent diffraction (Fig. 2.1.16b). To obtain a spatially coherent beam two paths through the grating pair are required. Compared to prism pairs (Sect. 2.1.5.2.3), pairs of diffraction gratings can generate higher dispersion in a compact setup. However, because of the limited diffraction efficiency of gratings, the losses of a grating pair are typically higher than acceptable for use in a laser cavity, except in Landolt-B¨ ornstein New Series VIII/1B1
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Table 2.1.9. Dispersion compensation, its defining equations and figures. c: light velocity in vacuum, λ: wavelength in vacuum, λ0 : center wavelength of pulse spectrum, ω: frequency in radians/second. Quantity
Defining equation
Gires–Tournois Interferometer (GTI) (Fig. 2.1.16a)
d: thickness of Fabry–Perot n: refractive index of material inside Fabry–Perot (airspaced n = 1) (Note: Material dispersion is neglected.) 2nd : round-trip time of the Fabry–Perot c Rt : intensity reflectivity of top reflector of Fabry–Perot (Bottom reflector is assumed to have a 100%-reflectivity.) t0 =
Dispersion: 2nd order
Four-grating compressor (Fig. 2.1.16b)
Dispersion: 2nd order
Dispersion: 3rd order
Four-prism compressor (Fig. 2.1.16c)
√ −2t20 (1 − Rt ) Rt sin ωt0 d2 φ = 2 √ dω 2 1 + Rt − 2 Rt cos ωt0 Lg : grating pair spacing Λ: grating period θi : angle of incidence at grating 2 −3/2 λ3 Lg λ d2 φ =− 2 2 1− − sin θi dω 2 πc Λ Λ λ 2 d3 φ d2 φ 6 π λ 1 + Λ sin θi − sin θi =− 2 2 dω 3 dω c λ 1− − sin θi Λ n: refractive index of prisms θB : angle of incidence of prism is at Brewster angle θB = arctan [n (λ0 )] α = π − 2θB : apex angle of prism
sin θB θ2 (λ) = arcsin n (λ) sin π − 2θB − arcsin n (λ) L: apex-to-apex prism distance h: beam insertion into second prism sin β =
Dispersion: 2nd order
Dispersion: 3rd order
h cos θ2 L cos (α/2)
λ3 d2 P d2 φ = dω 2 2 π c2 dλ2 2 2 2 2 ∂θ2 ∂n ∂n ∂ θ2 d P ∂ 2 n ∂θ2 = 2 L cos β L sin β − 2 + dλ2 ∂λ2 ∂n ∂n2 ∂λ ∂n ∂λ 2 2 ∂n ∂n 1 ∂2n + 2n − 3 L cos β ≈4 L sin β − 8 ∂λ2 n ∂λ ∂λ −λ4 d3 φ = 3 dω 4 π2 c3
2 d3 P d P 3 2 +λ 3 dλ dλ
d3 P d3 n dn d2 n ≈ 4 3 L sin β − 24 L cos β 3 dλ dλ dλ dλ2
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Bottom reflector R b = 100%
1
2
Top reflector Rt
AR−coating
I blue blue red
Glas substrate
d
x
θB
Spatially incoherent beam
Diffraction grating, e.g. Blaze grating
I
Air gap: tunable width and no absorption
I
red t
R GTI
a
[Ref. p. 134
t
b
Additional positive GDD due to prism material
t β L blue
red I blue
red t Spatially incoherent beam
c
λ1 Substrate
λ2
λ3
λ4
Wavelength λ [nm]
1000
800
600
400 0
d
1
4 2 3 Penetration depth [μm]
5
6
Fig. 2.1.16. Dispersion compensation techniques: (a) Gires–Tournois Interferometer (GTI), (b) grating pair, (c) prism pair, (d) chirped mirror (i.e. shown here: a double-chirped mirror).
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cases with a high gain (e.g., in fiber lasers). For this reason, grating pairs are normally only used for external pulse compression [84Tom]. The grating pairs alone can only be used to compensate for second-order dispersion. Higher-order dispersion limits pulse compression in the ultrashort pulse width regime. Therefore, a combination of a grating and prism compressor was used to generate the long-standing world record of 6-fs pulses with dye lasers [87For]. There are mainly two types of gratings: ruled or holographic. Removing material from a master substrate with a precise instrument called a ruling engine produces ruled gratings. Replicas of the ruled grating are then pressed and the pressings are coated. Holographic gratings are produced by interfering two laser beams on a substrate coated with a photoresist, which is subsequently processed to reproduce the sinusoidal interference pattern. Generally, replicas cannot be produced from holographic masters, i.e. they are more expensive. Higher damage threshold can be obtained with gold-coated ruled gratings (i.e. > 500 mJ/cm2 at 1 ps). The diffraction efficiency in this case is around 88 % to 92 % depending on the grating. Because four paths through the gratings are required for dispersion compensation and a spatially coherent beam, this amounts to at least about 30 % loss.
2.1.5.2.3 Prism pairs Prism pairs [84For] are well established for intracavity dispersion compensation. Negative dispersion is obtained with the wavelength-dependent refraction (Fig. 2.1.16c): The different wavelength components travel in different directions after the first prism and along parallel but separated paths after the second prism. The wavelength components can be recombined simply on the way back after reflection at a plane end mirror (of a standing-wave cavity) or by a second prism pair (in a ring cavity). Spatial separation of different wavelengths occurs only in a part of the cavity. The obtained negative GDD from the geometric effect is proportional to the prism separation, and an additional (usually positive) GDD contribution results from the propagation in the prism material. Thus, to obtain a spatially coherent beam two paths through the prism pair are required. The insertion loss is very small because the angle of incidence is at Brewster angle. The prism apex angle is chosen such that the incident beam at Brewster angle is also at the minimum deviation. Prism pairs offer two advantages. First, the pulse width can be varied by simply moving one of the prisms which adjusts the prism insertion and therefore the amount of positive GDD from the propagation in the prism material (see Fig. 2.1.16c). Second, the laser can be tuned in wavelength by simply moving a knife edge at a position where the beam is spectrally broadened. Both properties are often desired for spectroscopic applications, for example. However, the prism pair suffers from higher-order dispersion, which is the main limitation in ultrashort pulse generation in the sub-10-fs regime. Different prism materials introduce different amounts of higher-order dispersion. For compact lasers with pulse durations of few tens to hundreds of femtoseconds the more dispersive SF10-prisms are better because they require a smaller prism separation than fused quartz prism for example. But the smaller prism separation comes at the expense of a larger higher-order dispersion. Fused quartz is one of the best materials for ultrashort pulse generation with minimal higher-order dispersion. The higher-order dispersion of the prism pairs is dominated by the prism spacing, which is not changed significantly when we adjust the dispersion by inserting the prisms into the laser beam. More compact geometries for dispersion compensation make use of a single prism only [94Ram, 96Kop1]. In this case, the wavelength components are spatially separated in the whole resonator, not only in a part of it. Even without any additional prisms, refraction at a Brewster interface of the gain medium can generate negative dispersion. In certain configurations, where the cavity is operated near a stability limit, the refraction effect can be strongly increased [99Pas2], so that significant negative GDD can be generated in a compact cavity. The amount of GDD may then also strongly depend on the thermal lens in the gain medium and on certain cavity dimensions.
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For example, at a fused quartz prism spacing of 40 cm, the total dispersion that is produced by a double pass through the prism pairs amounts to −862 fs2 and a third-order dispersion of −970 fs3 at a center wavelength of 800 nm, assuming zero prism insertion into the beam (Table 2.1.9). We can reduce the negative dispersion by moving the prisms into the laser beam: Each additional millimeter of prism insertion produces a positive dispersion of 101 fs2 but only a third-order dispersion of 78 fs3 per cavity round trip. Thus, the prism pairs can generally only be used to compensate for either second- or third-order dispersion. With fused quartz prisms alone pulses as short as 10 fs can be produced with a Ti:sapphire laser [93Asa, 96Flu1]. Slightly shorter pulses can be achieved if the Ti:sapphire laser is operated at a center wavelength of approximately 850 nm, where nearzero second- and third-order dispersion can be obtained for a Ti:sapphire crystal of about 2 mm thickness. In this case 8.5 fs have been generated [94Zho]. Another dispersion compensation is then required for shorter pulse generation. Therefore, the chirped mirrors were designed to show the inverse higher-order group delay dispersion of the dispersion of the prism pair plus laser crystal to eliminate the higher-order dispersion and obtain a slightly negative but constant group delay dispersion required for an ideal soliton pulse.
2.1.5.2.4 Chirped mirrors Dielectric Bragg mirrors with regular quarter-wave layer stacks have a fairly small dispersion when operated well within their reflection bandwidth, but increasing dispersion at the edges of this range. Modified designs can be used to obtain well-controlled dispersion over a large wavelength range. One possibility already discussed is the use of a GTI structure (see Sect. 2.1.5.2.1). Another broad range of designs is based on the concept of the chirped mirrors [94Szi] (Fig. 2.1.16d): If the Bragg wavelength is appropriately varied within a Bragg mirror design, longer wavelengths can be reflected deeper in the mirror structure, thus acquire a larger phase change, which leads to negative dispersion. However, the straight-forward implementation of this idea leads to strong oscillations of the GDD (as a function of frequency) which render such simple designs useless. These oscillations can be greatly reduced by numerical optimizations which introduce complicated (and not analytically explainable) deviations from the simple chirp law. A great difficulty is that the figure of merit to optimize is a complicated function of many layer thickness variables, which typically has a large number of local maxima and minima and thus is quite difficult to optimize. Nevertheless, refined computing algorithms have lead to designs with respectable performance, which were realized with precision growth of dielectric mirrors. Such mirrors can compensate the dispersion in Ti3+ :sapphire lasers for operation with pulse durations well below 10 fs. Figure 2.1.16d shows a typical chirped mirror structure which schematically shows the path of a long-wavelength (i.e. 1000 nm) and short-wavelength (i.e. 650 nm) beam. This results in negative dispersion, because the long wavelengths are made to penetrate deeper into the mirror structure than short wavelengths. Figure 2.1.16d also shows the standing-wave electric field patterns in a chirped mirror structure versus wavelength. The negative dispersion of the mirrors is clearly illustrated by the dependence of penetration depth on wavelength for the range of 650 to 1050 nm. The highly transmissive region around 500 nm is used for pumping the Ti:sapphire laser through these chirped mirrors. According to [94Szi], chirping means that the Bragg wavelength λB is gradually increased along the mirror, producing a negative Group Delay Dispersion (GDD). However, no analytical explanation of the unwanted oscillations typically observed in the group delay and GDD of such a simple-chirped mirror was given. These oscillations were minimized purely by computer optimization. The original chirped mirror design was further refined by the Double-Chirped Mirror (DCM) [97Kae, 99Mat] concept which takes into account the impedance matching problem which occurs at the air–mirror interface and the grating structure in the mirror. An exact coupled-mode analysis [97Mat] was used to develop a double-chirp technique. The impedance matching concept allowed a much better insight to the design limitations and allowed for the first time for an analytical design with custom-tailored dispersion characteristics which required only minor numerical optimization Landolt-B¨ ornstein New Series VIII/1B1
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[99Mat]. The strong periodic variation in the group delay of the original chirped mirrors occurs due to impedance mismatch between the incident medium (i.e. typically air) and the mirror stack and also within the mirror stack. Using the accurate analytical expressions for phase, group delay, and GDD [99Mat], DCMs could be designed and fabricated with a smooth and custom-tailored GDD suitable for generating pulses in the two-cycle regime directly from a Ti:sapphire laser [99Sut, 99Mor1, 99Mor2]. A Double-Chirped Mirror (DCM) [97Kae, 99Mat] is a multilayer interference coating that can be considered as a composition of at least two sections, each with a different task. The layer materials are typically SiO2 and TiO2 . The first section is the AR coating, typically composed of 10 to 14 layers. It is necessary because the theory is derived assuming an ideal matching to air. The other section represents the actual DCM structure, as derived from theory. The double-chirp section is responsible for the elimination of the oscillations in the GDD from within the mirror stack. Double-chirping means that in addition to the local Bragg wavelength λB the local coupling of the incident wave to the reflected wave is independently chirped as well. The local coupling is adjusted by slowly increasing the high-index layer thickness in every pair so that the total optical thickness remains λB /2. This corresponds to an adiabatic matching of the impedance. The AR-coating, together with the rest of the mirror, is used as a starting design for a numerical optimization program. Since theoretical design is close to the desired design goal, a local optimization using a standard gradient algorithm is sufficient. At this point, only the broadband AR-coating sets a limitation on the reduction of the GDD oscillations. An AR-coating with a residual reflectivity of less than 10−4 is required for a DCM at a center wavelength of around 800 nm, which results in a bandwidth of only 250 nm [00Mat]. This bandwidth limitation cannot be removed with more layers in the mirror structure [96Dob]. The invention of the BAck-SIde-Coated (BASIC) mirrors [00Mat] or later the tilted front-side mirrors [01Tem] resolved this issue. In the BASIC mirror the ideal DCM structure is matched to the low-index material of the mirror which ideally matches the mirror substrate material. This DCM structure is deposited on the back of the substrate and the AR-coating is deposited on the front of the slightly wedged or curved substrate, so that the residual reflection is directed out of the beam and does not deteriorate the dispersion properties of the DCM structure on the other side of the substrate. Thus, the purpose of the AR-coating is only to reduce the insertion losses of the mirror at the air–substrate interface. For most applications it is sufficient to get this losses as low as 0.5 %. Therefore, the bandwidth of such an AR-coating can be much broader. Both the DCM and AR-coating multilayer structures can be independently designed and optimized. Based on this analysis, we designed a BAck-SIde-Coated Double-Chirped Mirror (BASIC DCM) that supports a bandwidth of 220 THz with group delay dispersion oscillations of about 2 fs2 (rms), an order-ofmagnitude improvement compared to previous designs of similar bandwidth [00Mat]. Ultrabroad BASIC DCMs with a bandwidth of 270 THz have also been used to compress supercontinuum of cascaded hollow fibers down to 4.6 fs [04San]. The trade-off is that the substrate has to be as thin as possible to minimize the overall material dispersion. In addition, the wedged mirror leads to an undesired angular dispersion of the beam. Another possibility to overcome the AR-coating problem is given with the idea to use an ideal DCM under Brewster-angle incidence [03Ste]. In this case, the low-index layer is matched to air. However, under p-polarized incidence the index contrast and therefore the Fresnel reflectivity of a layer pair is reduced and more layer pairs are necessary to achieve high reflectivity. This increases the penetration depth into the mirror which has the advantage that these mirrors can produce more dispersion per reflection but this means that scattering and other losses and also fabrication tolerances become even more severe. In addition, this concept is difficult to apply to curved mirrors. Furthermore, the spatial chirp of the reflected beam has to be removed by back reflection or an additional reflection from another Brewster-angle mirror. Other methods to overcome the AR-coating problem are based on using different chirped mirrors with slightly shifted GTI oscillations that partially cancel each other. Normally, these chirped mirrors are very difficult to fabricate [00Mat]. Many different growth runs normally result in strong Landolt-B¨ ornstein New Series VIII/1B1
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shifts of those GTI oscillations so that a special selection of mirrors makes it ultimately possible to obtain the right dispersion compensation. Some tuning of the oscillation peaks can be obtained by the angle of incidence [00Sut]. A specially designed pair of DCMs has been used to cancel the spurious GTI oscillation [01Kae] where an additional quarter-wave layer between the AR-coating and the DCM structure was added in one of the DCMs. Also this design has its drawbacks and limitations because it requires an extremely high precision in fabrication and restricts the range of angles of incidence. After this overview it becomes clear that there is no perfect solution to the challenge of ultrabroadband dispersion compensation. At this point ultrabroadband chirped mirrors are the only way to compress pulses in the one- to two-optical-cycle regime and normally a larger selection of chirped mirrors are required to “match and reduce” the residual unwanted GDD oscillations from all mirrors inside the laser cavity.
2.1.6 Mode-locking techniques 2.1.6.1 Overview Passive mode-locking mechanisms are well-explained by three fundamental models: slow saturable absorber mode-locking with dynamic gain saturation [72New, 74New] (Fig. 2.1.5a), fast saturable absorber mode-locking [75Hau1, 92Hau] (Fig. 2.1.5b) and slow saturable absorber modelocking without dynamic gain saturation which in the femtosecond regime is described by soliton mode-locking [95Kae1, 95Jun2, 96Kae] and in the picosecond regime by Paschotta et al. [01Pas1] (Fig. 2.1.5c). The physics of most of these techniques can be well explained with Haus’s master equation formalism as long as at steady state the changes in the pulse envelope during the propagation inside the cavity are small. At steady state the pulse envelope has to be unchanged after one round trip through the cavity. Passive mode-locking, however, can only be analytically modeled in the weak saturation regime, which is typically not the case in SESAM mode-locked solid-state lasers. However, this formalism still provides a useful approach to describe mode-locking techniques in an unified fashion. Recent numerical simulations show that analytical results with fast saturable absorbers only slightly underestimate numerical solutions and correctly describe the dependence on saturated gain, gain bandwidth and absorber modulation taking into account more strongly saturated absorbers and somewhat longer saturation recovery times in SESAM mode-locked solid-state lasers [01Pas1]. A short introduction to Haus’s formalism is given in Sect. 2.1.6.2 and Table 2.1.10. Afterwards we will describe all mode-locking techniques using this formalism and summarize the theoretical prediction for pulse shape and pulse duration (Table 2.1.11). For solid-state lasers self-Q-switching instabilities in passive mode-locking are a serious challenge. Simple guidelines to prevent those instabilities and obtain stable cw mode-locking are presented in Sect. 2.1.6.8.
2.1.6.2 Haus’s master equations Haus’s master equation formalism [95Hau2] is based on linearized differential operators that describe the temporal evolution of a pulse envelope inside the laser cavity. At steady state we then obtain the differential equation:
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
ΔA ≈ −iδL |A|2 A δL ≡
(2.1.47)
SPM
kn2 z AL
1 kn z 2
D≡
∂2 A ∂t2
ΔA ≈ iD
(2.1.41)
δL : SPM coefficient (2.1.44) n2 : nonlinear refractive index AL : laser mode area inside laser material (Note: Here we assume that the dominant SPM occurs in the laser material. Then z is equal to 2 times the length of the laser crystal in a standing-wave cavity.)
D: dispersion parameter (half of the total group delay dispersion per cavity round trip – Table 2.1.7) (2.1.40) d2 kn kn = dω 2
γA : absorber coefficient (2.1.18) and (2.1.35) q0 : maximum saturable amplitude loss coefficient Isat,A : saturation intensity AA : laser mode area in saturable absorber
Dispersion: 2nd order
q0 Isat,A AA
γA ≡
ΔA ≈ γA |A|2 A
(2.1.36)
Fast saturable absorber
ωm : loss modulation frequency in radians/second 2M : peak-to-peak modulation depth for amplitude loss coefficient
ψ: phase shift
2 M ωm 2
ΔA ≈ iψA
Ms ≡
Dg : gain dispersion (2.1.32) g: saturated amplitude gain coefficient Ωg : HWHM of gain bandwidth in radians/second Δνg : FWHM of gain bandwidth, i.e. Δνg = Ωg /π
Constant phase shift
ΔA ≈ −Ms t2 A
g Ωg2
Constants
l: amplitude loss coefficient
(2.1.34)
Loss modulator
Dg ≡
New constants
ΔA ≈ −lA
(2.1.32)
Gain
Linearized operator
∂2 ΔA ≈ g + Dg 2 A ∂t
Constant loss
Eq.
Laser cavity element
Table 2.1.10. Linearized operators that model the change in the pulse envelope A (t) for each element in the laser cavity and their defining equations. The pulse envelope is normalized such that |A (z, t)|2 is the pulse power P (z, t) (2.1.24). kn : wave vector in the dispersive media, i.e. kn = kn = n2π/λ, where λ is the vacuum wavelength. z: the relevant propagation distance for negative dispersion or SPM, respectively. c: vacuum light velocity. ω: frequency in radians/second.
Ref. p. 134] 2.1 Ultrafast solid-state lasers 103
(2.1.49)
(2.1.62)
(2.1.70)
(2.1.65)
(2.1.67)
(2.1.74)
Active ML: Amplitude loss modulation
Passive ML: Slow saturable absorber and dynamic gain saturation
Slow saturable absorber for solid-state lasers and strongly saturated absorbers (S > 3)
Fast Saturable Absorber (FSA)
Fully saturated ideal fast saturable absorber
Soliton mode-locking
soliton
soliton
numerical simulations
soliton
Gauss
Pulse shape
g ΔR for
τA 30 τp
2 |D| δL Ep
2g 1.12 ≈ q0 Δνg
g ΔR
for
|D| Dg = δL γA
τp,min = 1.7627
√
1 6 Ωg
3/4
−1/8
φs
τA g 3/2 q0
1/4 ≈ 0.45
1 Δνg
3/4
τA 1/4 g 3/8 1/8 ΔR φs
transform-limited soliton pulses for the total intracavity group delay dispersion (assuming negligible higher-order dispersion)
τp = 1.76
τp,min
1.76 = Ωg
only transform-limited soliton pulses for a well-defined intracavity group delay dispersion (assuming negligible higher-order dispersion): |D|/δL = Dg /γA
4Dg γA Ep
4 1 π Δνg
1.5 Δνg
τp = 1.76
τp,min ≈
τp ≈ 1.76 ×
Pulse duration (FWHM) Dg 2g 1 τp = 1.66 × 4 = 1.66 × 4 Ms M ω m Ωg
2.1.6 Mode-locking techniques
(2.1.76)
Eq.
ML technique
Table 2.1.11. Predicted pulse duration for the different ModeLocking (ML) techniques. The parameters used here are summarized and defined in Table 2.1.10. The pulse is transform-limited for proper dispersion compensation and is either an unchirped Gaussian or soliton pulse.
104 [Ref. p. 134
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 134]
TR
2.1 Ultrafast solid-state lasers
∂A (T, t) = ΔAi = 0 , ∂T i
105
(2.1.23)
where A is the pulse envelope, TR is the cavity round-trip time, T is the time that develops on a time scale of the order of TR , t is the fast time of the order of the pulse duration, and ΔAi are the changes of the pulse envelope due to different elements in the cavity (such as gain, loss modulator or saturable absorber, dispersion etc.) (Table 2.1.10). Equation (2.1.23) basically means that at steady state after one laser round trip the pulse envelope cannot change and all the small changes due to the different elements in the cavity have to sum up to zero. Each element is modeled as a linearized operator, which will be discussed in more detail below. 2 The pulse envelope is normalized such that |A (z, t)| is the pulse power P (z, t): E (z, t) ∝ A (z, t) ei[ω0 t−kn (ω0 )z]
2
|A (z, t)| ≡ P (z, t) ,
with
(2.1.24)
where E (z, t) is the electric field, ω0 the center frequency in radians/second of the pulse spectrum and kn = nk with k = 2π/λ the wave number with λ the vacuum wavelength and n the refractive index. Before we discuss the different mode-locking models we briefly discuss the linearized operators for the differential equations.
2.1.6.2.1 Gain A homogeneously broadened gain medium is described by a Lorentzian lineshape for which the frequency-dependent gain coefficient g (ω) is given by
g Δ ω2 2 g (ω) = for ((ω − ω0 )/Ωg ) 1 , (2.1.25) 2 ≈ g 1 −
Ωg2 ω − ω0 1+ Ωg where Δ ω = ω − ω0 , g is the saturated gain coefficient for a cavity round trip, and Ωg is the Half Width at Half Maximum (HWHM) of the gain bandwidth in radians/seconds. In the frequency domain the pulse envelope after the gain medium is given by A˜out (ω) = e g(ω) A˜in (ω) ≈ [1 + g (ω)] A˜in (ω)
for g 1 ,
(2.1.26)
where A˜ (ω) is the Fourier transformation of A (t). Equations (2.1.25) and (2.1.26) then give g g ∂2 (2.1.27) A˜out (ω) = 1 + g − 2 Δ ω 2 A˜in (ω) ⇒ Aout (t) = 1 + g + 2 2 Ain (t) , Ωg Ωg ∂t where we used the fact that a factor of Δ ω in the frequency domain produces a time derivative in the time domain. For example for the electric field we obtain: 1 ∂ ∂ ˜ (ω) eiωt dω = 1 ˜ (ω) iω eiωt dω E E (2.1.28) E (t) = ∂t ∂t 2π 2π and ∂2 ∂2 E (t) = 2 2 ∂t ∂t
1 2π
˜ (ω) eiωt dω E
=
1 2π
˜ (ω) −ω 2 eiωt dω , E
and similarly for the pulse envelope: ∂ ∂ 1 1 iΔωt ˜ A (t) = A (ω) e A˜ (ω) iΔω eiΔωt dω dω = ∂t ∂t 2π 2π Landolt-B¨ ornstein New Series VIII/1B1
(2.1.29)
(2.1.30)
106
2.1.6 Mode-locking techniques
[Ref. p. 134
and ∂2 ∂2 A (t) = ∂t2 ∂t2
1 2π
A˜ (ω) eiΔωt dω
=
1 2π
A˜ (ω) −Δω 2 eiΔωt dω .
(2.1.31)
For the change in the pulse envelope ΔA = Aout − Ain after the gain medium we then obtain: ∂2 g (2.1.32) ΔA ≈ g + Dg 2 A , Dg ≡ 2 , ∂t Ωg where Dg is the gain dispersion. 2.1.6.2.2 Loss modulator A loss modulator inside a laser cavity is typically an acousto-optic modulator and produces a sinusoidal loss modulation given by a time-dependent loss coefficient: l (t) = M (1 − cos ωm t) ≈ Ms t2 ,
Ms ≡
2 M ωm , 2
(2.1.33)
where Ms is the curvature of the loss modulation, 2M is the peak-to-peak modulation depth and ωm the modulation frequency which corresponds to the axial mode spacing in fundamental modelocking. In fundamental mode-locking we only have one pulse per cavity round trip. The change in the pulse envelope is then given by Aout (t) = e−l(t) Ain (t) ≈ [1 − l (t)] Ain (t) ⇒ ΔA ≈ −Ms t2 A .
(2.1.34)
2.1.6.2.3 Fast saturable absorber In case of an ideal fast saturable absorber we assume that the loss recovers instantaneously and therefore shows the same time dependence as the pulse envelope, (2.1.17) and (2.1.18): q (t) =
q0 ≈ q0 − γA P (t) , 1 + IA (t)/Isat,A
γA ≡
q0 . Isat,A AA
(2.1.35)
The change in the pulse envelope is then given by 2
Aout (t) = e−q(t) Ain (t) ≈ [1 − q (t)] Ain (t) ⇒ ΔA ≈ γA |A| A .
(2.1.36)
2.1.6.2.4 Group velocity dispersion (GVD) The wave number kn (ω) in a dispersive material depends on the frequency and can be approximately written as: 1 kn (ω) ≈ kn (ω0 ) + kn Δ ω + kn Δ ω 2 + . . . , (2.1.37) 2 ∂kn ∂ 2 kn and k = . In the frequency domain the pulse where Δ ω = ω − ω0 , kn = n ∂ω ω=ω0 ∂ω 2 ω=ω0 envelope in a dispersive medium after a propagation distance of z is given by A˜ (z, ω) = e−i[kn (ω)−kn (ω0 )]z A˜ (0, ω) ≈ {1 − i [kn (ω) − kn (ω0 )] z} A˜ (0, ω) ,
(2.1.38) Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 134]
2.1 Ultrafast solid-state lasers
107
where we used the slowly-varying-envelope approximation (which is applicable for pulse durations of more than 10 fs in the near infrared wavelength regime). Taking into account only the first-order and second-order dispersion terms we then obtain: 1 A˜ (z, ω) ≈ 1 − ikn Δ ωz − i kn Δ ω 2 z A˜ (0, ω) . (2.1.39) 2 The linear term in Δ ω determines the propagation velocity of the pulse envelope (i.e. the group velocity υg ) and the quadratic term in Δ ω determines how the pulse envelope gets deformed due to second-order dispersion. The influence of higher-order dispersion can be considered with more terms in the expansion of kn (ω) (2.1.37). However, higher-order dispersion only becomes important for ultrashort pulse generation with pulse durations below approximately 30 fs depending how much material is inside the cavity. Normally we are only interested in the changes of the pulse envelope and therefore it is useful to restrict our observation to a reference system that is moving with the pulse envelope. In this reference system we only need to consider second- and higher-order dispersion. In the time domain we then obtain for second-order dispersion: ∂2 1 1 d2 φ A (z, t) ≈ 1 + iD 2 A (0, t) , D ≡ kn z = , (2.1.40) ∂t 2 2 d ω2 where D is the dispersion parameter which is half of the total group delay dispersion per cavity round trip. Therefore we obtain for the change in the pulse envelope: ΔA ≈ iD
∂2 A. ∂t2
(2.1.41)
2.1.6.2.5 Self-phase modulation (SPM) The Kerr effect introduces a space- and time-dependent refractive index: n (r, t) = n + n2 I (r, t) ,
(2.1.42)
where n is the linear refractive index, n2 the nonlinear refractive index and I (r, t) the intensity of the laser beam, typically a Gaussian beam profile. For laser host materials, n2 is typically of the order of 10−16 cm2 /W and does not change very much for different materials. For example, for sapphire n2 = 3 × 10−16 cm2 /W, fused quartz n2 = 2.46 × 10−16 cm2 /W, Schott glass LG-760 n2 = 2.9 × 10−16 cm2 /W, YAG n2 = 6.2 × 10−16 cm2 /W, and YLF n2 = 1.72 × 10−16 cm2 /W. The nonlinear refractive index produces a nonlinear phase shift during pulse propagation: 2
φ (z, r, t) = −k n (r, t) z = −k [n + n2 I (r, t)] z = −knz − δL |A (r, t)| ,
(2.1.43)
where δL is the Self-Phase Modulation coefficient (SPM coefficient): δL ≡ kn2 z/AL ,
(2.1.44)
where AL is the laser mode area inside the laser medium. Here we assume that the dominant SPM inside the laser occurs in the gain medium. In this case, z is equal to twice the laser material length. Of course the mode area can be also very small in other materials. In this case, we will have to add up all the SPM contributions inside the laser resonator. The laser mode area AL is an “averaged value” in case the mode is changing within the gain medium. The electric field during propagation is changing due to SPM: E (z, t) = eiφ E (0, t) ∝ e−iδL |A(t)| A (0, t) eiω0 t−ikn (ω0 )z . 2
2
For δL |A| 1 we obtain: Landolt-B¨ ornstein New Series VIII/1B1
(2.1.45)
108
2.1.6 Mode-locking techniques 2 2 A (z, t) = e−iδL |A(t)| A (0, t) e−ikn (ω0 )z ≈ 1 − iδL |A (t)| A (0, t) e−ikn (ω0 )z .
[Ref. p. 134
(2.1.46)
After one cavity round trip we then obtain 2
ΔA ≈ −iδL |A| A .
(2.1.47)
2.1.6.3 Active mode-locking Short pulses from a laser can be generated with a loss or phase modulator inside the resonator. For example, the laser beam is amplitude-modulated when it passes through an acousto-optic modulator. Such a modulator can modulate the loss of the resonator at a period equal to the round-trip time TR of the resonator (i.e. fundamental mode-locking). The pulse evolution in an actively mode-locked laser without Self-Phase Modulation (SPM) and Group-Velocity Dispersion (GVD) can be described by the master equation of Haus [75Hau2]. Taking into account gain dispersion and loss modulation we obtain with (2.1.32) and (2.1.34) (Table 2.1.10) the following differential equation: ω m t2 1 ∂2 A (T, t) = 0 . (2.1.48) ΔAi = g 1 + 2 2 − l − M Ωg ∂t 2 i Typically we obtain pulses which are much shorter than the round-trip time in the cavity and which are placed in time at the position where the modulator introduces the least amount of loss. Therefore, we were able to approximate the cosine modulation by a parabola (2.1.33). The only stable solution to this differential equation is a Gaussian pulse shape with a pulse duration: τp = 1.66 × 4 Dg /Ms , (2.1.49) where Dg is the gain dispersion ((2.1.32) and Table 2.1.10) and Ms is the curvature of the loss modulation ((2.1.33) and Table 2.1.10). Therefore, in active mode-locking the pulse duration becomes shorter until the pulse shortening of the loss modulator balances the pulse broadening of the gain filter. Basically, the curvature of the gain is given by the gain dispersion Dg and the curvature of the loss modulation is given by Ms . The pulse duration is only scaling with the fourth root of √ the saturated gain (i.e. τp ∝ 4 g) and the modulation depth (i.e. τp ∝ 4 1/M ) and with the square root of the modulation frequency (i.e. τp ∝ 1/ωm ) and the gain bandwidth (i.e. τp ∝ 1/Δ ωg ). A higher modulation frequency or a higher modulation depth increases the curvature of the loss modulation and a larger gain bandwidth decreases gain dispersion. Therefore, we obtain shorter pulse durations in all cases. At steady state the saturated gain is equal to the total cavity losses, therefore, a larger output coupler will result in longer pulses. Thus, higher average output power is generally obtained at the expense of longer pulses (Table 2.1.2). The results that have been obtained in actively mode-locked flashlamp-pumped Nd:YAG and Nd:YLF lasers can be very well explained by this result. For example, with Nd:YAG at a lasing wavelength of 1.064 μm we have a gain bandwidth of Δλg = 0.45 nm. With a modulation frequency of 100 MHz (i.e. ωm = 2 π·100 MHz), a 10 % output coupler (i.e. 2g ≈ Tout = 0.1) and a modulation depth M = 0.2, we obtain a FWHM pulse duration of 93 ps (2.1.49). For example, with Nd:YLF at a lasing wavelength of 1.047 μm and a gain bandwidth of Δλg = 1.3 nm we obtain with the same mode-locking parameters a pulse duration of 53 ps (2.1.49). The same result for the pulse duration (2.1.49) has been previously derived by Kuizenga and Siegman [70Kui1, 70Kui2] where they assumed a Gaussian pulse shape and then followed the pulse once around the laser cavity, through the gain and the modulator. They then obtained a self-consistent solution when no net change occurs in the complete round trip. The advantage of Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 134]
2.1 Ultrafast solid-state lasers
109
Haus’s theory is that no prior assumption has to be made for the pulse shape. His theory then predicts a Gaussian pulse shape for actively mode-locked lasers, which then in principle justifies Kuizenga and Siegman’s assumption. Equation (2.1.49) shows that increasing the modulation frequency is an effective method to shorten the pulses. Harmonic mode-locking is a technique in which the cavity is modulated at a frequency that is some integer multiple of the fundamental pulse repetition rate with a period given by the cavity round-trip time. This technique was first introduced and analyzed by Becker et al. [72Bec] in a phase mode-locked Nd:YAG laser. Second-harmonic mode-locking of a flashlamppumped Nd:YAG laser at 1.06 μm resulted in less than 50 ps [83Joh, 85Joh] and at 1.32 μm in 53 ps [88Kel]. It has been well known for quite some time that the addition of a nonlinear index medium to a passively [84Mar, 85Mar] or actively [86Hau] mode-locked laser system can lead to shorter pulses. The bandwidth limitation that results from gain dispersion can be partially overcome by the spectral broadening caused by the nonlinearity. We can extend the differential equation (2.1.48) with the additional terms for SPM ((2.1.47) and Table 2.1.10): ω m t2 1 ∂2 2 − iδL |A| + iψ A (T, t) = 0 . ΔAi = g 1 + 2 2 − l − M (2.1.50) Ωg ∂t 2 i In this case, however, we have to include an additional phase shift ψ to obtain a self-consistent solution. So far, we always assumed ψ = 0. This phase shift is an additional degree of freedom because the boundary condition for intracavity pulses only requires that the pulse envelope is unchanged after one cavity round trip. The electric field, however, can have an arbitrary phase shift ψ after one round trip. This is normally the case because the phase and the group velocity are not the same. It is important to note, that for ultrashort pulses in the one- to two-cycle regime this becomes important and stabilization of the electric field with respect to the peak of the pulse envelope is required [99Tel]. 2 We can obtain an analytic solution of (2.1.50) if we assume a parabolic approximation for |A| :
2 2 t2 2 2 (2.1.51) |A| = |A0 | e−t /τ ≈ P0 1 − 2 . τ The solution of (2.1.50) is then a chirped Gaussian pulse 1 t2 A (t) = A0 exp − 2 (1 − ix) 2τ
(2.1.52)
with the chirp parameter x=
τ 2 φnl 2Dg
(2.1.53)
and the FWHM pulse duration τp = 1.66 · τ = 1.66 ·
4
Dg , Ms + φ2nl /4Dg
(2.1.54)
where φnl is the nonlinear phase shift per cavity round trip at peak intensity. Typically, the beam diameter is very small in the laser gain material, thus the dominant SPM contribution comes from propagation through the gain material: φnl = 2kLg n2 I0,L ,
(2.1.55)
where Lg is the length of the laser gain material (assuming a standing-wave cavity) and I0,L the peak intensity inside the SPM medium, i.e. the laser gain medium. Landolt-B¨ ornstein New Series VIII/1B1
110
2.1.6 Mode-locking techniques
[Ref. p. 134
This analytical result can explain the much shorter 7–12 ps pulses in actively mode-locked diode-pumped Nd:YAG [89Mak1] and Nd:YLF [89Mak2, 90Kel1, 90Wei, 90Juh] lasers because the laser mode area in those diode-pumped lasers is very small which results in significant SPM pulse shortening (2.1.54). For example, our experiments with an actively mode-locked diode-pumped Nd:YLF laser [95Bra2] are very well explained with (2.1.54). In this case the lasing wavelength is 1.047 μm, the gain bandwidth is Δλg = 1.3 nm, the pulse repetition rate is 250 MHz, the output coupler is 2.5 %, the average output power is 620 mW, the mode radius inside the 5 mm long Nd:YLF crystal is 127 μm × 87 μm and the loss modulation of the acousto-optic mode-locker is about 20 %. We then obtain a FWHM pulse duration of 17.8 ps (2.1.54) which agrees well with the experimentally observed pulse duration of 17 ps. Without SPM we would predict a pulse duration of 33 ps (2.1.49). Equation (2.1.54) would predict that more SPM continues to reduce the pulse duration. However, too much SPM will ultimately drive the laser unstable. This has been shown by the numerical simulations of Haus and Silberberg [86Hau] which predict that pulse shortening in an actively modelocked system is limited by roughly a factor of 2 in the case of SPM only. They also showed that the addition of negative GVD can undo the chirp introduced by SPM, and therefore both effects together may lead to stable pulse shortening by a factor of 2.5. However, experimental results with fiber lasers and solid-state lasers indicate that soliton shaping in the negative GVD regime can lead to pulse stabilization and considerable more pulse shortening. We have extended the analysis of Haus and Silberberg by investigating the possible reduction in pulse width of an actively mode-locked laser as a result of soliton-like pulse formation, i.e., the presence of SPM and an excessive amount of negative GVD [95Kae2]. We show, by means of soliton perturbation theory, that beyond a critical amount of negative GVD a soliton-like pulse is formed and kept stable by an active mode-locker. If the bandwidth of the gain is large enough, the width of this solitary pulse can be much less than the width of a Gaussian pulse generated by the active mode-locker and gain dispersion alone. We established analytically that the pulse shortening possible by addition of SPM and GVD does not have a firm limit of 2.5. Numerical simulations and experiments with a regeneratively actively mode-locked Nd:glass laser [94Kop2] confirm these analytical results. The pulse-width reduction achievable depends on the amount of negative GVD available. For an actively mode-locked Nd:glass laser a pulse shortening up to a factor of 6 may result, until instabilities arise.
2.1.6.4 Passive mode-locking with a slow saturable absorber and dynamic gain saturation Dynamic gain saturation can strongly support pulse formation in passive mode-locking and has allowed pulses with duration much shorter than the absorber recovery time. Dynamic gain saturation means that the gain undergoes a fast pulse-induced saturation that recovers between consecutive pulses. This technique has been used to produce sub-100-fs pulses with dye lasers and dye saturable absorbers even though the absorber recovery time was in the nanosecond regime. Dynamic gain saturation can only help if the following conditions are fulfilled (Fig. 2.1.5a): 1. The loss needs to be larger than the gain before the pulse: q0 > g0 ,
(2.1.56)
where q0 is the unsaturated loss coefficient (2.1.6) and g0 is the small signal gain coefficient in the laser. 2. The absorber needs to saturate faster than the gain. From (2.1.14) (i.e. slow saturable absorber and gain) then follows that
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 134]
2.1 Ultrafast solid-state lasers
111
Table 2.1.12. Femtosecond Rhodamin 6G dye laser with its saturable absorber DODCI at a wavelength of 620 nm. σL gain and σA absorber cross-section, τL upper-state lifetime, τA absorber recovery time. Dye material
Cross-section
Time
Rhodamin 6G DODCI Photoisomer
σL = 1.36 × 10−16 cm2 σA = 0.52 × 10−16 cm2 σ ˜A = 1.08 × 10−16 cm2
τL = 4 ns τA = 2.2 ns τ˜L = 1 ns
Esat,A < Esat,L ⇔
AA AL < , σA σL
(2.1.57)
where Esat,A and Esat,L are the saturation energy of the absorber and the gain, σA and σL the absorber and gain cross section, and AA and AL the laser mode area in the absorber and gain. 3. The absorber has to recover faster than the gain: τA < τL ,
(2.1.58)
where τA is the absorber recovery time and τL the upper-state lifetime of the gain medium (Table 2.1.1). Passively mode-locked dye lasers are based on this mode-locking technique and a more extensive review of ultrashort pulse generation with dye lasers is given in [88Sha, 90Die]. The most important dye laser for sub-100-fs pulse generation is the Colliding Pulse Mode-locked (CPM) laser [81For]. The design considerations of such a laser are very well described in [86Val]. This laser is based on Rhodamin 6G as the gain medium and on DODCI as the absorber [72Ipp]. From Table 2.1.12 follows that the conditions (2.1.56)–(2.1.58) are only fulfilled if the mode area in the absorber jet is smaller than in the gain jet. In addition, a six-mirror ring cavity design where the absorber and the gain jet are separated by 1/4 of the resonator round trip gives the two counter-propagating pulses the same gain and the absorber is more strongly saturated because of the two pulses colliding inside the saturable absorber jet (i.e. Colliding Pulse Mode-locking – CPM). This effectively shortens the pulses and increases the stability. The best performance of this laser was only obtained after both the gain and the absorber dyes have been freshly prepared, because both photodegrade within a relatively short time (i.e. 1–3 weeks). The best result was 27 fs pulses at a center wavelength of 620 nm with an average output power of 20 mW each in two output beams at a pulse repetition rate of 100 MHz [85Val, 86Val]. More typically, this laser produced slightly below 100 fs pulses. This laser was the “work horse” for all the pioneering work on sub-100-fs spectroscopy for nearly 10 years in the 1980’s. However, the rather large maintenance of this laser explains the success of the Ti:sapphire laser at the beginning of the 1990’s. Today, solid-state lasers with much shorter pulses, higher output powers and better stability have replaced practically all ultrafast dye laser systems. Another important application of this mode-locking technique are semiconductor lasers, which also have an upper-state lifetime in the nanosecond regime and a large gain cross section in the range of 10−14 cm2 . A more extensive recent review of ultrashort pulse generation with semiconductor lasers is given in [95Jia, 95Vai]. The CPM technique, as developed for dye lasers, has been also used for passively mode-locked semiconductor lasers [81Zie, 86Vas]. Wu and Chen et al. [90Wu, 92Che] monolithically incorporated the CPM technique in quantum-well lasers. Pulses of 0.64 ps at a repetition rate of 710 MHz were generated [91Che]. The master equation for this mode-locking mechanism (Fig. 2.1.5a) is given by [75Hau3, 94Ipp]: g0 d2 d A (T, t) = 0 . (2.1.59) ΔAi = g (t) − q (t) + 2 2 + tD Ωg dt dt i For a self-consistent solution we will have to include a time shift tD of the pulse envelope due to the saturation of the absorber. g (t) and q (t) are given by the slow-saturation approximation (2.1.14). Landolt-B¨ ornstein New Series VIII/1B1
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For an analytical solution we have to expand the exponential function up to the second order, i.e. x2 ex ≈ 1 + x + : 2 ⎤ ⎡ t σ 2 A q (t) = q0 exp ⎣− |A (t )| dt ⎦ AA hν −∞ ⎡ ⎛ t ⎞2 ⎤ t 2 σA σA 2 2 ⎢ ⎥ ⎝ (2.1.60) ≈ q0 ⎣1 − |A (t )| dt + |A (t )| dt ⎠ ⎦ 2 AA hν 2 (AA hν) −∞
−∞
and analogous for g (t). In this case we can obtain an analytical solution with a sech2 -pulse shape:
t (2.1.61) A (t) = A0 sech τ and a FWHM pulse duration τp ≈ 1.76 ×
4 1 , π Δ νg
(2.1.62)
where Δ νg is the FWHM gain bandwidth of the laser. In (2.1.62) the conditions (2.1.56)–(2.1.58) are assumed and in addition Esat,L Esat,A and Ep Esat,A (i.e. a fully saturated absorber). For the example of Rhodamin 6G and DODCI (Table 2.1.12) we then obtain for a gain bandwidth of Δ νg ≈ 4 × 1013 Hz a pulse duration of about 56 fs (2.1.62). Pulses as short as 27 fs have been demonstrated [85Val]. However, it was recognized early on that SPM together with negative dispersion results in soliton formation and further reduces pulse duration by about a factor of 2 in dye lasers [84Mar, 85Mar]. This would explain the difference in the theoretical prediction of (2.1.62) from the experimentally demonstrated 27 fs. However, at that time an analytic solution for the pulse-shortening effect was not presented. For semiconductor lasers we typically observe strongly chirped pulses [95Jia]. Therefore, we would have to include dispersion and self-phase modulation in the rate equation. This is not so easy because we would have to also include the refractive-index change that occurs during gain saturation.
2.1.6.5 Passive mode-locking with a fast saturable absorber In passive mode-locking the loss modulation is obtained by Self-Amplitude Modulation (SAM), where the pulse saturates an absorber, for example. In the ideal case, the SAM follows the intensity profile of the pulse. This is the case of an ideal fast saturable absorber. In this case, SAM produces a much larger curvature of loss modulation than in the sinusoidal loss modulation of active modelocking, because the mode-locked pulse duration is much shorter than the cavity round-trip time. Therefore, we would expect from the previous discussion of active mode-locking, that we obtain much shorter pulses with passive mode-locking. This is indeed observed. In the fast saturable absorber model no dynamic gain saturation is required and the short netgain window is formed by a fast recovering saturable absorber alone (Fig. 2.1.5b). This was initially believed to be the only stable approach to passively mode-lock solid-state lasers with long upperstate lifetimes. Additive Pulse Mode-locking (APM) was the first fast saturable absorber for such solid-state lasers (Sect. 2.1.4.4.2). However, APM required interferometric cavity-length stabilization. Kerr-Lens Mode-locking (KLM) [91Spe] (Sect. 2.1.4.4.3) was the first useful demonstration of an intracavity fast saturable absorber for a solid-state laser and because of its simplicity replaced Landolt-B¨ ornstein New Series VIII/1B1
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coupled cavity mode-locking techniques. KLM is very close to an ideal fast saturable absorber, where the modulation depth is produced either by the decreased losses because of self-focusing through a hard aperture [91Kel, 91Sal1, 91Neg] or by increased gain in the laser as a result of an increased overlap of the laser mode with the pump mode in the laser crystal [93Pic]. Only in the ultrashort pulse regime of a few optical cycles more complicated space–time coupling occurs and wavelength-dependent effects start to limit further pulse reduction. Besides the tremendous success of KLM, there are some significant limitations for practical or “real-world” ultrafast lasers. First, the cavity is typically operated near one end of its stability range, where the Kerr-lens-induced change of the beam diameter is large enough to sustain modelocking. This results in a requirement for critical cavity alignment where mirrors and the laser crystal have to be positioned to an accuracy of several hundred microns typically. Once the cavity is correctly aligned, KLM can be very stable and under certain conditions even self-starting. However, self-starting KLM lasers in the sub-50-fs regime have not yet been demonstrated without any additional starting mechanisms. This is not surprising, since in a 10-fs Ti:sapphire laser with a 100 MHz repetition rate, the peak power changes by 6 orders of magnitude when the laser switches from cw to pulsed operation. Therefore, nonlinear effects that are still effective in the sub-10-fs regime are typically too small to initiate mode-locking in the cw-operation regime. In contrast, if self-starting is optimized, KLM tends to saturate in the ultrashort pulse regime or the large Self-Phase Modulation (SPM) will drive the laser unstable. For an ideal fast saturable absorber, Haus et al. [92Hau] developed an analytic solution for the pulse width starting with the following master equation: 1 ∂2 2 (2.1.63) ΔAi = g 1 + 2 2 − l + γA |A| A (T, t) = 0 Ωg ∂t i not taking into account GVD and SPM. The solution is an unchirped sech2 -pulse shape
t (2.1.64) P (t) = P0 sech2 τ with a FWHM pulse width: τp = 1.7627 · τ = 1.7627
4Dg , γA Ep
(2.1.65)
where P0 is the peak power of the pulse, Ep is the intracavity pulse energy and Dg is the gain dispersion of the laser medium (2.1.32). The shortest possible pulses can be obtained when we use the full modulation depth of the fast saturable absorber. We only obtain an analytic solution if we assume an ideal fast absorber that saturates linearly with the pulse intensity (2.1.18) over the full modulation depth. This is clearly a strong approximation because (2.1.18) only holds for weak absorber saturation. For a maximum modulation depth and this linear approximation we then can assume that γA P0 = q0 . For a sech2 -shaped pulse (2.1.64), the pulse energy is given by Ep = I (t)dt = 2τ P0 . (2.1.66) The minimal pulse width for a fully saturated ideal fast absorber then follows from (2.1.65): 1.7627 2g τp,min = . (2.1.67) Ωg q0 This occurs right at the stability limit when the filter loss due to gain dispersion is equal to the residual loss a soliton undergoes in an ideal fast saturable absorber (2.1.19): Landolt-B¨ ornstein New Series VIII/1B1
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Filter loss =
Dg q0 = qs = residual saturable absorber loss . = 3τ 2 3
[Ref. p. 134
(2.1.68)
The residual saturable absorber loss qs results from the fact that the soliton pulse initially experiences loss to fully saturate the absorber (see Sect. 2.1.4.2.2). This residual loss is exactly q0 /3 for a sech2 -pulse shape and a fully saturated ideal fast saturable absorber. This condition results in a minimal FWHM pulse duration given by (2.1.67). Including GVD and SPM, i.e. soliton formation, in the fast saturable absorber model, an additional pulse shortening of a factor of 2 was predicted. However, unchirped soliton pulses (i.e. ideal sech2 -shaped pulses) are only obtained for a certain negative dispersion value given by |D| Dg = . δL γA
(2.1.69)
This is also where we obtain the shortest pulses with a fast saturable absorber. Here we assume that higher-order dispersion is fully compensated or negligibly small. In addition, computer simulations show that too much self-phase modulation drives the laser unstable. KLM is well described by the fast absorber mode-locking model discussed above even though it is not so easy to determine the exact saturable absorber parameters such as the effective saturation fluence. However, the linearized model does not describe the pulse generation with Ti:sapphire lasers in the sub-10-fs regime very well. Pulse-shaping processes in these lasers are more complex [91Bra, 92Kra2]. Under the influence of the different linear and nonlinear pulse shaping mechanisms, the pulse is significantly broadened and recompressed, giving rise to a “breathing” of the pulse width. The order of the pulse shaping elements in the laser cavity becomes relevant and the spectrum of the mode-locked pulses becomes more complex. In this case, an analytical solution can no longer be obtained. As a rough approximation, the pulses still behave like solitons and consequently these lasers are also called solitary lasers [91Bra].
2.1.6.6 Passive mode-locking with a slow saturable absorber without gain saturation and soliton formation Over many years we consistently observed in experiments that even without soliton effects the pulse duration can be much shorter than the absorber recovery time in SESAM mode-locked solidstate lasers. It has always been postulated that without soliton pulse shaping, we need to have a fast saturable absorber for stable mode-locking, which is in disagreement with our experimental observations. More recently, we therefore performed some more detailed numerical investigations [01Pas1]. For a strongly saturated slow absorber with a saturation parameter S > 3 and an absorber recovery time smaller than 10 to 30 times the pulse duration, we found a useful guideline for the predicted pulse duration 1.5 g τp,min ≈ . (2.1.70) Δ νg ΔR We neglected similar to the ideal fast saturable absorber mode-locking model, the effects of Kerr nonlinearity and dispersion in the cavity, phase changes on the absorber and spatial hole burning in the gain medium. Compared to the analytical solution of a fully saturated absorber (2.1.67) we would predict a slightly longer pulse duration given by a factor of about 1.3. Otherwise, the dependence with regards to gain saturation, gain bandwidth and absorber modulation depth has been explained very well with the analytical solution. Numerical simulations show that the pulse duration in (2.1.70) can be significantly shorter than the absorber recovery time and has little influence on the pulse duration as long as τA < 10 τp Landolt-B¨ ornstein New Series VIII/1B1
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to 30 τp . Numerical simulations show that this is a reasonable estimate and that with too long recovery time, the pulse does not simply become longer but unstable. At first this long recovery time might be surprising, because on the trailing edge of the pulse there is no shaping action of the absorber. There is even net gain, because the loss caused by the absorber is very small for the trailing edge (always assuming a fully saturated absorber), while the total loss for the pulse is larger and is balanced by the saturated gain in steady state. Thus, one might expect that this net gain after the pulse would destabilize the pulse – but this is not the case. The reason is that the pulses experience a temporal shift by the absorber, which limits the time in which noise behind the pulse can be amplified. The absorber attenuates mostly the leading wing of the pulse, thus shifting the pulse center backwards in each cavity round trip. This means that the pulse is constantly moving backward and swallows any noise growing behind itself. An upper limit on the recovery time than follows from the condition that this noise cannot grow too much. Note that weak reflections in the laser cavity could generate weak satellite pulses behind the main pulse. These satellite pulses could be stronger than the noise level and thus significantly reduce maximum tolerable recovery time of the absorber. So far we have not included any additional pulse-shaping effects such as SPM or solitons. Further simulations show that SPM alone in the positive dispersion regime should always be kept small because it always makes pulses longer and even destabilizes them, particularly for absorbers with small modulation depth [01Pas1]. This result might be surprising at first – but again the temporal delay caused by the absorber gives a simple explanation. SPM (with positive n2 , as is the usual case) decreases the instantaneous frequency in the leading wing and increases the frequency in the trailing wing. The absorber always attenuates the leading wing, thus removing the lower frequency components, which results in an increased center frequency and broader pulses due to the decrease in pulse bandwidth. For strong SPM the pulses become unstable. A rule of thumb is that the nonlinear phase shift for the peak should be at most a few mrad per 1 % of modulation depth. It is clear that SPM could hardly be made weak enough in the sub-picosecond regime. For this reason, soliton mode-locking is usually required in the sub-picosecond domain, because there the nonlinear phase changes can be much larger.
2.1.6.7 Soliton mode-locking In soliton mode-locking, the pulse shaping is done solely by soliton formation, i.e. the balance of Group-Velocity Dispersion (GVD) and Self-Phase Modulation (SPM) at steady state, with no additional requirements on the cavity stability regime as for example for KLM. In contrast to KLM we use only the time-dependent part of the Kerr effect at the peak intensity (i.e. n (t) = n+n2 I0 (t), (2.1.42)) and not the radially dependent part as well (i.e. n (r, t) = n+n2 I (r, t), (2.1.42)). The radially dependent part of the Kerr effect is responsible for KLM because it forms the nonlinear lens that reduces the beam diameter at an intracavity aperture inside the gain medium. Thus, this nonlinear lens forms an effective fast saturable absorber because the intensity-dependent beam-diameter reduction at an aperture introduces less loss at high intensity and more loss at low intensity. Such a radially dependent effective saturable however couples the mode-locking mechanism with the cavity mode. In contrast, soliton mode-locking does not depend on the transverse Kerr effect and has therefore the advantage that the mode-locking mechanism is decoupled from the cavity design and no critical cavity stability regime is required – it basically works over the full cavity stability range. In soliton mode-locking, an additional loss mechanism, such as a saturable absorber [95Kae1], or an acousto-optic modulator [95Kae2], is necessary to start the mode-locking process and to stabilize the soliton pulse-forming process. In soliton mode-locking, we have shown that the netgain window (Fig. 2.1.5c) can remain open for significantly more than 10 times longer than the ultrashort pulse, depending on the specific laser parameters [95Jun2, 96Kae]. This strongly relaxes Landolt-B¨ ornstein New Series VIII/1B1
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the requirements on the saturable absorber and we can obtain ultrashort pulses even in the 10-fs regime with semiconductor saturable absorbers that have much longer recovery times. With the same modulation depth, one can obtain almost the same minimal pulse duration as with a fast saturable absorber, as long as the absorber recovery time is roughly less than ten times longer than the final pulse width. In addition, high dynamic range autocorrelation measurements showed excellent pulse pedestal suppression over more than seven orders of magnitude in 130-fs pulses of a Nd:glass laser [95Kop1] and very similar to or even better than KLM pulses in the 10-fs pulse width regime [97Jun2]. Even better performance can be expected if the saturable absorber also shows a negative refractive-index change coupled with the absorption change as is the case for semiconductor materials [96Kae]. With a slow saturable absorber as a starting and stabilizing mechanism for soliton mode-locking, there remains a time window with net round-trip gain behind the pulse, where the loss of the still saturated absorber is smaller than the total loss for the pulse that is balancing the saturated gain. At a first glance it may seem that the discussion in the last section, Sect. 2.1.6.6, with slow saturable absorbers would apply here as well. However, there is another limiting effect which usually becomes more effective in soliton mode-locked lasers: The dispersion causes the background to temporally broaden and thus permanently loosing the energy in those parts which drift into the time regions with net loss. We can describe soliton mode-locking by the Haus’s master equation formalism, where we take into account GVD, SPM and a slow saturable absorber q (T, t) that recovers slower than the pulse duration (see Fig. 2.1.5c) [95Kae1, 96Kae]: ∂2 ∂2 2 ΔAi = −iD 2 + iδL |A (T, t)| A (T, t) + g − l + Dg 2 − q (T, t) A (T, t) ∂t ∂t i =0.
(2.1.71)
This differential equation can be solved analytically using soliton perturbation theory. The first bracket term of this differential equation determines the nonlinear Schr¨ odinger equation for which the soliton pulse is a stable solution for negative GVD (i.e. D < 0) and positive SPM (i.e. n2 > 0):
t e−iφs (z) . A (z, t) = A0 sech (2.1.72) τ This soliton pulse propagates without distortion through a medium with negative GVD and positive SPM because the effect of SPM exactly cancels that due to dispersion. The FWHM soliton pulse duration is given by τp = 1.7627 · τ and the time–bandwidth product by Δ νp τp = 0.3148. φs (z) is the phase shift of the soliton during propagation along the z-axis φs (z) =
1 1 kn2 I0 z ≡ φnl (z) , 2 2
(2.1.73)
where I0 is the peak intensity inside the SPM medium (i.e. typically the gain medium). Thus, the soliton pulse experiences during propagation a constant phase shift over the full beam profile. For a given negative dispersion and an intracavity pulse energy Ep we obtain a pulse duration τp = 1.7627
2 |D| , δ L Ep
(2.1.74)
for which the effects of SPM and GVD are balanced with a stable soliton pulse. This soliton pulse looses energy due to gain dispersion and losses in the cavity. Gain dispersion and losses can be treated as perturbation to the nonlinear Schr¨ odinger equation for which a soliton is a stable solution (i.e. second bracket term in (2.1.71)). This lost energy, called continuum in soliton perturbation theory, is initially contained in a low-intensity background pulse, which experiences negligible SPM, but spreads in time due to GDD (Fig. 2.1.17a). In soliton mode-locking a stable Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 134]
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Loss Group delay dispersion (GDD)
Continuum
Group delay dispersion (GDD)
Continuum
Gain
Gain
Pulse Pulse
a
Time t
b
Frequency n
Fig. 2.1.17. Soliton mode-locking in (a) time and (b) frequency domain. The continuum pulse spreads in time due to group velocity dispersion and thus undergoes more loss in the relatively slow absorber, which is saturated by the shorter soliton pulse. However, the longer continuum pulse has a narrower spectrum and thus undergoes more gain than the spectrally broader soliton pulse.
soliton pulse is formed for all group delay dispersion values as long as the continuum loss is larger than the soliton loss [96Kae] or the pulses break up in two or more pulses [97Aus]. Thus, for smaller negative dispersion the pulse duration becomes shorter (2.1.74) until minimal pulse duration is reached. With no pulse-break-up, the minimal pulse duration is given when the loss for the continuum pulse becomes equal to the loss of the soliton pulse. When the soliton pulse is stable, then the saturated gain is equal to the loss:
Ep Esat,A Dg 1 − exp − , (2.1.75) g = l + ls with ls = 2 + q0 3τ Ep Esat,A where l is the total saturated amplitude loss coefficient per cavity round trip (i.e. output coupler, residual cavity losses and nonsaturable absorber loss of the saturable absorber) and ls the additional loss experienced by the soliton as a result of gain filtering (2.1.68) and the amplitude loss coefficient for saturation of the slow absorber (2.1.15). Soliton perturbation theory then determines the roundtrip loss of the continuum pulse [96Kae]. The continuum is spread in time because of dispersion and therefore experiences enhanced loss in the recovering absorber that has been saturated by the much shorter soliton pulse. We then predict a minimum pulse duration for a soliton pulse [95Kae1, 96Kae]: !3/4
1/4 3/4
τA g 3/2 τA 1/4 g 3/8 1 1 τp,min = 1.7627 √ φ−1/8 ≈ 0.45 , (2.1.76) s 1/8 q0 Δ νg ΔR 6 Ωg φs where φs is the phase shift of the soliton per cavity round trip (assuming that the dominant SPM occurs in the laser gain medium), Δ νg the FWHM gain bandwidth and ΔR ≈ 2q0 (2.1.6). With (2.1.73) then follows φs = φs (z = 2Lg ) = kn2 Lg I0,L = 12 δL P0 , where δL is the SPM coefficient (2.1.47) and P0 the peak power inside the laser cavity. In (2.1.76) we assume a fully saturated slow saturable absorber and a linear approximation for the exponential decay of the slow saturable absorber. The analytical solution for soliton mode-locking (2.1.76) has been experimentally confirmed with a Ti:sapphire laser where a Fabry–Perot filter has been inserted to give a well-defined gain bandwidth [95Jun2]. However, this equation still does not tell us what soliton phase shift would be ideal. Equation (2.1.76) would suggest that very high values are preferred, which actually leads to instabilities. Also this equation is not taking into account that the soliton pulse may break up into two solitons which occurs more easily if the absorber is too strongly saturated. Numerical simulations can give better estimates for these open questions [01Pas1]. Landolt-B¨ ornstein New Series VIII/1B1
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In soliton mode-locking, the dominant pulse-formation process is assumed to be soliton formation. Therefore, the pulse has to be a soliton for which the negative GVD is balanced with the SPM inside the laser cavity. The pulse duration is then given by the simple soliton solution (2.1.74). This means that the pulse duration scales linearly with the negative group delay dispersion inside the laser cavity (i.e. τp ∝ |D|). In the case of an ideal fast saturable absorber, an unchirped soliton pulse is only obtained at a very specific dispersion setting (2.1.69), whereas for soliton mode-locking an unchirped transform-limited soliton is obtained for all dispersion levels as long as the stability requirement against the continuum is fulfilled. This fact has been also used to experimentally confirm that soliton mode-locking is the dominant pulse-formation process and not a fast saturable absorber such as KLM [97Aus]. Higher-order dispersion only increases the pulse duration, therefore it is undesirable and is assumed to be compensated. Solitons alone in the cavity are not stable. The continuum pulse is much longer and therefore experiences only the gain at line center, while the soliton exhibits an effectively lower average gain due to its larger bandwidth. Thus, the continuum exhibits a higher gain than the soliton. After a sufficient build-up time, the continuum would actually grow until it reaches lasing threshold, destabilizing the soliton. However, we can stabilize the soliton by introducing a relatively slow saturable absorber into the cavity. This absorber is fast enough to add sufficient additional loss for the growing continuum that spreads in time during its build-up phase so that it no longer reaches lasing threshold. The break-up into two or even three pulses can be explained as follows: Beyond a certain pulse energy, two soliton pulses with lower power, longer duration, and narrower spectrum will be preferred, since their loss introduced by the limited gain bandwidth decreases so much that the slightly increased residual loss of the less saturated saturable absorber cannot compensate for it. This results in a lower total round-trip loss and thus a reduced saturated or average gain for two pulses compared to one pulse. The threshold for multiple pulsing is lower for shorter pulses, i.e. with spectra which are broad compared to the gain bandwidth of the laser. A more detailed description of multiple pulsing is given elsewhere [98Kae]. Numerical simulations show, however, that the tendency for pulse break-up in cases with strong absorber saturation is found to be significantly weaker than expected from simple gain/loss arguments [01Pas1]. To conclude, soliton shaping effects can allow for the generation of significantly shorter pulses, compared to cases without SPM and dispersion. The improvement is particularly large for absorbers with a relatively low modulation depth and when the absorber recovery is not too slow. In this regime, the pulse shaping is mainly done by the soliton effects, and the absorber is only needed to stabilize the solitons against growth of the continuum. The absorber parameters are generally not very critical. It is important not only to adjust the ratio of dispersion and SPM to obtain the desired soliton pulse duration (2.1.74), but also to keep their absolute values in a reasonable range where the nonlinear phase change is in the order of a few hundred mrad per round trip (i.e. significantly larger than acceptable in cases without negative dispersion). Soliton formation is generally very important in femtosecond lasers, which has been already recognized in colliding pulse mode-locked dye lasers. However, no analytic solution was presented for the soliton pulse shortening. It was always assumed that for a stable solution the mode-locking mechanism without soliton effects has to generate a net gain window as short as the pulse (Fig. 2.1.5a and b). In contrast to these cases, in soliton mode-locking we present an analytic solution based on soliton perturbation theory, where soliton pulse shaping is clearly assumed to be the dominant pulse formation process, and the saturable absorber required for a stable solution is treated as a perturbation. Then, the net gain window can be much longer than the pulse (Fig. 2.1.5c). Stability of the soliton against the continuum then determines the shortest possible pulse duration. This is a fundamentally different mode-locking model than previously described. We therefore refer to it as soliton mode-locking, emphasizing the fact that soliton pulse shaping is the dominant factor.
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 134]
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2.1.6.8 Design guidelines to prevent Q-switching instabilities For picosecond solid-state lasers the self-amplitude modulation of a saturable absorber with a picosecond or tens of picoseconds recovery time is sufficient for stable pulse generation. A picosecond recovery time can be achieved with low-temperature grown semiconductor saturable absorbers where mid-gap defect states form very efficient traps for the photoexcited electrons in the conduction band (Sect. 2.1.4.3) . In the picosecond regime, we developed a very simple stability criterion for stable passive mode-locking without Q-switching instabilities [99Hoe1]: 2 Ep2 > Ep,c = Esat,L Esat,A ΔR .
(2.1.77)
The critical intracavity pulse energy Ep,c is the minimum intracavity pulse energy, which is required to obtain stable cw mode-locking, that is, for Ep > Ep,c we obtain stable cw mode-locking and for Ep < Ep,c we obtain Q-switched mode-locking. For good stability of a mode-locked laser against unwanted fluctuations of pulse energy, operation close to the stability limit is not recommended. Thus, a large modulation depth supports shorter pulses (Table 2.1.11), but an upper limit is given by the onset of self-Q-switching instabilities (2.1.77). In the femtosecond regime, we observe a significant reduction of the tendency of Q-switching instabilities compared to pure saturable absorber mode-locked picosecond lasers (2.1.77). This can be explained as follows: If the energy of an ultrashort pulse rises slightly due to relaxation oscillations, SPM and/or SAM broadens the pulse spectrum. A broader pulse spectrum, however, increases the loss due to the finite gain bandwidth, (2.1.68) and (2.1.74), which provides some negative feedback, thus decreasing the critical pulse energy which is necessary for stable cw modelocking. The simple stability requirement of (2.1.77) then has to be modified as follows [99Hoe1]: Esat,L gK 2 Ep2 + Ep2 > Esat,L Esat,A ΔR ,
(2.1.78)
where K is given by K≡
0.315 2π n2 Lg . 1.76 DAL λ0 Δ νg
(2.1.79)
Here we assume a standing-wave cavity and that the dominant SPM is produced in the laser medium. In other cases we have to add all other contributions as well. Theoretical results for the QML threshold, (2.1.77)–(2.1.79), have generally been found to be in good agreement with experimental values. However, inverse saturable absorption can show some significant improvement of the QML threshold. Two-Photon Absorption (TPA) has been widely used for optical power limiter [86Wal] and a roll-over which lowers the Q-switching threshold [99Tho]. In addition, for some recent high-repetition-rate lasers [04Pas] the QML threshold was found to be significantly lower than expected even taking into account TPA. It was shown that for some Er:Yb:glass lasers this could be explained with modified saturation characteristics of the used SESAMs, namely with a roll-over of the nonlinear reflectivity for higher pulse fluences [04Sch1]. However, for picosecond pulse durations TPA cannot explain the observed significant roll-over (Fig. 2.1.18). The reflectivity of a SESAM is generally expected to increase with increasing pulse energy. However, for higher pulse energies the reflectivity can decrease again; we call this a “rollover” of the nonlinear reflectivity curve caused by inverse saturable absorption (Fig. 2.1.18). We showed for several SESAMs that the measured roll-over is consistent with TPA only for short (femtosecond) pulses, while a stronger kind of nonlinear absorption is dominant for longer (picosecond) pulses [05Gra2]. The QML threshold criteria of (2.1.77) then have to be modified to [05Gra2] Ep2 >
Esat,A ΔR . 1 1 + Esat,L AA F 2
Landolt-B¨ ornstein New Series VIII/1B1
(2.1.80)
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Nonlinear reflectivity [%]
100.0
DRns
99.8
DR
99.6
ns,eff
DR
99.4 99.2
no ISA with ISA DReff
99.0 0.1
2
4 6 81 2 4 6 810 2 Saturation parameter S = F p / Fsat,A
4
6 8 100
[Ref. p. 134
Fig. 2.1.18. Nonlinear reflectivity as function of saturation parameter S which is equal to Fp /Fsat,A . Fp is the pulse fluence incident on the absorber mirror (i.e. pulse energy density) and Fsat,A is the saturation fluence of the absorber mirror. Inverse saturable absorption decreases the reflectivity at higher pulse energies such that a “roll-over” is observed. This decreases the effective modulation depth and increases the effective nonsaturable absorption. However, it improves the Q-switching mode-locking threshold.
For F2 → ∞ (i.e. without induced nonlinear losses) we retrieve the simpler equation (2.1.77). F2 is the inverse slope of the induced absorption effect and can be determined from nonlinear SESAM reflectivity measurements (Fig. 2.1.18) [05Gra2, 04Hai]: R ISA (Fp ) = R (Fp ) −
Fp , F2
(2.1.81)
where Fp is the pulse fluence incident on the SESAM (i.e. pulse energy density), R(Fp ) the measured nonlinear reflectivity without Inverse Saturable Absorption (ISA) and R ISA (Fp ) the measured reflectivity with inverse saturable absorption. The smaller the inverse slope of the roll-over F2 , the stronger is the roll-over. The stronger the roll-over, the smaller the maximum modulation depth of the SESAM.
2.1.6.9 External pulse compression SPM generates extra frequency components. The superposition with the other frequency components in the pulse can spectrally broaden the pulse (i.e. for positively chirped pulses assuming n2 > 0). SPM alone does not modify the pulse width, but with proper dispersion compensation a much shorter pulse can be generated with the extra bandwidth [80Mol]. The positively chirped spectrally broadened pulse then can be compressed with appropriate negative dispersion compensation, where the “blue” spectral components have to be advanced relative to the “red” ones. A careful balance between a nonlinear spectral broadening process and negative dispersion is needed for efficient compression of a pulse. Typically, self-phase modulation in a single-mode fiber with optimized length was used to linearly chirp the pulse, which is then compressed with a grating pair compressor [84Tom]. Ultimately, uncompensated higher-order dispersion and higher-order nonlinearities limit compression schemes. For pulses shorter than 100 fs, compression is typically limited to factors of less than 10. Compression of amplified CPM dye laser pulses with 50 fs duration produced the long-standing world record of 6 fs [87For]. Similar concepts have been used for external pulse compression of 13-fs pulses from a cavity-dumped Ti:sapphire laser [97Bal] and of 20-fs pulses from a Ti:sapphire laser amplifier [97Nis] resulting, in both cases, in approximately 4.5-fs pulses. In the latter case, the use of a noble-gas-filled hollow fiber instead of a normal fiber allows for much higher pulse energies. For example, pulse energies of about 0.5 mJ with 5.2-fs pulses and a peak power of 0.1 TW [97Sar]. More recently, adaptive pulse compression of a super-continuum produced in two cascaded hollow fibers generated 3.8-fs pulses with energies of up to 15 μJ [03Sch]. Further improvements resulted in 3.4-fs pulses but with only 500 nJ pulse energies [03Yam]. The pulse duration was fully characterized by Spectral-Phase Interferometry for Direct Electric-field Reconstruction (SPIDER) (Sect. 2.1.7.3). This is currently the world record in the visible and near-infrared spectral regime. Landolt-B¨ ornstein New Series VIII/1B1
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The extra bandwidth obtained with SPM can be extremely large producing a white-light continuum [83For], which can be used as a seed for broadband parametric amplification. Parametric processes can provide amplification with an even broader bandwidth than can typically be achieved in laser amplifiers. Noncollinear phase-matching at a crossing angle of 3.8 ◦ in beta barium borate (BBO) provides more than 150 THz amplification bandwidth [95Gal]. With this type of set-up, parametric amplification has been successfully demonstrated with pulse durations of less than 5 fs [99Shi, 02Zav].
2.1.7 Pulse characterization 2.1.7.1 Electronic techniques Electronic techniques for pulse-width measurements are typically limited to the picosecond regime. Photodetectors and sampling heads with bandwidths up to 60 GHz are commercially available. This means that the measured pulse duration is limited to about 7 ps. This follows from simple linear system analysis for which the impulse response of a photodetector or a sampling head can be approximated by a Gauss-function. The impulse response for a given system bandwidth B has a FWHM τ FWHM in units of ps: τ FWHM [ps] ≈
312 GHz . B [GHz]
(2.1.82)
The impulse response of a measurement system can be determined from the impulse response of each element in the detection chain: τ 2FWHM = τ12 + τ22 + τ32 + . . . , (2.1.83) where for example τ1 is the FWHM of the impulse response of the photodetector, τ2 of the sampling head and so on. Thus, with a 40 GHz sampling head and a 60 GHz photodetector we only measure a impulse response with FWHM of 9.4 ps.
2.1.7.2 Optical autocorrelation Optical autocorrelation techniques with second-harmonic generation of two identical pulses that are delayed with respect to each other are typically used to measure shorter pulses [80Sal, 83Wei]. We distinguish between collinear and non-collinear intensity autocorrelation measurements for which the two pulse beams in the nonlinear crystal are either collinear or non-collinear. In the non-collinear case the second-harmonic signal only depends on the pulse overlap and is given by I2ω (Δt) ∝ I (t)I (t − Δt) dt . (2.1.84) The FWHM of the autocorrelation signal I2ω (Δt) is given by τAu and determines the FWHM pulse duration τp of the incoming pulse I (t). However, τAu depends on the specific pulse shape (Table 2.1.13) and any phase information is lost in this measurement. So normally, transformlimited pulses are assumed. This assumption is only justified as long as the measured spectrum also agrees with the assumption of pulse shape and constant phase (i.e. the time–bandwidth product corresponds to a transform-limited pulse, Table 2.1.13). For passively mode-locked lasers, for Landolt-B¨ ornstein New Series VIII/1B1
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[Ref. p. 134
Table 2.1.13. Optical pulses: defining equations for Gaussian and soliton pulse shapes, FWHM (fullwidth-half-maximum) intensity pulse duration τp , time–bandwidth products Δνp τp for which Δνp is the FWHM of the spectral intensity, FWHM intensity autocorrelation pulse duration τAu . Pulse shape
2
t τ2 t Soliton: I (t) ∝ sech2 τ
Gauss:
I (t) ∝ exp
τp /τ
Δνp τp
τp /τAu
ln 2
0.4413
0.7071
1.7627
0.3148
0.6482
2
√
example, that allow for parabolic approximation of pulse-formation mechanisms one expects a sech2 temporal and spectral pulse shape (Sects. 2.1.6.4–2.1.6.7). Passively mode-locked solid-state lasers with pulse durations well above 10 fs normally generate pulses close to this ideal sech2 shape. Therefore, this non-collinear autocorrelation technique is a good standard diagnostic for such laser sources. For ultrashort pulse generation in the sub-10-fs regime this is generally not the case anymore. Experimentally, this is clearly indicated by more complex pulse spectra. Interferometric AutoCorrelation (IAC) techniques [83Min] have been used to get more information. In IAC a collinear intensity autocorrelation is fringe-resolved and gives some indication how well the pulse is transform-limited. However, we still do not obtain full phase information about the pulse. The temporal parameters have usually been obtained by fitting an analytical pulse shape with constant phase to the autocorrelation measurement. Theoretical models of the pulse-formation process motivate the particular fitting function. For lasers obeying such a model the a-priori assumption of a theoretically predicted pulse shape is well-motivated and leads to good estimates of the pulse duration as long as the measured spectrum also agrees with the theoretical prediction. However, we have seen that fits to an IAC trace with a more complex pulse spectrum tend to underestimate the true duration of the pulses. Problems with IAC measurement for ultrashort pulses are also discussed in the two-optical-cycle regime [04Yam]. For few-cycle pulses, a limitation in a noncollinear beam geometry arises because of the finite crossing angle of two beams. In this case the temporal delay between two beams is different in the center and in the wings of the spatial beam profile. This geometrical artifact results in a measured pulse duration that is longer than the actual pulse duration τp : 2 τp,meas = τp2 + δτ 2 .
(2.1.85)
For a beam diameter d and a crossing angle θ between the two beams this results in an δτ of δτ =
√ d θ θd 2 tan ≈ √ c 2 2c
(2.1.86)
with the speed of light c and the additional approximation for a small crossing angle θ. For example a crossing angle of 1.7 ◦ and a beam diameter of 30 μm results in δτ = 2.1 fs. For an actual pulse duration of 10 fs (resp. 5 fs) this gives a measured pulse duration of 10.2 fs (resp. 5.4 fs) which corresponds to an error of 2 % (resp. 8 %). This means this becomes more severe for pulse durations in the few-cycle regime. However, if the crossing angle is significantly increased this can become also more important for longer pulses. For this reason, in the few-cycle-pulse-width regime collinear geometries have always been preferred to avoid geometrical blurring artifacts and to prevent temporal resolution from being reduced.
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2.1.7.3 New techniques: FROG, FROG-CRAB, SPIDER, . . . For a more precise measurement, a variety of methods have been proposed to fully reconstruct both pulse amplitude and phase from measured data only [91Chi, 93Kan, 95Chu2, 96Rhe, 98Iac]. Initially, especially Frequency-Resolved Optical Gating (FROG, [93Kan, 97Tre]) and Spectral Phase Interferometry for Direct Electric-field Reconstruction (SPIDER, [98Iac, 99Iac]) have found widespread use.
2.1.7.3.1 FROG, SHG-FROG, FROG-CRAB Frequency-Resolved Optical Gating (FROG) [93Kan, 97Tre] is a characterization method based on the measurement of a spectrally resolved autocorrelation signal followed by an iterative phaseretrieval algorithm to extract the intensity and phase of the laser pulse. In a general sense the FROG technique uses a gate G(t) that is being used to measure the spectrum S(ω, τ ) of a series of temporal slices: 2 S (ω, τ ) = G (t − τ ) E (t) eiωt dt , (2.1.87) where E(t) is the electric field of the pulse that needs to be characterized and τ the time delay between the gate and the pulse. The gate can either be an amplitude or phase gate [93Bec, 03Kan]. The most commonly used FROG is based on an amplitude gate using Second-Harmonic Generation (SHG) and the pulse that needs to be characterized (i.e. “blind FROG” because the gate is unknown): G (t) = χ(2) E (t) .
(2.1.88)
This is generally referred to as SHG-FROG. Collinear SHG-FROG has been demonstrated using type II phase matching in the 20-fs [99Fit] and sub-10-fs [00Gal1] pulse-width regime. An example for a phase gate would be cross phase modulation using again the same pulse for the gate: 2 (2.1.89) G (t) = exp −ikn2 |E (t)| . The iterative retrieval algorithm is not very intuitive and rather complex and is based on a Principal Component Generalized Projections Algorithm (PCGPA) which starts in an initial guess for G(t) and E(t) that is than being compared to the measured S(ω, τ ) [99Kan]. For femtosecond pulses in the visible to infrared regime nonlinear optics can be used to obtain very good FROG traces. In the XUV and attosecond-pulse-width regime this becomes more complicated. We basically need a non-stationary filter in the XUV with a response time on the order of the attosecond-pulse duration. A phase gate can be obtained using photoionization of an atom in the presence of a weak InfraRed (IR) pulse that has been used to generate the attosecond pulses and therefore is precisely synchronized. As long as the XUV pulse is shorter than the IR period the temporal information of the XUV pulse is mapped into the electron energy distribution in the linear part of the optical IR field. This technique is referred to as Frequency-Resolved Optical Gating for Complete Reconstruction of Attosecond Burst (FROG-CRAB) where the linear phase modulation is obtained through the photoionization of atoms by the short XUV pulse in the presence of a weak linear part of the IR field and the spectrometer is being replaced by the electron energy detection [05Mai]. The XUV pulse is then converted in a modulated electron wave packet.
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2.1.7 Pulse characterization
[Ref. p. 134
2.1.7.3.2 SPIDER Spectral Phase Interferometry for Direct Electric-field Reconstruction (SPIDER) measures the spectral interference of a pulse with a frequency-shifted replica [98Iac, 99Iac]: 2 ˜ ˜ (ω − ω0 − δω) eiωτ , S (ω, τ ) = E (ω − ω0 ) + E (2.1.90) ˜ (ω) is the Fourier-transformation of the electric field E(t). To access the spectral phase where E it is necessary to produce two time-delayed replicas by a predetermined delay τ of the pulse and with a spectral shear δω between their carrier frequencies. The spectral shear between the central frequencies of the two replicas is generated by upconversion of the two replicas with a strongly chirped pulse using sum-frequency generation in a nonlinear optical crystal. The strongly chirped pulse is generated by propagating another copy of the original pulse through a thick glass block. The spectral shear arises because the time delay between the replicas assures that each replica is upconverted with a different portion of the chirped pulse containing a different instantaneous frequency [99Gal]. The time delay τ between the replica is kept constant during the measurements and therefore only a 1D trace needs to be measured for the resulting SPIDER interferogram 2 2 ˜ ˜ ISPIDER (ω) = E(ω) + δω) + E(ω ˜ ˜ + δω) cos [ϕ(ω + δω) − ϕ(ω) + ωτ ] . +2 E(ω) E(ω (2.1.91) The phase information can be extracted from the cosine term by the following, purely algebraic, method: The Fourier transform to the time domain of the SPIDER interferogram consists of a peak at zero time and two side peaks located near τ and −τ . The two side peaks contain equivalent phase information and are equal. One of the peaks is isolated by applying a suitable filter function and an inverse Fourier transform back to the frequency domain yields a complex function z(ω), whose complex phase gives access to the pulse spectral phase: arg (z(ω)) = ϕ(ω + δω) − ϕ(ω) + ωτ . A separate measurement of the linear phase term ωτ by spectral interferometry of the short unsheared pulse replicas is subtracted from the previous expression to yield the spectral phase difference Δϕ(ω) = ϕ(ω + δω) − ϕ(ω). From an arbitrarily chosen starting frequency ω0 one obtains the spectral phase ϕ(ω) at evenly spaced frequencies ωi = ω0 + i · δω by the following concatenation procedure: ϕ(ω0 ) = ϕ0 , ϕ(ω1 ) = Δϕ(ω0 ) + ϕ(ω0 ) = ϕ(ω0 + δω) − ϕ(ω0 ) + ϕ(ω0 ) = ϕ(ω0 + 1 · δω) , .. .
(2.1.92)
ϕ(ωi+1 ) = Δϕ(ωi ) + ϕ(ωi ) . The constant ϕ0 remains undetermined but is only an offset to the spectral phase, which does not affect the temporal pulse shape and we may thus set it equal to zero. The spectral phase is written as: ϕ(ωi+1 ) =
i
Δϕ(ωk ) .
(2.1.93)
k=0
If δω is small relative to features in the spectral phase, Δϕ(ω) corresponds in first order to the first derivative of the spectral phase and we can approximate the spectral phase by: ω 1 Δϕ(ω ) dω . (2.1.94) ϕ(ω) δω ω0 The integral expression for the spectral phase has the advantage that all the measured sampling points of the interferogram can be used instead of only using a subset with sampling according Landolt-B¨ ornstein New Series VIII/1B1
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to the spectral shear as with the concatenation method. The phase information of the resulting interferogram allows the direct reconstruction of the spectral phase of the input pulse. Combined with the measured spectrum of the pulse the actual pulse can be calculated without any prior assumptions. Three design parameters determine the range of pulse durations that can be measured by a certain SPIDER apparatus: the delay τ , the spectral shear δω and the group-delay dispersion GDDup used to generate the strongly linearly chirped upconverter pulse. These three parameters are related as: δω =
τ . GDDup
(2.1.95)
The delay τ , which determines the positions of the two side peaks of the Fourier transform of the interferogram, is chosen in such a way as to assure that the side peaks are well-separated from the center peak. On the other hand, the fringe spacing of the interferogram is proportional to 2π/τ and thus τ must be sufficiently small such that the spectrometer is able to fully resolve the fringes. The stretching factor GDDup is then chosen such that the spectral shear δω, which determines the sampling interval of the reconstructed spectral phase, is small enough to assure correct reconstruction of the electric field in the time domain according to the Whittaker–Shannon sampling theorem [00Dor]. The constrained relationship for τ and δω expressed by (2.1.95) means that with a particular SPIDER setup, only pulses with a limited range of pulse durations can be measured. A set-up for the sub-10-femtosecond regime in described in [99Gal].
2.1.7.3.3 Comparison between FROG and SPIDER techniques The highest acquisition rates for single-shot pulse characterization reported so far were 1 kHz using SPIDER [03Kor] and 30 Hz using FROG [03Gar]. FROG is not well suited for high acquisition rates for two reasons: FROG requires the measurement of a 2D trace which makes the acquisition itself inherently slow and moreover the FROG algorithm uses an iterative process which requires a minimum number of steps for convergence depending on the complexity of the measured pulse. SPIDER however only requires the acquisition of two 1D spectra: the so-called SPIDER interferogram and the optical spectrum of the pulse. Furthermore, the SPIDER algorithm is deterministic since it is based on two Fourier transforms with intermittent spectral filtering to reconstruct the spectral phase of the pulse. An additional Fourier transform is then required to calculate the electric field in the time domain and therefore the pulse reconstruction is fast. SPIDER is thus well suited for high acquisition rates and real-time operation. SPIDER has been shown to achieve high accuracy, i.e. the reconstructed electric field matches well with the physical field of the pulse [02Dor1], and high precision [02Dor2], implying a small spread between several reconstructions of the field obtained from the same data. In particular the SPIDER technique is reliable in the presence of limited experimental noise [00And, 04Jen]. SPIDER offers more bandwidth than any other technique and we even can measure pulses in the single-cycle regime [03Sch]. In addition, SPIDER still gives valid results even if the beam profile is not spatially coherent anymore because we can spatially resolve these measurements [01Gal]. A direct comparison between FROG and SPIDER techniques in the sub-10-femtosecond regime is given in [00Gal2]. Only fully characterized pulses in phase and amplitude will provide reliable information about pulse shape and pulse duration – this becomes even more important for pulses with very broad and complex spectra. In such a situation any other technique, such as fitting attempts to IAC traces, is very erroneous and generally underestimates the pulse duration.
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2.1.8 Carrier envelope offset (CEO)
[Ref. p. 134
2.1.8 Carrier envelope offset (CEO)
TR
Electric field E
Progress in ultrashort pulse generation [99Ste] has reached a level where the slowly-varyingenvelope approximation starts to fail. Pulse durations of Ti:sapphire laser oscillators have reached around 5 fs which is so short that only about two optical cycles of the underlying electric field fit into the full-width half maximum of the pulse envelope. For such short pulses the maximum electric-field strength depends strongly on the exact position of the electric field with regards to the pulse envelope, i.e. the Carrier Envelope Offset (CEO) [99Tel]. In passively mode-locked lasers this carrier envelope offset is a freely varying parameter because the steady-state boundary condition only requires that the pulse envelope is the same after one round trip (Fig. 2.1.19). Therefore the CEO phase may exhibit large fluctuations, even when all other laser parameters are stabilized. We have discussed the physical origin of these fluctuations before [02Hel2, 02Hel1]. Because nonlinear laser–matter interaction depends strongly on the strength of the electric field, this CEO fluctuations cause strong signal fluctuations in nonlinear experiments such as high-harmonic generation [00Bra], attosecond pulse generation [01Dre], photoelectron emission [01Pau1] etc.
Time t
Fig. 2.1.19. Electric field E(t) of three subsequent pulses from a mode-locked laser with a pulse repetition rate of TR = 1/frep . The envelope ±A(t) is shown as dashed lines. The electric-field patterns of the pulses experience large pulse-to-pulse fluctuations.
Different techniques have been proposed to stabilize these CEO fluctuations in the time domain [96Xu1] and in the frequency domain [99Tel]. The frequency-domain technique is based on the frequency comb generated from mode-locked lasers (Sect. 2.1.2.2) and is much more sensitive and is the technique that is being used today. Optical frequency comb techniques recently received a lot of attention and were also an important part of the 2005 Nobel Prize in Physics for Theodor W. H¨ ansch and John L. Hall in the area of laser-based precision spectroscopy [05Nob]. In the following we follow the notation and derivation of Helbing et al. [03Hel]. A very stable frequency comb is generated with a mode-locked laser which follows directly from the time domain: Etrain (t) = A (t) exp (iωc t + iϕ0 (t)) ⊗
+∞
δ (t − mTR ) ,
(2.1.96)
m=−∞
where Etrain (t) is the electric field of a pulse train (Fig. 2.1.19), ωc is the (angular) carrier frequency which is the center of gravity of the mode-locked spectrum, A(t) the pulse envelope, and ϕ0 (t) the absolute phase of the pulse. The change of the carrier-envelope offset phase ϕ0 in (2.1.96) per round trip is given by: Δϕ0 = Δϕ GPO mod 2π .
(2.1.97)
The Group-Phase Offset (GPO) only arises from the first-order dispersion of the material along the beam path: L 2 L 1 ω dn(ω, x) 1 dx = Δϕ GPO = −ω − dx , (2.1.98) vg vp c dω 0 0 where vg is the group velocity and vp is the phase velocity (Table 2.1.7). Landolt-B¨ ornstein New Series VIII/1B1
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Intensity I
rep
Frequency n 0 CEO
Fig. 2.1.20. Equidistant frequency comb of a mode-locked laser. The comb lines are spaced by the repetition rate frep and exhibit a nonvanishing offset frequency fCEO at zero frequency unless the electric field pattern exactly reproduces from pulse to pulse.
We define the (angular) carrier-envelope offset frequency as
Δϕ0 Δϕ GPO ∂ ϕ GPO mod 2π . 2π fCEO = ωCEO = Δϕ0 frep = ≡ mod 2π ≡ TR TR ∂t
(2.1.99)
Taking into account the varying carrier-envelope offset phase the electric field of the pulse train becomes: Etrain (t) = A (t) exp (iωc t + i ωCEO t) ⊗
+∞
δ (t − mTR ) .
(2.1.100)
m=−∞
The Fourier-transformation of (2.1.100) then results in the frequency comb as shown in Fig. 2.1.20: ˜train (f ) = A˜ (f − fc ) · E
+∞
δ (f − mfrep − fCEO ) .
(2.1.101)
m=−∞
The whole equidistant frequency comb is shifted by fCEO due to the per round trip carrier-envelope offset phase shift of Δϕ0 . Therefore, a mode-locked laser generates an equidistant frequency comb with a frequency step given by the pulse repetition frequency frep which can be measured and stabilized with very high precision [86Lin, 86Rod, 89Rod, 89Kel]. The uniformity of the modelocked frequency comb has been demonstrated to a relative uncertainty below 10−15 [99Ude]. The timing jitter in the arrival time of the pulses (i.e. variations in frep ) produces a “breathing” of the fully equidistant frequency comb. The additional freedom of the frequency offset to DC of this frequency comb is given by the CEO frequency fCEO (Fig. 2.1.20) and every “tick of the frequency ruler” then can be described by [99Tel] fm = mfrep + fCEO
(2.1.102)
with m being an integer number. The timing jitter of the CEO results in a translation of the full frequency comb. Note that the equidistant frequency-comb spacing is given by the round-trip propagation time of the pulse envelope (i.e. by the group velocity and not the phase velocity). This means that the axial modes of a mode-locked laser are not the same as the ones from a cw laser for which the phase velocity determines the axial mode spacing. Even though a measurement of the repetition rate is straightforward, it is virtually impossible to access the CEO-frequency directly, as the laser spectrum contains no energy close to zero frequency. One therefore has to use an indirect way to measure the second comb parameter. Depending on the available optical bandwidth different techniques have been proposed by Telle et al. [99Tel] such as f -to-2f , 2f -to-3f heterodyne techniques and others. Selecting some low-frequency portion of the comb and frequency doubling it gives rise to the comb
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2.1.8 Carrier envelope offset (CEO) ¦rep
Intensity
¦1 = ¦CEO +m¦rep
[Ref. p. 134
2¦2 = 2¦CEO +2m¦rep
¦1
Frequency ¦CEO = 2¦1 -¦2
0
¦2 = ¦CEO +2n¦rep
¦CEO
¦CEO ¦2 2¦1
a
Repetition rate
Power density [dBc]
CEO- beat 0 -20
Spurious
- 40
-60
0
b
20
40 60 Frequency [MHz]
80
100
Fig. 2.1.21. f -to-2f interference technique to measure the CEO frequency according to [99Tel]: (a) Mode beating of fundamental and second harmonic frequency comb results in the carrier envelope offset frequency fCEO = 2f1 − f2 , where frep is the pulse repetition rate frequency, fCEO is the carrier envelope offset frequency and m is an integer number. (b) Mode beating signal measurement with a microwave spectrum analyzer which shows a strong peak at the pulse repetition rate and the two CEO beats at fCEO and frep − fCEO with a signal-to-noise ratio of more than 40 dB. This is ideal for a stabilizing feedback loop using a weak modulation of the pump laser power to compensate for the CEO fluctuations.
2fm = 2fCEO + 2mfrep .
(2.1.103)
If the fundamental comb spectrum covers more than an optical octave it will also contain modes at f2m = fCEO + 2mfrep .
(2.1.104)
Beating the combs of (2.1.103) and (2.1.104), therefore extracts the CEO-frequency from the comb spectrum [99Tel]: fCEO = 2fm − f2m = (2fCEO + 2mfrep ) − (fCEO + 2mfrep ) ,
(2.1.105)
see Fig. 2.1.21. Today the most common technique is based on this f -to-2f heterodyne technique because of its simplicity and because an octave-spanning spectrum can be generated with external spectral broadening in a microstructure fiber for example [00Jon, 00Apo]. With this technique we achieved a long-term CEO stabilization with residual 10 attosecond timing jitter which corresponds to 0.025 rad rms CEO phase noise in a (0.01 Hz–100 kHz) bandwidth [02Hel1]. The f -to-2f interference technique requires an octave-spanning spectrum. So far, all attempts to generate this spectrum directly from a laser source have only reached unsatisfactory control of the CEO frequency, which was mainly caused by poor signal strength. Therefore most experiments required additional spectral broadening, e.g. in an external microstructure fiber. The continuum generation process with its strong nonlinearity, however, introduces additional CEO noise. It is important to note that the CEO stabilization is achieved for the pulses after the microstructure fiber, which means that the pulses directly from the Ti:sapphire laser will exhibit excess CEO phase noise even with a perfectly working CEO stabilization. The relative phase between the carrier and the envelope of an optical pulse is the key parameter linking the fields of precision frequency metrology and ultrafast laser physics. As we have discussed, the spectrum of a mode-locked laser consists of a comb of precisely equally spaced frequencies. The uniformity of this frequency comb has been demonstrated to a relative uncertainty below 10−15 Landolt-B¨ ornstein New Series VIII/1B1
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[99Ude]. Knowledge of only two parameters, the comb spacing and a common offset frequency of all modes, provides one with a set of reference frequencies, similar to the tick marks on a ruler. The beat (difference-frequency) signal of this unknown frequency with the closest frequency in the ruler always gives a beat signal smaller than the comb period. Thus, an optical frequency in the 100 THz regime can be translated down to a microwave frequency in the range of 100 MHz, which can then be measured very accurately. This can be used for an all-optical atomic clock that is expected to outperform today’s state-of-the-art cesium clocks [02Ude]. The mode-locked laser provides a phaselocked clockwork mediating between radio frequencies and the Terahertz frequencies of the lines in the optical comb, effectively rendering optical frequencies countable. Details on precision frequency measurements with mode-locked laser combs can be found in [99Rei, 01Hol, 01Cun, 02Bau].
2.1.9 Conclusion and outlook We have shown that the technology of ultrafast lasers has become very refined and is now suitable for application in many areas. Points of particular importance in this respect are: – The transition from dye lasers to solid-state lasers, which can be compact, powerful, efficient and long-lived. It has been shown that solid-state lasers can generate pulses which are even shorter pulses than those generated in dye lasers with much more average output power. – The development of high-power and high-brightness diode lasers for direct pumping of solidstate lasers. This has lead not only to very efficient and compact lasers, but also to lasers with more than 1000 W of average output power. – The development of novel saturable absorbers such as KLM which has pushed the frontier in ultrashort pulse duration into the two-optical-cycle regime using novel chirped mirrors for dispersion compensation. New parameters such as the Carrier Envelope Offset (CEO) of the electric field underneath the pulse envelope have become important for many different applications. – The development of SEmiconductor Saturable Absorber Mirrors (SESAMs) which passively mode-lock many different diode-pumped solid-state lasers without Q-switching instabilities and can be optimized for operation in very different parameter regimes such as laser wavelength, pulse duration, pulse repetition rate and power levels. SESAMs can be optimized independently of the cavity design. This allowed for pushing the frontier in ultrafast solid-state lasers by several orders of magnitude: femtosecond mode-locked lasers with close to 100 W of average output power and more than 1 μJ of pulse energies and different lasers with high pulse repetition rates up to 160 GHz have been demonstrated so far. For the next few years we expect many new exciting developments in the field of diode-pumped solid-state lasers: – Very high power levels (> 100 W of average power) should become possible with passively modelocked thin-disk lasers. Pulse durations just below 1 ps are feasible and with new materials the regime of 200 fs or even below should become accessible with similarly high powers. – Nonlinear frequency conversion stages (based on second-harmonic generation, sum frequency mixing, or parametric oscillation) will be pumped with high-power mode-locked lasers to generate short and powerful pulses at other wavelengths. The high power makes the nonlinear conversion efficiencies very high with very simple arrangements [01Sue, 05Mar]. This will be of interest for application in large-screen RGB display systems, for example [04Bru, 06Inn]. – Simple external pulse compression combined with novel high-average-power solid-state lasers now allows for peak intensities as high as 12 MW with 33-fs pulses at the full pulse repetition rate of the laser oscillator [03Sue]. This could be focused to a peak intensity of 1014 W/cm2 , a Landolt-B¨ ornstein New Series VIII/1B1
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regime where high-field laser physics such as high-harmonic generation [88Fer, 94Lew, 98Sal] and laser-plasma-generated X-rays [91Mur] are possible at more than 10 MHz pulse repetition rate. This improves signal-to-noise ratios in measurements by 4 orders of magnitude compared to the standard sources at kHz repetition rates. This would be important for low-power applications such as X-ray imaging and microscopy [02Sch1], femtosecond EUV and soft-X-ray photoelectron spectroscopy [01Bau] and ultrafast X-ray diffraction [99Sid, 01Rou]. – Very high pulse repetition rates with 100 GHz should be possible from passively mode-locked diode-pumped solid-state lasers at different wavelengths, even in the wavelength range around 1.5 μm and 1.3 μm for telecom applications. – As an alternative to ion-doped gain media at high pulse-repetition rates (i.e. > 1 GHz) optically pumped VECSELs and even hopefully electrically pumped VECSELs will become very interesting alternatives [06Kel]. The integration of the SESAM into the VECSEL structure will provide even more compact ultrafast lasers [07Maa]. – So far octave-spanning frequency combs have been mostly generated with KLM Ti:sapphire lasers and supercontinuum generation in a microstructured fiber. However, many applications need more compact sources. The progress in femtosecond diode-pumped solid-state lasers and VECSELs reported here will make this possible in the near future. Thus, all these examples show that the development of ultrafast diode-pumped sources has not come to its end but will continue to deliver superior performances for many established and new applications. In addition, research to produce pulses of even shorter duration is underway. Currently, the most promising path to attosecond pulse generation and attosecond spectroscopy is high-harmonic generation (recent reviews are given with [98Sal, 95DiM, 04Ago]). High-order-Harmonic Generation (HHG), being an up-conversion process, provides a laser-like source of temporally and spatially coherent radiation consisting of odd multiples of the laser driving frequency down to the XUV region of the spectrum. Since its discovery in 1987 in Chicago and Saclay [88Fer, 87McP], it has been speculated early on that pulses from existing sources of high-harmonic generation exhibit attosecond time signature [95Cor, 96Ant]. Meanwhile much progress has been made and by controlling its properties, Attosecond Pulse Trains (APT) [01Pau2] and isolated attosecond pulses [02Dre] have been successfully produced and applied in first proof-of-principle experiments. The higher orders are produced simultaneously and fully phase-coherent with the driving IR field, which makes this source ideally suited for two-color or even multi-color pump probe experiments. Furthermore, it is important to note, that much of this progress is directly related to advancements in laser science. Isolated attosecond pulse generation depends on the maximum amplitude of the driving pulse’s electric field, i.e. the exact position of the electric field with regard to the pulse envelope (Carrier Envelope Offset: CEO) [99Tel]. Generally in mode-locked lasers, the CEO phase exhibits large fluctuations, which have to be measured and be corrected for. Until recently the only successful demonstration of CEO-phase-locked intense pulses was based on a CEO-stabilized Ti:sapphire laser, chirped-pulse amplification and pulse compression in a hollow fiber (Sect. 2.1.6.9). Meanwhile, there are some new promising ways to achieve this goal. One is based on Chirped-Pulse Optical Parametric Amplification (CPOPA) [92Dub] and the other on pulse compression through filamentation [04Hau1]. We have demonstrated CEO-phase-stabilized CPOPA for the first time with near-transform-limited 17.3-fs pulses [04Hau2]. But even more amazing was that even though filamentation is a highly nonlinear process involving plasma generation, the CEO stabilization was maintained and intense CEO-stabilized pulses as short as 5.1 fs with 180 μJ pulse energy have been generated [05Hau]. It is expected that both pulse duration and energies will be further improved in the near future. For example just recently CPOPA resulted in 9.8 fs pulses with 10.5 mJ at 30 Hz pulse repetition rate [05Wit]. We would expect that with attosecond time resolution we open up a new world of physics with as much impact as has been demonstrated in the 70’s and 80’s with the transition from picosecond to femtosecond time resolution. First time-resolved measurements have been done [02Dre]. At this
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point, however, we still have some significant challenges to tackle before we demonstrate standard attosecond pulse generation and attosecond spectroscopy. Solving all of these challenges will make the research in ultrashort pulse generation very exciting and rewarding for many years to come.
2.1.10 Glossary A AA AL Ap B b D Dg Dp DR (t) d E Ep Ep,c Ep,out Esat,A Esat,L Etrain F2 Fin Fout Fp,A Fsat,A Fsat,L fCEO frep G(t) g g0 h I IA Iin (t) Iout (t) Isat,A k kn L La Landolt-B¨ ornstein New Series VIII/1B1
pulse envelope (2.1.23) laser mode area on saturable absorber (Table 2.1.5) laser mode area in laser gain media pump mode area system bandwidth (2.1.82) depth of focus or confocal parameter of a Gaussian beam dispersion parameter (2.1.40), i.e. half of the total group delay dispersion per cavity round trip gain dispersion ((2.1.32) and Table 2.1.10) width of the pump source (i.e. approximately the stripe width of a diode array or bar or more accurately given in Sect. 2.1.3.2) differential impulse response of a saturable absorber mirror measured with standard pump probe (Sect. 2.1.4.2) thickness of Fabry–Perot (Table 2.1.9) electric field of the electromagnetic wave intracavity pulse energy critical Ep (2.1.77) output pulse energy absorber saturation energy (Table 2.1.5) laser saturation energy electric field of a pulse train (2.1.96) inverse slope of roll-over (2.1.81) incident saturation fluence on SESAM (2.1.9) reflected saturation fluence on SESAM (2.1.9) incident pulse fluence on saturable absorber (Table 2.1.5) absorber saturation fluence (Table 2.1.5) laser saturation fluence (2.1.1) and (2.1.2) carrier envelope offset (CEO) frequency (2.1.99) pulse repetition frequency gate (see Sect. 2.1.7.3.1) saturated amplitude laser gain coefficient small signal amplitude laser gain beam insertion into second prism (Table 2.1.9) intensity incident intensity on saturable absorber (Table 2.1.5) incident intensity onto the saturable absorber (2.1.8) reflected intensity from the saturable absorber (2.1.8) absorber saturation intensity (Table 2.1.5) vacuum wave number, i.e. k = 2 π/λ wave number in a dispersive medium, i.e. kn = nk (2.1.24) apex-to-apex prism distance (Table 2.1.9) absorption length
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2.1.10 Glossary
[Ref. p. 134
Lg l
length of laser gain material or grating pair spacing (Table 2.1.9) total saturated amplitude loss coefficient (Table 2.1.10). l includes the output coupler, all the residual cavity losses and the unsaturated loss of the saturable absorber. lout amplitude loss coefficient of output coupler ls amplitude loss coefficient of soliton due to gain filtering and absorber saturation (2.1.75) M modulation depth of loss modulator (2.1.33) M1 , M2 , M3 , . . . different mirrors in laser cavity M 2 factor defining the laser beam quality (2.1.3) M2 2 Mfast M 2 factor in the “fast” axis, perpendicular to the pn-junction of the diode laser 2 Mslow M 2 factor in the “slow” axis, parallel to the pn-junction of the diode laser Ms curvature of loss modulation ((2.1.33) and Table 2.1.10) n refractive index of a dispersive medium n2 nonlinear refractive index (Fig. 2.1.13, (2.1.42)) P power P (z, t) pulse power (2.1.24) Pabs absorbed pump power Pav,out average output power q saturable amplitude loss coefficient (i.e. nonsaturable losses not included) (2.1.7) q0 unsaturated amplitude loss coefficient or maximal saturable amplitude loss coefficient (2.1.6) qp total absorber loss coefficient which results from the fact that part of the excitation pulse needs to be absorbed to saturate the absorber ((2.1.11) and (2.1.15)) qs residual saturable absorber amplitude loss coefficient for a fully saturated ideal fast absorber with soliton pulses R(Fp,A ) measured nonlinear reflectivity of a SESAM (Fig. 2.1.9) R(t) impulse response of a saturable absorber mirror (Sect. 2.1.4.2) RISA measured nonlinear reflectivity with inverse saturable absorption (ISA) (2.1.81) top intensity reflectivity (Table 2.1.9) Rt total net reflectivity (2.1.9) Rtot S(ω, τ ) spectral interference of a pulse with a frequency-shifted replica (2.1.90) T time that develops on a time scale of the order of TR (2.1.23) group delay (Table 2.1.7) Tg Tout intensity transmission of the laser output coupler cavity round-trip time TR t fast time of the order of the pulse duration (2.1.23) t0 round-trip time of Fabry–Perot (Table 2.1.9) time shift (2.1.59) tD pump volume Vp vg group velocity (Table 2.1.7) phase velocity (Table 2.1.7) vp beam waist W0 W0,G beam waist of a Gaussian beam optimized beam waist for efficient diode pumping (2.1.5) W0,opt z pulse propagation distance z0 Rayleigh range of a Gaussian beam, i.e. z0 = π W02 /λ α β γA ΔA
apex angle of prism (Table 2.1.9) angle in prism compressor (Fig. 2.1.16c and Table 2.1.9) absorber coefficient ((2.1.18), (2.1.35) and Table 2.1.10) change in the pulse envelope Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 134] ΔR ΔRns ΔT ΔTns Δλg Δνg Δνp ΔϕGPO δL δτ θ θB θG θi Λ λ λ0 λeff λn ν νpump σA σL σLabs τ0 τA τAu τc τL τp τp,min Φ(ω) Φ0 ϕ0 (t) φnl φnl (z) φs φs (z) ψ Ωg ω ω0 ωc ωCEO ωm
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modulation depth of a saturable absorber mirror (Fig. 2.1.9 and Table 2.1.5) nonsaturable reflection loss of a saturable absorber mirror (Fig. 2.1.9 and Table 2.1.5) modulation depth of saturable absorber in transmission nonsaturable transmission loss of saturable absorber FWHM gain bandwidth Δνg Δλg FWHM gain bandwidth, i.e. = ν0 λ0 FWHM of pulse intensity spectrum group phase offset ((2.1.97) and (2.1.98)) SPM coefficient (2.1.44) temporal delay between two beams (2.1.86) divergence angle of a pump source (i.e. the beam radius increases approximately linearly with propagation distance, defining a cone with half-angle θ) Brewster angle (Table 2.1.9) divergence angle of a Gaussian beam, i.e. θG = λ/(π W0,G ) (2.1.3) angle of incidence (Table 2.1.9) grating period (Table 2.1.9) vacuum wavelength of light center vacuum wavelength effective wavelength (2.1.4) wavelength in a dispersive medium with refractive index n, i.e. λn = λ/n frequency pump photon frequency absorber cross section gain cross section absorption cross section of the three-level gain medium initial transform-limited pulse duration (2.1.20) recovery time of saturable absorber (Table 2.1.5) FWHM of intensity autocorrelation pulse photon cavity lifetime upper-state lifetime of laser gain material FWHM intensity pulse duration minimal τp frequency-dependent phase shift (Sect. 2.1.5.1) phase shift at center angular frequency ω0 absolute phase of pulse (2.1.96) nonlinear phase shift per cavity round trip (2.1.73) nonlinear phase shift of a pulse with peak intensity I0 during propagation through a Kerr medium along the z-axis, i.e. φnl (z) = kn2 I0 z (2.1.73) phase shift of the soliton per cavity round trip phase shift of the soliton during propagation along the z-axis (2.1.73) phase shift (Table 2.1.10) Half-Width-Half-Maximum (HWHM) gain bandwidth of laser in radians/second, i.e. Ωg = π Δνg radian frequency center radian frequency carrier radian frequency (2.1.96) carrier envelope offset (CEO) frequency in radians/second (2.1.99) modulation frequency in radians/second
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Harmer, A.L., Linz, A., Gabbe, D.R.: Fluorescence of Nd3+ in lithium yttrium fluoride; J. Phys. Chem. Solids 30 (1969) 1483–1491. Treacy, E.B.: Optical pulse compression with diffraction gratings; IEEE J. Quantum Electron. 5 (1969) 454–458.
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80Mol 80Sal
81For 81Zie
83For 83Joh 83Min
83Wei
84For 84Mar
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86Hau 86Kno
86Lin 86Mou 86Rod
86Ros 86Sie 86Val
86Vas
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87Bad
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References for 2.1 Kim, K., Lee, S., Delfyett, P.J.: 1.4 kW high peak power generation from an all semiconductor mode-locked master oscillator power amplifier system based on eXtreme Chirped Pulse Amplification(X-CPA); Opt. Express 13 (2005) 4600–4606. Kisel, V.E., Troshin, A.E., Shcherbitsky, V.G., Kuleshov, N.V., Matrosov, V.N., Matrosova, T.A., Kupchenko, M.I., Brunner, F., Paschotta, R., Morier-Genoud, F., Keller, U.: Femtosecond pulse generation with a diode-pumped Yb3+ :YVO4 laser; Opt. Lett. 30 (2005) 1150–1152. Lagatsky, A.A., Rafailov, E.U., Sibbett, W., Livshits, D.A., Zhukov, A.E., Ustinov, V.M.: Quantum-dot-based saturable absorber with p-n junction for mode-locking of solid-state lasers; IEEE Photon. Technol. Lett. 17 (2005) 294–296. Lecomte, S., Kalisch, M., Krainer, L., Sp¨ uhler, G.J., Paschotta, R., Krainer, L., Golling, M., Ebling, D., Ohgoh, T., Hayakawa, T., Pawlik, S., Schmidt, B., Keller, U.: Diodepumped passively mode-locked Nd:YVO4 lasers with 40-GHz repetition rate; IEEE J. Quantum Electron. 41 (2005) 45–52. Lecomte, S., Paschotta, R., Pawlik, S., Schmidt, B., Furusawa, K., Malinowski, A., Richardson, D.J., Keller, U.: Synchronously pumped optical parametric oscillator with a repetition rate of 81.8 GHz; IEEE Photon. Technol. Lett. 17 (2005) 483–485. Lin, J.H., Yang, W.H., Hsieh, W.F., Lin, K.H.: Low threshold and high power output of a diode-pumped nonlinear mirror mode-locked Nd:GdVO4 laser; Opt. Express 13 (2005) 6323–6329. Lindberg, H., Sadeghi, M., Westlund, M., Wang, S., Larsson, A., Strassner, M., Marcinkevicius, S.: Mode locking a 1550 nm semiconductor disk laser by using a GaInNAs saturable absorber; Opt. Lett. 30 (2005) 2793–2795. Liu, J., Mateos, X., Zhang, H., Wang, J., Jiang, M., Griebner, U., Petrov, V.: Continuous-wave laser operation of Yb:LuVO4 ; Opt. Lett. 30 (2005) 3162–3164. Mairesse, Y., Quere, F.: Frequency-resolved optical gating for complete reconstruction of attosecond bursts; Phys. Rev. A 71 (2005) 011401. Mandrik, A.V., Troshin, A.E., Kisel, V.E., Yasukevich, A.S., Klavsut, G.N., Kuleshov, N.V., Pavlyuk, A.A.: CW and Q-switched diode-pumped laser operation of Yb3+ :NaLa(MoO4 )2 ; Appl. Phys. B 81 (2005) 1119–1121. Marchese, S.V., Innerhofer, E., Paschotta, R., Kurimura, S., Kitamura, K., Arisholm, G., Keller, U.: Room temperature femtosecond optical parametric generation in MgOdoped stoichiometric LiTaO3 ; Appl. Phys. B 81 (2005) 1049–1052. Naumov, S., Fernandez, A., Graf, R., Dombi, P., Krausz, F., Apolonski, A.: Approaching the microjoule frontier with femtosecond laser oscillators; New J. Phys. 7 (2005) 216. http://nobelprize.org/physics/laureates/2005/adv.html – load down text with advanced information. Petit, J., Goldner, P., Viana, B.: Laser emission with low quantum defect in Yb:CaGdAlO4 ; Opt. Lett. 30 (2005) 1345–1347. Rivier, S., Mateos, X., Petrov, V., Griebner, U., Aznar, A., Silvestre, O., Sole, R., Aguilo, M., Diaz, F., Zorn, M., Weyers, M.: Mode-locked laser operation of epitaxially grown Yb:KLu(WOO4 )2 composites; Opt. Lett. 30 (2005) 2484–2486. Romero, J.J., Johannsen, J., Mond, M., Petermann, K., Huber, G., Heumann, E.: Continuous-wave laser action of Yb3+ -doped lanthanum scandium borate; Appl. Phys. B 80 (2005) 159–163. Roser, F., Rothhard, J., Ortac, B., Liem, A., Schmidt, O., Schreiber, T., Limpert, J., T¨ unnermann, A.: 131 W 220 fs fiber laser system; Opt. Lett. 30 (2005) 2754–2756. Rutz, A., Grange, R., Liverini, V., Haiml, M., Sch¨ on, S., Keller, U.: 1.5 μm GaInNAs semiconductor saturable absorber for passively modelocked solid-state lasers; Electron. Lett. 41 (2005) 321–323. Schlatter, A., Krainer, L., Golling, M., Paschotta, R., Ebling, D., Keller, U.: Passively mode-locked 914-nm Nd:YVO4 laser; Opt. Lett. 30 (2005) 44–46. Landolt-B¨ ornstein New Series VIII/1B1
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Schlatter, A., Rudin, B., Zeller, S.C., Paschotta, R., Sp¨ uhler, G.J., Krainer, L., Haverkamp, N., Telle, H.R., Keller, U.: Nearly quantum-noise-limited timing jitter from miniature Er:Yb:glass lasers: Opt. Lett. 30 (2005) 1536–1538. Schibli, T.R., Minoshima, K., Kataura, H., Itoga, E., Minami, N., Kazaoui, S., Miyashita, K., Tokumoto, M., Sakakibara, Y.: Ultrashort pulse-generation by saturable absorber mirrors based on polymer-embedded carbon nanotubes; Opt. Express 13 (2005) 8025–8031. Sorokin, E., Naumov, S., Sorokina, I.T.: Ultrabroadband infrared solid-state lasers; IEEE J. Sel. Topics Quantum Electron. 11 (2005) 690–712. Sp¨ uhler, G.J., Krainer, L., Innerhofer, E., Paschotta, R., Weingarten, K.J., Keller, U.: Soliton mode-locked Er:Yb:glass laser; Opt. Lett. 30 (2005) 263–265. Sp¨ uhler, G.J., Krainer, L., Liverini, V., Sch¨ on, S., Grange, R., Haiml, M., Schlatter, A., Pawlik, S., Schmidt, B., Keller, U.: Passively mode-locked multi-GHz 1.3-μm Nd:vanadate lasers with low timing jitter; IEEE Photon. Technol. Lett. 17 (2005) 1319– 1321. Sp¨ uhler, G.J., Weingarten, K.J., Grange, R., Krainer, L., Haiml, M., Liverini, V., Golling, M., Schon, S., Keller, U.: Semiconductor saturable absorber mirror structures with low saturation fluence; Appl. Phys. B 81 (2005) 27–32. Su, K.W., Lai, H.C., Li, A., Chen, Y.F., Huang, K.E.: InAs/GaAs quantum-dot saturable absorber for a diode-pumped passively mode-locked Nd:YVO4 laser at 1342 nm; Opt. Lett. 30 (2005) 1482–1484. Uemura, S., Torizuka, K.: Center-wavelength-shifted passively mode-locked diodepumped ytterbium(Yb): Yttrium aluminum garnet(YAG) laser; Jpn. J. Appl. Phys. Part 2 44 (2005) L361–L363. Voitikov, S.V., Demidovich, A.A., Batay, L.E., Kuzmin, A.N., Danailov, M.B.: Subnanosecond pulse dynamics of Nd:LSB microchip laser passively Q-switched by Cr:YAG saturable absorber; Opt. Commun. 251 (2005) 154–164. Wang, Y.G., Ma, X.Y., Fan, Y.X., Wang, H.T.: Passively mode-locking Nd:Gd0.5 Y0.5 VO4 laser with an In0.25 Ga0.75 As absorber grown at low temperature; Appl. Opt. 44 (2005) 4384–4387. Witte, S., Zinkstok, R.T., Hogervorst, W., Eikema, K.W.E.: Generation of few-cycle terawatt light pulses using optical parametric chirped pulse amplification; Opt. Express 13 (2005) 4903–4908. Zhang, B.Y., Li, G., Chen, M., Yu, H.J., Wang, Y.G., Ma, X.Y.: Passive mode locking of diode-end-pumped Nd:GdVO4 laser with an In0.25 Ga0.75 As output coupler; Opt. Commun. 244 (2005) 311–314. Zhang, Q., Jasim, K., Nurmikko, A.V., Ippen, E., Mooradian, A., Carey, G., Ha, W.: Characteristics of a high-speed passively mode-locked surface-emitting semiconductor InGaAs laser diode; IEEE Photon. Technol. Lett. 17 (2005) 525–527. Cascales, C., Serrano, M.D., Esteban-Beteg´on, F., Zaldo, C., Peters, R., Petermann, K., Huber, G., Ackermann, L., Rytz, D., Dupr´e, C., Rico, M., Liu, J., Griebner, U., Petrov, V.: Structural, spectroscopic, and tunable laser properties of Yb3+ -doped NaGd(WO4 )2 ; Phys. Rev. B 74 (2006) 174114–174128. Dewald, S., Lang, T., Schr¨ oter, C.D., Moshammer, R., Ullrich, J., Siegel, M., Morgner, U.: Ionization of noble gases with pulses directly from a laser oscillator; Opt. Lett. 31 (2006) 2072–2074. Grange, R., Zeller, S.C., Sch¨ on, S., Haiml, M., Ostinelli, O., Ebn¨ other, M., Gini, E., Keller, U.: Antimonide semiconductor saturable absorber for passive mode locking of a 1.5-μm Er:Yb:glass laser at 10 GHz; IEEE Phot. Tech. Lett. 18 (2006) 805–807. Holtom, G.R.: Mode-locked Yb:KGW laser longitudinally pumped by polarizationcoupled diode bars; Opt. Lett. 31 (2006) 2719–2721.
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References for 2.1 Innerhofer, E., Brunner, F., Marchese, S.V., Paschotta, R., Arisholm, G., Kurimura, S., Kitamura, K., Usami, T., Ito, H., Keller, U.: Analysis of nonlinear wavelength conversion system for a red-green-blue laser projection source; J. Opt. Soc. Am. B 23 (2006) 265– 275. Keller, U., Tropper, A.C.: Passively modelocked surface emitting semiconductor lasers; Physics Report 429 (2006) 67–120. Li, G., Zhao, S., Yang, K., Li, D.: Control of the pulse width in a diode-pumped passively Q-switched Nd:GdVO4 laser with GaAs saturable absorber; Opt. Materials, to be published. Lorenser, D., Maas, D.J.H.C., Unold, H.J., Bellancourt, A.R., Rudin, B., Gini, E., Ebling, D., Keller, U.: 50-GHz passively mode-locked surface emitting semiconductor laser with 100 mW average output power; IEEE J. Quantum Electron. 42 (2006) 838– 847. Major, A., Cisek, R., Barzda, V.: Femtosecond Yb:KGd(WO4 )2 laser oscillator pumped by a high power fiber-coupled diode laser module; Opt. Express 14 (2006) 12163–12168. Marchese, S.V., S¨ udmeyer, T., Golling, M., Grange, R., Keller, U.: Pulse energy scaling to 5 μJ from a femtosecond thin disk laser; Opt. Lett. 31 (2006) 2728–2730. Ostinelli, O., Haiml, M., Grange, R., Almuneau, G., Ebn¨ other, M., Gini, E., M¨ uller, E., Keller, U., B¨ achtold, W.: Highly reflective AlGaAsSb/InP Bragg reflector at 1.55 μm grown by MOVPE; J. Cryst. Growth 286 (2006) 247–254. Plant, J.J., Gopinath, J.T., Chann, B., Ripin, D.J., Huang, R.K., Juodawlkis, P.W.: 250 mW, 1.5 μm monolithic passively mode-locked slab-coupled optical waveguide laser; Opt. Lett. 31 (2006) 223–225. Rivier, S., Mateos, X., Liu, J., Petrov, V., Griebner, U., Zorn, M., Weyers, M., Zhang, H., Wang, J., Jiang, M.: Passively mode-locked Yb:LuVO4 oscillator; Opt. Express 14 (2006) 11668–11671. Thibault, F., Pelenc, D., Druon, F., Zaouter, Y., Jacquemet, M., Georges, P.: Efficient diode-pumped Yb3+ :Y2 SiO5 and Yb3+ :Lu2 SiO5 high-power femtosecond laser operation; Opt. Lett. 31 (2006) 1555–1557. Xue, Y., Wang, C., Liu, Q., Li, Y., Chai, L., Yan, C., Zhao, G., Su, L., Xu, X., Xu, J.: Characterization of diode-pumped laser operation of a novel Yb:GSO crystal; IEEE J. Quantum Electron. 42 (2006) 517–521. Zaouter, Y., Didierjean, J., Balembois, F., Leclin, G.L., Druon, F., Georges, P., Petit, J., Goldner, P., Viana, B.: 47-fs diode-pumped Yb3+ :CaGdAlO4 laser; Opt. Lett. 31 (2006) 119–121. Zeller, S.C., Grange, R., Liverini, V., Rutz, A., Sch¨ on, S., Haiml, M., Pawlik, S., Schmidt, B., Keller, U.: A low-loss buried resonant GaInNAs SESAM for 1.3-μm Nd:YLF laser at 1.4 GHz; Appl. Phys. Lett., submitted. Zhou, X., Kapteyn, H., Murnane, M.: Positive-dispersion cavity-dumped Ti:sapphire laser oscillator and its application to white light generation; Opt. Express 14 (2006) 9750–9757. Bellancourt, A.R., Rudin, B., Maas, D.J.H.C., Golling, M., Unold, H.J., S¨ udmeyer, T., Keller, U.: First demonstration of a modelocked integrated external-cavity surface emitting laser (MIXSEL); Conference on Lasers and Electro-Optics (CLEO ’07), Baltimore, USA, May 8–10 (2007) upgraded to invited talk CWI1. Fong, K.H., Kikuchi, K., Goh, C.S., Set, S.Y., Grange, R., Haiml, M., Schlatter, A., Keller, U.: Solid-state Er:Yb:glass laser mode-locked by using single-wall carbon nanotube thin film; Opt. Lett. 32 (2007) 38–40. Garc´ıa-Cort´es, A., Cano-Torres, J.M., Serrano, M.D., Cascales, C., Zaldo, C., Rivier, S., Mateos, X., Griebner, U., Petrov, V.: Spectroscopy and Lasing of Yb-Doped
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NaY(WO4 )2 : Tunable and Femtosecond Mode-Locked Laser Operation; IEEE J. Quantum Electron. 43 (2007) 758–764. Li, W., Hao, Q., Zhai, H., Zeng, H., Lu, W., Zhao, G., Zheng, L., Su, L., Xu, J.: Diodepumped Yb:GSO femtosecond laser; Opt. Express 15 (2007) 2354–2359. Maas, D.J.H.C., Bellancourt, A.R., Rudin, B., Golling, M., Unold, H.J., S¨ udmeyer, T., Keller, U.: Vertical integration of ultrafast semiconductor lasers; Appl. Phys. B 88 (2007) 493–497. Marchese, S.V., Hashimoto, S., B¨ ar, C.R.E., Ruosch, M.S., Grange, R., Golling, M., S¨ udmeyer, T., Keller, U., L´epine, G., Gingras, G., Witzel, B.: Passively mode-locked thin disk lasers reach 10 μJ pulse energy at megahertz repetition rate and drive high field physics experiments; CLEO Europe 2007, Munich, Germany, June 17–22 (2007) Talk CF3-2-MON. Palmer, G., Siegel, M., Steinmann, A., Morgner, U.: Microjoule pulses from a passively mode-locked Yb:KY(WO4 )2 thin-disk oscillator with cavity dumping; Opt. Lett. 32 (2007) 1593–1595. Rivier, S., Schmidt, A., Petrov, V., Griebner, U., Kr¨ ankel, C., Peters, R., Petermann, K., Huber, G., Zorn, M., Weyers, M., Klehr, A., Ebert, G.: Ultrashort pulse Yb:LaSc3 (BO3 )4 mode-locked oscillator; Opt. Express, submitted. Saarinen, E.J., Harkonen, A., Herda, R., Suomalainen, S., Orsila, L., Hakulinen, T., Guina, M., Okhotnikov, O.G.: Harmonically mode-locked VECSELs for multi-GHz pulse train generation; Opt. Express 15 (2007) 955–964. Sorokina, I.T., Sorokin, E.: Chirped-mirror dispersion controlled femtosecond Cr:ZnSe laser; Advanced Solid-State Photonics OSA Technical Digest, Vancouver, Canada, Jan. 28–31 (2007) WA7. Zeller, S.C., S¨ udmeyer, T., Weingarten, K.J., Keller, U.: Passively modelocked 77 GHz Er:Yb:glass laser; Electron. Lett. 43 (2007) 32–33.
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3.1 Gas laser systems R. Wester
3.1.1 Introduction The first gas laser was realized by A. Javan, W.R. Bennett and W.R. Herriot [61Jav] in 1961 about half a year after T.H. Maiman [60Mai] had achieved the first experimental realization of a laser, a solid-state ruby laser. A. Javan et al. used a mixture of the noble gases He and Ne. Since then a great number of further laser-active transitions have been discovered [98Web, 80Bec]. The basic condition for laser operation is that the higher energy level of the laser transition is more heavily occupied than the lower energy level, the transition must be inverted. In systems which are in thermodynamic equilibrium the lower energy levels are always stronger occupied than the higher levels. Thus inversion is only possible in states of thermodynamic non-equilibrium. States of non-equilibrium can be generated by various mechanisms. A hotter system, which can consist of free electrons or photons, can be coupled to the colder laser medium. Inversion can be realized when the net excitation rate of the upper laser level exceeds the net excitation rate of the lower level. Another approach is to heat the laser medium, during which it is in thermodynamic equilibrium and then cool it down fast. During relaxation the system can pass through non-equilibrium states. These kind of lasers include gas-dynamic lasers and recombination lasers. Solid-state crystal and liquid lasers can only be pumped by photons. Excitation by free electrons or fast cooling as well as excitation by chemical processes is the domain of gas lasers. The pumping of laser transitions with free electrons can be divided according to two main arrangements. In electron-guns electrons are emitted from a cathode and accelerated to energies in the range of several 10 keV to several MeV which then can be injected into a laser medium. Especially in the case of excimer lasers electron-beam pumping leads to otherwise unobtainable excitation efficiencies and pulse lengths. One disadvantage, however, is the technical complexity and low repetition rate of the electron-guns. The second mechanism for generating free electrons is to simultaneously use the gaseous laser medium as a gas discharge. The electrons are generated in the laser gas by electron collision ionization and heated by an externally applied electric field far above the gas-kinetic temperature of the laser gas. This is possible because the coupling of the translational degrees of freedom of electrons and gas particles is weak due to the large difference in mass weight between electrons and gas particles. Various types of gas discharges can be used. These range from direct current discharges via high-frequency and microwave discharges through to optical discharges, which involve heating the electrons with the beam of another laser. The most frequently used are direct-current and highfrequency discharges. This is mainly due to the ease of technical realization but also for physical reasons. Some types of lasers require pulsed excitation. Gas discharges are systems consisting of free electrons, charged and uncharged heavy particles (atoms, molecules etc. and their ions), photons and electromagnetic or static electric fields and in certain cases also static magnetic fields. The treatment of gas discharges includes elements of electrodynamics, statistical physics, kinetics, atomic and molecular physics, collision theory and radiation processes.
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3.1.2 Threshold pump power density
[Ref. p. 197
The most important elementary processes in gas discharges are electron collision ionization and electron collision excitation. For a discharge to be self-sustaining the number of free electrons which are produced by electron collision ionization must equal or exceed the number of electrons which recombine with ions in the discharge volume or at the discharge walls or which are lost by attachment to electro-negative gas components. The relevant laser levels are populated either directly or indirectly by electron collision excitation processes. The rate coefficient of an electron collision process depends on the electron distribution function, the partial density of the respective gas component and the respective cross section. The electron distribution function on the other hand is determined by the partial densities of all gas components, including those components which are produced by the gas discharge itself, by the relevant cross sections and by the electric field within the discharge region. The electric field is a function of the external electrical circuit, the geometry of the discharge chamber and the space charges in the discharge. The space-charge distribution is determined by the electric field and the number of free charge carriers which is determined by electron ionization. All this processes are interrelated and have in general to be treated self-consistently. The electron distribution function is the solution of the Boltzmann equation. There exist several approximate solution approaches. Most frequently applied are the two-term approximation and Monte-Carlo simulation. The two-term approximation is computationally fast but the approximations made are not always justifiable. Monte-Carlo simulations do not imply the same approximations as the two-term approximation but are computationally much more expensive. With the knowledge of the electron distribution function the rate coefficients of all the electron collision processes can be calculated. The rate coefficients together with transport coefficients which can be deduced from the electron energy distribution function too can be used to calculate the charge carrier densities and the densities of excited states. There are gas lasers with flowing gas medium, either for cooling and recirculation purposes or as in the case of gas-dynamic lasers for the excitation process. In gas-dynamic lasers the gas is compressed and subsequently expanded through a Laval nozzle. During expansion the gas is cooled rapidly so that inversion can occur during the relaxation of the gas.
3.1.2 Threshold pump power density The requirements for minimum pump power density for laser activity to commence vary considerably according to laser type. The values range from less than 1 W cm−3 for HeNe lasers to over 1 MW cm−3 for excimer lasers1 . In order to determine the required pulse pump power density the balance for the occupation of the laser levels and the light amplification must be considered. Figure 3.1.1 shows a diagram of the level scheme of a laser. In a simplified rate-equation approach the temporal development of the occupation density of the upper laser level can be written as: ∞ ∞ dN2 ηp2 N2 − A21 N2 − = − B21 f (ν)ρν (ν) dνN2 + B12 f (ν)ρν (ν) dνN1 (3.1.1) hν τ2 dt 0 0 with η = ηp ηQ . N2 is the occupation density of the upper laser level, N1 is the occupation density of the lower laser level, A21 is the Einstein coefficient for spontaneous emission, τ2 is the time constant for collisional deexcitation of the upper laser level, B21 is the Einstein coefficient for stimulated emission, B12 is 1
For the excitation of x-ray lasers much higher power densities still are required. Landolt-B¨ ornstein New Series VIII/1B1
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173
Pump level(s) Ep Upper laser level
E2 p2
A21
B21 r
E1 -1
t1 E0
B12 r
Lower laser level
Ground level
N2 -
t2 1 N1
Fig. 3.1.1. Diagram of the level scheme in the special case of a four-level laser. In general the lower laser level is not the ground state of the atom or molecule and the pump levels are often above the upper laser level.
the Einstein coefficient for absorption, and f (ν) is the spectral line shape of the laser transition2 . ρν (ν) is the spectral energy density of the radiation field: ρν (ν) =
Iν (ν) . c
(3.1.2)
Iν (ν) is the spectral intensity and c the speed of light. The energy difference between the upper and lower laser levels is equal to the photon energy hν = E2 − E1 . p2 is the power density for the excitation of the pump levels, ηp is the pump efficiency and ηQ is the so-called quantum efficiency. It is defined as the quotient of the energy difference between the upper and lower laser levels and the energy difference between pump level(s) and ground level: ηQ =
E2 − E1 . Ep − E0
(3.1.3)
The Einstein coefficients are linked by the following relations: 8π ν 2 hνB21 (ν) , c3 g1 B12 (ν) = g2 B21 (ν) . A21 =
(3.1.4) (3.1.5)
The first factor in (3.1.4) is the mode density, i.e. the number of modes of the radiation field per volume element in the frequency interval dν is: dNν =
8π ν 2 dν . c3
(3.1.6)
Equation (3.1.4) states that the rate of spontaneous decay is as large as the rate of stimulated transitions if exactly one photon is present in each radiation mode. g1 and g2 in (3.1.5) are the statistical weights of the two levels. The line profile of the transition is normalized in the following way: ∞ f (ν)dν = 1 . (3.1.7) 0
In general the spectral width of the laser transition is large compared to the spectral width of the laser radiation field, i.e. the integrals in (3.1.1) result in: 2
In general f (ν) is modified by saturation effects [74Sar], but near threshold these can be neglected.
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0
∞
f (ν)ρν (ν)dν = f (νr )ρ = f (νr )
[Ref. p. 197
I . c
(3.1.8)
νr is the optical resonator eigenfrequency, possibly shifted by mode pulling or pushing [74Sar]. At threshold the radiation field is small and stimulated emission and absorption can approximately be neglected in (3.1.1). In the steady state the threshold condition obeys the relation: (3.1.9) ηp2 ≥ hν A21 + τ2−1 N2 , which follows from (3.1.1). The spectral amplification of the radiation when passing through the laser medium is given by: dI(ν) = g(ν)I(ν)dz .
(3.1.10)
g(ν) is the gain per length. The spectral intensity increases along the length element dz: dIν (ν) = (B21 N2 − B12 N1 )
hν f (ν)Iν (ν)dz . c
Comparing (3.1.10) and (3.1.11) the gain can be written as: hν g2 B21 f (ν) N2 − N1 . g(ν) = c g1
(3.1.11)
(3.1.12)
Assuming that the lower laser level is much less occupied than the upper level it follows that: g(ν) ≈
hν c2 B21 f (ν)N2 = f (ν)A21 N2 . c 8π ν 2
With (3.1.9) one therefore gets the normalized pump power density: ηp2 8π hν 3 τ2−1 1 = . 1+ g(ν) c2 A21 f (ν)
(3.1.13)
(3.1.14)
The normalized pulse power density is proportional to ν 3 , i.e. the requirements for pump power density increase sharply with the frequency of the laser radiation [74Rho]. Besides this the normalized pump power density depends on the losses due to collisional deexcitation and the line profile. With the normalization (3.1.7) the value of the function f at the center frequency of the transition is inversely proportional to the line width, i.e. the pump power requirement increases linearly with increasing line width. The line width is determined by various factors. Alongside natural line broadening Doppler broadening and pressure broadening are important mechanisms for gas lasers.
3.1.2.1 Line Broadening 3.1.2.1.1 Natural line broadening For isolated atoms at rest only natural line broadening occurs. Excited states of atoms or molecules decay exponentially with the time constant given by the inverse of the Einstein coefficient A21 . According to the Wigner–Weisskopf theory of spontaneous emission [30Wei] the exponential decay is due to the interaction of the atoms with the vacuum fields of the infinitely many modes of free space. The line width can be explained as the result of the energy–time uncertainty relation [74Sar]. The line width is thus proportional to the Einstein coefficient A21 which varies with frequency as ν 3 : Δ νN ∼ A21 ∼ ν 3 .
(3.1.15) Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 197]
3.1 Gas laser systems
175
The line shape is a Lorentzian profile: fN (ν) =
ΔνN 2 . 2 π 4 (ν − ν0 )2 + Δ νN
(3.1.16)
At the center frequency ν0 one gets: π Δ νN 1 = ∼ ν03 . fN (ν0 ) 2
(3.1.17)
With this it follows from (3.1.14) that the normalized pump power density varies with the sixth power of the frequency: ηp2 ∼ ν06 . g(ν0 )
(3.1.18)
Natural line broadening is significant above all at high frequencies in or above the soft x-ray range. This helps to show why the practical realization of x-ray lasers is such a tough problem [90Elt].
3.1.2.1.2 Doppler broadening Natural line broadening and pressure broadening are homogeneous line-broadening mechanisms, i.e. all emitting particles have the same transition frequency and line width. In contrast to this in the case of Doppler broadening the line width results from the superposition of the velocitydependent Doppler-shifted transition frequencies of particles with different velocities. This kind of line broadening is called inhomogeneous broadening. If the particle velocities have a Maxwell distribution the resulting line shape is a Gaussian distribution [64Gri]: √ 1 2 ln 2 4 ln 2 2 fD (ν) = √ (3.1.19) exp − (ν − ν ) 0 2 Δ νD π Δ νD with the line width: √ 2kB T Δ νD = 2 ln 2 ν0 . M c2
(3.1.20)
M is the mass of the emitting particle. The value of the line profile at the center frequency is given by: √ 1 2kB T = π ν0 . (3.1.21) f (ν0 ) M c2 The normalized pump power density is therefore proportional to the fourth power of the laser frequency: ηp2 ∼ ν04 . g(ν0 )
(3.1.22)
3.1.2.1.3 Pressure broadening At higher particle densities or pressures pressure broadening occurs [64Gri, 97Dem1]. Pressure broadening results from stochastic perturbation of the atomic ore molecular levels by other particles. These can be neutral atoms or molecules, ions or electrons. In the latter case the mechanism Landolt-B¨ ornstein New Series VIII/1B1
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[Ref. p. 197
is called Stark broadening [64Gri]. Besides broadening a shift of the center frequency can result. Again, the line form is a Lorentzian profile: fp (ν) =
Δ νp 2 . π 4 (ν − ν0 )2 + Δ νp2
(3.1.23)
The line width is independent of the frequency. When the broadening results from the perturbation by neutral atoms or molecules the line width can be estimated by [85Bor]: Δ νp =
1 , πτ
(3.1.24)
where τ is the mean collision time of the particles. The mean collision time is proportional to the particle density or pressure, which is why this broadening mechanism is also called pressure broadening. The normalized pump power density equation (3.1.14) therefore becomes: ηp2 ∼ ν03 . g(ν0 )
(3.1.25)
3.1.3 Excitation mechanisms Gas laser pumping can be accomplished by several different mechanisms. To these belong highenergy electron-beam excitation, photo-excitation, creation of population inversion by fast gas dynamical cooling of the laser gas and by exploiting exothermic chemical reactions. By far the most important gas laser excitation mechanism however is gas discharge excitation. This is mainly due to the technical simplicity of gas discharge excitation compared to the other excitation mechanisms and because many of the lasers which are used for industrial and medical applications can best be excited by a discharge as is the case for HeNe, CO2 , excimer and rare gas ion lasers.
3.1.3.1 Gas discharge excitation The dimension of the gas volume to be excited in direction of the optical axis of the laser generally is much greater than its transversal dimensions. Accordingly there are two different discharge arrangements: With longitudinal discharge excitation the electrical current flows in the direction of the optical axis whereas with transversal excitation the current flows perpendicular to the optical axis (Fig. 3.1.2). Depending on the laser system under consideration the discharge parameters can vary significantly. The pressures can range from below 1 hPa up to 1 MPa. Discharges can be operated continuously or pulsed. The electric current flowing through the discharge can be Direct Current (DC) or Alternating Current (AC) with frequencies ranging from some kHz up to microwave frequencies3 . In most cases the discharges are self-sustaining, which means that the necessary free electrons are produced by the discharge itself in contrast to electron-beam ionization where high-energy electrons are injected from outside. In self-sustaining discharges production and loss of free electrons must counterbalance. Free electrons are produced by ionization of molecules or atoms. The necessary energy can be supplied by other free electrons during collisions, by photons or by excited atoms ore molecules which transfer their excitation energy. The latter process is called Penning 3
The discharge for laser excitation can even be sustained by another laser. In this case the discharge is called optical discharge [95Igo]. Landolt-B¨ ornstein New Series VIII/1B1
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Glass tube
End mirror
177
Partial-reflecting mirror Laser beam
Longitudinal gas discharge Anode
U
End mirror
Cathode
Cathode
Partial- reflecting mirror Laser beam
Anode U
Fig. 3.1.2. Schematic drawing of longitudinal and transversal gas discharge excitation.
Transversal gas discharge
ionization. The most important process for free-electron production is electron impact ionization. The ionization rate of electron impact ionization strongly depends on the mean energy of the free electrons which itself is an increasing function of the electrical field strength. The electron loss processes, e.g. diffusion to the discharge walls, electron–positive-ion recombination and electron attachment by electro-negative gas components, are much less dependent on the electron energy and thus on the electrical field strength. For steady-state conditions the mean electron energy acquires a certain value depending on the specific gas discharge under consideration. Discharges are treated in more detail in Sect. 3.1.4.
3.1.3.2 Electron-beam excitation In the case of electron-beam excitation electrons are accelerated to energies in the range between several 10 keV up to several MeV and injected through a window into the gas volume to be excited [83Buc, 97Dym1] (Fig. 3.1.3). There are three kinds of electron source: 1. The electrons are produced in a low-pressure discharge and extracted by applying high-voltage pulses. 2. Thermal electron emission from hot cathodes. 3. Electron field emission from cold cathodes. Vacuum diodes with cold field emission electrodes are especially employed for high-current sources. The cold cathodes are either metal structures with tips or edges or made from graphite. The metal or graphite surfaces are not completely smooth, there are micro-tips. When the high voltage is
End mirror
Active volume
Partial- reflecting mirror Laser beam
HV
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Fig. 3.1.3. Schematic representation of an electron-beam-excited laser.
178
3.1.3 Excitation mechanisms
[Ref. p. 197
applied correspondingly high field strengths occur at the tips or edges. This would generally not be sufficient to cause a significant field emission flow from the cathode but the field strength is further enhanced at the micro-tips. The field emission current emitted from the micro-tips is high enough to cause evaporation of the cathode material. The plasma thus formed now acts as a cathode with a very small working function. The current emitted from the plasma is only limited by the space charges of the electrons [74Che]. The cathodes have a limited life time due to the removal of material. The electron window is usually a titanium sheet with a thickness of several 10 μm. Because of the pressure difference between the vacuum diode and the gas discharge chamber, which usually is above 1000 hPa, the sheet must be held on a support structure. The support structure absorbs some of the electrons. The sheet is thermally loaded due to the impacting electrons and, like the cathode, has only a limited life time. This and the necessity for shielding the x-rays produced by the high-energy electrons turns electron-beam excitation into a laboratory technique (e.g. laser fusion). Depending on their energy the range of the electrons in the gas can exceed the transversal gas volume dimension so that during transversal injection only a part of the electron energy can be exploited. Axial injection on the other hand is technically more difficult to achieve. Reducing the electron energy increases the efficiency of energy absorption in the gas but also the energy losses in the window. The main advantage of electron-beam excitation is that electron generation and laser excitation are separated. Instabilities such as those in gas discharges cannot develop. Electron-beam excitation has been used for the excitation of excimer lasers with large active volumes and with pulse lengths of several 100 ns which is not possible with discharge excitation. Electron-beam-sustained discharges are an attempt to combine the two techniques [82Bot, 82Qua]. An electron beam is injected into a gas volume for ionization and at the same time a pulsed voltage is applied to the gas. The voltage is chosen so that it is not sufficient for self-sustained burning of the discharge but in combination with the electron beam a discharge can operate. The advantage is that although the discharge is not as unstable as a self-sustaining discharge not all the excitation energy has to be supplied by the electron beam. This technique has been used for example for the excitation of large discharge volume atmospheric pressure excimer [97Sha], CO2 [90Gor, 95Sid, 94Mil] and CO lasers [74Pug, 97Dym1, 97Dym2, 89Ana1, 89Ana2, 96Bor].
3.1.3.3 Gas-dynamic excitation With the excitation procedures described so far a cold equilibrium state is assumed and the attempt is made to achieve inversion between two states by precise excitation of states, e.g. by transferring energy into the system’s inner degrees of freedom. With gas-dynamic excitation the starting state is a hot state of thermodynamic equilibrium and inversion is achieved by removing energy from the inner degrees of freedom [81Dor, 69Bas, 81Los]. This is achieved in practice by cooling previously heated laser gas as it passes through a Laval nozzle (Fig. 3.1.4). The energy in the inner degrees of freedom and in the non-directional kinetic energy is transformed into directional kinetic flow energy. If this takes place fast enough states of thermodynamic non-equilibrium are passed through in the occupation of the inner degrees of freedom. Depending on the time constants for collisional transitions to other states inversion can occur. This technique is suitable for molecular lasers where the laser levels are vibrational-rotational states of the electronic ground state, e.g. CO2 [93Sai, 97Ita] and CO [94Caf] lasers. For an ideal gas the temperature T along the flow channel is given by [81Los]: T = T0 −
VG2 . 2cp
(3.1.26)
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Exhaust
End mirror
T
179
Laser beam
Active volume p
Supersonic flow p0
T0
Laval nozzles
Ignition chamber Fuel input
Fig. 3.1.4. Schematic representation of a gasdynamic laser. Fuel is burned in an ignition chamber. With this temperatures of up to 1600 K are reached and CO2 molecules are produced.
cp is the heat capacity at constant pressure, T0 is the gas temperature within the ignition chamber and VG the gas velocity in the flow duct. In a Laval nozzle VG can exceed the velocity of sound and T can reach values below 300 K. Supersonic flow cooling is also used as an efficient cooling mechanism for CO lasers whose efficiency sharply increases with decreasing temperature [88Kov].
3.1.3.4 Chemical excitation In many gas lasers excited by electrical discharges or high-energy electron beams chemical reactions among gas constituents take place either as an interfering byproduct of the excitation (CO2 lasers [78Shi, 95Ley, 97Cen, 94Cen]) or as a necessary part of the excitation process (excimer lasers [84Rho]). Besides this the pumping energy can partly or entirely being supplied by exothermic chemical reactions. The most prominent chemical lasers are the HF and DF [90Bas, 77Ber, 98Kut] and the Chemical Oxygen-Iodine Laser (COIL) [90Bas, 98Mas, 97Vet, 98Vet2, 98Vet1, 98Wak]. The HF molecule is produced by reactions that involve atomic F or H, respectively: F + H2 → HF(ν) + H , F2 + H → HF(ν) + F . The HF(ν) molecule is formed in a vibrationally excited state which is the upper laser level or relaxes to this level. There are several schemes to initialize the chain reaction above [90Bas]: F2 + wall → 2F , F2 + H2 → 2F + HF + H , F2 + ΔE → 2F . ΔE is the electron or photon energy sufficient for F2 dissociation. The HF laser can be operated without auxiliary means but in many cases discharges or electron beams are used to initiate the reaction [98Kut]. When H is replaced by D the energy spacing of the vibrational states changes. Vibrationally excited DF(ν) can very efficiently transfer its vibrational energy to CO2 molecules which are then used as lasing medium. lasers excitation energy is transferred from an excited oxygen molecule In oxygen–iodine O2 1 Δ to an iodine molecule. The oxygen excitation takes place outside the active region after which oxygen and iodine are mixed. Again the O2 1 Δ can be produced entirely by chemical reactions but often gas-discharge electrons are used for this purpose [98Wak, 90Bas].
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3.1.4 Gas discharges Gas discharges are interacting many-particle systems consisting of free electrons, charged and uncharged heavy particles (atoms, molecules and their ions), photons, electrical fields and in some cases also magnetic fields. The first systematic observations concerning the phenomenon of charge transfer in gases were carried out in the 17th century. The first real gas discharges became possible with the development of the voltaic cell. In 1803 Petroff discovered the arc discharge at atmospheric pressure and in 1831 Faraday discovered the glow discharge. The treatment of gas-discharge physics includes elements of electrodynamics, statistical physics, atomic and molecular physics, collision theory, chemical reactions and radiation process physics. Apart from procedural complexity the theoretical treatment of gas discharges is also made difficult by the inherent space dependency of the processes resulting from the finite size of the gas discharges and the presence of walls. With transient or periodical excitation there is an additional time dependency. A further difficulty which is worthy of mention is the often insufficient knowledge concerning effective cross sections for the relevant collision processes. The predictions of gas-discharge physics are therefore frequently imprecise, with even deviations of several 10 % mostly being considered as precise.
3.1.4.1 Elementary processes in gas discharges Figure 3.1.5 schematically shows some of the most important elementary processes involved in gas discharges. Charged particles, electrons and ions, take energy from the electromagnetic field and transfer it through collisions to other particles. Particles may collide with particles of the same type or with particles of different types. The energy transfer per collision between the heavy particles – ions and atoms – is very large due to their equal or roughly equal mass so that a Maxwell velocity distribution among the translational degrees of freedom is established very quickly. In most cases it Energy and momentum transfer
Electromagnetic field Energy and momentum transfer Elastic and inelastic collisions
Electrons fe (x, v, t)
Superelastic collisions Ion, fi Atom, fa
+
-
Ionization Recombination
Detachment Continuous radiation Line radiation
Ion, fi
-
Attachment
-
Atom, fa Line radiation Radiation, r ( n)
Fig. 3.1.5. Overview of some of the most important elementary processes in a gas discharge. fe , fa and fi are the distribution functions of electrons, neutral atoms or molecules and ions, respectively. Landolt-B¨ ornstein New Series VIII/1B1
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can be assumed that atoms and ions have equal mean translational energies or temperatures. The electrons can also effectively transfer energy between themselves through collisions but this does not apply for collisions with heavy particles. Thus the electrons do not generally have a Maxwell distribution unless the degree of ionization, the ratio of electron density to heavy-particle density, has a value of more than around 10−4 [72Eck]. This is only the case for a few laser gas discharges, e.g. rare gas ion lasers and some excimer laser discharges. Apart from the cathode region the electrons take considerably more energy from the electrical field than the positive ions due to their small mass and their higher drift velocity. The electrons give off their energy mainly through inelastic collisions because the energy loss through elastic collisions between electrons and heavy particles is very small4 . Inelastic collisions excite the inner degrees of freedom of the heavy particles which is the actual aim of laser gas discharges. In some types of laser the excitation efficiency, i.e. the ratio between the power pumped into the level relevant to the laser and the power taken from the electric field, can be up to 90 % (CO2 lasers). In most laser gas discharges the interaction distance among most particles is much smaller than the mean particle separation. This is not true for electrons and ions but in most cases their densities are much smaller than the densities of the uncharged particles. Besides some exceptions the interaction between particles can be treated as two-particle collisions. Every collisional process has a reversal process. When an electron collides with a previously excited particle the excitation energy can be transferred back to the electron. After the collision the electron has a higher energy than before. These collisions are called collisions of the second kind or super-elastic collisions. If the electron’s energy is high enough it can free another electron from the atomic unit during a collision with a heavy particle, the atom is ionized. The reversal process is recombination, the capture of an electron by a positively charged ion. There are several different recombination processes. Because energy and momentum balance have to be fulfilled during a collision it is not possible that an electron is captured by an ion without another particle or a photon being involved. When a photon is emitted the process is called photo-recombination. The third particle can be an electron or a heavy particle, the latter being most likely in high-pressure discharges. Besides volume recombination processes wall recombination can occur; in this case the excess momentum and energy are transferred to the atoms of the discharge walls. Wall recombination is the dominant recombination process in low-density discharges (HeNe, rare gas ion lasers). In the case of electro-negative gas components electrons can be captured by neutral atoms or molecules, which is called electron attachment, the reverse process is detachment. Attachment processes can be dissociative and non-dissociative, respectively. Attachment cross sections depend on the electron energy. In some cases the cross section is non-zero for vanishing electron energy so that even low-energy electrons are efficiently attached (e.g. F2 ). In other cases the attachment process has a threshold energy (e.g. CO2 ). Heavy particles can exchange excitation energy. The rate of energy transfer strongly decreases with increasing difference of the excitation energies of the involved levels. This process is explicitly exploited in some lasers. In HeNe lasers He atoms are excited by electron impact whereas Ne, the laser-active gas component, is mainly pumped by energy transfer from excited He atoms. In the case of CO2 lasers the efficiency can be enhanced considerably by adding N2 to the gas mixture because the N2 vibrational levels of the electronic ground state can more efficiently be pumped by electron impact than CO2 . The N2 vibrational energy can very rapidly be transferred to CO2 molecules because the energy difference between the N2 vibrational levels and the upper CO2 laser level is quite small. Alongside particle collisions radiation processes are among the most important processes in gas discharges. Excited neutral gas particles or ions can transfer their excitation energy to a photon during a radiative transition to an energetically lower level, the energy difference between the 4
In gas discharges with a high content of He and with small molecular densities the relative electron energy loss due to elastic collisions with He atoms can become comparatively high because of the small mass of He.
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levels being equal to the energy of the emitted photon. Here too a reversal process does exist, the absorption of a photon with the required energy. In general the processes which take place must be treated self-consistently. For instance, the electrical field is determined by the space-charge field of the electrons and ions and the dynamics of the particles is determined by the electrical and magnetic fields. The electron distribution function depends not only on the electromagnetic field and the gas components but also on their state of excitation. The state of excitation of the gas components in turn depends on the electron distribution function. If the dependencies described are not too strong the problems can be separated out. If, for example, the density of the excited particles is small compared to the particle density in the ground state then the influence of the excited particles on the electron distribution function is negligible.
3.1.4.2 Electron distribution function The electron distribution function fe (V , r) is a solution of the Boltzmann equation: ∂fe e δfe E · ∇V fe = . + V · ∇fe − ∂t me δt C
(3.1.27)
The distribution function fe (V , r) gives the density of the electrons at a point in phase space, that is to say that fe (V , r) d3 V d3 r is the number of electrons in the phase space element d3 V d3 r, where r is the spatial coordinate and V is the electron velocity. E is the macroscopic electrical field that accelerates the electrons. e is the electron charge, me is the electron mass. If there is a magnetic field the Lorentz force must be added. The second term on the left-hand side describes the changes of the distribution function in real space. The third term on the left-hand side correspondingly describes the changes of the distribution function in velocity space due to acceleration through macroscopic fields. The term on the right-hand side of (3.1.27) is the so-called collision integral. The collision term describes the change of the velocity distribution in the velocity space due to collisions. The Boltzmann approach for the collision integral is based on the assumption that the mean time between two collisions is far greater than the interaction time of a collision. Whereas the terms on the left-hand side of (3.1.27) describe a continual change of position in the phase space the electrons change their position in velocity space discontinuously during a collision. Both the direction and the magnitude of the velocity are generally changed by a collision. In the case of two-particle collisions the collision integral has the following general form [46Hol]:
δfe δt
∞ (V ) = C
[fe (V ) a(V , V ) − fe (V ) a(V , V )] d3 V .
(3.1.28)
−∞
a(V , V ) is the probability per time that an electron with the velocity V will have a collision and that after that collision it will have the velocity V . a(V , V ) is proportional to the cross collision sections and the gas density. Integration of the distribution function over the velocity space gives the electron density: ∞ ne (r, t) =
fe (V , r, t) d3 V .
(3.1.29)
−∞
A general solution of the Boltzmann equation has not yet been found. A numerical solution of the whole of (3.1.27) in the 6-dimensional phase space is hardly possible even with today’s computers. Landolt-B¨ ornstein New Series VIII/1B1
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3.1.4.2.1 Similarity laws Several similarity laws apply to gas discharges (see [69Pfa] for an extensive discussion). The momentum transfer collision frequency is proportional to the density of the collision partners. For a given gas composition the densities Nj are proportional to the overall heavy-particle density.
Dividing (3.1.27) with the collision integral (3.1.28) by the overall particle density N = j Nj shows that the solutions of the Boltzmann equation (3.1.27) remain unchanged if the quotient of field strength and particle density is kept constant5 : E = const. with E = |E| , N i.e. the dependence of the distribution function on the parameters E and N can be reduced to the single parameter E/N . Furthermore, the results remain unchanged if the time scale is varied with the density so that N t = const. remains constant. The same applies for the spatial coordinates: N z = const.
3.1.4.2.2 Characteristic frequencies Various characteristic frequencies can be distinguished in gas discharges. Among them are the electron momentum transfer frequency νm , the electron energy transfer frequency νu , excitation νex and ionization frequencies νion and in the case of high-frequency discharges the excitation frequency ω. Under typical conditions of laser gas discharges the electron momentum transfer frequency is much higher than the electron energy transfer frequency νm νu and the excitation frequencies are higher than the ionization frequency νex νion . In high-frequency gas discharges different temporal behavior of the gas discharge is observed depending on the frequency range. At small excitation frequencies ω νm , νu the distribution function instantaneously follows the electrical field. The distribution function can be calculated by solving the time-independent Boltzmann equation. The respective instantaneous value has to be used for the field strength: f (u, t, E(t)/N ) = f (u, (E0 /N ) cos ωt)
(3.1.30)
with the electron energy u=
me 2 V . 2
On the other hand if the excitation frequency is large compared to the energy transfer frequency, νu ω, the isotropic part of the distribution function is only weakly modulated within a period. The time-independent form of the Boltzmann equation can be employed again in the two-term approximation. The effective field strength has to be used for the field-strength value [83Fer, 95Rai]:
νm E0 . (3.1.31) f (u, t, E/N ) = f u, Eeff = 2 + ω2 2N νm 5
The collision integral (3.1.28) is valid for two-particle collisions only. The similarity laws discussed here are thus only valid if three-body collisions can be neglected [69Pfa].
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If the frequency is in the range of the energy transfer frequency νu ≈ ω νm the timedependent Boltzmann equation must be solved. In that case the distribution function is a function explicitly dependent on time: E (t) . (3.1.32) f (u, t, E) = f u, t, N 3.1.4.2.3 Rate coefficients The rate Rab of a process that excites an atom or molecule from state a to state b is given by: Rab = kab Na ne .
(3.1.33)
Rab is the number of excitation processes per time and volume. Na is the density of particles in state a, ne is the density of free electrons and kab is the rate coefficient of this process. The rate coefficient can be calculated by integrating the product of the relevant collision cross section and the electron flux |V | fe (V , r) over all velocities: 1 kab (r) = ne
∞
σab (|V |) |V | fe (V , r) d3 V .
(3.1.34)
−∞
The pump power density is: p = (Eb − Ea ) ne Na kab .
(3.1.35)
Ea and Eb are the energies of the lower and upper level, respectively. The rate coefficient of ionization results by analogy with the ionization collision cross section inserted in (3.1.34).
3.1.4.2.4 Approximate solutions of the Boltzmann equation There are several procedures for the approximate solution of the Boltzmann equation for laser gas discharges. Monte-Carlo particle simulations [85Bir, 91Bir, 85Pen] make possible the calculation of distribution functions in phase space without the introduction of special approximations. The very long computing times are the price which has to be paid for this. A significant reduction of the computing times can be achieved if the gas discharges are treated in the framework of a hydrodynamic description [92Lis]. The transport equations for density, momentum and energy can be deduced as moments of the Boltzmann equation by multiplying the Boltzmann equation by 1, mV and (m/2)V 2 , respectively, and integrating over the velocity space. The resulting equations include coefficients that still can only be calculated when the distribution function in velocity space is known. This problem can be dealt with by assuming the distribution function to be separable in real and velocity space which is valid when the electron distribution function only depends on the local electrical field, which is generally the case in the discharge body, but in the sheath regions near the electrodes, especially near the cathode, this might be a very rough approximation. Maxwell distributions can usually be assumed for the distribution functions of the heavy particles. At degrees of ionization above around 10−4 electron–electron collisions make the electron distribution function tend towards a Maxwell distribution too. The Maxwell distribution contains three parameters: 1. electron density ne (r), 2. electron temperature Te (r), 3. electron drift velocity superposed onto the isotropic thermal movement V 0 (r):
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3.1 Gas laser systems
f (V , r) = ne (r)
me 2π kB Te (r)
2
me (V − V 0 (r)) exp − 2kB Te (r)
185
.
(3.1.36)
For most gas lasers the assumption of a Maxwell distribution of the electrons is no more than a very rough approximation. A further method of solving the Boltzmann equation by approximation becomes possible when the mean random velocity of the electrons is much higher than the electron drift velocity. In this case the distribution function is almost isotropic. By using spherical coordinates in velocity space the distribution function can be expanded in an infinite series of Legendre polynomials. Approximate solutions can be found by truncating the series after a few terms. The most simple approximation can be found by retaining only the first two terms. This two-term approximation is a good approximation when the electron distribution function is almost isotropic. The assumption of isotropy is fulfilled in close approximation by gas discharges in which elastic collisions between electrons and heavy particles are considerably more frequent than inelastic electron collisions. The elastic collisions cause the distribution function to become isotropic because only a very small part of the electron energy is given off during elastic collisions while the direction of the electrons can change greatly. The elastic collisions dominate when the mean electron energy is small compared to the threshold energy of the inelastic collisions. This is generally true with atomic gases and typical electrical field strength in the bulk of laser gas discharges. In the case of molecular gases, however, threshold energies for rotational and vibrational excitation are in the range of or even below the value of the mean electron energy. The assumption of isotropy is not very well fulfilled in these cases, but comparative Monte-Carlo calculations have shown that the two-term approximation is still approximately applicable in the case of molecular gases and electrical-field-strength values typical for laser gas discharges [84Bra]. Higher-order solutions are described in [85Phe] and [96Lof] who retain six terms of the Legendre series. The Legendre-series approach generally is applied to the discharge bulk with the assumption of slowly varying electric field and densities. In this case the distribution in velocity space can be assumed only to depend on the local electric field. The spatial variation of the electron density is determined by the electron density equation with rate and transport coefficients taken from the solution of the electron distribution function in local-field approximation. In the sheath regions of discharges especially the cathode region this approach is only a rough approximation.
3.1.4.2.5 Charged-particle densities The particle densities are solutions of the continuity equations [91Rai]: ∂ni = −∇ · (V i ni ) + Si . ∂t
(3.1.37)
ni is the particle density (electrons, positive and negative ions), the particle flux densities are given by: V i ni = sign(qi )μi E ni − Di ∇ni .
(3.1.38)
μi is the mobility and Di the diffusion coefficient of the particle types i (i = electrons, positive ions, negative ions). qi is the electrical charge of the particles. The Si are source terms. For a mixture consisting of uncharged heavy particles, electrons, positive and negative ions these are: E E N ne − ka N ne − kr,ep ne np + kd nn , (3.1.39) Se = ki N N E N ne − kr,ep ne np − kr,pn np nn , Sp = ki (3.1.40) N E N ne − kr,pn nn np − kd nn . Sn = ka (3.1.41) N Landolt-B¨ ornstein New Series VIII/1B1
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Three-particle recombination is neglected here. The ionization rate coefficient ki (E/N ) and the electron attachment rate coefficient ka (E/N ) strongly depend on the reduced field strength, whereas the photon–electron-ion recombination coefficient kr,ep , the ion–ion recombination coefficient kr,pn and the detachment coefficient kd are generally only slightly dependent on the reduced field strength. The electron mobility μi and diffusion coefficient Di and the rate coefficients can either be taken from measurements or can be calculated when the electron distribution function is given [83Fer]. The electron distribution function can e.g. be calculated employing the two-term approximation.
3.1.4.2.6 Ambipolar diffusion In the case of transversal excitation the particle flux density is strongly dependent on the applied electric field which is enhanced in the sheath regions near the electrodes by space-charge fields. In this case numerical methods have to be employed to solve the continuity equations6 . In the case of longitudinal excitation there is no external field component perpendicular to the discharge tube walls. The particle currents to the wall are only due to diffusion and space-charge fields which occur when particle density gradients are present. Because of their much smaller mass the electrons have a considerably larger mobility than the ions which means that even if the mean energy is the same their coefficient of diffusion is greater. The electrons move away from the region of maximum density while the ions almost remain. This creates space charges and a corresponding space-charge field leads to an electron drift which counteracts the electron diffusion and to an ion drift in the same direction as the ion diffusion. The space-charge field increases until the particle fluxes are of equal amount. When the mean free path of the particles is small compared to the discharge radius the differences in density are small enough to be neglected to first approximation, the gas discharge plasma is quasi-neutral in this cases. The electrical field strength can be eliminated and the electron and ion fluxes can be described using a single equation and a single effective coefficient of diffusion: V i ni = Da ∇ni .
(3.1.42)
This effective coefficient of diffusion is called ambipolar diffusion coefficient [91Rai, 71Nas]: Da =
De μp + Dp μe . μe + μp
(3.1.43)
An ambipolar diffusion coefficient can also be defined if negative ions are present alongside the positive ions but the equations for this are far more complicated. The electrons and ions hitting the wall are attached and subsequently recombine with each other with the wall atoms acting as collision partners. The electron and ion densities can be regarded to vanish at the walls which sets the boundary condition for the continuity equations7 . In the case that electron attachment and volume recombination can be neglected the diffusion equation for electrons and positive ions can be written: E ΔDa n + ki Nn = 0 . (3.1.44) N In circular geometry the solution is the Bessel function: 2.405 r . n(r) = n(0) J0 R 6 7
(3.1.45)
In many cases the local-field approximation is invalid in the sheath regions and other methods have to be employed. The densities do not vanish exactly at the wall but about one mean free path behind the wall [64McD]. Landolt-B¨ ornstein New Series VIII/1B1
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R is the discharge tube radius. In steady state the ionization rate coefficient has to obey the condition: 2 Da 2.405 E = ki , (3.1.46) N N R which indeed is a condition for the reduced field strength E/N . This is the Schottky theory of the positive column which is valid when the mean free path of the gas particles is small compared to the tube radius R. A similar theory applies to the free fall case if the mean free path is large compared to the tube radius [29Ton].
3.1.4.3 Electromagnetic field The charged particles in gas discharges, especially the electrons, take energy from the electrical field. A self-consistent treatment of gas discharges must therefore include the calculation of the electrical or more general electromagnetic field. The electrical field determines the particle energy, the particle densities, space charges and particle current densities retroact on the fields. The electromagnetic field is the solution of the Maxwell equations: ∂B , ∂t ∇·D = ρ,
∇×E = −
∇×H =j+ ∇·B =0.
∂D , ∂t
(3.1.47) (3.1.48)
In the simplest case the following relations apply: B = μ0 H ,
D = 0 E ,
j = σE .
(3.1.49)
μ0 is the vacuum magnetic susceptibility, 0 the vacuum electrical susceptibility and σ the conductivity. Alongside time-independent fields with harmonic time dependence are of particular interest. With A = A0 exp [iωt] the Maxwell equations result in: ∇ × E 0 = −iωB 0 , σe ω ∇ × B 0 = iμ0 0 ω 1 + E 0 = i 2 p E 0 , iω 0 c ∇ · ( p E 0 ) = 0 .
(3.1.50) (3.1.51) (3.1.52)
E 0 and B 0 are complex field amplitudes. σe is the electron conductivity (it is assumed that the contribution of the ions is negligible) [83Fer]: σe = ene μe = ωp2 =
e2 ne . me 0
0 ωp2 , νm + iω
(3.1.53) (3.1.54)
ωp is the plasma frequency, p the plasma dielectric constant:
p = 1 +
ωp2 ωp2 σe νm =1− 2 − i . 2 2 ω + νm iω 0 ω ω 2 + νm
(3.1.55)
The electrical field and if necessary the electromagnetic field obeys the Maxwell equations together with appropriate boundary conditions. Self-magnetic fields are of minor importance in laser gas discharges although in some cases, e.g. ion lasers, external magnetic fields are employed. The absorbed power density is: Landolt-B¨ ornstein New Series VIII/1B1
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3.1.4 Gas discharges pe = Re (j · E 0 ) = Re (σe ) E 0 · E ∗0 = ω 0 Im ( p ) E 0 · E ∗0 .
[Ref. p. 197 (3.1.56)
In the small-frequency limit ω νm this becomes: pe =
e2 ne 2 E , me νm
E 2 = E 0 · E ∗0 .
(3.1.57)
The momentum-transfer frequency is proportional to the heavy-particle density: νm = km N . In many cases km is only slightly dependent on N or E. Equation (3.1.57) can thus be written: 2 E e2 pe = ne N . (3.1.58) me km N The reduced field strength E/N is for a given discharge system almost independent of the gas and the electron density, i.e. the power density is in good approximation proportional to ne and N .
3.1.4.4 Neutral gas Alongside electrical field strength the density of the heavy particles is one of the most important influencing factors for the behavior of gas discharges. Together with the field E the gas density determines the reduced field strength E/N . The rate coefficients of collisions that involve gas particles increase linearly with the gas density. This is also true for the absorbed power density (3.1.58). The continuity equation and the momentum and energy balance equations read: ∂ρ + ∇ · (V ρ) = 0 , (3.1.59) ∂t ∂V + ρ (V ∇) V = −∇p + ηΔV , (3.1.60) ρ ∂t ∂ρ
+ ∇ · (ρ V ) = −∇ · q + w (r) . (3.1.61) ∂t V is the gas velocity, ρ the mass density, the energy density, p the gas pressure, η the dynamic viscosity, q the heat flux density and w the heat source. For an ideal gas = cv T , with the heat capacity cv and the gas temperature T . According to Fourier’s law the energy flux is given by: q = −λ∇T
(3.1.62)
with the heat conductivity λ. Even if the pump power is deposited homogeneously within the active volume thermal conductivity and convection lead to inhomogeneities in temperature and density. In pulsed laser systems the expansion of the heated gas results in shock waves that are reflected at the gas vessel boundaries. The superposition of the reflected waves leads to gas density fluctuations that have a negative impact on subsequent pulses unless the fluctuations have decayed or have been blown out of the active region by gas flow [94Ima, 84Buf, 82Tou]. The active medium of high-average-power systems has to be replaced continuously. In most systems this is accomplished by a fast recirculated gas flow where the gas is cooled by the use of heat exchangers outside the active region. The gas density fluctuates due to non-smooth variations of the flow duct and at high flow velocities due to turbulence. Gas density fluctuations can be the starting point of gas discharge instabilities with the consequence that discharge power is deposited only within some small regions of the whole active volume. The second impact is that the propagation of the laser field is distorted by the density fluctuations. This reduces the beam quality of the laser. Thus laser development aims at low fluctuating gas flows [94Hab].
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3.1.4.5 Discharge instabilities For efficient laser excitation the active medium has to be pumped homogeneously and the optical properties of the laser medium have to be homogeneous as well. Gas discharges for the excitation of gas lasers are necessarily far from thermodynamic equilibrium. Various instabilities can develop in such systems which lead to inhomogeneities which can degrade the laser performance considerably [76Nig, 73Haa, 95Loo, 91Wes4, 78Bro, 75Jac, 73Nig, 76Egg, 95Dre, 93Bie]. At low pressures discharge striations can occur. The reason for this kind of instability is that the average ionization rate increases when the electric field is not constant but modulated along the field direction because the ionization rate increases more than linearly as function of the electric field [76All]. This kind of instability has no great importance for laser gas discharges. In electron-beam-sustained discharges with electro-negative gas components and with the ionization being dominated by the beam electrons instabilities can occur which are due to electron attachment [74Dou]. When the attachment rate increases with increasing reduced field strength, as is the case e.g. for CO2 , the electron density decreases because the ionization rate due to the beam electrons is independent of the field strength. According to Ohm’s law locally decreasing electron density leads to an increase of the local field strength, which in turn makes the attachment rate increase further, an instability develops. Of much greater impact are instabilities that lead to filamentation of the discharge. Filaments are channels of highly increased current density in the direction of the electric field. In the filaments the electron density and the power density are enhanced compared to the undisturbed state. The filaments influence laser activity mainly by two mechanisms. Firstly the local discharge parameters, e.g. gas temperature, electron density and mean energy, can acquire values which are not optimal for laser excitation. For example the lower laser level of CO2 is only 0.16 eV (corresponding to 1850 K) above the ground state, so that the lower laser level can thermally be occupied in hot filaments which considerably decreases efficiency. Secondly, the propagation of the radiation field is stochastically disturbed by the spatially inhomogeneous gas discharge; this seriously degrades the beam quality. It is therefore necessary to operate the discharges within parameter ranges where these are stable. There are several filament-forming mechanisms. In the case of CW (continous wave) or long-pulse-duration (> μs) discharges thermal instabilities have to be considered. Filamentation in high-pressure glow discharges will be discussed in Sect. 3.1.4.6.1.
3.1.4.5.1 Thermal instabilities The mechanism for the development of thermal instabilities can be schematically represented as follows: E ↑ → δTe ↑ → δne ↑ . δne ↑ → δ σE 2 ↑ → δT ↑ → δN ↓ → δ N When the electron density increases locally the absorbed power density increases accordingly. As a consequence temperature rises and the gas density decreases. This leads to an increase of the reduced field strength which in turn leads to a rise of the electron temperature and of the ionization rate. As a consequence the electron density further increases, the discharge is unstable. This simple scheme only applies in cases where the field strength of the discharge remains constant. But this is not generally the case. This can be shown schematically as follows: δ σE 2 ↑↓ δne ↑ → δσ ↑ → δE ↓ ← . (3.1.63) E ↑↓ δN ↓ δ N
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3.1.4 Gas discharges
[Ref. p. 197
If the electron density rises or the gas density falls the conductivity increases. According to Ohm’s law this leads to a reduction of the electrical field strength. The extent of the change of N and E, respectively, dictates whether the power density σE 2 rises or falls and whether the reduced field strength E/N rises or falls. For an effective stabilization the field strength must decrease as strongly as possible with increasing conductivity [76Nig, 73Haa, 95Loo].
3.1.4.6 Discharge types Gas discharges can be divided into various types. These differ according to the geometric arrangement, type of excitation (DC, high-frequency, microwave, pulsed or continuous wave), pressure range and processes at the boundaries, especially the cathode of the discharge. Although many of the basic processes are similar for different laser gas discharges the varying pressure, fields and gas components result in differences in the behavior of discharges which require separate treatment. The processes at the walls of the discharge and in particular at the electrodes have a considerable effect on the behavior of the discharge. Arc discharges for example are characterized by a high current density at the cathode; with glow discharges the potential difference in the cathode area is high. Alongside DC discharges it is above all high-frequency discharges, and in individual cases microwave discharges, which are used for the excitation of gas lasers. In Table 3.1.1 some of the types of gas discharges used for the excitation of gas lasers are listed. Table 3.1.1. Some of the types of gas discharges used for the excitation of gas lasers. Discharge type
Laser types
Gas pressure [hPa]
Power density [W cm−3 ]
Excitation frequency [Hz]
Longitudinal DC glow discharge
CO2 CO HeNe
10 . . . 60 10 . . . 60 0.1 . . . 2
10 . . . 20 10 . . . 20 0.01 . . . 1
– – –
Transversal DC glow discharge
CO2 CO
10 . . . 60 10 . . . 60
10 . . . 20 10 . . . 20
– –
Pulsed discharge at atmospheric pressure (TEA)
CO2 excimer
103 . . . 104 2 · 103 . . . 4 · 103
103 . . . 104 105 . . . 106
– –
Wall-stabilized arc discharge
Ar II, Kr II
0.1 . . . 1.5
102 . . . 103
–
Transversal AC discharge
CO2
20 . . . 100
1 . . . 30
104 . . . 106
Transversal HF discharge
CO2
60 . . . 200
1 . . . 80
4 · 106 . . . 2 · 108
Microwave discharge
CO2 excimer HeNe
20 . . . 100 103 . . . 2 · 103 0.1 . . . 2
50 . . . 100 104 . . . 105 0.01 . . . 1
2.45 · 109 2.45 · 109 2.45 · 109
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3.1.4.6.1 Glow discharges Glow discharges are self-sustaining discharges with a cold cathode from which electrons are emitted by secondary processes. The importance of secondary emission in glow discharges depends decisively on the excitation frequency. In DC glow discharges electron emission from the cathode is a precondition for the self-sustained burning of the discharge. If the excitation frequency is sufficiently high discharges can burn self-sustaining without secondary processes. The name glow discharge comes from the bright glow near the cathode which is due to the electrons that are released from the cathode surface by secondary processes and accelerated by the high space-charge field in the cathode region [91Rai]. Many gas lasers are excited by glow discharges. HeNe lasers are operated at pressures of around 1 hPa with low power densities. The discharge vessels are small-diameter tubes. The main electron loss mechanism is diffusion to the tube wall and subsequent wall-recombination. CO2 lasers can be operated continuously at pressures of 10 . . . 150 hPa or in a pulsed mode at pressures above 1000 hPa. Low-pressure CO2 lasers are today most commonly excited with high-frequency glow discharges but DC glow discharges as well are used. In the low-power region lasers can be operated sealed-off. The heat generated in the discharge is carried off through the walls. Heat conduction thus limits the extractable power. In case of high-power lasers fast gas flow is employed for heat removal. Longitudinal as well as transversal flow systems have been developed. The latter arrangement has been the preferred arrangement for high-power systems in the beginning but because of the better beam quality of longitudinal flow systems this arrangement is now even employed for CO2 lasers with output powers of up to 40 kW [94Hab]. Pulsed glow discharges at pressures above 1000 hPa are used e.g. for the excitation of highpressure CO2 , CO and excimer lasers. This kind of discharge is discussed in more detail below. 3.1.4.6.1.1 Secondary processes Electrons can be attached to solids or solid surfaces with bonding energies of several eV. At least this energy must therefore be applied in order to release an electron from a solid or a surface. The necessary energy can be transferred to the solid in various ways. In gas discharges photons with high enough energies are emitted which can release electrons from the wall. Electrons which hit the surface with sufficiently high velocities can generate secondary electrons [91Rai] too. But electrons with sufficient energy generally don’t hit surfaces in gas discharges (surface discharges and highfrequency discharges with very low neutral particle densities are exceptions). This is different for positively charged ions. Here both the kinetic energy and the ionization energy of the ions can be transferred to the solid electrons. Energy transfer from the kinetic energy is only noticeably at energy values of over 200 eV [60Bat, 61Bat, 68Kre], which means that under most gas discharge conditions transfer of the ionization energy dominates. The ionization energy must be high enough to release two electrons. One electron serves to neutralize the ion while the second is emitted as a free electron. Besides ionization energy from ions excitation energy from excited particles can cause electron emission. Because the particles must exist long enough in the excited state to arrive at the wall this mechanism is only relevant for particles in meta-stable states. For these states electrical dipole transitions are forbidden, which results in comparatively long radiation lifetimes even at high levels of excitation energy. In low- to medium-pressure glow discharges the most important process besides photo-effect is secondary emission by impacting positive ions [91Rai]. In this case the voltage drop across the cathode sheath is not a monotonic increasing function of the discharge current density but decreases at low current densities and increases at high current densities. The current density at the minimum of the voltage drop is called normal current density. Its value depends on the cathode material, the gas composition and the gas density. The normal current density scales as jn /N = const.
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3.1.4 Gas discharges
[Ref. p. 197
Glow discharges are preferably operated near the normal current density, which means that at low pressures current densities are quite small. In the case of HeNe lasers large-area cold cathodes are used in order to achieve the discharge currents necessary for efficient laser operation of about 50 mA. Rare gas ion lasers are also operated at low pressures but with much higher currents. In this case cold cathodes are no longer suitable, therefore thermal electron emission from hot cathodes is exploited.
3.1.4.6.2 High-pressure glow discharges For lasers that need very high pumping power densities large volume glow discharges at pressures above 1000 hPa are used besides high-electron-energy electron-beam pumping and in case of molecular lasers gas-dynamic pumping. Because of their technical complexity the latter two methods are normally only used for special applications, e.g. for very-high-power lasers or for the excitation of large volumes. High-pressure glow discharges are also called TEA discharges. This means Transversal-Electrically excited at Atmospheric pressure. The electrical pulse lengths are in the range of 10 ns in the case of N2 and excimer lasers and up to several μs in the case of CO2 and CO lasers, respectively. Pulse length in the 10 ns range can only be realized with low inductive pulse forming networks [95Mas, 93Yat] and fast high-power switches. The main problem with high-pressure glow discharges is their inherent tendency to arcing or filamentation. There are several processes that result in filamentation. Without preionizing there are only a small number of electrons present in the discharge volume at discharge ignition time. A single electron that is accelerated in a high electric field can build up a streamer by an electron avalanche that results in a discharge channel through which all the power can flow. In order to avoid this sufficient preionization is necessary [74Pal, 80Suz, 98Fee, 93Mue, 89Tuc, 94Pro, 91Bur]. The criterion is that the mean distance of the electrons at discharge ignition has to be small enough that the avalanche heads overlap before the space-charge fields in front of the avalanches reach the value of the external applied field [74Pal]. There are two main preionization schemes: The first one is preionizing by photons emerging from small discharges, either spark discharges or sliding/corona discharges [98See, 97Kuz, 97Fed, 97Zha, 97Bar, 95Sat, 88Mat]. The photons created in this discharges release electrons from the electrode surfaces and ionize gas particles. The second scheme is x-ray preionization which ionizes the atoms and molecules in the discharge volume [94Ber, 99Fee]. The minimum values of the preionization electron density and the rate of preionization depend on the gas composition and the gas pressure [76Egg, 97Bre]. Even in sufficiently preionized discharges several kinds of instabilities can develop. In CO2 lasers thermal instabilities [75Jac, 76Egg, 74Nig, 73Haa] and in the case of electron-beam ionization attachment instabilities [74Dou, 76Nig] have been observed. Thermal instabilities are more severe as they greatly degrade efficiency and beam quality. In excimer lasers depletion of the strongly attaching halogens, e.g. HCl, is a major reason for instabilities [95Dre, 78Bro]. An important prerequisite for instabilities to develop is an inhomogeneity within the discharge. Small fluctuations of the electron or gas density, respectively, can be sufficient for this [91Wes4], but in high-pressure glow discharges hot spots on the cathode surface have been identified to be a major starting point for instabilities. This has been investigated in detail by [95Dre] and [93Bel] for the case of HeCl4 excimer lasers. Uniform field electrodes are a prerequisite for uniform excitation of high-pressure glow discharges [93Ish, 95Ish].
3.1.4.6.3 High-frequency glow discharges In recent years high-frequency discharges for the excitation of CO2 lasers have extensively been investigated [92Vit, 94Vit, 93Zha, 92Ter, 85Vid, 91Wes3]. This type of discharge has replaced DC discharges to a great extent in the excitation of CO2 lasers. Although at first only small lasers Landolt-B¨ ornstein New Series VIII/1B1
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with powers below 100 W were excited using high-frequency discharges, high-power CO2 lasers with high-frequency excitation are now available with output powers of up to 40 kW [94Hab]. The excitation frequencies for waveguide lasers8 range from 100 MHz to 150 MHz [94Vit]. High-power systems are usually operated at frequencies of 13.6 MHz and 27 MHz, respectively. The disadvantage of the high cost of high-frequency excitation of CO2 lasers compared to DC-excitation is compensated for by a series of advantages. High-frequency discharges are significantly more stable than DC discharges as far as the development of thermal instabilities is concerned [95Loo, 81Mys2, 81Mys1, 82Mys1, 82Mys2, 91Wes4, 91Wes1]. This means that much higher power densities can be achieved with high-frequency discharges than with DC discharges. Up to 60 W cm−3 have been achieved with low-pressure stationary high-frequency-excited discharges, whereas a maximum of 20 W cm−3 is possible with DC-excited discharges. This permits more compact laser construction. One of the reasons for this greater stability is that it is possible to coat the metallic electrodes with a dielectric material. Apart from increasing stability this also reduces gas degradation to around 10 % of the value typical for DC-excited lasers. For lasers which are used commercially gas consumption is an important cost factor. High-frequency discharges can be modulated with frequencies up to around 200 kHz whereas DC discharges can only be modulated with frequencies of several kHz. The high-frequency power can be coupled to the discharge in various ways. For galvanic coupling the high-frequency power is applied to the non-coated metallic electrodes. This corresponds to DC excitation. Opposed to the case of DC excitation the electrodes for high-frequency excitation can be coated with a non-conducting dielectric material. The current through the dielectric is displacement current. A further power input method is inductive coupling. This involves placing a coil around the discharge volume. The voltage applied to the ends of the coils generates an electrical field in the direction of the coil axis. The current in the coil generates a longitudinal magnetic field which induces an azimuthal electrical field. The excitation of the discharge occurs as a result of both components of the electrical field although within the usual operating parameters of CO2 gas discharges the axial field dominates. Inductive excitation of CO2 lasers is hardly ever used in practice as this arrangement is not very stable. The excitation processes in the volume of high-frequency discharges, the positive column, are hardly different from the processes in DC discharges. Differences can be observed in the boundary regions and in the stability behavior. The latter are caused above all by the differences between boundary regions and the varying interaction of gas discharge and electrical field.
3.1.4.6.3.1 Boundary layers in high-frequency discharges In DC discharges characteristic regions are formed in front of the cathode and the anode. These regions are connected by the positive column. In high-frequency discharges the polarity of the voltage changes periodically and with it the structure of the discharge. As a result of the temporally variable electrical field strength the particle current is supplemented by the displacement current which permits current conduction even at near-zero charged-particle densities [80Cha, 91Rai, 93God]. This is of particular importance for the boundary layers in which most of the current can be carried by the displacement current. High-frequency discharges with capacitive coupling can operate in two modes, the α-mode and the γ-mode [57Lev, 91Rai, 86God]. In α-mode the secondary processes are of little importance for the maintenance of the discharge, high-frequency discharges can even exist completely without secondary processes. This form of discharge is a particular feature of high-frequency excitation but does only exist at small current densities and thus small voltage drops across the discharge boundaries. In the sheath regions near the discharge electrodes the electron density is much smaller than the positive-ion density. The 8
Waveguide lasers have a closed wave guide for optical radiation instead of the usual open optical resonators.
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3.1.4 Gas discharges
[Ref. p. 197
field strength in the boundary layers of high-frequency discharges in α-mode can be approximated to [91Rai]: e np d ,
0
E=
(3.1.64)
where d is the layer thickness. In α-mode the layer thickness is proportional to the drift distance of the electrons in the volume of the discharge: d=
0
T /2
VD sin (ωt) dt =
2VD . ω
(3.1.65)
VD is the amplitude of the electron drift velocity in the discharge volume. The field strength in the vicinity of the boundary layer increases when the frequency decreases or when the ion density increases. If the voltage drop across the boundary layer, V =
e np d 2 ,
0
(3.1.66)
exceeds a value corresponding to the breakdown voltage of a discharge with the electrode gap d, then a second breakdown can take place in the boundary layer, the discharge goes into γ-mode. In γ-mode the processes at the electrodes correspond extensively to those in DC glow discharges. Secondary electrons are released from the surface by impacting ions and then accelerated in the space-charge field where they generate electron–ion pairs by collisional ionization. But the structure of the boundary layers is not identical to those in DC discharges due to the periodical voltage reversal and the displacement current.
3.1.4.6.4 Microwave discharges Alongside DC and high-frequency discharges microwave discharges are used for the excitation of gas lasers, in most cases with a frequency of 2.45 GHz. This includes CO2 lasers [96Vio, 78Han, 91Wes2, 99Ike, 93Bie, 90Fre], CO lasers [80Hof, 93Luo], HeNe lasers [88Ima, 99Ima, 85Mou] and excimer lasers [85Chr, 81Men, 82Wis, 84Wis, 97Dem2, 90Kli]. The widely varying electron and gas densities involved in the different gas discharges make different discharge layouts necessary for each type of laser. The value of the plasma dielectric constant (3.1.55) is of decisive importance for the coupling of the gas discharge plasma and the electromagnetic field. Table 3.1.2 shows how the figures relate. Table 3.1.2. Electron and gas densities and value of the plasma dielectric constant (3.1.55) for different laser types. Laser type CO2 Ar II excimer
ne [cm−3 ] 10
3 · 10 1014 . . . 1015 1014 . . . 1015
N [cm−3 ] 18
p 19
10 . . . 10 1016 . . . 3 · 1016 5 · 1019 . . . 1020
0.9 + i 0.2 −700 + i 40 0 + i 1000
The boundary condition for the normal component of the field strength is:
a Ea = p Ep .
(3.1.67)
Ea is the normal field component outside the discharge plasma, Ep is the normal field inside the plasma, a,p are the dielectric constants of the exterior region and the plasma, respectively. When Landolt-B¨ ornstein New Series VIII/1B1
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Ea and a are kept constant the field inside the plasma increases with increasing electron density until the critical electron density, nc =
ω 2 me 0 , e2
(3.1.68)
is reached [91Wes2]. Above the critical density the plasma field decreases with further increasing electron density. Discharges are only stable when the field inside the discharge decreases strong enough with increasing electron density. This means that below the critical electron density the discharge is always unstable. The electron density that is commonly realized in medium-pressure CO2 lasers of about 1. . . 3 · 1010 cm−3 is well below the critical value9 of a 2.45 Ghz discharge of 1011 cm−3 . Stationary conditions cannot be expected until electron densities are reached which are around one order of magnitude higher than the common values. If no suitable counter-measures are taken, such as fast gas flow and special microwave resonator design [96Vio] or pulsed operation with a small pulse/pause ratio [91Wes2], the gas becomes overheated and thermal instabilities are likely to occur. In the case of Ar II and excimer lasers high p values lead to small values of the normal components of field strength in the gas discharge plasma related to the values of the exterior region, and to a skin depth in the mm-range. In order to achieve the required field strengths inside the discharge the outer field-strength values must be very high. The small skin depth limits the use of microwave excitation for both these types of laser to transversal discharge dimensions in the order of mm.
3.1.4.6.5 Arc discharges Inversion of the laser levels depends upon there being a sufficiently large difference between the electron and gas temperatures10 . This can be achieved, for example, in pulsed operation if the pulse length is small compared to the thermalization time constant. In stationary operation the energy transfer from the electron gas to the heavy-particle gas at the necessary temperature difference must not exceed the energy output to the exterior. This condition can in general only be fulfilled at sufficiently low gas densities. The current densities and as a consequence also the power densities in low-pressure glow discharges are relatively small. This small values are sufficient for HeNe and CO2 lasers. This does not apply, however, for ion lasers, e.g. Ar II or Kr II lasers. In these cases the laser transitions are transitions between electronic levels of the ions and not the neutral atoms. For the amplification to be sufficient the ion density must be in the range of several percent of the neutral gas density. At gas densities in the hPa range this means power densities of up to 1 kW cm−3 . This values can be realized with arc discharges. Arc discharges are characterized by thermal electron emission or field emission both of which are processes which lead to considerably high current densities at the cathode. With glow cathodes use is made of the thermionic effect which permits current densities of up to several 100 A cm−2 . Apart from the portion which goes into the laser radiation field and leaves the gas-discharge volume the power coupled into the discharge must be removed through the walls which must be cooled for this reason. Because the gas temperature is kept stable by cooling the walls this type of discharge is called a wall-stabilized arc discharge11 . Apart from heat removal the walls also act as a sink for the electrons and ions. Electrons and ions which hit the wall remain attached there and recombine with each other. Due to the considerably higher velocity of the electrons many more electrons than ions reach the wall initially. 9 10 11
The critical electron density at 27 MHz is only around 107 cm−3 . For electrons it is better to talk of average energy as there is generally no Maxwell distribution. Temperature stabilization in arc discharges can also be achieved by gas flow.
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3.1.4 Gas discharges
[Ref. p. 197
The wall is therefore negatively charged whereas in the region adjacent to the wall a positive space charge exists which gives rise to a space-charge field. The ions are accelerated by this field towards the wall whereas the electrons are decelerated. In steady state the number of ions and electrons hitting the wall are equal. The wall potential, and thus the energy of the ions hitting the wall, is about 5 times the mean electron energy [29Ton]. The mean electron energy in rare gas ion lasers amounts to 3 . . . 7 eV so that the energy of the ions hitting the wall reaches values of up to 35 eV. At these ion energies wall material can be sputtered off which is one of the main technological problems of ion lasers. Electrons and ions take momentum from the electrical field: dpe = −eE , dt
dpi = eE . dt
This takes place in opposite directions and with equal amounts. Electrons and ions give off the momentum taken from the field to other particles and to the wall. Because of the space-charge field in the vicinity of the walls the ions give off more of their momentum to the wall than the electrons that are deflected by the space-charge field. On the average the total momentum transferred to the neutral gas particles is in the direction of the mean electron momentum [81Ebe, 95Val, 68Che2, 68Che1]. This phenomenon is called electrophoresis. In addition to electrophoresis there is also cathophoresis which is caused by the ion flow [98Mur]. The ions drifting to the cathode recombine there and collect around the cathode. Electrophoresis and cathophoresis act in opposite directions, the direction and amount of the resulting gas flow depends on the discharge parameters. In order to compensate for the gas flow through the gas discharge tube so-called bypass pipes must be installed parallel to the discharge tube through which the gas can flow back. The bypass pipes must have a sufficient diameter to allow high enough back-flow at low pressure differences; on the other hand the discharge must not burn through the bypass pipes which is a considerable design problem. Instabilities can limit the usable parameter range of arc discharges [77Lue].
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197
References for 3.1 29Ton
Tonks, L., Langmuir, I.: A General Theory of the Plasma of an Arc. Phys. Rev. 34 (1929) 876.
30Wei
Weisskopf, V., Wigner, E.: Berechnung der nat¨ urlichen Linienbreite auf Grund der Diracschen Lichttheorie. Z. Phys. 63 (1930) 54.
46Hol
Holstein, T.: Energy distribution of electrons in high frequency gas discharges. Phys. Rev. 70 (1946) 367.
57Lev
Levitskii, S.M.: An investigation of the breakdown potential of high-frequency plasma in the frequency and pressure transition region. Sov. Phys. Tech. Phys. (English Transl.) 2 (1957) 887.
60Bat
Batanov, G.M., Petrov, N.N.: Emission of Electrons from Glass by Helium and Argon Ions. Sov. Phys. Solid State (English Transl.) 1 (1960) 1701. Maiman, T.H.: Stimulated Optical Radiation in Ruby. Nature (London) 187 (1960) 493.
60Mai
61Bat 61Jav
Batanov, G.M., Petrov, N.N.: Secondary Emission from no. 46 Glass under the Effect of Positive Ions of some Gases. Sov. Phys. Solid State (English Trsnsl.) 3 (1961) 1839. Javan jr., A., Bennett, W.R., Herriot, D.R.: Population Inversion and Continuous Optical Maser Oscillator in a Gas Discharge Containing a He-Ne Mixture. Phys. Rev. Lett. 6 (1961) 106.
64Gri 64McD
Griem, Hans R.: Plasma Spectroscopy, New York: McGraw Hill, 1964. McDaniel, E.W.: Collision Phenomena in Ionized Gases, New York: Wiley, 1964.
68Che1
Chester, A.N.: Experimental Measurement of Gas Pumping in an Argon Discharge. Phys. Rev. 169 (1968) 184. Chester, A.N.: Gas Pumping in Discharge Tubes. Phys. Rev. 169 (1968) 172. Krebs, K.H.: Electron Ejection from Solids by Atomic Oarticles with Kinetic Energy. Fortschr. Phys. 16 (1968) 419.
68Che2 68Kre
69Bas
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71Nas
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Haas, R.A.: Plasma Stability of Electric Discharges in Molecular Gases. Phys. Rev. A 8 (1973) 1017. Nighan, W.L., Wiegand, W.J., Haas, R.A.: Ionization instability in CO2 laser discharges. Appl. Phys. Lett. 22 (1973) 579.
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76All 76Egg
Allis, W.P.: Review of Glow Discharge Instabilities. Physica C 82 (1976) 43. Egger, H., Dufour, M., Seelig, W.: Inhomogeneities in TEA laser discharges. J. Appl. Phys. 47 (1976) 4929. Nighan, W.L.: Principles of Laser Plasmas, chapter Stability of High-Power Molecular Laser Discharges, New York: Wiley, 1976.
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Myshenkov, V.I., Yatsenko, N.A.: Influence of interelectrode distance on the maximum transverse size of a spatially uniform plasma column. Sov. Phys. Tech. Phys. (English Transl.) 26 (1981) 1199. Myshenkov, V.I., Yatsenko, N.A.: Prospects for using high-frequency capacitive discharges in lasers. Sov. J. Quantum Electron. (English Transl.) 11 (1981) 1297. Botti, E., Martelucci, S., Quartieri, J.: High-Power Electron Beam Preionized CO2 Laser Modelling. II. Analysis of Plasma Characteristics. Nuovo Cimento B 69 (1982) 47. Myshenkov, V.I., Yatsenko, N.A.: Stability of a composite discharge sustained by static and rf electric fields. II. Structure of a high-current rf capacitive discharge. Sov. J. Plasma Phys. (English Transl.) 8 (1982) 306. Myshenkov, V.I., Yatsenko, N.A.: Stability of a composite discharge sustained by static and rf electric fields. II. Mechanism for the stabilizing effect of an rf field on the positive column of a dc discharge. Sov. J. Plasma Phys. (English Transl.) 8 (1982) 397. Quartieri, J., Mastrocinque, G.: High-Power Electron Beam Preionized CO2 Laser Modelling. III. Kinetic and Fluid-Dynamic Model. Nuovo Cimento B 78 (1982) 21. Tough, R.J.A., Willetts, D.V.: Density perturbations induced by a discharge in a laser. J. Phys. D 15 (1982) 2433. Wisoff, P.J.K., Medelsohn, A.J., Harris, S.E., Young, J.F.: Improved Performance of the Microwave-Pumped XeCl Laser. IEEE J. Quantum Electron. 18 (1982) 1839. Buchnev, V.M., Klementov, A.D., Sergeev, P.B.: High-efficiency electron-beam-excited KrF excimer laser. Sov. J. Quantum Electron. (English Transl.) 13 (1983) 1364. Ferreira, C.M., Loureiro, J.: Electron energy distributions and excitation rates in highfrequency argon discharges. J. Phys. D 16 (1983) 2471. Braglia, G.L., Romano, L.: Monte Carlo and Boltzmann Two-Term Calculations of Electron Transport in CO2 . Lett. Nuovo Cimento 40 (1984) 513. Buffa, R., Fini, L., Matera, M.: Gas Density Perturbations in High Repetition Rate Static Fill TEA Lasers. Opt. Commun. 50 (1984) 397. Rhodes, Ch.K. (ed.): Excimer Lasers, New York: Springer-Verlag, 1984. Wisoff, P.J.K., Young, J.F.: Active Mode Locking of a Microwave-Pumped XeCl Laser. IEEE J. Quantum Electron. 20 (1984) 195. Birdsall, Ch.K., Langdon, A.B.: Plasma Physics Via Computer Simulation, New York: McGraw-Hill, 1985. Born, M.: Optik, Berlin: Springer-Verlag, 1985. Christensen, C.P., Waynant, R.W., Feldman, B.J.: High efficiency microwave discharge XeCl laser. Appl. Phys. Lett. 46 (1985) 321. Moutoulas, C., Moisan, M., Bertrand, L., Hubert, J., Lachambre, J.L.: A high-frequency surface wave pumped He-Ne laser. Appl. Phys. Lett. 46 (1985) 323. Penetrante, B.M., Bardsley, J.N., Pitchford, L.C.: Monte Carlo and Boltzmann calculations of the density gradient expanded energy distribution functions of electron swarms in gases. J. Phys. D 18 (1985) 1087. Phelps, A.V., Pitchford, L.C.: Anisotropic scattering of electrons by N2 and its effect on electron transport. Phys. Rev. A 31 (1985) 2932. Vidaud, P., He, D., Hall, D.R.: High efficiency rf excited CO2 laser. Opt. Commun. 56 (1985) 185. Godyak, V.A.: Soviet Radio Frequency Discharge Research. Monograph Series on Soviet Union, Falls Church, Va.: Delphic Associates, 1986.
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References for 3.1 Imankulov, Z.I., Mirinoyatov, M.M.: Distribution of the gain in an He-Ne laser over the cross section of the discharge tube with a transverse microwave discharge. Sov. J. Quantum Electron. (English Transl.) 18 (1988) 1235. Kovsh, I.B., Mikulin, E.I., Potatov, V.N.: Efficient methods for cooling an eletricdischarge CO laser. Sov. Phys. Tech. Phys. (English Transl.) 33 (1988) 210. Matousek, P., Vrbova, M.: Preionization of TEA CO2 laser by sliding discharge. Czech. J. Phys. Sect. B 38 (1988) 1375. Anan’ev, V.Yu., Danilychev, V.A., Ionin, A.A.: Pulsed electron-beam-controlled carbon monoxide laser amplifiers. I. Amplification of radiation from a CO laser operating in the free-running regime. Sov. J. Quantum Electron. 19 (1989) 4. Anan’ev, V.Yu., Danilychev, V.A., Ionin, A.A.: Pulsed electron-beam-controlled carbon monoxide laser amplifiers. II. Amplification of radiation pulses from an electronbeam-controlled CO laser with controlled spectral and temporal characteristics. Sov. J. Quantum Electron. (English Transl.) 19 (1989) 10. Tucker, J.E.: High Pressure Infrared Xenon Laser with X-Ray Preionization. IEEE Photon. Technol. Lett. 1 (1989) 193. Basov, N.G., Bashkin, A.S., Igoshin, V.I., Oraevsky, A.N., Shcheglov, V.A.: Chemical Lasers, Berlin, Heidelberg: Springer-Verlag, 1990. Elton, R.C.: X-Ray Lasers, Boston: Academic Press, 1990. Freisinger, B., Frohwein, H., Pauls, M., Pott, G., Schaefer, J.H., Uhlenbusch, J.: Excitation of CO2 lasers by microwave discharges; CO2 Lasers and Applications II. Proc. SPIE 1276 (1990) 29. Gordeeva, M.N., Yachnev, I.L.: Lasing dynamics of an electron-beam controlled CO2 laser. Sov. J. Quantum Electron. (English Transl.) 20 (1990) 1162. Klingenberg, H.H., Gekat, F., Splinder, G.: L-band microwave pumped XeCl laser with preionization. Appl. Opt. 29 (1990) 1246. Birdsall, C.K.: Particle-in-Cell Charged-Particle Simulations, Plus Monte Carlo Collsions With Neutral Atoms, PIC-MCC. IEEE Trans. Plasma Science 19 (1991) 65. Buranov, S.N., Gorokhov, V.V., Karelin, V.I.: Wide-aperture source of x-ray radiation for preionization of the large-volume electric-discharge lasers. Sov. J. Quantum Electron. (English Transl.) 21 (1991) 806. Raizer, Yu.P.: Gas Discharge Physics, Berlin: Springer-Verlag, 1991. Wester, R.: Frequency dependence of thermal volume instabilities in high frequency CO2 laser discharges. J. Appl. Phys. 70 (1991) 3449. Wester, R., Seiwert, S.: Investigation of microwave excited CO2 laser discharges. J. Phys. D 24 (1991) 1102. Wester, R., Seiwert, S.: Numerical modelling of RF excited CO2 laser discharges. J. Phys. D 24 (1991) 1371. Wester, R., Seiwert, S., Wagner, R.: Theoretical and experimental investigations of the filamentation of high-frequency excited CO2 laser discharges. J. Phys. D 24 (1991) 1796. Lister, G.G.: Low-pressure gas discharge modelling. J. Phys. D 25 (1992) 1649. Terai, K., Murata, T., Kobayashi, S., Tamagawa, T.: Laser Pulsing Characteristics of RF Excited High Power CO2 Laser at a Frequency of 1 MHz. Proc. LAMP (Laser Advanced Materials Processing) ’92, 1992, p. 79. Vitruk, P.P., Baker, H.J., Hall, D.R.: The characteristics and stability of high power transverse radio frequency discharges for waveguide CO2 slab laser excitation. J. Phys. D 25 (1992) 1767.
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Belasri, A., Boeuf, J.B., Pitchford, L.C.: Cathode sheath formation in a dischargesustained XeCl laser. J. Appl. Phys. 74 (1993) 1553. Bielesch, U., Budde, M., Fischbach, M., Freisinger, B., Schaefer, J.H., Uhlenbusch, J., Vioel, W.: Q-switched multikilowatt CO2 laser system excited by microwaves, 9th International Symposium on Gas Flow and Chemical Lasers. Proc. SPIE 1810 (1993) 57. Godyak, V.A.: A comparison of RF Electrode Sheath Models. IEEE Trans. Plasma Sci. 21 (1993) 378. Ishii, A., Okita, Y., Yasuoka, K., Tamagawa, T.: Uniform Field Electrodes for HighPower and High-Repetiton TEA CO2 Lasers. Jpn. J. Appl. Phys. 32 (1993) 88. Luo, X., Schafer, J.H., Uhlenbusch, J.: Microwave excited high power cw CO laser at room temperature. Opt. Commun. 102 (1993) 65. M¨ uller, T., Neuber, A., Seelig, W.: Densities and Life Time of Electrons in KrF∗ Laser Gas Mixtures during the X-Ray Preionization. Contrib. Plasma Phys. 33 (1993) 183. Saito, H.: Review on High-Power Gas Dynamic CO2 Laser. Rev. Laser Eng. (Reza Kenkyu) 21 (1993) 485. Yatsui, K., Masugata, K., Kurihara, K., Satoh, I., Igawa, H., Imada, G., Sakugawa, T., Kataoka, Y., Shibata, K., Shigeta, M.: All-solid-state excitation circuit using saturable transformer for excimer laser excitation. 9th International Symposium on Gas Flow and Chemical Lasers. Proc. SPIE 1810 (1993) 396. Zhang, X.S., Baker, H.J., Hall, D.R.: Flowing gas operation of a planar discharge rf excited CO2 laser. J. Phys. D 26 (1993) 359. Bernard, N., Hofmann, T., Fontaine, B.L., Forestier, B.M., Delaporte, P.C., Sentis, M.L.: High pulse rate frequency (PRF) long-pulse x-ray preionized spiker-sustainer XeCl laser [2502-64], Tenth International Symposium on Gas Flow and Chemical Lasers, H¨ ugel, H., Bohn, W.L. (eds.). Proc. SPIE 2502 (1994) 433. Caffaro, M.G., Caffaro, M.A.G.: A Generalized Model for Carbon Monoxide GasDynamic Laser. Mod. Phys. Lett. B 8 (1994) 1913. Cenian, A., Chernukho, A., Borodin, V.: Modeling of Plasma-Chemical Reactions in Gas Mixtures of CO2 Lasers II. Theoretical Model and its Verification. Contrib. Plasma Phys. 35 (1994) 273. Habich, U., Du, K., Ehrlichmann, D., Jarosch, U., Niehoff, J., Plum, H.-D., Meyer, R., Wolf, N., Loosen, P., Beck, T., Hertzler, C., Wollermann-Windgasse, R.: Developement of an industrial CO2 laser with more than 40-kW output power: recent results [2502-03], Tenth International Symposium on Gas Flow and Chemical Lasers. Proc. SPIE 2502 (1994) 20. Imada, G., Igawa, H., Masugata, K., Masuda, W., Yatsui, K.: Propagation of shock waves in a discharge-pumped XeCl excimer laser; Gas, Metal Vapor, and Free-Electron Lasers and Applications. Proc. SPIE 2118 (1994) 51. Miller, A.W., Wallace, S., Schwarzenberger, P.M.: Performance Optimization of an Electron-Beam Sustained CO2 Laser. GEC J. Res. 11 (1994) 167. Pronko, M.S.: Controlling Output Gain Uniformity by Spatial Variation of the X-Ray Preionization in a Large Aperture Discharge Pumped KrF Amplifier. IEEE J. Quantum Electron. 30 (1994) 2147. Vitruk, P.P., Baker, H.J., Hall, D.R.: Similarity and Scaling in Diffusion-Cooled RFExcited Carbon Dioxide Lasers. IEEE J. Quantum Electron. 30 (1994) 1623. Dreiskemper, R., B¨otticher, W.: Current Filamentation of Strongly Preionized High Pressure Glow Discharges in Ne/Xe/HCl Mixtures. IEEE Trans. Plasma Sci. 23 (1995) 987.
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References for 3.1 Igoshin, V.I., Pichugin, S.Yu.: Excimer-Laser Excitation by Optical Discharge. High Energy Chem. (English Transl.) 29 (1995) 59. Ishii, A., Yasuoka, K., Okita, Y., Tamagawa, T.: 3 kHz XeCl Excimer Laser Using New Type of Electrode. Jpn. J. Appl. Phys. 34 (1995) 2324. Leys, C. van, Egmond, C., Desoppere, E.: Dissociation levels in fast-axial-flow CO2 lasers: A quantitative model. J. Appl. Phys. 78 (1995) 2265. Loosen, P., Wester, R.: Parameter limits of thermal instabilities in high-frequency CO2 laser discharges. J. Phys. D 28 (1995) 849. Masugata, K.: A new pulse compression circuit for low impedance pulse power generation. Rev. Sci. Instrum. 66 (1995) 5640. Raizer, Yu.P., Shneider, M.N., Yatsenko, N.A.: Radio-Frequency Capacitive Discharges, New York: CRC Press, 1995. Sato, Y., Inoue, M., Nagai, H.: Development of a 2-kW XeCl Laser with a Surface Corona Preionization Scheme and a Spiker-Sustainer Circuit (Invited Paper). IEEE J. Sel. Topics Quantum Electron. 1 (1995) 811. Sidorov, A.I., Chirkov, V.N., Yachnev, I.L.: Formation of a smooth radiation pulse in an electron-beam-controlled CO2 laser. Sov. J. Quantum Electronics (English Transl.) 25 (1995) 544. Valentini, H.-B., Wolff, D., Glauche, E.: Axial neutral gas transport in the low-pressure direct current positive column including the radial variation of the electron temperature. J. Phys. D 28 (1995) 716. Borodin, A.M., Gurashvili, V.A., Shchekotov, E.Yu.: Electron-beam-controlled CO laser with supersonic flow of the active mixture. Sov. J. Quantum Electron. (English Transl.) 26 (1996) 307. Loffhagen, D., Winkler, R.: Time-dependant multi-term approximation of the velocity distribution in the temporal relaxation of plasma electrons. J. Phys. D 29 (1996) 618. Viol, W., Uhlenbusch, J.: Generation of CO2 laser pulses by Q-switching and cavity dumping and their amplification by a microwave excited CO2 laser. J. Phys. D 29 (1996) 57. Baranov, I.Ya.: Preionization of the Positive Column of a High-Frequency Capacitive Discharge by Electrons from the Electrode Sheath in a Molecular Gas Flow. Plasma Phys. Rep. 23 (1997) 75. Brenning, N., Axnas, I., Eninger, J.E.: High Pressure Pulsed Avalanche Discharges: Formulas for Required Preionization Density and Rate for Homogeneity. IEEE Trans. Plasma Sci. 25 (1997) 83. Cenian, A., Chernukho, A., Kukietto, P., Zaremba, R., Borodin, V.: Improvement of self-regeneration of gas mixtures in a convection-cooled 1.2 kW CO2 laser. J. Phys. D 30 (1997) 1103. Demtr¨oder, W.: Laser Spectroscopy, Berlin: Springer-Verlag, 1997. Dem’yanov, A.V., Lo, D., Napartovich, A.P.: Numerical Modeling of a XeCl Laser Excited by Microwave Discharge. Appl. Phys. B 65 (1997) 445. Dymshits, B.M., Alexandrov, B.S.: Multi-megawatt supersonic e-beam sustained CW CO lasers: estimations of their energy characteristics and operating regimes, XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference. Proc. SPIE 3092 (1997) 448. Dymshits, B.M., Alexandrov, B.S., Belavin, V.A., Koretsky, J.P.: Supersonic CO laser: status and prospects, XII International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference. Proc. SPIE 3574 (1997) 235. Fedorov, A.I.: Discharge excimer lasers with a automated spark preionization. Atmospheric Oceanic Opt. 10 (1997) 796. Landolt-B¨ ornstein New Series VIII/1B1
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Itaya, Y., Kawamura, Y., Kobayashi, N., Takami, Ch., Hasatani, M.: CO2 gas dynamic laser driven by methane-air combustion. XII International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference. Proc. SPIE 3092 (1997) 452. Kuznetsov, A.A., Novgorodov, M.Z., Tikhonov, V.M.: Small-size slab CO2 -laser excited with a DC discharge with short-pulse preionization. Atmos. Oceanic Opt. 10 (1997) 810. Shaw, M.J.: Prospects for high average power electron-beam-pumped KrF lasers for inertial confinement fusion and industrial applications. XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference. Proc. SPIE 3092 (1997) 154. Vetrovec, J.: Prospects for an industrial chemical oxygen-iodine laser. In: Proc. SPIE, XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, Vol. 3092, p. 723, 1997. Zhang, B., Yukimura, K.: Spectrum Observation of Pulsed Arc Discharge for KrF Excimer Laser Preionization. Sci. Eng. Rev. Doshisha Univ. 37 (1997) 253. Feenstra, L., Hoekstra, O.B., Peters, P.J., Witteman, W.J.: Timing of the x-ray preionization of a discharge-pumped ArF excimer laser with different excitation circuits, XII International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference. Proc. SPIE 3574 (1998) 67. Kutumov, C.A., Klimuk, E.A., Troshchinenko, G.A.: Electric discharge repetitively pulsed HF/DF chemical laser operating on the mixture F2 + H2 (D2 ). XII International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference. Proc. SPIE 3574 (1998) 601. Masuda, W., Hishida, M., Abe, Y.: Numerical simulation of a supersonic mixing chemical oxygen-iodine laser with ramp nozzle arrays [3574-81]. Proc. SPIE 3574 (1998) 584. Murphy, A.B.: Cataphoresis in electric arcs. J. Phys. D 31 (1998) 3383. Seelig, W., Onkels, E.D.: Quantitative comparison of different preionization schemes of KrF laser discharges. Appl. Phys. B 67 (1998) 33. Vetrovec, J.: Electrochemical production of basic hydrogen peroxide and chlorine for use in chemical oxygen-iodine laser. In: Proc. SPIE, XII International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, Vol. 3574, p. 305, 1998. Vetrovec, J.: Conceptual design of an industrial chemical oxygen-iodine laser [3574-61]. In: Proc. SPIE, XII International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, Vol. 3574, p. 461, 1998. Wakazono, T., Hashimoto, K., Takemoto, T., Uchiyama, T., Muro, M.: Chemical oxygen-iodine laser using rf-discharge dissociation of I2 . XII International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference. Proc. SPIE 3574 (1998) 290. Weber, Marvin J.: Handbook of Laser Wavelengths, Boca-Raton: CRC Press, 1998. Feenstra, L., Bastiaens, H.M.J., Wittemann, W.J.: On the long pulse operation of an x-ray preionized, gas discharge pumped ArF excimer laser. Appl. Phys. Lett. 75 (1999) 1033. Ikeda, T., Danno, M., Tanaka, J.: A New Helical Coupling Microwave Antenna Excited High-Power CO2 Laser Using a Cyclindrical Resonant Cavity. IEEE J. Quantum Electron. 35 (1999) 721. Imankulov, Z.I., Mirinoyatov, M.M., Usmanov, T.: Influence of a magnetic field on the power and noise of the radiation of an He-Ne laser with a transverse microwave discharge. Sov J. Quantum Electron. (English Transl.) 29 (1999) 792.
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3.2 CO2 laser and CO laser
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3.2 CO2 laser and CO laser ¨l J. Uhlenbusch, W. Vio
3.2.1 CO2 laser The CO2 laser is generally regarded as the industrial workhorse of the laser world because it is used to carry out such wide range of applications. A large-scale application of the CO2 laser is its use for material processing and specific surgical tasks. The advantages of the CO2 laser are: the high efficiency for conversion of electrical energy into laser photons (overall device-efficiencies of 10 % are possible), the relatively simple technical realization and operation, the possibility to scale CO2 lasers over two orders of magnitude in laser output power (for example from 50 W to 5 kW) by using the same technical realization concept, and the high security of the human eye at the CO2 laser wavelengths between 9.2 μm and 10.8 μm.
3.2.1.1 Fundamentals of CO2 laser discharge The CO2 laser makes use of a suitable gas mixture of CO2 , N2 , and He. Laser action takes place between two vibrational levels of the CO2 molecule, while N2 and He improve the laser efficiency. The gas mixture is often excited by an electrical glow discharge. At a reduced electrical field E/n of 2 · 10−20 V m2 (which corresponds to an electron energy of about 1 eV) applied to a gas mixture with a particle density n about 60 % of the incoupled electrical power is used for the vibrational excitation of nitrogen. The pumping of the upper laser level is very efficiently achieved by resonant energy transfer from vibrationally excited N2 molecules. In a so-called gas-dynamic laser the preheated gas mixture is rapidly cooled down due to a nozzle while maintaining the vibrational excitation of N2 . The majority gas He, because of its high thermal conductivity (about six times as large as that of CO2 and N2 ), helps to keep the CO2 cool by conducting heat away to the walls of the container. A low translational temperature for CO2 is necessary to avoid population of the lower laser level by thermal excitation. The deexcitation of the lower laser level occurs by distributing the vibrational energy among the symmetric stretching mode and the bending mode via resonant energy transfer and finally by transferring this vibrational energy to translational energy of the colliding partners. This energy is most likely to be transferred to lighter atoms, i.e., to He in this case. Thus He helps to empty the population from the lower laser level. In sealed-off systems laser action would cease in a few minutes. This is because CO2 compared with the precursor gas is dissociated by the electrical discharge resulting in a modified CO2 –CO–O2 composition. Therefore, some kind of catalyst must be present in the closed cycle to promote the regeneration of CO2 from the CO. A simple way to achieve this is to add a small amount of H2 O (1 %) to the gas mixture. This leads to the regeneration of CO2 , probably through the reaction CO∗ + OH → CO∗2 + H
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[Ref. p. 212
involving vibrationally excited CO and CO2 molecules. The relatively small amount of H2 O vapor required may be added in form of H2 and O2 . In fact, since O2 is produced during the dissociation of CO2 , it is found that only H2 needs to be added. The gas mixture in sealed-off lasers also contains a low amount of Xe (a few per cent). The influence of Xe is mainly due to its effect on the electron energy distribution; the number of electrons with energy smaller than 4 eV increases whereas the number of those with larger energies decreases. This change of electron energy distribution has a favorable effect on the vibrational excitation of N2 and reduces the degree of dissociation of CO2 . Thus Xe increases the laser output power and efficiency compared with a mixture without Xe [87Wit]. The most important laser parameter can be scaled at a constant gas temperature and at a constant degree of ionization ne /n (ne : electron density) as follows: At a discharge pressure above 2 kPa (as usual in modern CO2 laser) the small-signal gain g0 is independent of the discharge pressure p: g0 = f (p) .
(3.2.2)
The saturation intensity IS is proportional to the square of the discharge pressure: IS ∼ p2
(3.2.3)
and the laser output power P L per discharge volume V is also proportional to the square of the discharge pressure: PL ∼ p2 . (3.2.4) V The condition of a constant degree of ionization cannot be realized in cw CO2 lasers, because the electrical discharge tends with growing pressure to develop electro-physical instabilities. To avoid these instabilities, the electron density must be raised slower than the discharge pressure. The practical consequence is that the laser output power per discharge volume grows as PL (3.2.5) ∼ pm , V where the exponent m has a value between 1 and 2 [92Hue]. The CO2 laser discharge can be excited by DC [87Wit, 92Hue], high frequency (10 kHz . . . 3 MHz) [90Kuz, 94Kle, 00Wie], RF (13 . . . 1500 MHz) [96Wit] and microwave (2.45 GHz) [92Bie]. Most of the CO2 lasers operated today use the RF-excitation, which presents many advantages over the DC-excitation, e.g. 1. the avoidance of anodes and cathodes, which eliminates the associated gas chemistry problem at the cathode; and 2. the occurrence of a stable discharge at higher discharge pressures. As drawback appears the high cost of the RF-generators. Therefore, low-cost all-solid-state generators with frequencies up to 3 MHz are used in some novel laser systems [00Wie, 04Wie].
3.2.1.2 Practical design of cw CO2 lasers From the point of view of their constructional features, design, and technical realization of the gas cooling one distinguishes between five types of cw CO2 lasers: 1. 2. 3. 4. 5.
sealed-off lasers, lasers with slow axial flow, lasers with fast axial flow, transverse-flow lasers, and gas-dynamic lasers. Landolt-B¨ ornstein New Series VIII/1B1
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3.2.1.2.1 Sealed-off lasers To reduce the dissociation of CO2 with subsequent irreversible chemistry of dissociation products on the surface of the discharge tube in a sealed-off laser, typically small amounts of Xe, H2 and O2 are added to the laser gas (see Sect. 3.2.1.1 above). Lifetimes for sealed-off laser tubes in excess of 10,000 h have been demonstrated. The heat removal is provided by radial conduction of heat to the tube walls, which are cooled externally by a suitable coolant (usually water). The output power produced by lasers with cylindrical tubes is proportional to the discharge length (∼ 60 W/m), but independent of the tube diameter. Therefore, the tube diameter can be reduced to about a few millimeters (1 . . . 4 mm) without loosing laser power, but then a situation is reached where the laser radiation is guided by the inner walls of the tube. Such waveguide CO2 lasers have a low diffraction loss. Tubes of BeO or Al2 O3 have been found to give the best performance. This technological constraint limits the power which may be extracted from an individualelement laser device. The laser array concept provides one attractive approach to laser power scaling. In the conceptually simplest form of array, consisting of a set of independent laser oscillators, the output power from each laser is uncorrelated with that of its neighbors, thus each operating at a different frequency and/or random phase. The total output power from N such identical oscillators in an incoherent array is then N times the power of each individual laser [96Wit]. The concept of stripline CO2 laser represents an extension of the CO2 waveguide laser principle towards higher laser power [90Now, 91Now]. The stationary laser gas is electrically excited by a RF discharge between large area electrodes. In order to keep the mean gas temperature at a sufficiently low level, a discharge gap of 1 . . . 2.5 mm is needed for an efficient cooling of the laser gas by heat diffusion to the water-cooled electrodes. A RF frequency of about 100 MHz is needed to keep the discharge boundary layers small, which do not contribute to laser excitation. In such cases, the linear power scaling of conventional diffusion-cooled lasers is replaced by an area scaling. The laser output power P L is proportional to the electrode area A and inversely proportional to the discharge gap d [91Now]: PL ≈
3 mm A ·W. · d cm2
(3.2.6)
For discharge gaps smaller than 1 mm the waveguide losses become significant as well as the changing excitation conditions and the problem of spatial discharge inhomogeneity at the required higher RF frequencies. Therefore, the laser power prediction of (3.2.6) fails for very small electrode gaps.
3.2.1.2.2 Lasers with slow axial flow Operation of the first CO2 laser was achieved in a laser of this type [64Pat]. The gas mixture slowly flows along the laser tube (≈ 1 cm/s) to remove the dissociation products, that would otherwise contaminate the laser active medium. The laser output power scales with the discharge length (∼ 100 W/m). Slow-flow axial-flow lasers excited with a DC-discharge are low-cost devices and therefore are still used in industry [97Poe].
3.2.1.2.3 Lasers with fast axial flow To overcome the output limitations of the above type of CO2 laser the laser gas mixture is blown through the tube at very high speed (≈ 100 m/s). In this case the heat is removed simply by Landolt-B¨ ornstein New Series VIII/1B1
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exchanging the hot laser gas, which is then cooled outside the tube by a suitable heat exchanger before being returned to the tube. Much higher output power if compared with the slow-flow system per unit discharge length can be obtained (∼ 1 kW/m or even greater). This convective cooling is limited due to choking when the laser gas reaches the sound barrier at the end of the discharge tube. Besides cooling, the mixture, while it is outside the laser tube, can also be regenerated. A complete sealed-off operation is not possible, but the laser gas exchange can be kept very low [92Hue]. The high electric power input is effectively realized by RF-excitation.
3.2.1.2.4 Transverse-flow lasers Another way of circumventing the power limitation of a slow-axial-flow laser is to move the gas mixture perpendicular to the discharge. If the flow is fast enough, the heat, as in the case of fastaxial-flow lasers, gets carried away by convection rather than diffusion to the walls. The discharge is usually applied in the direction perpendicular to the resonator axis and perpendicular to the gas flow. Compared to the fast-axial-flow lasers, these lasers appear to be simpler devices in view of the reduced flow speed and flow resistance requirement for transverse rather than axial flow. However, the beam quality of fast-axial-flow lasers is considerably better, because of the cylindrical symmetry.
3.2.1.2.5 Gas-dynamic lasers In a gas-dynamic CO2 laser the population inversion is not produced by an electrical discharge but by rapid expansion of a gas mixture (containing CO2 ) which has initially been heated to a high temperature. The operation principle can be summarized as follows. The gas mixture is first held at high temperature (≈ 1400 K) and pressure (≈ 1.7 MPa) in thermal equilibrium. The population of the upper laser level of CO2 will be about 9 % of the ground-state population. The lower-level population is, of course, higher than this (≈ 24 %), and there is no population inversion. Since this gas mixture expands adiabatically through an expansion nozzle, the translational temperature of the mixture will be reduced to a much lower value. The relaxation of vibrational energy into translational energy to the equilibrium values behind the nozzle happens faster for the lower laser level than for the upper one. Thus there will exist a fairly extensive region downstream from the expansion zone where population inversion occurs. Gas-dynamic CO2 -lasers have been reported that produce output power of several 10 kW with a laser efficiency of about 1 % [81Los].
3.2.1.3 Practical design of pulsed CO2 lasers 3.2.1.3.1 Transversely excited atmospheric-pressure lasers In a cw Transversely Excited (TE) CO2 laser, it is not easy to increase the laser gas pressure above 0.02 MPa. Above this pressure and at the current densities normally used glow discharge instabilities with subsequent arcing set in. To overcome this difficulty, the voltage can be applied to the transverse electrodes in the form of a pulse. If the pulse duration is shorter than a microsecond, the discharge instabilities have no time to develop and the operating pressure can then be increased up to and even above atmospheric pressure. These lasers are therefore referred to as TEA lasers, the abbreviation standing for Transversely Excited at Atmospheric pressure. These lasers thus produce a pulsed output and are capable of large output energies per unit volume of the discharge (≈ 70 J/liter). To avoid arc formation, some form of preionization is also applied (UV- or e-beam or corona preionization). Landolt-B¨ ornstein New Series VIII/1B1
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The first peak of a TEA laser pulse is usually called the gain-switched peak or gain spike. About one third of the total laser pulse energy is found in the gain spike, which has a duration of typically 70 ns. After this spike the gain recovers by energy transfer from the vibrationally excited nitrogen to the upper laser level of CO2 . The restored gain causes a pulse tail with a duration of about 800 ns. For low pulse repetition rates (≈ 1 Hz), it proves unnecessary to exchange the gas mixture. For higher repetition rates (up to a few kilohertz) the gas mixture streams transversely to the resonator axis and is cooled by a suitable heat exchanger. Another interesting characteristic of these lasers is their relatively broad line width (≈ 4 GHz at p = 1 atm = 0.1 MPa, due to collision broadening). Thus, by mode-locking TEA lasers optical pulses with less than 1 ns duration can be produced. 3.2.1.3.2 Q-switched low-pressure lasers Several low-pressure lasers for industrial applications use current switching techniques for enhancing instantaneous power. A peak power excess a few times higher than average power can be obtained. As the collisional energy transfer from vibrationally excited N2 to the upper laser state, which is the dominant pumping mechanism for CO2 lasers, is inherently slow at low gas pressure (≈ 0.01 MPa), no gain-switched spike is observed and modulation is even impossible at frequencies above 10 kHz. By insertion of a fast Q-switch into the resonator, continuous discharge CO2 lasers yield highpeak-power pulses at multi-kHz repetition rate [93Fus, 96Vio]. The Q-switching can be realized by a mechanical chopper disc or by a CdTe Pockels cell. By mechanical Q-switching laser pulses with a pulse repetition rate of 4 . . . 200 kHz and TEM00 beam quality can be produced. Peak powers of 0.9 MW at a pulse repetition rate of 10 kHz and 0.2 MW at a 100 kHz repetition rate are reported [96Vio]. The pulse duration is about 0.2 μs. The maximum average power of 7 kW in the Q-switched mode reaches nearly the maximum cw laser power of 10 kW of the laser system used. The laser pulse duration can be shortened by the combination of cavity dumping and electrooptical Q-switching. This pulsed operation leads to laser pulses with 35 ns pulse duration and 1.9 MW maximum power at a pulse repetition rate of 10 kHz and an average laser power of 0.8 kW [96Vio].
3.2.2 CO laser The CO laser like the CO2 laser is a powerful coherent infrared light source with lasing on a multitude of lines between 4.8 μm and 6.7 μm. Despite of its high quantum efficiency and its favorable wavelength the industrial application of this laser is still of minor importance, but it is well established for a special type of molecular spectroscopy allowing very sensitive detection of molecular species.
3.2.2.1 Fundamentals of CO laser process The CO laser gas mixture consists of CO, N2 , He, Xe, and O2 . Lasing takes place due to rovibrational transitions between neighbored (Δv = 1) high-lying vibrational levels.
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The excitation of the CO vibration from the ground state is by inelastic electron collisions via negatively charged CO compound states, which rapidly decay into the first ten excited vibrational states of CO. Typical discharge conditions assumed, between 30 % and 90 % of the electron energy can be transferred to the vibrational levels of CO, an average electron temperature of 0.75 eV provided. The presence of N2 supports partially the excitation of CO by V–V collisions and has additionally an effect to optimize the E/n values of the discharge. The initial excited-state population of the vibrational levels relaxes rapidly by a selective relaxation process, which results from the anharmonicity of the CO molecule. This quasi-resonant/near-resonant V–V transfer process is much faster than V–T relaxation and is responsible for the so called V–V pumping effect, which means, that CO molecules in quantum levels above v − 1 cannot relax by collisions, if the energy discrepancy by anharmonicity is larger than the average translational energy. For this specific quantum number v the relation v − 1 ≈ 2.59 × 10−2 TGas /K is valid. The anharmonic pumping, however, is not so effective that complete inversion between two vibrational levels occurs, but partial inversion for rotational-state densities belonging to transitions from J to J + 1 (P-branch) or J to J − 1 (R-branch) is possible. Laser action reduces the population of the upper rotational level belonging to the upper vibrational state, for the lower state a growth of the population is inevitable. As a consequence this loss from the upper laser level causes lasering between the next higher vibrational state and the one under consideration, and so on. In particular in a pulsed CO laser a cascading behavior of laser output with slightly different wavelengths is observed. Starting with an a–b transition (upper/lower state), after a certain time delay a transition (a+1)–(b+1) oscillates, then (a+2)–(b+2) oscillates, and so on. The cascading behavior and the slow relaxation by V–T processes are responsible for the high quantum efficiency of the CO laser. Trace additions of several gases are known to significantly affect CO laser power, efficiency and service life. The gases He and Xe have a similar meaning as in case of the CO2 laser. The additive He lowers the gas temperature near the discharge axis and a higher current density enhancing the output power is allowed. Xe has, like in a sealed-off CO2 laser, a beneficial effect on the electronic distribution function by the Ramsauer effect. O2 removes CN radicals, has a positive effect on the electron–ion recombination process [77Mor] and prevents the formation of unwanted carbon layers. The discharge is poisoned by CO2 generated during operation. It must be removed by a zeolite trap. The gas temperature of the active medium is a very important parameter, which determines the output power, the gain, the efficiency and the spectral position of the emitted laser light. With decreasing temperature the output power grows, the small-signal gain is enhanced (typically 0.2 m−1 at T = 293 K and 0.9 m−1 at T = 77 K), and the emitted spectrum shifts towards lower vibrational transitions with preference for rotational transitions with low quantum number J.
3.2.2.2 Practical design of cw CO lasers Design and operation of CO lasers are very related to those known from CO2 lasers. A very drastic difference between the two types is the required expensive cooling in case of the CO laser of the entire discharge structure and of portions of the laser gas lines down to liquid nitrogen temperature, if their high-power operation (> 5 kW) is wanted. The need for the complex cooling system hampered considerably the commercial use of CO lasers for material treatment. Several quite different CO laser types have been developed: sealed-off lasers, lasers with axial and transversal flow, and pulsed CO lasers.
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3.2.2.2.1 Sealed-off lasers The lifetime of sealed-off CO lasers is most probably limited by decomposition of the precursor gas filling, generation of unwanted dissociation products, formation of sputtered films, gas clean up by those films and deposition of material, e.g. carbon. These processes are accompanied by a gradual decrease of laser output power. A continuous gas flow helps to circumvent some of the problems. As is reported in literature [71Fre] not only the initial gas filling for long-life operation is crucial, but also the construction material including the choice of the electrode material. In particular the presence of H2 (or H2 O) is believed to poison the active medium, quite in contrast to the CO2 laser, where H2 or H2 O are used as a catalyst. Therefore, in [78Mur] a heated palladium diffusion tube was used to remove hydrogen. A very efficient, long-life (110 hours) laser system at room temperature is described in [80Pet]. The authors use gold electrodes (instead of platinum) and a small zeolite cell as an absorber of water that is released from the wall, electrodes etc. Power output from a discharge of ∼ 1 m length and internal diameter of 6 mm was maximum 28.5 W multiline in a gas mixture containing 7.9 Pa O2 , 145 Pa N2 , 263 Pa Xe, 316 Pa CO, 35.5 hPa He. At 16 mA discharge current an efficiency of 15 % was achieved. The application in spectroscopy requires a wavelength-tuning of the CO laser, which can be easily performed by an intracavity grating. Several hundred rovibrational lines can be attained by this technique. Line widths of less than 100 kHz are possible, if Lamb-dip stabilization is provided [87Sch].
3.2.2.2.2 Lasers with axial and transversal flow Very early papers [65Pat, 65Leg] have verified laser oscillation in a flowing CO and N2 mixture. High-power cw operation at say 100 W was realized by [70Epp]. A 600 W cryogenic system with convective flow and a longitudinal discharge is described in [77Lim]. More powerful cryogenic CO lasers with DC excitation up to 3.1 kW [87Sai] and electron beams excited with 10 kW [85Bas] were used with benefit for isotope separation and material processing (cutting, welding, surface hardening, crystal growth). Since the early days of CO laser operation one tried to get rid of the cryogenic cooling. One way which has received a lot of attention is to generate CO laser action by supersonic expansion. The first experiments used aerodynamically-stabilized glow discharges for excitation located in the subsonic plenum upstream of the nozzle [77Dai] and the laser resonator non-coincident with the discharge. Similar devices applying RF- and microwave excitation with output power of several 100 watts were developed [80Sch1, 80Sch2]. A novel CO laser development provides laser activity at room temperature without making use of supersonic flow with coincident resonator axis and discharge. Laser oscillation is observed at high-lying vibrational quantum numbers v = 9 . . . 8 to v = 13 . . . 12 on 10 lines with an efficiency comparable to the closed-cycle gas-dynamic cw CO laser [93Luo, 96Shi].
3.2.2.2.3 Pulsed CO lasers Pulsed electron-beam-sustained cryogenic discharges with superimposed subsonic flow deliver the highest electrical efficiency and specific energy, e.g. 200 J from a volume of 2 l at a maximum efficiency of 63 % [74Man] and 1600 J from a volume of 16 l at a maximum efficiency of 40 % [77Bon]. Typical laser pulse lengths are 50 μs. The application of a supersonic flow (Mach-number 3 . . . 4) improves the uniformity of cooling and as a consequence the optical quality of the laser beam.
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References for 3.2
References for 3.2 64Pat
Patel, C.K., Faust, W.L., McFarlane, R.A.: Bull. Am. Phys. Soc. 9 (1964) 500.
65Leg 65Pat
Legay-Sommaire, H., Henry, L., Legay, F.: C. R. Acad. Sci. (Paris) 260 (1965) 3339. Patel, C.K.N.: Appl. Phys. Lett. 7 (1965) 246.
70Epp
Eppers, W.C., Osgood jr., R.M., Greason, P.R.: IEEE J. Quantum Electron. 6 (1970) 145.
71Fre
Freed, C.: Appl. Phys. Lett. 18 (1971) 458.
74Man
Mann, M.M., Rice, D.K., Equchi, R.G.: IEEE J. Quantum Electron. 10 (1974) 682.
77Bon 77Dai 77Lim 77Mor
Boness, M.J.W., Center, R.E.: J. Appl. Phys. 48 (1977) 2705. Daiber, J.W., Thompson, H.M.: IEEE J. Quantum Electron. 13 (1977) 10. Lim, D.G., Mendoza, P.J., Cohn, D.B.: Rev. Sci. Instrum. 48 (1977) 1430. Morgan, W.L., Fisher, E.R.: Phys. Rev. A 16 (1977) 1186.
78Mur
Murray, G.A., Smith, A.L.: J. Phys. D 11 (1978) 2477.
80Pet 80Sch1 80Sch2
Peters, P.J.M., Witteman, W.J., Zuidema, R.J.: Appl. Phys. Lett. 37 (1980) 119. Schall, W., Hoffmann, P., Schock, W., H¨ ugel, H.: J. Phys. (Paris) 41 (1980) C9. Schock, W., Schall, W., H¨ ugel, H., Hoffmann, P.: Appl. Phys. Lett. 36 (1980) 793.
81Los
Losev, S.A.: Gasdynamic Laser, Berlin: Springer-Verlag, 1981.
85Bas
Basov, N.G.: IEEE J. Quantum Electron. 21 (1985) 342.
87Sai 87Sch
Saito, H.: Rev. Sci. Instrum. 58 (1987) 1417. Schneider, M., Hinz, A., Grok, A., Evenson, K.M., Urban, W.: Appl. Phys. B 44 (1987) 241. Witteman, W.J.: The CO2 laser, New York: Springer-Verlag, 1987.
87Wit 90Kuz 90Now
Kuzumoto, M., Ogawa, S., Tanaka, M., Yagi, S.: IEEE J. Quantum Electron. 26 (1990) 1130. Nowack, R., Opower, H., Schaefer, U., Wessel, K., Hall, Th.: Proc. SPIE 1276 (1990) 18.
91Now
Nowack, R., Opower, H., Wessel, K., Kr¨ uger, H., Haas, W.: Laser Optoelektronik 3 (1991) 68.
92Bie 92Hue
Bielesch, U., Budde, M. , Fischbach, M., Freisinger, B., Sch¨ afer, J.H., Uhlenbusch, J., Vi¨ ol, W.: Laser Optoelektronik 24 (1992) 68. H¨ ugel, H.: Strahlwerkzeug Laser, Stuttgart: Teubner, 1992.
93Fus 93Luo
Fuss, W., Loosen, P., M¨ arten, O., Schmid, W.E.: Proc. SPIE 1810 (1993) 79. Luo, X., Sch¨ afer, J.H., Uhlenbusch, J.: Opt. Commun. 102 (1993) 65.
94Kle
Klein, J., Otto, G., Habich, U., Loosen, P.: EuroLaser 2 (1994) 48.
96Shi
Shimizu, K., Taniwaki, M., Sato, S.: Opt. Lett. 21 (1996) 125. Landolt-B¨ ornstein New Series VIII/1B1
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96Vio 96Wit
Vi¨ ol, W., Uhlenbusch, J.: J. Phys. D 29 (1996) 57. Witteman, W.J., Ochkin, V.N.: Gas lasers – recent developments and future prospects, Netherlands: Kluwer Academic Publishers, 1996.
97Poe
P¨ ohler, M., Osterburg, L.: Laser-Praxis, 1997, LS8.
00Wie
Wieneke, S., Born, S., Vi¨ ol, W.: J. Phys. D: Appl. Phys. 33 (2000) 1282.
04Wie
Wieneke, S., Uhrlandt, C., Vi¨ ol, W.: Laser Phys. Lett. 1 (2004) 241.
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3.3 Femtosecond excimer lasers and their applications ´ri, G. Marowsky, P. Simon S. Szatma
3.3.1 Introduction In the short-wavelength region the well-known capability of lasers for effective temporal and spatial concentration of energy is more pronounced. This is the main reason why intensities up to 1020 W cm−2 are reached by table-top short-pulse, short-wavelength excimer laser systems. On the other hand, excimer lasers are known to have relatively moderate energy storage capabilities, imposing severe limitations on the amplification of short pulses. For these reasons special techniques are needed to have access to the whole stored energy of such amplifiers, which is a basic condition to utilize the potential advantages of short-wavelength lasers. The scope of the next sections covers the comparison of high-power lasers of different wavelengths (Sect. 3.3.1.3), introducing the advantageous features of short-wavelength (Sect. 3.3.1.1) and dual-wavelength lasers (Sect. 3.3.1.2), the comparison of the different seed pulse generation schemes, with special emphasis on those based on pulsed dye lasers (Sect. 3.3.1.4), the discussion of the amplification of short pulses in different excimers (Sect. 3.3.2), and the identification of those factors which limit the performance of short-pulse excimer laser systems at present (Sect. 3.3.3). The following subsections are devoted to answer the points listed in Sect. 3.3.3 for the case of KrF by introducing several new methods (spatially evolving chirped-pulse amplification (Sect. 3.3.3.1), off-axis amplification (Sect. 3.3.3.2.2 to Sect. 3.3.3.2.4), interferometric multiplexing (Sect. 3.3.3.3.3), active spatial filtering (Sect. 3.3.3.4.3), spectral filtering (Sect. 3.3.3.4.4), and different beam homogenization methods (Sect. 3.3.3.4.6) which are regarded – or already proven – to be straightforward in increasing the maximum brightness of laboratory-scale short-pulse excimer systems. In Sect. 3.3.3.4 considerations for the avoidance of phase and pulse front distortions for large-aperture beams and focusing experiments are reported. Some historical developments of short-pulse amplification in excimers are also traced, highlighting those advances which resulted in the most significant increase in brightness while keeping the complexity of the system moderate. Section 3.3.4 is devoted to applications. Two major fields of applications are reviewed: application of short laser pulses for plasma generation (Sect. 3.3.4.1), and micromachining of materials by short UV pulses (Sect. 3.3.4.2).
3.3.1.1 Advantages and difficulties associated with short-wavelength lasers Lasers are known as light sources where the energy carried in the beam can efficiently be concentrated both spatially and temporally. In this respect short-pulse UltraViolet (UV) excimer lasers, whose wavelengths extend into the deep ultraviolet, have a unique potential. Considering that for a fixed normalized bandwidth Δλ/λ (= Δ ν/ν) the temporal compression of a pulse is theoretically proportional to the frequency ν and that the spatial concentration scales with the square of the frequency, the maximum intensity I that can be achieved by a light pulse of a certain energy E Landolt-B¨ ornstein New Series VIII/1B1
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scales with the third power of the frequency, as I ∼ E ν3 .
(3.3.1)
On the other hand this scaling is only true as long as the pulse has the maximum quality allowed by the uncertainty principle and diffraction: The pulse is transform- and diffraction-limited. This implies that the theoretically third-order increase of the achievable intensity is only possible if the spatial and temporal quality of the pulse is kept at the physical limits. Such a high-quality pulse is easily available in the long-wavelength (InfraRed, IR) region, based on standard laser technology. However to reach these limits becomes more and more difficult as the wavelength becomes shorter. The basic reason for that lies in the well-known frequency scaling of the Einstein A and B coefficients, as A ∼ B ν3 .
(3.3.2)
It means that the probability for an inverted material to radiate spontaneously instead of amplifying through stimulated emission (lasing) increases with the third power of the frequency. This also means a drastic decrease of the lifetime of spontaneous emission (typically down to nanoseconds for ultraviolet excimers). Therefore, the gradual evolution of the temporal, spatial and spectral quality of the pulse through the many roundtrips in the laser cavity is not possible for the presently available UV-lasing materials. The only way to convert the optical energy of an UV-emitting material into a short-wavelength electromagnetic field of the highest possible spatial and temporal quality is optical amplification. Even this can only be realized with stringent limitations (see Sect. 3.3.3). These are the reasons why short-wavelength, short-pulse, high beam-quality laser systems are generally dual-wavelength systems. In these systems the high-quality pulses are generated in the long-wavelength region and then generally shifted into the short-wavelength region through frequency upconversion. UV gain modules are used as optical amplifiers for the amplification of the frequency-converted pulses. In most of the applications the high photon energy is of great advantage; a given energy gap can be overcome easier and with less photons. The good temporal and spatial concentration promotes the study of high-intensity laser–matter interactions. In micromachining the short wavelength enhances the spatial resolution. Temporal concentration allows reaching the same processing result with less energy which – together with the increased absorption in the UV – results in sharp and well-defined contours.
3.3.1.2 General features of dual-wavelength laser systems The schematic of a dual-wavelength laser system is shown in Fig. 3.3.1. At first glance such a system has a disadvantage connected to its complexity. On the other hand, complexity also means more free parameters which can be adjusted independently for optimum operation. The advantages are as follows: 1. The first wavelength can be chosen in a region where the techniques for short-pulse generation are well-developed and the necessary lasing materials are available. 2. The second wavelength can be matched to those excimer frequencies where efficient short-pulse amplification can be performed. Long−wavelength oscillator preamplifier
Frequency converter
Short−wavelength amplifier
Fig. 3.3.1. Schematics of a dual-wavelength laser. Landolt-B¨ ornstein New Series VIII/1B1
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3. In dual-wavelength systems a significant part of the needed amplification can be realized at longer wavelengths, where the effect of spontaneous emission is less dominant, and 4. the Amplified-Spontaneous-Emission (ASE) appearing in the form of a low-intensity temporal noise can effectively be filtered by the frequency converter through its nonlinear response. 5. Using a newly developed technique the nonlinear response of the frequency converter can also be used for efficient improvement of the directional properties of the beam (Sect. 3.3.3.4.3), and 6. for efficient control of the spectral properties of the signal pulse (Sect. 3.3.3.4.4). As a result, after frequency conversion diffraction- and transform-limited pulses of μJ to mJ energy can be produced. After moderate amplification the diffraction- and transform-limited behavior of the pulses can be preserved, and the noise can be kept on a very low level. These features are essential for utilizing the great potential of pulses of short wavelength for efficient spatial and temporal concentration of the energy. At certain wavelengths direct generation of pulses in the UV is possible by excimers with high efficiency [79Rho]. The bandwidth of the gain curve of excimers allows the amplification of subpicosecond pulses [87Doe, 91McI, 92Sza]. Among the various excimers XeF, XeCl, KrF and ArF are the most often used and are the main candidates for short pulse amplifiers, having their wavelengths at 351, 308, 248 and 193 nm, respectively. (In spite of the great success of short-pulse amplification using the XeF (C → A) transition [92Hof2], in the present study this excimer transition is disregarded because of the longer (visible) wavelength. Also F2 has been left out because of its very low efficiency and the technical difficulties associated with the short (λ = 157 nm) wavelength [93Mom2].)
3.3.1.3 Comparison of high-power solid-state and excimer lasers In view of the recent advances in femtosecond solid-state technology, solid-state-based high-power laser systems have become an important work-horse in high-intensity experiments [93Rou, 95Zho, 96Bar, 97Ant, 97Stu, 98Yam]. Alternatively excimer-based short-pulse laser systems can also be used as a driver for such experiments [86Glo2, 86Sch, 87Sza5, 88Bar, 88Rob, 88Sza3, 88Wat, 89End, 89Luk, 89Sza2, 90Ros, 90Tay2, 92Alm, 92Miz, 93Bou, 93Mos1, 93Sha]. Due to their different wavelengths a different regime of laser–matter interactions can be investigated, therefore these laser systems can be regarded as complementary sources. For the comparison of solid-state and excimer-based laser systems, the most important features are summarized in Table 3.3.1. It is known that the saturation energy density of solid-state materials is in the J cm−2 range, while for excimers it is ∼1000 times smaller, lying in the mJ cm−2 regime [77Tom, 80Ban, 82Buc, 82Cor, 84Sza, 86Glo1, 87Sza4, 88Mil2, 88Tay1, 88Zha2, 90Tay1, 93Mom1, 93Mos2]. This is roughly proportional to the maximum extractable energy from a given crosssection; that is why solid-state lasers can be much more efficiently used for high-energy application. The host material is solid-state and noble gas for solid-state and excimer lasers, respectively. The noble gas host material with its low density and low nonlinearity results in ease of propagation of the beam in excimer amplifiers, without the danger of self-focusing, phase front distortion and self-phase modulation. Due to the different intensity levels for the appearance of nonlinearities in excimers and solid-state systems and due to the very different values of their saturation energy density, direct amplification of subpicosecond pulses is only possible in excimers. In solid-state systems, saturated amplification of subpicosecond pulses corresponds to an intensity level at which nonlinearities prevent any operation. The so-called Chirped-Pulse Amplification (CPA) [85Str, 88Mai] scheme is devoted to overcome this problem, where the intensity of the pulse is lowered in the amplifier by temporal stretching and compression of the pulse duration before and after the amplification, respectively. The maximum peak power of short-pulse solid-state systems is two
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Table 3.3.1. Comparison of solid-state and excimer-based laser systems.
Saturation energy density Wavelength Min. pulse duration Max. energy Host material Nonlinearities Short-pulse amplification Max. peak power Energy contrast Focusability Max. focused intensity Storage time
Solid state
Excimer
∼ J cm−2 800–1064 nm ∼ 20 fs high solid state yes complicated ∼ 100 TW 10−4 moderate 1020 W/cm2 ∼ μs
∼ mJ cm−2 193–308 nm ∼ 100 fs low noble gas no simple ∼ several TW 10−7 good 1019 W/cm2 ∼ ns
orders of magnitude higher than that of short-pulse excimer systems [97Stu, 98Yam, 88Wat, 89End, 94Ros, 97Ome] (Table 3.3.1). On the other hand, because of the incomplete compression of the temporally stretched pulses in the CPA scheme, a significant background level – carrying generally more than 10−4 times the signal energy – is obtained [90Per, 91Yam]. Due to the direct amplification of short pulses in excimers, the main limitation for the contrast is the Amplified-SpontaneousEmission (ASE) level [90Kue, 90Sha, 90Sza2], which – by proper choice of the operational conditions of the amplifier (see later) – can be reduced in the far-field below 10−7 times the energy of the main pulse [92Alm]. This represents an intensity contrast of 1010 –1011 . Such clean pulses have great advantages over pulses of limited contrast in many plasma-physics experiments [88Mur, 90Nam, 92Teu]. The minimum focal spot area is > 10 times smaller for excimer systems, provided by the significantly (3–4 times) shorter wavelength and by the less nonlinearity and/or optical distortion of the gaseous active medium [88Rob, 89Luk, 90Ros, 90Tay2, 92Alm, 93Sha]. That is why the focusability of excimer-based systems is good as can be seen in Table 3.3.1, resulting in more than one order of magnitude increase of the brightness and of the focusable intensity for the same peak power. As a result of this fact the focusable intensity of short-pulse excimer systems approaches that of solid-state systems [97Ant, 97Stu, 89Luk, 96Sza]. The comparison is not complete without the different energy storage capabilities of both active media. The storage time for solid-state materials is in the μs regime, allowing complete extraction of the stored energy by a single short pulse. This implies that the values for the maximum peak power, brightness and focused intensity of solid-state lasers listed in Table 3.3.1 correspond to almost complete energy extraction. On the other hand in excimer amplifiers, due to the short (ns) storage time of the active medium [79Rho], only a small fraction (< 1/10) of the overall stored energy is available for a single short pulse [91McI, 92Sza]. Since no practical way has been found up to now for successive replenishment of the gain in excimers by optical multiplexing of subpicosecond pulses, the data listed in Table 3.3.1 for excimers were obtained mainly in single beam amplification experiments using not more than 10 % of the available energy. If a generally applicable interferometric beam recombination method was found for optical multiplexing, it might solve the inherent energy extraction problem of excimers caused by their short storage time and low saturation energy density. This would be of an importance comparable to that of the Chirped-Pulse Amplification (CPA) scheme used in short-pulse solid-state systems, and could make the excimer-based short-pulse laser systems competitive with solid-state systems even in maximum peak power. In this case, the brightness of excimer systems is expected to be significantly higher than that of long-wavelength systems, which – combined with the expected future improvement of the performance of short-wavelength focusing optics – can lead to the highest focused intensities (in excess of 1020 W cm−2 ) achievable by table-top laser systems. The Landolt-B¨ ornstein New Series VIII/1B1
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availability of such a laser system to many laboratories would open a new strong-electric-field regime of study for matter–field interaction.
3.3.1.4 Seed pulse generation 3.3.1.4.1 General features of hybrid dye/excimer lasers As shown in Sect. 3.3.1.1 the pulse-shortening methods used for solid-state and dye lasers are hardly applicable to excimers. Therefore, excimers are mainly used for amplification of frequencyconverted short pulses which are generated by means of dye, or more recently also solid-state lasers. Since the saturation energy of excimers is very similar to that of dyes (several mJ cm−2 ) the principles of construction for the dye and excimer amplifier chains are similar. With such a hybrid dye/excimer laser one has a chance to get short ultraviolet pulses with parameters comparable to those generated by dye lasers in the visible. Since excimer amplifiers can easily be scaled up to high energies, this arrangement is not only a simple extension of the dye laser tuning range to a shorter wavelength, but is also an effective way for the generation of high-power pulses in the TW range. If the short pulses are generated in a classical way – by the use of cw mode-locked or Colliding Pulse Mode-locked (CPM) dye lasers – the whole arrangement is quite complex, where synchronous operation of numerous lasers is needed [82Cor, 86Glo1, 86Glo2, 86Sch, 88Bar, 88Mil2, 88Rob, 88Tay1, 88Wat, 89End, 89Luk, 90Ros, 90Tay2, 90Tay1, 92Miz, 93Bou, 93Mos2, 93Mos1, 93Sha]. Due to the limited wavelength range of cw lasers, complicated frequency conversion schemes are necessary to reach certain excimer wavelengths [82Cor, 86Glo1, 86Sch, 88Bar, 88Mil2, 88Rob, 88Tay1, 88Wat, 89End, 89Luk, 90Ros, 90Tay2, 90Tay1, 92Hof1, 92Miz, 93Bou, 93Mom1, 93Mos2, 93Mos1, 93Sha]. These problems do not arise and the arrangement can be significantly simplified when an excimer laser-pumped pulsed dye laser can be used for short-pulse generation. In such an arrangement the same excimer laser is used for the pumping and for the amplification, providing automatic synchronization between the amplifier and the pulse to be amplified. In this case the only question is how the necessary subpicosecond pulse duration can be obtained starting with a 10-ns long pump pulse. In the case of cw mode-locked dye or solid-state lasers, significant pulse shortening is achieved as a result of the stepwise evolution of the pulse shape during many round trips. For a pulsed laser, stable pulse shortening in the range of 104 –105 must be achieved within a single shot. In order to fulfill this stringent requirement, a special dye laser system has been developed. This laser system has gradually evolved in the last years. The latest, most advanced version is shown in Fig. 3.3.2 [88Sza3, 89Sza3, 89Sza2]. This arrangement uses an excimer-pumped cascade pulsed dye laser [63Fra, 80Wya, 84Chr, 87Sza1, 88Sza2, 89Sza1] which generates subpicosecond pulses tunable over the whole visible spectrum, which are amplified up to typically 150 μJ. When the wavelength of the dye laser is set to be twice the wavelength of the excimer amplifier, the frequency-doubled pulses can be used as seed pulses for amplification in the excimer amplifier. Frequency doubling is performed just before the excimer amplifier. The ultraviolet seed pulses have an energy in the order of 15 μJ. These pulses are then amplified in the amplifier channel of the twin-tube excimer laser filled with the appropriate gas mix.
3.3.1.4.2 Hybrid solid-state/excimer lasers Short-pulse solid-state laser systems presently reach significantly higher peak powers than excimer systems. In spite of this fact there is an increasing number of applications where the output pulses of such high-power solid-state lasers – after frequency conversion – serve as seed pulses that are further amplified in excimer amplifiers. The main motivations of doing this are to have higher photon energies and better directional properties of the output beam. Recent developments of the Landolt-B¨ ornstein New Series VIII/1B1
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248 nm < 0.5 ps ~15 μJ EMG 150 excimer laser 248 nm 0.5 ps 15-30 mJ SHG 497 nm 0.5 ps ~150 μJ
308 nm 15 ns 60 mJ
QCDL 340 nm ~200 ps
Bethune − cell
SCDL 365 nm ~15 ps
SA
GSA ~9 ps
DFDL 497 nm 0.5 ps
Fig. 3.3.2. Experimental arrangement using pulsed dye lasers for short-pulse generation.
Ti:sapphire technology made these schemes even more attractive since now the 248 nm wavelength of the most efficient excimer KrF (see Sect. 3.3.2) can be reached through frequency tripling. Another advantage of these systems over hybrid dye/excimer lasers is that using the CPA technique very high energies can be reached already at the fundamental wavelength, which – even combined with the less efficient frequency tripling – ensures higher seed pulse energies than that of dye lasers followed by frequency doublers. Using solid-state based schemes, seed energies typically on the mJ-level are reached, where moderate amplification (G0 ≈ 102 –103 ) results in output pulses of ∼ 100 mJ energy with a very low level of ASE background. A practical advantage of this approach is that a laboratory which already has a high-power solid-state laser system can convert it into a high-brightness UV laser system with minor investment (with the addition of a frequency converter and excimer amplifier). This makes it possible to have both systems simultaneously, allowing much more applications with two different (complementary) pump wavelengths.
3.3.2 Short-pulse amplification properties of excimers Starting with input pulse energies of several μJ, by double-pass amplification, the pulse energy can be boosted up typically to 1, 5, and 10 mJ using XeF [88Zha2], XeCl [87Sza2], and KrF [88Sza3] gas fills, respectively. The output pulses exhibit an inherent chirp in all cases. This is the least pronounced for XeF, having practically the same 560-fs pulse duration for the direct output and for the compressed pulse [88Zha2]. In XeCl, pulse compression results in a more significant decrease of the pulse duration down to between 220 fs [87Sza2] and 170 fs [88Zha1]. The pulse shortening is especially pronounced at 248 nm, where the typical compressed pulse duration is below 100 fs [87Sza5, 88Sza3]. The shortest pulse duration obtained at 248 nm is 45 fs [89Sza3]. Because of the lack of a suitable frequency-doubling crystal, the 193 nm wavelength of ArF could only be reached by a more complicated frequency conversion scheme [89Sza4]. In a double-pass Landolt-B¨ ornstein New Series VIII/1B1
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1 78 %
0
t = 85 ps
Logarithm of the gain ln g [arb.units]
-1
a
-2
0
100
5 65 % 4 t = 53 ps 3 2 1 b 0 0 100
5 4 3 2 1 0
200
200
300
400
300
25 % t = 57 ps
0
c
100
200 Time t [ps]
300
Fig. 3.3.3. Recovery of the gain in (a) XeF, (b) XeCl, and (c) KrF followed over 300 ps.
amplification scheme – similar to the former experiments – 0.5 mJ pulses are typically obtained, with a compressed pulse duration of ∼ 300 fs [89Sza4, 90Sza4]. It is seen from these results that – with the exception of ArF – a theoretical minimum pulse duration, limited by gain bandwidth, has been reached for all the excimers. The different performance of the various excimers is characterized by the different values of the output energy from a given cross section and by the different pulse durations. A quantitative comparison of the excimers as short-pulse amplifiers can only be obtained by the measurement of their gain dynamics. The gain dynamics measurements were performed for XeF [88Zha2], XeCl [82Cor, 87Sza4] and KrF [84Sza, 87Sza4, 88Tay1] using the well-known pump-and-probe technique. Figures 3.3.3a– c show the results of the gain dynamics measurements for XeF, XeCl, and KrF indicating a t ≈ 50–90 ps gain recovery with 78 %, 65 %, and 25 % relative amplitude, respectively (taken from [87Sza4, 88Zha2]). This recovery is attributed to the rotational relaxation of the B-state and the C → B-state relaxation, with significant contribution of the relaxation of the ground state in case of XeF and XeCl [87Sza4, 88Zha2]. It is found that in XeF only 22 %, in XeCl 38 %, while in KrF 75 % of the stored energy is extractable for pulses shorter than ∼ 5 ps. This corresponds to the different measured values of the saturation energy density of εsat = 0.2 mJ cm−2 [88Zha2], 0.85 mJ cm−2 [87Sza4, 90Tay1] and 2 mJ cm−2 [82Buc, 84Sza, 87Sza4, 88Tay1], respectively. A qualitative gain recovery measurement has been performed for ArF [93Mom1], giving information mainly on the long-term recovery. The “effective” saturation energy density of ArF is determined to be 1.9 mJ cm−2 [93Mom1] and 2.3 mJ cm−2 [93Mos2], including the effect of windows. This corresponds to a saturation energy density of 3.6 mJ cm−2 , corrected for window transmissions [93Mos2], suggesting a performance similar to KrF as far as short-pulse amplification is concerned. The gain dynamics measurements were repeated with subpicosecond temporal resolution for XeCl and KrF [87Sza4] (Fig. 3.3.4). The gain curve obtained for XeCl revealed a damped sinusoidal oscillation, with a period of 1.28 ps and a damping time of ∼ 12 ps, superimposed on the slowly rising Landolt-B¨ ornstein New Series VIII/1B1
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3.3.2 Short-pulse amplification properties of excimers
5 4 75 % 3 25 % 2 1 0
2 1 0
1.28 ps
240 fs 0
a 4 3
[Ref. p. 248
5
10
75 % 25 %
Fig. 3.3.4. Logarithm of the gain in (a) XeCl and (b) KrF vs. delay between the saturating and the probe pulse, followed over 10 ps with pump and probe beams of parallel polarization.
260 fs 0
b
5 Time t [ps]
10
Table 3.3.2. Dependence of saturation energy density (εsat ) on the pulse duration (τp ) in the case of different excimers. Pulse duration τp
Bandwidth Δλ [˚ A]
Saturation energy density εsat [mJ cm−2 ]
< 16 < 16
≈ 2.5 ≈ 0.8 . . . 1.0
< 15 < 15
≈ 2.7 ≈ 2.0
XeCl 20 ps ≤ τp ≤ 1 ns 150 fs ≤ τp ≤ 5 ps KrF 200 ps ≤ τp 100 fs ≤ τp ≤ 5 ps
baseline (Fig. 3.3.4a). This is attributed to quantum beats observed for the first time in stimulated emission [87Sza4, 87Sza3]. In KrF only a short-term recovery is seen (Fig. 3.3.4b). When these measurements were repeated with pump-and-probe beams of parallel and orthogonal polarization, the difference of the gain in the first picosecond was revealed to be a molecular reorientation effect [87Sza4]. From these results a molecular reorientation time of T /4 = 1.1 ps and 0.7 ps is obtained for XeCl and KrF, respectively [87Sza4]. The detailed study of the gain dynamics of XeCl and KrF made it possible to estimate the dependence of their “effective” saturation energy density on the amplified pulse duration. The results are summarized in Table 3.3.2 [87Sza4]. These results are found to be consistent with theoretical considerations [89Kan] and other experimental results [77Tom, 80Ban, 82Buc, 82Cor, 84Sza, 86Glo1, 87Sza4, 88Mil2, 88Tay1, 88Zha2, 90Tay1], showing that KrF is expected to show similar performance both for the short signal-pulse and for the long ASE background. This has great importance in minimizing the ASE background in high-energy amplifier chains. From these results one can conclude that for physical reasons KrF is superior to XeF and XeCl, and mainly for practical reasons is still more advantageous than ArF as a short-pulse amplifier.
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3.3.3 Critical issues for a high-power excimer amplifier The development of large-aperture, high-power excimer amplifier chains showed that there are numerous specific problems to be considered when building and operating such a laser system. The most important ones are: – – – – –
nonlinear effects (absorption, self-focusing) in the windows; ASE content, nonsaturable absorption in the active medium (limitations on the cross section); limited energy storage time of the active medium; shape of the phase front (focusability); shape of the pulse front (spatially dependent temporal broadening across the beam).
In the following sections a detailed study of these problems and possible solutions will be given, considering primarily KrF as the active medium.
3.3.3.1 Nonlinear effects, attainment of minimum pulse duration (spatially evolving chirped-pulse amplification) The power density of the unfocused output beam of high-brightness KrF laser systems is in the range of 10 GW cm−2 . At these high power-densities, nonlinearities in air [91McI] and in the window materials become important [79Liu, 88Tay2]. The nonlinearities (self-focusing and self-phase modulation) in air can be minimized by minimizing the length of the light pass, or by the use of noble-gas filled tubes. The use of tubes is also desirable to eliminate phase front aberrations caused by air turbulence. The nonlinearities in the windows are more difficult to avoid. Our investigations showed that practically all UV transparent materials show increased absorption (2- and 3-photon absorption) for pulses at these intensities [89Sim]. The observed loss is found to be the combined effect of self-focusing, multi-photon absorption and color center formation [89Sim]. The relative importance of these mechanisms is different for different wavelengths, different materials and even for different samples [88Tay2, 89Kim, 89Sim, 89Tom, 90Gow, 90Hat, 90Sza1]. On the other hand, saturation of the amplifiers – and therefore a certain energy density at the output window – is needed in order to keep the extraction efficiency high. This means that in the case of excimer lasers it is also desirable to manipulate the pulse duration – similar to the well-known Chirped-Pulse Amplification (CPA) scheme applied for solid-state lasers [85Str, 88Mai] – but with a moderate (up to 10) stretching/compression factor. The conventional CPA scheme has been tested both for XeCl [91Gos] and KrF [94Hou2, 94Hou1, 94Ros, 96Div]. Because of the technical difficulties associated with the compression of the high-power ultraviolet amplified pulse in the conventional CPA scheme, a special amplification scheme has been developed where the chirp and the pulse duration develop in space [90Sza3], called the Spatially evolving Chirped-Pulse Amplification scheme (SCPA) [90Sza5]. The basic idea behind the SCPA is the spatial evolution of the pulse duration after a dispersive element. This can be seen in Fig. 3.3.5a, where a grating is inserted into a positively chirped beam. Due to the angular dispersion of the grating, the different spectral components (shown by solid and dotted lines) are separated in a direction perpendicular to the propagation. Since the pulse front is tilted, the above displacement of the spectral components leads to a spatial separation of the pulse fronts of the different spectral components also in a direction parallel to the propagation. This means a spatially evolving negative chirp. For the dispersion constant of the single dispersive element, one gets the same expression as is obtained for pulse compressors. This means that by the use of a single dispersive element in a properly chosen position, one can tilt the pulse front and simultaneously compress the pulse duration of a positively chirped input pulse. This behavior can be useful in Traveling-Wave Excitation (TWE)
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a G
A
OS
B
1 Beam stop
a b
Fig. 3.3.5. (a) Schematic of the pulse fronts of different spectral components after diffraction on a grating. (b) Schematic arrangement to realize spatially evolving chirped-pulse amplification.
experiments but it can be shown by simple geometrical considerations that in the plane of optimum pulse compression – which is always parallel to the grating – the maximum pulse front tilt introduced by a single grating is limited: not enough for TWE [90Sza3]. There are several newly developed methods existing to increase the pulse front tilt. The most straight-forward method is the use of optical imaging, as shown in Fig. 3.3.5b. The positively chirped incoming beam – after diffraction by the grating G – is optimally compressed in the plane A, which is then imaged by an optical image system OS to the plane B. Since optical imaging leaves the absolute value of the delay between the two marginal rays unchanged, the increase of the tangent of the pulse front tilt is proportional to the demagnification. Assuming a perfect image system in the position of OS – which has to have the same path length between any pair of object and image points for any rays and any spectral components – the same compressed pulse duration is seen in the plane B as in plane A, while the pulse duration in between these two planes (seen also by OS) is longer. If an amplifier system is inserted between plane A and OS (see Fig. 3.3.5b), it will then see long pulse duration and therefore moderate intensities. Moreover, a single lens following the amplifier can generate the ultimate shortest pulse duration at the target plane. The spatial evolution of the chirp and the pulse duration makes it possible to simulate the conventional CPA schemes, however in a much simpler manner: without the use of pulse stretchers and compressors, and only using the previously described spatial evolution of the pulse duration. By the use of the SCPA scheme, it is achieved that the amplifier is working at moderate intensities, while the minimum compressed pulse duration with a variable pulse front tilt can be created at the target plane, using only a single focusing element following the amplifier. This can have great importance in large-scale TWE experiments such as X-ray laser experiments. Another interesting feature of this SCPA arrangement is that the different spectral components are spatially separated in the amplifier in a similar manner as in the amplification schemes suggested in [92Chr, 92Din]. This allows one to amplify pulses of broader bandwidth than in the conventional schemes [92Chr], resulting in even shorter compressed pulse widths than ever achieved by excimer amplifiers.
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3.3.3.2 Amplification in media having nonsaturable absorption 3.3.3.2.1 ASE content, nonsaturable absorption, limitations on the cross-section It has already been shown by gain dynamics measurements why KrF is the best candidate as an efficient amplifying medium. In that case, extraction efficiency was defined as the ratio of the extractable energy for short (τ < 5 ps) and long (τ > 100 ps) pulses, with regard to the experimentally observed ∼ 50 ps long recovery of the gain [87Sza4, 88Zha2]. In practical cases, however, one has to consider more effects, which significantly influence the efficiency, such as ASE, nonsaturable absorption, and limited storage time of the amplifying medium. In case of a short-wavelength laser system with a short energy storage time [79Rho] ASE is often a limiting factor [90Kue, 90Sha, 90Sza2]. Since at the excimer wavelengths no effective saturable absorbers are available [89Nis], spatial filtering is the only way to avoid gain depletion, however, leaving the ASE content in the direction of the signal unchanged. This ASE content can only be reduced by proper choice of the operational conditions of the amplifier, generally at the expense of efficiency [90Kue, 90Sha, 90Sza2, 92Alm]. Unfortunately, discharge-pumped KrF amplifiers are only efficient when the electric excitation is fast, necessitating a small discharge loop [78Gre, 78Sze]. This limits the cross-section of the discharge and prefers elongated, pencil-like pumped geometries. This geometry is not suitable for short-pulse amplifiers having significant nonsaturable absorption [63Fra, 87Til, 92Sza]. This problem will be examined in a specific example: in the case of KrF, having g0 /α = 10 [82Gow, 87Jar] (where g0 is a small-signal gain, α is the absorption coefficient). Figure 3.3.6a shows the local extraction efficiency defined as η(ε) =
1 dε , g0 dz
(3.3.3)
and the contrast coefficient defined as c = geff /(g0 − α) ,
(3.3.4)
geff = lim (1/ΔL) ln(Eout /Ein ) ,
(3.3.5)
ΔL→0
where L is the length of the amplifier, as a function of the normalized energy density ε∗ = ε/εsat for KrF [92Alm]. Since in many applications the contrast is of comparable importance to the extraction 1.0
Local extraction efficiency η Gain contrast coefficient c
η
g0 /α = 10
0.6
0.2 Efficiency
0.4
c
S Contrast
0.1
0.2
0 0
4 2 6 8 X Y 2 Normalized energy density ε [mJ/cm ]
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Stabilization coefficient S
0.3
Stability
0.8
Fig. 3.3.6. Local extraction efficiency η (dashed line), gain contrast coefficient c (solid line), and stabilization coefficient s (dotted line) as function of the normalized energy density in a KrF amplifier. The optimum operation with regard to both efficiency and contrast for a preamplifier and a final amplifier is marked by X and Y , respectively. (For the definition of s see Sect. 3.3.3.4.6.)
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3.3.3 Critical issues for a high-power excimer amplifier
[Ref. p. 248
efficiency, the operation of KrF amplifiers generally must be optimized for both efficiency and contrast. It is seen from these curves that both requirements can never be fulfilled at the same time, one can only have a trade-off when operating the amplifier close to the saturation energy density. This optimized operation can be best attained by an amplifier for which the overall increase of the local energy density is limited, corresponding to a limited gain–length product gL, due to the steep slopes of the curves around the optimum value. It is also seen that for a given amplifier length, the input and output energy densities are determined if “optimized” operation is required. Since in preamplifiers both the optimum extraction efficiency and high gain contrast are of the same importance, the optimum operational condition for such an amplifier is obtained at an energy density, where the product of the efficiency and the gain contrast coefficient ηc is maximal. This condition is marked by X in Fig. 3.3.6, where the energy density is εx ≈ 1.1 εsat . In power amplifiers extraction efficiency plays a more important role than gain contrast. Here we set the optimum where η 10 c is maximal. This weighting factor results in an operational condition, which coincides with the experimentally determined optimum. This condition is fulfilled at an energy density of εy ≈ 2.2 εsat (marked by Y in Fig. 3.3.6). If optimized operation is required, the momentary stored energy of the amplifier given by Estored = εsat Ag0 L
(3.3.6)
should be comparable to the optimum value of the extractable energy (Eout = 2.2 εsat A). If we set this ratio to Eout /Estored = 1 ,
(3.3.7)
an upper limit of gL = 2.2 is obtained, for the maximum gain–length product of an “efficiently used” discharge-pumped KrF power amplifier (for details see Sect. 3.3.3.2.3). This corresponds to L = 10 cm, for a typical case, when g0 = 0.2 cm−1 [87Sza4]. It is seen that from the optical point of view a “short” amplifier is ideal; on the other hand, the cross-section is limited by the fast pump circuit. These requirements would certainly limit the active volume and therefore the maximum stored energy, unless a transformation is found which properly converts the “geometrical” cross section and length of the amplifier into a new cross section and length, which are seen by the pulse to be amplified.
3.3.3.2.2 Off-axis amplification Figure 3.3.7 shows a simple solution where the effective cross-section of the pencil-like dischargepumped excimer amplifier is increased by tilting the input beam with respect to the geometrical axis of the amplifier [91Sza, 92Alm]. This off-axis arrangement is also capable of solving the inherent inhomogeneity problem of these amplifiers, caused by the inhomogeneous transversal distribution of the deposited energy in the discharge. In the off-axis mode, it is the more homogeneous longitudinal distribution, which mainly determines the intensity homogeneity of the output beam. Therefore, a more homogeneous, nearly flat-topped intensity distribution can be obtained after amplification. The most important characterization of an “ordinary” amplifier can be given by its input– output characteristics, which determines the contrast, the efficiency, and the gain. In an off-axis
Amplifying medium β
x
On−axis
z
z’
x’
Off −a
xis Fig. 3.3.7. The off-axis amplification geometry. Landolt-B¨ ornstein New Series VIII/1B1
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Fig. 3.3.8. (a) Output energy, (b) energy extraction efficiency, (c) gain contrast vs. off-axis angle and input energy. The curves connect the points of the surfaces with equal elevation given by the labels.
amplifier the off-axis angle is a new independent variable. Then the run of the two independent variables (the input energy and the applied off-axis angle) produce a surface which gives the output energy. The output energy, global efficiency and contrast are shown in Figs. 3.3.8a–c for an amplifier of d = 2.7 cm gap separation, where the length and width of the discharge are L = 86 cm and w = 0.85 cm, respectively, and g0 = 0.1 cm−1 . In Fig. 3.3.8a it is seen that a certain output energy can be reached with a wide variety of off-axis angle–input energy pairs. The minimum of a certain contour line gives the so-called optimum off-axis angle from the point of view of energy extraction efficiency, where the most energy can be extracted with minimum input energy. With more input energy available, the same output energy can be reached at two different angles. Smaller off-axis angles belong to higher input energy densities due to the smaller free off-axis aperture. If the experimental geometry makes it possible it is better to use an arrangement with larger off-axis angle. This relaxes the nonlinear effects in the window material [88Tay2, 89Sim] and improves the contrast. The efficiency curves in Fig. 3.3.8b are basically similar to that of Fig. 3.3.8a. The contrast shown in Fig. 3.3.8c is a monotonic function of both α and Ein . The larger the off-axis angle or the smaller the input energy the better the contrast. The on-axis and off-axis schemes can be best compared by comparing the performance of an on-axis amplifier, and an optimally chosen off-axis pre- and power-amplifier. For this comparison the data of a commercially available EMG 150 amplifier were taken: L = 45 cm, w = 0.6 cm,
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Efficiency h
0.7
0
a
0
Input energy Ein [mJ ]
10
Gain contrast c
0.7
× 10 0
b
0
Input energy Ein [mJ ]
10
Fig. 3.3.9. Efficiency (a) and gain contrast defined as g/g0 (b) of the EMG 150 amplifier as function of input energy, when used in the on-axis (solid line) and optimally chosen off-axis preamplifier (dotted line) and power amplifier (dashed line) mode.
g0 = 0.19 cm−1 . In Fig. 3.3.9 the overall efficiency (Fig. 3.3.9a) and the gain contrast (Fig. 3.3.9b) is plotted as a function of the input energy for this amplifier, when operated in the on-axis mode (solid line), the optimally chosen off-axis preamplifier (dotted line), and final amplifier mode (dashed line). The last two operational conditions correspond to those marked by X and Y in Fig. 3.3.6, respectively. It is seen from Fig. 3.3.9a that the on-axis and the off-axis power amplifier mode have comparable efficiency, while the off-axis preamplifier shows a somewhat lower efficiency. In the on-axis mode the maximum efficiency is obtained at low input energies (Ein ≈ 2 mJ), while in off-axis amplifiers the efficiency curve is monotonically increasing in the studied input energy range (Ein ≤ 10 mJ). An enormous change in performance of the on-axis and off-axis amplifiers is seen in the gain contrast curves (Fig. 3.3.9b). The contrast drops below a few percent in the on-axis mode for input energies in the mJ range. However, in the case of off-axis preamplifiers it is around 60–70 % for similar input energies. Even in the case of off-axis power amplifiers – which are optimized mainly for efficiency – the contrast is in the range of 20–40 %, when amplification of input pulses in the mJ range is needed. It is worth noting that the theoretically predicted high extraction efficiency of the on-axis scheme (solid line in Fig. 3.3.9a) is difficult to reach experimentally for two reasons. One is that in this case the output energy density is relatively high (three to five times εsat ) which corresponds to high intensities for subpicosecond pulses (several GW cm−2 ), where nonlinear effects in window materials are important [79Liu, 88Tay2, 89Sim, 89Tom, 90Hat]. The second is related to the low gain contrast of this scheme, shown by the solid line in Fig. 3.3.9b. This low gain contrast means an extremely high value of the small-signal gain, which often leads to gain depletion by ASE [90Sha, 90Sza2]. This decreases the stored energy of the amplifier and therefore the output energy. Our experiments show that without special measures against nonlinear effects and gain depletion, the off-axis preamplifier shows an efficiency comparable to the on-axis one. This makes the advantages of the off-axis amplification scheme – represented by the significantly better contrast and phase front of the beam – even more pronounced.
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3.3.3.2.3 Multiple-pass off-axis amplification schemes Another interesting feature of the off-axis amplification scheme is that it allows the optimization of the operational conditions not only for a single amplification pass, but also for multiple passes using the same amplifier [91Sza, 92Alm]. A practical example for a three-pass arrangement is shown in Fig. 3.3.10, where the increasing beam diameter is always optimally matched to the increased effective cross-section of the amplifier by proper choice of the divergence angle of the beam and the off-axis angles of the different passes. It can be achieved that each of the amplification passes is in the earlier defined optimized condition, which makes it possible to optimally extract the stored energy of the same amplifier in subsequent steps. The applicability of the off-axis amplification scheme for multiple-pass amplification in discharge-pumped gain modules of different discharge parameters has been analyzed by computer model calculations [95Alm]. It has been shown that in a wide range of the momentarily stored energy of the gain module, a three-pass off-axis amplification scheme is suitable for achieving the theoretically extractable energy with 10–20 μJ input energy, when the overall contrast is 5–10 %. It suggests high-contrast amplification of 10–20 μJ input energies up to 100 mJ output energy by the use of a single amplifier [95Alm]. From the result of these calculations it follows that an optimized multiple-pass short-pulse excimer amplifier should have the following features. During the first amplification the input has to be boosted up to the same magnitude as the momentarily stored energy. This is the necessary condition for possible optimization of the efficiency of the amplifier in the subsequent passes. The amplifier gain length should make it possible to do this in one amplification pass. The optimum energy density for the power amplification can be determined from the small-signal gain and the absorption coefficient. With a cylindrical expansion scheme one should avoid the loss of the useful aperture in the second and third passes. The final output aperture should be enough to keep the energy density at moderate values (about two times the saturation energy density) for the desired final output energy. In the final amplification pass the gain must be more than 2, in order to get a positive net gain with respect to optical losses. According to our theoretical considerations and experimental results, from an amplifier having similar geometrical discharge properties like commercial KrF lasers, one can expect an output energy similar to the momentarily stored energy with the overall contrast of 5–10 % in a three-pass arrangement [95Alm]. Output
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3.3.3.2.4 Requirements for the discharge geometries of off-axis amplifiers The off-axis amplification scheme relaxes the requirements for discharge-pumped gain modules. For practical reasons, discharge-pumped excimer amplifiers are preferable to e-beam-pumped amplifiers, when moderate output energies (up to several 100 mJ), high pulse-repetition rates and ease of operation are required [87Sza5, 88Wat, 89End, 89Luk, 89Sza2, 90Tay2, 92Miz, 93Bou]. In the conventional amplification schemes, the large cross-section necessary for high-energy shortpulse amplification was achieved by increasing both the gap separation d and the width w of the discharge of the discharge-pumped gain modules [82Wat, 91Miz, 91Nod, 91Rac], as also seen in the construction of the amplifiers used in [87Sza5, 88Wat, 89End, 89Luk, 90Tay2, 92Miz, 93Bou]. This, however, significantly increased the cross-section of the discharge loop, thus limiting the speed of electric excitation and leading to enhanced instabilities and inhomogeneities of the discharge. Hence, in most cases, complicated X-ray preionization was necessary for stable operation. With the off-axis amplification scheme, the size of the amplified beam can be significantly increased in one dimension. Therefore, large and square beam cross-sections can be obtained even with discharges of small w/d aspect ratios. In the following a rough estimation will be given for the w/d aspect ratio of discharges which already meet the requirements of the off-axis amplification. Assuming that in the off-axis amplification geometry the effective beam cross-section is increased to Aout = d2 , allowing an output beam of square cross section, and the amplifier is operated at an energy density optimized for power amplifiers εout ≈ 2.2 εsat [92Alm]. Then the output energy is expressed as Eout ≈ 2.2 εsat A = 2.2 εsat d2 .
(3.3.8)
On the other hand the momentarily stored energy Estored is given by Estored = εsat gLdw .
(3.3.9)
For the optical parameters of excimers and for the commonly used pencil-like discharge geometries, Amplified Spontaneous Emission (ASE) develops in the on-axis direction when gL ∼ 7. When this “limit” is reached the ASE stabilizes the gain–length product to this value, which then becomes practically insensitive to the pumping conditions. This, however limits the stored energy to Estored ≈ 7 εsat dw .
(3.3.10)
It is pointed out in Sect. 3.3.3.2.3 that the maximum energy Eout that can be obtained through multiple-pass amplification of a short pulse in an excimer amplifier is comparable to the stored energy Estored of that amplifier [95Alm]. From this comparison 1 w ≈ (3.3.11) d 3 is obtained. Most of the commercial discharge-pumped excimer lasers have discharges of this aspect ratio. It is known that such discharges are more stable, the discharge loop can be made relatively small even for large gap separations, allowing high-speed charging circuits with relatively low operational voltages. Under these circumstances, simple UV preionization is expected to be sufficient. Moreover, the charging circuit can be optimized for other parameters such as maximum momentarily stored energy, maximum efficiency, high stability, minimum temporal jitter of the gain etc. The development of such a discharge-pumped KrF gain module – tailored to the needs of the off-axis amplification – is described in [94Kov] with the preliminary amplification experiments.
3.3.3.3 Limited energy storage time (interferometric multiplexing) In excimer amplifiers – due to the short storage time of the active medium – successive replenishment of the momentarily stored energy is the only way to have access to the whole stored energy Landolt-B¨ ornstein New Series VIII/1B1
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[79Rho, 91McI, 92Sza], which is given roughly by Etot = Estored T /τ ,
(3.3.12)
where T is the gain window and τ is the recovery time of the gain. Since for KrF T /τ ≥ 10, significant increase of the extractable energy is expected by successive depletion of the gain [92Sza]. This can either be done by multiple-pass amplification of a single pulse [86Glo2, 86Sch, 87Sza5, 88Bar, 88Rob, 88Sza3, 88Wat, 89End, 89Sza2, 92Miz, 93Mos1] or by optical multiplexing [81Mur, 87Ros, 88Ray, 90Ros, 90Wat, 91Paw, 93Sha].
3.3.3.3.1 Limitations on multiple-pass amplification Multiple-pass amplification is technically simpler, however, in the conventional amplification scheme it does not allow the amplifier to operate under the optimum operational conditions for each pass. The optimum condition sets the energy density inside the amplifier to a given value with regard to extraction efficiency and a signal-to-background ratio (contrast). As shown in the former section, this restriction is especially acute for KrF excimer amplifiers [90Kue, 90Sha, 90Sza2] exhibiting significant nonsaturable absorption [82Gow, 87Jar, 87Til] and having no effective saturable absorbers available at that wavelength [89Nis]. (The saturable absorber suggested for 248 nm [89Nis] exhibits a moderate ratio of the primary to the excited absorption cross-section and can only be completely bleached at E > 30 mJ cm−2 , where severe nonlinearities are expected to occur using subpicosecond pulses [88Tay2, 89Sim].) It is shown [92Alm, 92Sza] that the local energy density range, where the operation of a short-pulse KrF amplifier can be regarded as optimal, is very narrow: It extends from 0.5 εsat to 3 εsat (see Fig. 3.3.6). This condition can only be fulfilled for an amplifier of low small-signal gain (G0 ≈ 10) and is certainly impossible to realize for a conventional multiple-pass arrangement, where the output of a given amplification pass is an input for the next pass [88Sza3, 88Wat, 89End, 92Miz] in the same amplifier. The off-axis amplification scheme [91Sza] solves part of the above mentioned problems for discharge-pumped excimer amplifiers [91Sza, 92Alm, 92Sza]: It decreases the small-signal gain seen by the signal pulse and allows optimum operational conditions for a limited number (n ≈ 3) of amplification passes by proper choice of the off-axis angle enclosed by the pencil-like amplifier and the beam [91Sza, 92Alm]. This makes it possible to optimally extract the stored energy of the same amplifier in limited subsequent steps. Since the ideal number of the successive amplification steps in KrF amplifiers is T /τ ≥ 10 [92Sza, 93Sza] the off-axis amplification scheme only relaxes but does not solve the problem of energy extraction for a single short-pulse.
3.3.3.3.2 Optical multiplexing In optical multiplexing, the beam to be amplified is split into partial beams, which are arranged in the multiplexer to form a pulse train with a separation comparable to the recovery time of the amplifier. After amplification the partial beams are recombined to form a single pulse again (demultiplexing) (Fig. 3.3.11a). The key point of any kind of multiplexing is how accurately the recombination of the partial beams can be performed. In the conventional multiplexing schemes, recombination is far from that of interferometric accuracy, which imposes severe limitations on the focusability of the final beam. Synchronism can generally be obtained only for longer than picosecond pulses [87Ros, 91Paw], or in some cases even no attempt has been made for beam recombination [92Miz, 90Wat, 81Mur]. The beam combination method based on Raman conversion [90Ros, 93Sha] lowers the requirements for the recombination accuracy, however, it is rather complex and shown to be best fitted for longer (≥ 10 ps) pulses.
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Multiplexer
Amplifier
[Ref. p. 248
Demultiplexer
a Output
Multiplexer Amplifier
Input Demultiplexer
b
Fig. 3.3.11. The principle of (a) conventional and (b) interferometric multiplexing.
3.3.3.3.3 Interferometric multiplexing For the reasons listed in the former section, a new multiplexing method is being developed which does not suffer from the earlier listed shortcomings of the conventional ones. This novel method is based on a common optical arrangement used both for multiplexing and for demultiplexing (Fig. 3.3.11b). In this way automatic (phase-locked) synchronization of the partial beams is achieved for any alignment of the multiplexer (demultiplexer), and any kind of distortion and/or misalignment is automatically compensated. With this scheme, optimum focusability is expected for the output, where the minimum focal spot size is already determined by the diffraction limit of the whole recombined beam [92Sza, 93Sza]. This significantly increases the brightness and therefore the maximum focusable intensity. Figures 3.3.12a and b show a possible realization for the case of two multiplexed beams, using a Sagnac-interferometer with polarization (Fig. 3.3.12a) or geometrical splitting (Fig. 3.3.12b). Each arrangement can be scaled up to multiple beams and for multiple-pass (off-axis) amplification geometries [93Sza]. Detailed considerations for the accuracy of the superposition of the beams and preliminary experiments for two and four multiplexed beams are presented in [93Sza]. Amplification of input pulses of ∼ 0.5 mJ energy up to 110 mJ is demonstrated in a four-beam multiplexing scheme, using a slightly modified commercial excimer gain module in a double-pass off-axis geometry [93Sza]. Output
Amplifier Input
Polarization− sensitive reflector
a Input Output
b
Fig. 3.3.12. Possible realization of interferometric multiplexing using (a) polarization or (b) geometrical splitting.
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3.3.3.4 Focusability of short-wavelength high-intensity lasers The importance of the shape of the phase and pulse front of high-power excimer beams can easily be understood if one imagines that the output of a 100 fs/TW excimer laser system is a 30 μm thick slice where the wavelength and the pulse length are only a small fraction of the beam cross-section. In this case even the smallest distortions can easily be comparable to the wavelength or to the pulse length. The distortion of the phase front can be solved in principle by the use of well-corrected optics; a condition which is generally difficult to fulfill in practice for large-aperture UV beams.
3.3.3.4.1 Pulse front distortion, spatially dependent temporal broadening It is shown in [88Bor, 88Sza1, 89Bor] that in the case of short-wavelength, femtosecond pulses and large-aperture beams, the shape of the phase front and the pulse front can be significantly different, where the difference can easily be comparable to or larger than the pulse duration. This deviation comes from the difference of phase and group velocities in optical materials, which introduces a delay ΔT between the phase and pulse fronts. ΔT is given as ΔT = −(λ/c) ΔL dn/dλ ,
(3.3.13)
where dn/dλ is the dispersion and ΔL is the length of the material traversed by the pulse [88Bor, 88Sza1, 89Bor]. At the same time, when a short pulse passes through a material, its duration is broadened. The broadening ΔT ∗ is given by ΔT ∗ = (Δλ/c) ΔL dng /dλ ,
(3.3.14)
where dng /dλ is the group velocity dispersion of the material. This implies that for refractive optical components having different thickness across the beam, the shape of the pulse front changes and the pulse duration becomes spatially modulated [88Sza1]. The pulse front delay for a single thin lens is given by ΔT =
λ h2 1 dn · · · , c 2 r dλ
(3.3.15)
where h is the distance of the ray from the optical axis and r is the radius of curvature of the lens [88Sza1, 89Bor, 88Bor, 88Ihl]. It is also shown in [88Sza1, 89Bor, 88Bor] that the spatially dependent pulse front delay can be avoided by the use of achromats, where 1 dni =0 ri dλ
(3.3.16)
is fulfilled. On the other hand, a lens system hardly can be compensated for pulse front distortion and broadening at the same time. This would require dng /dλ = const. dn/dλ
(3.3.17)
to be fulfilled for all materials used in the lens system [88Sza1]. This is true for many materials [85Bor] at wavelengths far from the absorption edge of those materials. However, when working close to the absorption edge (in the UV) the above condition is not valid anymore [84Sil]. It means that a lens system generally cannot be compensated for pulse front distortion and spatially modulated broadening at the same time [88Sza1]. This restricts one to use only reflective optics in high-power UV systems [92Alm, 92Sza]. A more accurate treatment of this problem is given in [92Fed, 92Bor1]. Landolt-B¨ ornstein New Series VIII/1B1
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3.3.3.4.2 Origin of phase-front distortions in dual-wavelength laser systems Short-pulse excimer laser systems are generally dual-wavelength lasers, where the generation and the final amplification of the pulse is done at two different wavelengths. For KrF lasers the short pulses are normally generated at twice [88Sza3, 96Sza] or three times [89Luk, 90Wat, 93Nab, 97Ome] the desired wavelength of 248 nm, which necessitates a frequency doubling or tripling stage before UV amplification. In such systems the main sources of eventual distortion of the phase front of the output beam are as follows: – phase distortion and intensity-modulation of the beam at the fundamental wavelength; – phase distortion and intensity-modulation accumulated during UV amplification.
3.3.3.4.3 Active spatial filtering It follows that diffraction-limited beam quality and a well-determined intensity distribution of the frequency-converted beam is very important. Considering that phase distortions and intensity modulations are maintained or even magnified in conventional frequency-conversion schemes, the requirements for the beam quality at the fundamental wavelength are even more pronounced. Normally, spatial filtering is a widely used technique to improve the directional properties and intensity distribution of the beam by allowing the transmission of only the first spatial-component at the Fourier plane. Generally two lenses (or mirrors) in a confocal arrangement are used for Fourier-transformation and retransformation. Selection of the different spatial components is accomplished by a pinhole of appropriate size. It is obvious that in a long amplifier chain the earlier the beam is filtered the less energy is lost, and the construction of the spatial filter is easier. However, if spatial filtering is accomplished at the front end, the chance that additional distortions are accumulated during amplification is higher. Therefore, in hybrid dye/excimer or solid-state/excimer [88Sza3, 89Luk, 90Wat, 94Sza, 96Sza] laser systems the best choice is, if spatial filtering is done around the frequency converter. The main problem associated with the pinhole-based arrangement is that the direction of the beam has to be matched to the optical axis of the arrangement with an accuracy comparable to the diffraction-limited divergence of the beam. However, this accuracy is generally not allowed by the limited pointing stability of such laser beams, leading to unpredictable transmission of the beam and early damage of the pinhole. The limited pointing stability of large laser systems is generally originated by the limited stability of the optical components, including the oscillator, amplifier chain and target area. The larger the beam size for a given wavelength, the more stringent these requirements are. A novel beam filtering method [97Sza] is based on replacing the pinhole by a nonlinear component which – due to its intensity- (or energy-density-) dependent transmission – automatically selects the more intense central spatial-component, resulting in an output beam of well-determined energy distribution even for input beams of fluctuating directional properties. Numerical calculations showed this method capable of effectively filtering the beam using saturable absorbers, frequency doublers and nonlinear components having a step-function-like transmission. In all cases similar results were obtained; the noisy intensity distribution of an input beam could be improved significantly over a wide range of intensities [97Sza]. Figures 3.3.13b, c, d show the calculated output profile, when a step-function-like filter, a saturable absorber and a frequency doubler are used as a nonlinear component for spatial filtering of an input beam whose intensity profile is shown in Fig. 3.3.13a. It is seen from Fig. 3.3.13 that a well-characterized Gaussian-like intensity profile is obtained at the output, which is insensitive to the operational condition of the active filter; practically the same distribution is obtained, when the input intensity is varied over more than one order of magnitude (corresponding to the dotted, solid and dashed curves of Fig. 3.3.13b, c, d, respec-
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Fig. 3.3.13. (a) Noisy intensity profile assumed for the input beam; (b), (c), (d) calculated intensity distributions for the output beam, filtered by a step-function-like filter (b), a saturable absorber (c) and a frequency doubler (d). The dotted, solid and dashed curves correspond to different peak intensities of the central diffraction-lobe at the Fourier plane.
tively). The output beam distribution is the least sensitive to the operational conditions in the case of a frequency doubler (Fig. 3.3.13d) where even the beam divergence is halved because of the two times shorter wavelength. The feasibility test of the nonlinear component-based Fourier filtering was performed in a dual-wavelength laser system using the frequency doubler (see Fig. 3.3.1) as the nonlinear component. The input beam was obtained from a subpicosecond distributed feedback dye laser oscillator–amplifier arrangement operating at 497 nm [88Sza3, 88Sza2, 89Sza1]. Using a Bethune-type amplifier [81Bet] a typical intensity profile for the fundamental beam is shown in Fig. 3.3.13a. However, when the frequency doubler was operated at the Fourier-plane of a confocal telescope, the size of the doubled output beam shrank, and the intensity distribution became free of modulation, in agreement with the results of the calculations (solid and dashed curves in Fig. 3.3.13d). Figures 3.3.14c, d show the intensity distributions of the input and the filtered output beams along the central line – indicated as a solid line in Fig. 3.3.14a, b – respectively. The significant improvement in the homogeneity is clearly seen by comparing the corresponding pictures/distributions.
3.3.3.4.4 Spectral filtering The earlier described beam filtering method minimizes the dependence of the directional properties of the frequency-doubled input beam on the properties of the fundamental generated in the dye laser system, and produces a harmonic of diffraction-limited beam quality from a fundamental beam of practically arbitrary directional properties. Using frequency doubling as an intensity-dependent
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a
b
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0 2
c
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3
x [mm]
4
5
2
d
3
x [mm]
4
5
Fig. 3.3.14. Measured distribution of the input beam (a) and the filtered output beam (b) using a frequency doubler as a nonlinear component. (c), (d) Intensity distribution of the input and output beam along the central horizontal line in (a) and (b).
nonlinear process, it has been demonstrated that the spatial dependence of the energy-flow can be used for the improvement of the directional properties of the beam. Since the temporal and spectral properties of the pulse are connected (through Fourier transformation), utilizing the temporal dependence of the energy-flow through the nonlinear element, Second Harmonic Generation (SHG) can also be used for spectral modification (spectral filtering) of the pulse. It is well known, that the combined effect of Self-Phase Modulation (SPM) and Group-Velocity Dispersion (GVD) in a fiber results in a broadening of the bandwidth carrying strong spectral modulations [84Tom]. This already allowed the generation of 55 fs tunable pulses by DistributedFeedback-Dye-Laser- (DFDL-) based pulsed dye laser [91Sim]. On the other hand, in most experiments, careful control over the spectral, consequently also the temporal shape of a pulse is required. As has been pointed out recently [96Zha], effective subpulse suppression occurs upon frequency doubling. Analogous to the active spatial filtering [97Sza], the possibility of active spectral filtering of a femtosecond pulse through frequency doubling has been demonstrated both experimentally and theoretically [98Sim]. It was shown, that a complete removal of the modulations in the second harmonic spectrum, hence a smooth temporal envelope is achieved, when frequency doubling is done with the compressed pulse. For theoretical and experimental verification of this idea, SHG was performed behind a grating, which introduced a spatially evolving negative chirp on the originally positively chirped pulse,
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Fig. 3.3.15. Measured and calculated spectra of frequency-doubled femtosecond pulses corresponding to different positions of the doubling crystal. The distance of the BBO from the plane of the best compression in a spatially changing chirp scheme is indicated on each graph. At the bottom, the fundamental spectrum, that was also used as input spectrum for the calculations, is shown.
whose spectrum showed the typical modulation occurring during fiber-chirping (lower curves in Fig. 3.3.15). The upper curves in Fig. 3.3.15 show the measured and calculated spectra of the frequency-doubled pulses when the SHG element is positioned at different distances behind the grating. The measurements – in agreement with the calculations – show strong dependence of the spectrum on the position of SHG [98Sim]. At the position of optimum pulse compression the spectral modulation of the original pulse is completely removed and a smooth spectrum is obtained for the frequency-doubled pulse. It can also be shown that the spectral and temporal purity of such pulses is much better than that of the fundamental, and the time–bandwidth product can be pushed to the theoretical limit. Even starting with such clean pulses, during amplification in KrF some spectral modulation is accumulated [96Sha]. The spectral narrowing observed during amplification in KrF [94Div] is balanced by the spectral broadening of femtosecond pulses when the amplifier is driven into saturation [95Die]. The broad bandwidth and the high spectral purity of the output pulse is a basic condition to get the maximum spectral brightness for high-intensity laser systems, moreover, such clean pulses can also find numerous applications in time-resolved spectroscopy.
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3.3.3.4.5 Optimization of off-axis amplifiers for minimum phase-front distortion It is seen that optical components can easily introduce phase or pulse front distortion in largeaperture ultraviolet beams, leading to poor focusability and/or increased pulse duration in the focus. Both effects dramatically decrease the focused intensity. At this point we note that an important practical advantage of the multiple-pass off-axis arrangement depicted in Fig. 3.3.10 [92Alm, 92Sza] is that multiple-pass amplification is realized by using no optical components except plane mirrors and plane-parallel windows. Both components can easily be fabricated with diffraction-limited quality for the ultraviolet up to large apertures. One can assume that in an inhomogeneously pumped amplifier the distortions seen by the pulse are proportional to the smallsignal gain times length product of the amplifier [95Ros]. In this case the amplification referred to a given distortion of the pulse can be expressed by a quantity that is proportional to the contrast coefficient defined in Sect. 3.3.3.2.1 (see also Fig. 3.3.6). As it is seen on the contrast curves of Fig. 3.3.9b, one of the main advantages of the off-axis scheme is that amplification of the signal can be maximized for a given gain–length product g0 l of the amplifier, consequently for the same optical distortion seen by the pulse. This is achieved by operating the amplifier in the optimum – as defined in Sect. 3.3.3.2.1 –, where the gain is close to the small-signal gain, and energy extraction is already satisfactory [92Alm, 92Sza]. Moreover, in the off-axis amplification scheme, it is the more homogeneous longitudinal distribution of the discharge which is seen by the pulse. Therefore, direct refractive index distortions and nonuniform-gain induced phase-front distortions – which are mainly important in the transversal direction – are integrated by the signal beam [91Sza, 92Alm]. Due to these three advantageous features of the off-axis amplification scheme, the distortions experienced by the signal beam are expected to be minimum. In order to quantitatively characterize the distortion, one can assume that the amplification of the signal pulse corresponding to a given phase-front distortion can be described by a quantity that is proportional to the ratio of the gain and the small-signal gain (G/G0 ) [94Sza, 96Sza]. In order to show the dependence of G/G0 on the operational conditions of the amplifiers, a local quantity called local contrast coefficient c has been introduced [92Alm] (see also Sect. 3.3.3.4.6). In Fig. 3.3.6 the local extraction efficiency η and the local contrast coefficient c both are plotted as a function of the normalized energy density in a KrF amplifier (taken from [92Alm]). As already shown in [92Alm, 94Sza], one of the main advantages of the off-axis amplification scheme is that by proper choice of the beam cross-section, the energy density in the amplifier can be lowered to optimize both efficiency and contrast. This means maximum gain for a given g0 l product and consequently maximum gain for the same optical distortion seen by the signal beam. It can be seen from Fig. 3.3.6 that optimum operation is achieved by running the amplifier in an energy density range where the gain is close to the small-signal gain, resulting in low ASE background while at the same time the energy extraction is reasonably high.
3.3.3.4.6 Beam homogenization method for short-pulse excimers It is known that intensity modulations across a beam reduce the energy concentrated in the focal spot, due to diffraction into higher-order spatial coordinates in the far field. Starting with a diffraction-limited UV input beam, there are two origins of such inhomogeneities occurring during amplification: one is related to the inhomogeneous distribution of the gain of excimer amplifiers across the beam, the other is connected to self-focusing of the laser beam in the window materials. It can be seen from Fig. 3.3.7 that in the off-axis amplification scheme the intensity distribution across the amplified beam is determined by the usually homogeneous longitudinal distribution of the discharge. Therefore, direct refractive index distortions and nonuniform gain-induced phase-front distortions, which are important mainly in the transversal direction, are integrated by the signal beam [91Sza, 92Alm, 94Sza]. This advantage of the off-axis amplification scheme over the conventional one was also demonstrated by interferometric phase-front distortion measureLandolt-B¨ ornstein New Series VIII/1B1
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ments [95Ros]. The second origin of inhomogeneities occurring during amplification is shown to be caused by self-focusing in the window material and/or diffraction on imperfect surfaces of the windows [97Feu]. This results in a spatially developing grainy structure superimposed on the original smooth beam profile. Various methods have been developed for the homogenization of laser beams [91Yam, 92Sez, 86Glo2, 86Sch, 87Sza5]. The normally used homogenization technique for powerful ns-excimer lasers is based on overlapping of many partial beams generated by two crossed arrays of cylindrical lenses [88Rob]. This technique, however, is not suitable for ultrashort laser pulses, since it leads to an unwanted increase of the pulse duration and/or an uncontrolled interference pattern. Spatial filtering of high-power beams by a small pinhole is not feasible because of the fast deterioration of the pinhole by the very high intensity at the focus. As a result, no practical beam homogenization method is available at present for high-power short-pulse UV beams. The most effective way of homogenizing the beam profile is to use properly adjusted saturation of the amplification [97Feu]. The efficiency of the amplifier’s homogenization can be described best by the global stabilization given by S = (ΔEin /Ein ) / (ΔEout /Eout ) .
(3.3.18)
It was shown in [97Feu] that one can optimize the amplifier parameters to obtain the highest stabilization. The stabilization per unit amplifier length defined as s=
lim ln(S)/g0 Δl
g0 Δl→0
(3.3.19)
has a maximum at a normalized energy density of 1.8 mJ cm−2 , as shown in Fig. 3.3.6 by the dotted line. (For further details see [97Feu].) It is seen that the operational regime corresponding to ideal stabilization coincides with the optimum found for efficiency, contrast and minimum optical distortion. In all cases, the amplifier must be operated around the saturation energy density. As already shown, this can be easily done by using the off-axis amplification scheme [94Sza]. In order to experimentally verify the improvement of the output beam homogeneity by the stabilization effect of the amplifier, the intensity distribution at the output window was recorded for different amplification parameters (see Fig. 3.3.16). Figure 3.3.16a was recorded without operation of the amplifier. This corresponds to a global stabilization of S = 1. Figure 3.3.16b shows the output profile for an output energy density of about 1.8 mJ cm−2 (ε = 0.9). To obtain this energy density, the small-signal gain of the KrF amplifier was decreased using a gas mixture with reduced F2 content. Figure 3.3.16c was recorded with a new gas fill resulting in an output energy density of 3.4 mJ cm−2 (ε = 1.7). The graphs on the right side of each image show the intensity distribution of a horizontal cut through the images. The homogenizing effect of the saturated amplification on the output beam profile is readily seen from the figure.
3.3.3.4.7 Focusability measurements Due to the above advantageous features of the off-axis amplification scheme, the distortions experienced by the signal beam are minimized, as already supported by former focusability measurements [92Alm, 94Sza]. We found that using the optical scheme of Fig. 3.3.2 (which allows output energies of up to 30 mJ in a 500 fs pulse from commercially available gain modules) diffraction-limited beam quality can routinely be obtained at the output. Using an f /20 focusing lens of diffractionlimited performance, both the diameter of the central diffraction lobe and the energy concentrated in the central spot show less than 5 % deviation from the theoretical value for a flat-top beam profile. Considering this diffraction-limited divergence of the beam, the peak brightness of the system is B = 1020 W cm−2 sterad−1 , which could, in principle, result in a peak focused intensity of I ≈ 8 × 1019 W cm−2 for a circular beam using an f /1 focusing optics of diffraction-limited performance. This is a noticeable performance for a laboratory-scale system.
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Intensity I [arb.units]
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Fig. 3.3.16. Records of the beam profile and the corresponding intensity distribution at the output window of the amplifier for a small-signal gain of (a) g0 = 0, (b) g0 = 0.16 cm−1 , (c) g0 = 0.2 cm−1 .
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0
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4 x [mm]
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4 2 m] 0 y [m
Fig. 3.3.17. Intensity distribution of the local spot of the KrF beam using an f /1.4 off-axis paraboloid mirror. The half-width of the distribution and the theoretical limit (in brackets) are also indicated. The central spot carries ≥ 60 % of the total energy. For further details see text.
An f /1.4 off-axis paraboloid mirror of 5 cm diameter of excellent surface conformity was made available by Optical Surface Limited, England. Performing the focusing experiments with this mirror and by careful adjustment of the saturation level for best homogenization, the intensity distribution shown in Fig. 3.3.17 was obtained. It can be seen from the figure that the half width of the central peak is 480 nm, close to the diffraction-limited spot size of 360 nm. The energy concentrated in the central diffraction lobe is more than 60 % of the whole energy of the beam, close to theoretical value of ≈ 83 % [94Sza]. The exact value of the energy in the central spot and of the background was determined by a pinhole measurement. In this measurement, the intensity distribution obtained at the focal plane of the off-axis paraboloid was magnified by a microscope objective. At the image plane, a pinhole allowing only transmission of the central diffraction lobe and its near vicinity was inserted. The size of the pinhole was chosen so that free transmission of the central lobe was easy to achieve, and the dynamic range of the beam analyzer system (LaserLaboratorium G¨ ottingen) allowed accurate determination of the ratio of the central spot energy and the background energy. From the measured data a peak focused intensity of I ≥ 1019 W cm−2 results for this table-top laser system [96Sza]. In conclusion, we have demonstrated that by taking proper care of the directional properties of short-pulse ultraviolet excimer laser systems, large focused intensities (I ≥ 1019 W cm−2 ) can be achieved with table-top lasers of moderate peak power. Up to now such intensities have only been produced by large laser systems. Work is in progress to further develop and finally combine these ideas in order to extract all the stored energy of excimers by a femtosecond pulse in a diffraction-limited beam, which – with optimum focusing – could lead to a table-top excimer laser system, giving intensities up to 1020 W cm−2 . An instrument of this nature will certainly find broad application in many laboratories.
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3.3.4 Application of short laser pulses 3.3.4.1 Application of short laser pulses for plasma generation Since the discovery of Q-switched lasers high-intensity focused radiation has become available to generate plasmas which emit radiation in the VUV and X-ray spectral range. In recent decades the study of laser-produced plasmas has been mainly motivated by Inertial Confinement Fusion (ICF) researches. For this purpose nanosecond-duration, short-wavelength lasers proved to be appropriate because of higher absorption of the radiation and higher conversion to X-rays [88Mea]. The reason is that most of the nonlinear processes scale with Iλ2 , consequently unwanted, competing effects are of much more importance for long-wavelength radiation. Nonlinear interactions, i.e. Raman- and stimulated Brillouin scattering and filamentation reduce light absorption for longer wavelengths. Besides the main research line of ICF [82Mey] these large laser facilities served also to determine radiation properties of highly ionized matter, determining opacities in the soft X-ray spectral range and bringing even astrophysical problems into the laboratories [87Gol, 92DaS, 94Eid, 95Foe, 96Foe2]. In recent years the availability of table-top, short-pulse laser systems gave new impetus for small-scale researches in the field of X-ray generation and spectroscopy of laser-produced plasmas. Recent developments of high-power lasers of ∼ 100 fs duration yielded bright laser plasma XUV sources of extremely short duration. There is a great demand for the generation of short and/or coherent X-ray pulses. The possible applications of these new XUV sources are X-ray microscopy, lithography, holography, investigation of biological specimen etc. Here some of the possible applications of short-pulse high-power excimer laser systems for this purpose will be highlighted. As a consequence of the high focusability of these pulses, intensities in the order of 1020 W cm−2 can easily be obtained with modest energies. A general problem of high-power laser-plasma interactions is the low absorption of the laser radiation at high intensities. Absorption of 800 and 400 nm radiation of 120 fs duration was found to be as low as 10 % at 1017 –1018 W cm−2 intensities with decreasing absorption for increasing intensity, independently of the target material [88Mil1, 95Pri]. Therefore, it is an interesting possible advantage, that recent absorption experiments revealed substantial absorption up to 70 % at intensities in excess of 1018 W cm−2 for KrF lasers of 380 fs duration [96Teu]. The observed high absorption is attributed to the anomalous absorption [92And], i.e. that the mean free path of the electrons in the accelerating laser field is longer than the skin depth in the solid plasmas. A further reason is that Iλ2 remains relatively low for KrF lasers, which might be of special importance in this case, where the ASE of the laser might create a preplasma. The higher absorption in the preplasma of the 248 nm beam might have contributed to the high total absorption as well. However, it is very probable that the ponderomotive pressure strongly pushes the preplasma, causing a steep density profile appropriate for the anomalous skin-effect [96Teu]. The observed high absorption of light leads to more efficient conversion to X-rays, too. Detailed spectroscopy of KrF laser produced plasmas in the soft X-ray, i.e. sub-keV range [96Kru], shows strong line-radiation of the He- and H-like highly ionized low-Z materials (C, F, and O), corresponding to a temperature of 200–500 eV of the high-density (> 1023 cm−3 ) plasma. Even higher (higher than 1 keV) temperatures could be derived from X-ray spectroscopy of the keV X-rays of Si and Al plasmas [96Teu]. Thus X-ray spectroscopy of KrF laser produced plasmas on solid surfaces can generate bright X-ray lines up to 10 keV photon energies [96Teu]. It is to be noted that, when speaking of X-ray spectroscopy of laser plasmas generated by ultrashort laser pulses, one must distinguish between thermally excited continuum radiation and X-rays generated by fast processes. The time-scale of thermal generation of X-rays is determined by hydrodynamical processes, which are slow, consequently the cooling of the hot material is also slow, therefore the X-ray pulses have a typical pulse duration of at least 1 ps [88Mil1].
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It is also possible to generate X-rays of several keV energy by illuminating gas jets by the subps ultra-intense radiation. There is a high electron density (1024 cm−3 ) in the clusters of high-Z noble gases, consequently multiphoton ionization and further ionization via intra-cluster inelastic electron–atom collisions generate hollow atoms with inner-shell vacancies. X-ray spectroscopy of such targets revealed intense L-band X-ray emission of Xe44+ and Xe45+ [94McP]. The emission of these lines is of nonthermal origin. The short bursts might be even shorter than the abovementioned 1 ps X-ray pulse duration. Multiphoton ionization and especially Optical Field Ionization (OFI) might be a possible excitation scheme for X-ray lasers when the main goal is to generate X-ray lasers of short wavelengths. One of the most widely discussed developments in recent years is the OFI laser on the Lyman-α transition of H-like lithium [94Nag]. In this scheme singly ionized Li preplasma was generated on solid Li surface by a 10-ns laser, then a high-power KrF laser was focused on it, yielding a nonlinear growth of the Ly-α line with g = 20 cm−1 gain. In order to increase the gain–length product gL, successful experiments were carried out in a LiF microcapillary up to 5 mm length [96Kor], obtaining gL ∼ = 5.5 gain on the 13.5 nm Ly-α line. The inversion was again obtained by a sub-ps KrF excimer laser system. Another possible method of generating coherent radiation in the XUV range is high-harmonic generation. Harmonic generation in gases produces odd-integer harmonics. The available highest harmonic order is determined by the Emax ∼ = Ip + 3 Up equation [92Kra], where Emax is the maximum harmonic photon energy, Ip is the ionization potential and Up is the ponderomotive potential, Up is given by the expression Up = e2 E 2 /4me ω 2 , where e is the electron charge, E is the electric field amplitude, me is the electron mass, and ω is the laser carrier frequency. Note that in this expression of the ponderomotive energy the often-mentioned Iλ2 scaling of the nonlinear processes can immediately be seen. Due to this scaling most of the efforts for high-harmonic generation were carried out with long-wavelength lasers in neutral gases [97Cha], where the wavelength of the highest harmonic has reached the so-called water-window at 2.7 nm. It is also possible to generate harmonics by ultrashort ultraviolet pulses using ions as a nonlinear medium as well. Here ionic nonlinearities produce the harmonics while the temperature is kept low. One of the first efforts was to produce high harmonics of preionized rare-gas-like alkaline ions [92Aki] by a KrF laser. High-density gas-jets served as source of He and Ne ions, where the 37th harmonics, corresponding to 6.7 nm wavelength was obtained in He+ ions [96Pre]. Both odd and even harmonics can be generated up to a high order on the steep density gradient of a laser-plasma on solid surfaces [96Nor]. According to recent theoretical expectations no strict cutoff of harmonics is expected in this case [96Gib]. Harmonic generation by UV lasers might especially be effective as the starting frequency is short and it is not the final energy but the order of harmonics which obeys the general Iλ2 scaling [96Gib]. Really, VUV harmonics were observed by using modest laser intensities [96Foe1]. However, the first efforts with higher, relativistic powers did not increase significantly the available harmonic order [98Cha]. Although high-harmonic generation was observed from very low laser intensities (well below the threshold of plasma generation [92Far]) up to relativistic 1019 W cm−2 [96Nor] intensities, further efforts are needed to clear the role of the laser wavelength and pulse duration on this mechanism of harmonic generation. An entirely different and surprising possible application of ultrashort laser pulses is the Inertial Confinement Fusion (ICF). The conventional method of ICF is that after the ablation of the fusion pellet by a high-power pulse of more than 10 ns duration a high-temperature hot spot of 5 keV temperature is generated in its center, surrounded by the main fuel of higher density and lower temperature. In case of symmetric heating the central spark will ignite the main fuel where the fusion burn occurs [82Mey, 76Kid]. As this scheme needs MJ laser energies for successful ignition, a new scheme, a so-called fast ignitor was proposed, which uses high-intensity lasers [94Tab]. The new scheme might reduce the required pumping energy down to the 100 kJ range. This is based on the positive use of the otherwise deteriorating nonlinear processes in the following way. After the capsule had reached high density through implosion, a hole is bored by a high-intensity ultrashort pulse through the capsule corona composed of the ablated material. Then the fuel is ignited by Landolt-B¨ ornstein New Series VIII/1B1
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suprathermal electrons produced in the high-intensity laser plasma interaction propagating from the critical density to the high-density core. In order to understand this process we must go back to the early 1960ties, i.e. to the first suggestion of self-focusing of laser light [62Ask]. Selffocusing caused by the ponderomotive force [80Bal], nonuniform heating [81Bak, 83Bak] and finally relativistic self-focusing [92Bor2] was observed, leading to high concentration of the radiation into a filament with a channel width of less than 1 μm [92Bor2]. This could make it possible to bore a hole [97Esa] into the plasma corona pushing the critical density close to the high-density capsule by the ponderomotive force. A fast ignitor requires 1020 W cm−2 intensities, and the generated forward propagating hot electrons must be of 1 MeV energies which is typical for interactions at these intensities and for the KrF wavelength [96Teu]. Longer-wavelength lasers may generate electrons of even higher energies up to 10 MeV, which is too hot for efficient ignition. The 248 nm radiation of KrF lasers and the recent progress in the achievable focused intensities make these lasers the best choice for a fast ignitor in ICF experiments.
3.3.4.2 Micromachining of materials with subpicosecond UV pulses Laser micro-machining of solids is nowadays a well-accepted technology for the manufacturing of components in electronics, aerospace, optics, medical, and photovoltaic industries. Furthermore, laser etching of sub-micron-sized features in dielectric materials is a well-established technique in photolithography for the fabrication of microelectronic devices. Usually the laser devices used for these applications are standard CO2 , Nd:YAG, or excimer lasers with nanosecond or longer pulse durations. However, there are specific classes of technologically important materials imposing severe limitations for the applicability of conventional laser sources if fabrication of sub-micron structures is required. These are mainly highly conducting or transparent materials. In case of solids with high heat conductivity, such as metals or semiconductors, fast lateral spreading of the absorbed energy outward from the irradiated zone prohibits the creation of structures below one micron, if conventional laser sources are used. It has been shown [94Mat] that the size of the heat-affected area, characterized by the thermal diffusion length Lth , depends on the thermal diffusivity κ of the material and the pulse duration τ : √ (3.3.20) Lth = 2κτ . Intuitively, it is expected that the limiting effect of the heat conductivity can be neglected, if Lth ≤ α−1 , α−1 being the penetration depth of the laser radiation. For most metals (or semiconductors) this condition is fulfilled for pulses shorter than a couple of picoseconds. Indeed, experimental evidence for a dramatic reduction of the heat-affected zone, by using sub-picosecond pulses for the irradiation of metal and semiconductor surfaces, has been provided [95Kru, 95Pre1, 96Mom]. Another challenging class of materials for sub-micron structuring represent transparent solids having little absorption even in the ultraviolet spectral range. In general, a prerequisite for precise surface ablation is a high optical absorption. Most materials are strongly absorbing in the deep UV, but there are some exceptions such as fused silica, fluoride crystals, diamond, sapphire, Teflon, etc., having only little absorption in the UV part of the spectrum. Subpicosecond lasers can be new tools for the precise micro-machining of these materials. Ultrashort pulses generate extremely high peak powers (∼ TW cm−2 ) carrying only moderate energies. At such high power levels multiphoton absorption becomes dominant and establishes the condition for the concentration of the irradiated energy in a thin surface layer necessary for precise machining. At the same time, the relatively low energy of the pulse insures that little or no optical damage occurs to the neighboring zones or to the bulk material. A further aspect is that, applying standard laser pulses with pulse durations of the order of 10 ns, coupling of the laser energy into the sample, the ablation process, and the removal of the
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material all happen at the same time, and hence the role of each part for the ablation process cannot be clearly identified. This may be sufficient for many practical purposes. For a detailed understanding of the ablation process, however, it is highly desirable to separate the individual roles of energy coupling into the sample, incubation, ablation, and removal of material. Taking a typical etch rate of 1 μm/pulse, and a supersonic velocity of material removal of 1000 m s−1 corresponding to 1 μm ns−1 , for standard 20-ns excimer laser pulses only the very first part of the laser pulse will see a virgin sample, whereas already after 5 ns material has moved 5 μm away from the sample and therefore may reduce the intensity of the incident pulse. Using ultrashort laser pulses, energy coupling into the sample, incubation, ablation, and removal of material can be separated, since the material will, for example, only move 0.3 nm in 300 fs. In this way plasma shielding of the incoming laser beam common to conventional nanosecond-pulse laser ablation is practically absent [87Kue]. The increasing demand for precise material processing is undoubtedly one of the driving forces for laser development. Nowadays, short-pulse laser systems operating on as high as the terawatt power level are table-top devices, thus making such sources accessible to many laboratories and recently also to industry. This revolutionary development was highly accelerated by the invention of the amplification of temporally stretched pulses followed by pulse compression (Chirped-Pulse Amplification, CPA). This technique is perfectly fitted to solid-state laser systems operating in the InfraRed (IR) part of the spectrum, thus concentrating a tremendous scientific potential to the development of these systems. Consequently, only limited effort has been made to develop alternative compact, high-brightness lasers such as excimer-based laser systems, although these are the only sources capable of amplifying radiation in the UltraViolet (UV) part of the spectrum. Fortunately, pioneering work of a few groups has led to a yet remarkable parallel development of excimer-based high-brightness systems. In fact, UV excimer short-pulse lasers can deliver similar focused intensities and average powers to those of solid-state IR laser systems. Worldwide advances in subpicosecond-pulse solid-state laser technology induced many research groups to exploit their applicability in materials processing. In a number of studies it has been shown that using these new lasers, as well as other infrared or visible short-pulse lasers, much better etch quality can be achieved than with nanosecond-pulse sources. Excellent results on short-pulse ablation of polymers, metals, semiconductors, ceramics and biological tissues have been reported [94Kau1, 94Kau2, 94Kum, 96Chi]. However, fabrication of feature sizes below one micron is hardly possible with these sources. A fundamental advantage of UV sources compared to IR systems is the focusability of the laser beam, inversely scaling with the wavelength. Spatial concentration of the energy and the resulting spatial resolution is clearly the most important figure of merit in sub-micrometer material processing. A KrF laser system running at 248 nm provides a more than three times better spatial resolution as compared to a Ti:sapphire laser operating at 780 nm, allowing the production of accordingly smaller feature sizes. Actually, subpicosecond excimer laser systems combine the merits of short pulse duration for minimum thermal load and hence clean structures, and short wavelength for small feature sizes. Recently the ablation of sub-micron structures at 248 nm on copper and silicon representing the material classes of metals and semiconductors has been demonstrated [96Sim, 97Sim]. Highly reproducible periodic line structures with a line-spacing below 400 nm, and individual holes with diameters below 500 nm have been produced on the sample surface by single-laser-shot exposure (Fig. 3.3.18). Irradiation was carried out in a mask projection set-up using a Schwarzschild-type reflective objective with pulses of 160 fs to 50 ps durations. Besides metals and semiconductors LiNbO3 has also attracted much interest in integrated optics applications. An integrable, narrow-band, fixed-frequency light source is one of the key components for applications in optical communication. Optically pumped Ti:Er:LiNbO3 Distributed Bragg Reflector (DBR) waveguide lasers are good candidates for such systems. Single-frequency lasers at 1531 nm and 1561 nm have been demonstrated recently. The key component of these lasers, the narrow-band Bragg reflector gratings, were fabricated by using holographic exposure and a Landolt-B¨ ornstein New Series VIII/1B1
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Fig. 3.3.18. Ablation of sub-micron structures at 248 nm on copper and silicon surfaces. With short pulses (500 fs . . . 50 ps) individual holes with diameters less than 500 nm and periodic line structures with a line-spacing below 400 nm have been produced by single-shot exposure.
m]
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Fig. 3.3.19. Atomic Force Microscope (AFM) picture of periodic line structures of 360 nm spacing on LiNbO3 surfaces fabricated with short UV pulses. The modulation depth can be adjusted by varying the fluence and the number of pulses.
set of dry-etching techniques. This fabrication technology is time-consuming and expensive. These facts initiate the search for alternative techniques allowing simpler grating fabrication with easy adjustment of the grating period Λ in the range of 345–360 nm and a groove depth of about 250–300 nm. Pulsed laser ablation patterning is a simple method for surface micro-machining. Excimer lasers provide the ability to create sub-micron structures. Due to the short wavelength a lateral resolution of several hundred nanometers can be achieved. In addition, the high UV-absorptivity of many materials provides a small penetration depth enabling exact control of the ablation depth. Previously, using conventional excimer lasers, the fabrication of periodic line structures of 2 μm spacing on LiNbO3 surfaces has been demonstrated. With nanosecond-pulse sources, however, heat diffusion seems to prevent the fabrication of sub-μm grating structures. Very recently, however, it has been shown that applying 248-nm subpicosecond pulses, grating-like structures with periods of about 360 nm can be created with single exposure [97Che] (Fig. 3.3.19). The modulation depth can be adjusted by varying the fluence and the number of pulses. This method seems to be appropriate to fabricate Bragg reflectors in LiNbO3 -based waveguides. Another important material in various areas of optical technology is Ta2 O5 . Due to its good transparency and the high refractive index (n > 2.2 in the visible range) it is often used for multilayer dielectric mirrors or masks and also for planar waveguides in optical communications technology and in integrated optical sensors. The thermal properties of Ta2 O5 are similar to those of LiNbO3 , so that fabrication of sub-μm structures has only become possible with 248 nm subpicosecond pulses. In a recent work a smooth and homogeneous structure was achieved over an irradiated area of as big as 300 μm × 300 μm resulting in a sinusoidal modulation profile [99Bei] (Fig. 3.3.20). Short-pulse excimer lasers have also been demonstrated to be powerful tools for sub-micronscale deposition of metal and oxide structures. The ability to deposit patterns, spots, and lines with sub-μm resolution has a great potential in microelectronics and optoelectronics fabrication industries, and in holographic recording. In a recent work [98Zer] direct micro-deposition of high-
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500 nm Fig. 3.3.20. Sub-micrometer sinusoidal modulation profile on Ta2 O5 using 248 nm femtosecond pulses. A smooth structure has been achieved over an area of 300 μm × 300 μm.
Fig. 3.3.21. Direct micro-deposition of Cr dots on glass substrates using subpicosecond KrF laser pulses (Scanning Electron Microscope (SEM) picture).
Table 3.3.3. List of papers in which demonstrations of high-quality patterning of various targets are reported. Material Polymers Metals Semiconductors Fused silica Diamond Ceramics C60 , C70 Ta2 O5 In2 O3 LiNbO3 YBa2 Cu3 O7
Fig. Fig. 3.3.18, Fig. 3.3.21 Fig. 3.3.18
Fig. 3.3.20 Fig. 3.3.19
Ref. [87Kue, 89Kue1, 89Kue2] [94Pre, 95Pre1, 96Sim, 97Sim, 98Zer] [96Her, 96Sim, 97Sim] [92Ihl] [95Pre1] [95Ihl] [92Zha] [99Bei] [98Zer] [97Che, 90Beu] [94Pro, 90Hei]
quality patterns with sub-μm features has been demonstrated (Fig. 3.3.21). Using a subpicosecond KrF laser, deposition of chromium (Cr) and indium oxide (In2 O3 ) on glass and silicon substrates has been achieved, with the Laser-Induced Forward Transfer (LIFT) technique. This approach exploits all advantages over conventional methods including simplicity in terms of vacuum handling, deposition purity, and high-accuracy sub-μm pattern transfer. For an overview, a list of papers is given in Table 3.3.3, in which demonstrations of high-quality patterning of various targets using subpicosecond excimer laser pulses are reported.
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References for 3.3
References for 3.3 62Ask
Askarian, G.A.: Zh. Eksp. Teor. Fiz. 42 (1962) 1567.
63Fra
Frantz, L.M., Nodvik, J.S.: J. Appl. Phys. 34 (1963) 2346.
76Kid
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77Tom
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255
3.4 Ion lasers and metal vapor lasers W. Seelig
3.4.1 Introduction Since the first ion laser was built in 1964 [64Bel, 00Bri], several hundreds ion laser transitions in the visible and near UV spectral range have been reported [66Bri]. Generation of these ion transitions requires low-pressure arc discharges containing noble gases or metal vapors to provide electron densities exceeding 1013 cm−3 . The corresponding high threshold current densities for ion laser excitation of more than 100 A cm−2 mostly permit only quasi-cw pulsed mode operation. The spectral range of ion lasers is the largest of all lasers, down to the X-ray region if high-Z ions are considered. Although the pump power densities increase rapidly with the laser frequency and other excitation methods must be used, some similarities to visible-range ion lasers are present. This review is restricted to classical visible and near-ultraviolet ion lasers. These are commercial systems and, in particular, noble gas ion lasers with high continuous power levels. Historically ion lasers and metal vapor lasers are closely related. The first metal vapor laser was the optically pumped cw Cs laser. [62Rab]. Difficulties with alkali metals and high temperatures have stimulated the search of other potential laser media, e.g. Hg with well-established lamp technology. So the first gas discharge metal vapor laser was a Hg I laser [63Rid]. The first gas ion laser invented by Bell [64Bel] also used mercury, the first laser with doubly ionized Hg was demonstrated by Gerritson and Goedetier [64Ger]. More important was the discovery of the continuous 488 nm Ar ion laser action in Ar–Hg-mixture discharges by Bridges et al [64Bri]. The He–Hg+ laser inspired Fowler and Silfvast to the search for new laser transitions in other He–metal discharges. A result was the continuous He–Cd+ laser, a successful commercial metal vapor laser [66Sil]. The discovery of the Cu I and Au I laser, another type of metal vapor laser, by Walter et al. [66Wal1, 66Wal2] in 1965 has started the very successful development of self-terminating resonancemetastable metal vapor lasers with repetitively pulsed metal–noble-gas low-pressure discharges. The Cu I laser is the most powerful, efficient, and best developed metal vapor laser. Oscillating on the Cu I transitions at 510.6 nm and 578.2 nm wavelength, average output powers of up to 500 W have been demonstrated from oscillators. Commercial lasers are available with output powers of up to 120 W at an efficiency of 1 %. Typical laser pulses have 10 . . . 100 ns in duration at pulse repetition rates of up to 200 kHz with peak powers of up to several hundred kW. Different metal vapor lasers are the subjects for a few thousand contributions in the scientific literature. In a comprehensive book C.E. Little [99Lit] gives a current review. This contribution is concentrated on commercially available laser systems. Therefore, the last part is restricted to the copper vapor laser, representing the class of self-terminating metal vapor high-power lasers.
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3.4.2 Properties of gas discharge laser media
[Ref. p. 272
3.4.2 Properties of gas discharge laser media The capability of materials to amplify light of a specific wavelength if two excited levels are inversely populated, is characterized by the small-signal gain g0 . To establish population inversion, spontaneous emission losses must be compensated by a pumping mechanism. For this balance the necessary pump power density for the laser threshold P (e.g. g0 = 10−2 cm−1 ) can be estimated (Fig. 3.4.1). Here η is the fluorescence efficiency which – for most laser media – is in the percent range [84See]. 10 7
S [W cm-2 ]
10 5
10 3
10 1
10-1 10
1000 100 Laser wavelength l [nm]
Fig. 3.4.1. Threshold energy current density S = P η/g0 versus laser wavelength λ (Dopplerbroadened gas laser transitions).
There are two remarkable items resulting from these considerations: 1. P increases with more than λ−4 for short wavelengths, i.e. generation of short-wavelength laser radiation requires active media of high power density. 2. The pump power density threshold for many gas lasers is by orders of magnitude lower than it is for solid-state or dye lasers because of the narrow fluorescence line width. This is of advantage for continuous operation. Here only laser transitions in the visible and UV spectral range of atoms or ions excited in lowpressure gas discharges are considered. The lines are Doppler-broadened, and the λ−4 -dependence of the threshold energy density is realized: ΔνD ηP > 5 · 10−22 , g0 λ3 √ Δ ν D = v¯ ln 2/λ0 , v¯ = 8 kT /mπ S=
(3.4.1) (3.4.2)
with Δ ν D : Doppler width, T : gas temperature, m: atomic mass, k: Boltzmann constant. In the gas discharge the electron gas transforms the input energy into excitation energy of the laser levels. The pumping process by electron collisions is limited by its inverse destructive process of inversion due to electron collisions of second kind. Using the relation of Klein–Rosseland [21Kle]
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
-3
Electron density ne [cm ]
10
3.4 Ion lasers and metal vapor lasers
257
20
Ù
ne
1017 1014 Ú
ne h g0 L
1011 10 8 1
100 10 Laser wavelength l [nm]
1000
Fig. 3.4.2. Electron-density region of laserrelevant plasma.
σ21 ve g1 ω = exp , σ12 ve g2 kTe
(3.4.3)
a condition for the electron temperature Te in the plasma results. σ12 , σ21 are the cross sections of electrons interacting with the laser atoms, g1 , g2 are the statistical weights of the lower (1) and upper (2) state, respectively. ve is the electron velocity, and ω = 2π/λ. Usually the difference between the lifetimes is about one order of magnitude or less, and from (3.4.3) results: kTe ≥ ω .
(3.4.4)
kTe /me /2L (L: active length) gives the lowest necessary
ˇ e = 0.4 g0 L/ηλ5/2 . ne > n
(3.4.5)
Equation (3.4.1) and P < 3ne kTe electron density n ˇ e for laser action:
Fluorescence quenching of the laser radiation dominates if ne > A21 / σ−2 ve . Using the maximum possible value of the destruction cross section by electron collisions σ−2 ve ∼ = π2 2 /me 2π me kTe , A21 = f21 · 2e20 ω 2 /4π ε0 c3
(3.4.6)
(3.4.7) (3.4.8)
with A21 : Einstein coefficient, f21 : oscillator strength, ω: frequency of the laser transition, me : electron mass yields the inequation: ne < n ˆe ∼ = 103 /λ5/2 .
(3.4.9)
n ˆ e : highest electron density for laser action. kT ≥ hω and (3.4.5), (3.4.9) give the region of laserrelevant plasmas (Fig. 3.4.2). These results are valid in a wide range of laser wavelengths from the visible to the XUVspectrum. Especially the power limits of self-terminating pulse lasers can be estimated using (3.4.9). Landolt-B¨ ornstein New Series VIII/1B1
258
3.4.2 Properties of gas discharge laser media
[Ref. p. 272
Quasi-cw or continuously operating lasers have more restrictive conditions given by bottle necks in their laser mechanism which lead to an increased lifetime of the lower laser level. In the shortwavelength regime radiation trapping is important. The ensemble average value of the radiative decay time τ1 of the lower laser level is characterized by the escape factor F , were τ10 is the rad. lifetime of the single atom: 1/τ1 = F/τ10 .
(3.4.10)
F can be calculated using for instance the theory of Holstein [51Hol], but the theory is not applicable to values of F > 1/4. For large F -values which are of interest for lasers the simpler approximation τ1 = τ10 + g1 λ310 RN/4π2 v¯ gN
(3.4.11)
gives good results [78Ban]. N is the ground-state density, gN its statistical weight, R the radius of the active medium, v¯ the thermal velocity, and λ10 the wavelength of the escaped radiation from the lower laser level to the ground state. Based on this relation, and on stationary rate equations of the lower-laser-level population inequalities for the maximum laser output power and conditions for the ground-state densities of laser atoms/ions can be estimated. The population density of the lower laser level N1 is given by N1 g2 τ 1 ρ g2 N2 N1 N2 − N1 = 1− (3.4.12) − − P1 < P L = B21 ω g1 τ1 τ2 τ1 g1 τ2 with ρ: energy density of the radiation field, g2 , g1 : statistical weights, N2 : population density of the upper laser level, N2 > g2 N1 /g1 , τ2 , τ1 : time constants of the upper and lower laser level, respectively, P1 : pumping rate into the lower laser level, P2 : pumping rate into the upper laser level, B21 : Einstein coefficient of stimulated emission. For a closed cycle of the process with a time constant τN it is necessary that v. N = (P1 + P2 )τN = PΣ τN > PΣ R/¯
(3.4.13)
For a three-level laser process results with (3.4.11): g2 τ10 g2 λ310 R2 PΣ − P L R2 < PΣ R2 1 − g1 τ2 gN 4 π2 τ2 v¯2 and P L < PΣ
1−
g2 τ10 g2 λ310 RN − g1 τ2 gN 4 π2 τ2 v¯
(3.4.14)
.
(3.4.15)
P L · ω is the laser output power per volume unit. Equation (3.4.15) gives upper limits of the ground-state density of atoms or ions, respectively. The right term of (3.4.14) becomes maximal for 1 g1 τ10 + τ2 (3.4.16) τ1 = 2 g2 and an equation for the specific output power ΦL of the laser results: ΦL = π R2 P L ω < π2
gN τ2 kT ω . g2 m λ310
(3.4.17) Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
259
Equation (3.4.17) is also valid for a four-level laser process. λ10 is always the wavelength corresponding to the energy gap between ground state and lower laser level. From (3.4.17) results: If only ion levels are involved in the cw laser process then T represents the ion temperature. For atom lasers T is the neutral gas temperature. In a powerful laser discharge the ion temperatures are up to two orders of magnitude higher compared to the neutral gas temperatures. Furthermore, the distances between the ion energy levels are larger compared to the atomic levels due to the stronger binding of the lightning electron, so for ions λ10 can be smaller than for atoms of the same gas. So the maximum laser output power of cw ion lasers can be more than two orders of magnitude higher compared to cw atom lasers.
3.4.3 Noble gas ion lasers 3.4.3.1 Excitation mechanism Noble gas ion lasers are powerful continuous sources of coherent radiation in the visible and nearUV spectrum. High-power radiation of several ten watts has been generated continuously from many ionic transitions excited in highly ionized low-pressure arc discharges [66Paa, 71Bri, 69Her, 70Boe, 74Aki, 76Lue1, 76Bur, 77Lue1, 73Alf, 68Her, 86Apo]. Among these, the argon ion laser with continuous emission up to 0.5 kW in the visible is the most prominent. The behavior of the Ar II 4p–4s transitions turns out to be typical for most of the ion laser transitions in noble gases and metal vapors, respectively. In theoretical and experimental investigations [68Her, 69Her] the Ar II laser has therefore been studied as a model for continuous ion lasers in general. The energy levels of the argon ion contributing to the laser process are the excited level groups Ar II 4p (upper laser level), and Ar II 4s, Ar II 3d next to the ion ground state Ar II 3s2 3p4 3p. Figure 3.4.3 shows a generalized energy level diagram for the Ar II 4p–4s laser transitions. From quantum-mechanical selection rules the Ar II 4s–3p is an allowed transition while the Ar II 4p–3p transition is forbidden, so that radiative decay of the 4p to the ion ground state is of the type 500 nm
70 nm
Ar II 4p −→ Ar II 4s −→ Ar II 3p . The 4p decay time exceeding that of the 4s by an order of magnitude, consequently the selection rules and the high decay rate of the 4s term automatically insure a population inversion of strongly allowed transitions of the type 4p → 4s in argon, provided that the supply rate of excited 4p and 4s ions is of the same magnitude. This means, incident radiation in the 500 nm region will be amplified. In steady-state gas discharges with average electron energies of a few eV stepwise excitation will consequently dominate over all other excitation processes: e + A+ → e + A+ ∗ .
(3.4.18)
This has in fact be verified by theoretical modeling in agreement with a number of experiments performed with noble-gas lasers [68Her, 67Boe, 67Bei, 67Gor, 65Lab, 66Rud]. In the case of predominant stepwise excitation the number of lasing atoms PL generated per unit time in the unit volume of the active medium rises quadratically with the electron density ne , and the output power per unit length Φ may be written as Φ ∝ R2 PL = f (kTe )R2 n2e , Landolt-B¨ ornstein New Series VIII/1B1
(3.4.19)
260
3.4.3 Noble gas ion lasers
Energy E [eV]
t ~7.5 ns t~ 9.1 ns 33.0 32.9 32.8
284 267
2
4s P
16.0 15.9 15.8 15.7
285
1/2
266
3/2
t~ 0.36 ns ~ 72 nm
265
-1
35.2
286
457.9 nm 476.5 nm 496.5 nm 488.0 nm 514.5 nm
3
4p D
287
Energy E [10 cm ]
4 0
288
3/2 1/2 3/2 5/2 1/2 3/2 5/2 7/2
⎫ ⎬ ⎭
4p P
4p2D0
⎫ ⎬ ⎭
35.4
2 0
1/2 ⎫ ⎬ ⎭
35.6
289
4p2S0 ⎫ ⎬ ⎭
35.8
[Ref. p. 272
264 129
1/2 +
5
Ar 3p
128
2 0
P
3/2
127 126
0
Ar
0
Fig. 3.4.3. Generalized energy level diagram for the Ar II 4p–4s laser transitions.
if quenching of inversion is neglected. Maximum pumping rates PL for Ar II laser levels have been calculated [68Her, 75Lue] to occur for neutral gas densities N according to N R = const. = 3 · 1014 (cm−2 ) .
(3.4.20)
Low-pressure arc discharges with a mean electron energy of about kTe = 4 eV satisfy this condition. “Boltzmann-invariant similarity laws” [69Pfa] for the electron distribution function in optimized laser plasmas are the consequence. Substituting (3.4.20) into (3.4.19) the maximum power per unit length can be written as Φ ∝ (ne /N )2 ∝ (ne R)2 ,
(3.4.21)
x = ne /N is about the degree of ionization. The output power of ion lasers is limited for two reasons that set an upper limit to both discharge parameters x and kTe : 1. The processes leading to an inversion density are quenched a) by collisional depopulation of the upper laser level and b) by radiation trapping that limits the decay of the lower laser level [75Lue]. 2. The range of parameters favorable for high inversion densities may not be achieved in stable low-pressure arc discharges [71Bri]. The effects that quench the inversion are well known in the case of Ar II lasers and have been described quantitatively [75Lue]. According to (3.4.19), collisional depopulation of the upper laser level by electrons sets an upper limit for ne . Hence (3.4.21) Φ ∝ R2 ,
(3.4.22)
and a large tube radius should be used for high-power generation. Radiation trapping of the lowerstate decay depends on the optical thickness k0 · R of the 70-nm VUV resonance radiation, where Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
k0 = 7 · 10−14 ne · (kTi )−1/2
261 (3.4.23)
with k0 : absorption coefficient, Ti : ion temperature. An upper limit for k0 R results, and Φ ∝ (kTi )1/2 .
(3.4.24)
So high ion temperatures must be achieved in the laser plasma, large R values are helpful, but kTi < kTe sets an upper limit. Different experiments confirm the following relations for the temperatures in the Ar ion laser plasma [73Her]: Ti = Ti0 + 0.90 (jR) , Ta = Ta0 + 0.75 (jR)
(3.4.25)
with Ti0 = 2800 K, Ta0 = 1500 K, 15 < jR (A cm−1 ) < 150, j: current density.
3.4.3.2 Operating characteristics Continuous ion lasers are sophisticated sealed off devices. Their operation conditions are close to the destruction limits of the tube material. More than 99.8 % of the input energy heats the tube walls with energy flux densities of 1 kW cm−2 . Due to radial ion currents up to 10 A cm−2 with ion energies > 20 eV rapid sputtering occurs for the most wall materials. The discharge density of 1015 cm−3 requires Ultra-High Vacuum (UHV) cleanness (without any vapor impurities). Furthermore, discharge instabilities (e.g. [03Don]) can avoid good operation conditions.
3.4.3.2.1 Neutral gas depletion A stationary low-pressure arc can only be stable if the ion wall current is equal or smaller than the back flow of neutral gas from the tube wall into the plasma volume. The comparison between the radial current density of ions and neutral atoms gives 0.55 ne (kTe /m)1/2 = N (kTa /2πm)1/2 ,
(3.4.26)
where Ta is the temperature of the neutral atoms and m is the atom mass. Equation (3.4.26) is independent of the discharge diameter and of the discharge gas. It can be used to calculate the macroscopic parameter of the stability limit. The parameter jR and pR allow a geometricindependent representation [77Lue1]. Figure 3.4.4 shows the plasma parameter kTe versus ne R for stable Ar II laser arc discharges (ΔN ∝ g0 ).
Landolt-B¨ ornstein New Series VIII/1B1
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3.4.3 Noble gas ion lasers
[Ref. p. 272
7.5
Plasma parameter kTe [eV]
Unstable discharge
5.0
Stable discharge ΔN ≥ 0 2.5
ΔN<0
0 1
2
5 -2 13 ne R [10 cm ]
10
20
Fig. 3.4.4. Plasma parameter kTe versus ne R for stable Ar II laser arc discharges (ΔN ∝ g0 ).
3.4.3.2.2 Axial gas pumping Axial gas pumping creates density gradients between the cathode and the anode [68Che]. The gas pumping in ion laser plasmas is due to the balance of axial momentum: In the plasma column electrons and ions gain equal but opposite momentum from the electric field. In a first approximation only the momentum of electrons can be transmitted to the neutral gas, the momentum of ions is transmitted to the wall. In the low-pressure discharges the radial potential distribution is reflecting nearly all electrons, whereas the ions are accelerated towards the wall [29Lan, 76Lue2]. As a result, a pressure gradient occurs in direction to the anode. This gradient can be reduced by connecting anode and cathode vessels with a bypass. For an Ar laser plasma the following relation is found by a first approximation [77Lue2]: j = 6 · 105 (R1 /R)4 (x/L1 ) (Δp/p)
(3.4.27)
with R1 : radius of the (external) bypass tube, L1 : length of the (external) bypass tube, p: filling pressure, x: degree of ionization. In general, a sufficient bypass should have a cross section which is one order of magnitude larger than the discharge cross section.
3.4.3.2.3 Transition regions Equation (3.4.26) suggests that neutral gas depletion sets a general upper limit to stable ion laser discharges. In a real discharge device, however, other current limiting effects are to be expected, which are due to axial density gradients and due to space-charge layers [71Bri]. A comparison of axial current density with neutral current density due to thermal remotion leads in a first approximation [69And] to N (kTa /2 π m)1/2 ≥ 2(me /m)1/2 · j .
(3.4.28)
This effect can be overcome by the design of the discharge tube ends [71Bri] in connection with magnetic fields. Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
263
3.4.3.2.4 Magnetic fields Magnetic fields have in most cases a positive effect on the ion laser plasma. Instabilities are results of mismatching to the discharge geometry or of the self-magnetic field of the discharge current. Axial magnetic fields are used to reduce sputter effects, and for stabilization of the arc column. Such fields mainly influence the electrons. The reduction of their radial mobility by the magnetic field leads to a decrease of the radial electric field, especially to a reduction of the negative wall potential, and therefore of the ion impact energy. The quenching of the radial ion current sets a limit for the magnetic field strength Bz [74Ban]: Bz R 1.5 (V s/m) .
(3.4.29)
Axial magnetic fields are indispensable for arc-stabilization in modern ion laser tube structures. During a long period of development all these problems have been solved. Modern commercial ion laser devices use copper–tungsten disc discharge tubes with integrated bypass, axial magnetic fields to stabilize the arc discharge and prevent sputtering damage. The use of tungsten in the central part is necessary. This metal has the highest sputter threshold energy and UHV-capabilities. Figure 3.4.5 shows a schematic cross section of the W–Cu discharge tube structure. Figure 3.4.6 shows a commercial ion laser tube construction. Cooled magnet
Magnet
Anode
Water Ceramic envelope Copper
Heated cathode Water cooling
Tungsten disk Bore Gas reservoir
Gas return holes Ceramic ring Brewster window Fig. 3.4.5. Schematic cross section of the W–Cu discharge tube structure.
Fig. 3.4.6. Commercial ion laser tube construction.
3.4.3.2.5 Summary of operation parameters The operation parameters of Ar II/Ar III lasers are summarized in Figs. 3.4.7–3.4.11 using the generalized scaling parameters [73Her, 77Lue1, 78Lue]. The results of the Ar laser are transferable to other ion lasers with relatively small modifications. Furthermore of commercial interest is Kr with lines in the red part of the spectrum. The following commercial lasers are usually available: Ar II: Output power up to 30 W, 10 lines in the range 454.5 . . . 528.7 nm with 40 % output power in 488 nm and in 514.5 nm too; efficiency 1 ◦/◦◦ . Landolt-B¨ ornstein New Series VIII/1B1
264
3.4.3 Noble gas ion lasers Doppler width DnD [GHz] 3
4
6
[Ref. p. 272
9 -1
[W m ]
200 12
Max.output power per unit length fL
-1
-1
Small-signal gain g0 [% cm ]
1.0
0.5
0
50
100
150 -1
jR [A cm ] Fig. 3.4.7. Small-signal gain of the 488 nm Ar II line of a high-power laser (R = 0.6 cm) versus product of radius and mean current density jR.
100 50 +
Ar visible 10 5 ++
Ar UV 1
20
50
100 -1 jR [A cm ]
200
Fig. 3.4.8. Maximum output power of the Ar II/Ar III laser (all lines) per unit length versus product of radius and mean current density jR.
1
^
Ez R [ V ]
2
0
0
200
100 -1
jR [A cm ]
300
Fig. 3.4.9. Product of axial field strength and radius Ez R versus jR for optimum laser operation.
Ar III: Output power up to 5 W, 2 lines, 50 % on 363.7 nm and 50 % on 351 nm. Kr II: Output power up to 20 W, 13 lines in the range 406.7 . . . 799.3 nm; efficiency 1 ◦/◦◦ . More details, other wavelengths, and the actual state of the art are summarized in Laser Focus World [04LFW]. For about twenty years basic research of continuous (low-Z) ion lasers is well established. Some results are applicable to new XUV high-Z ion lasers. By means of continuous ion lasers a series of new research fields have been opened in the past. Until now Ar/Kr ion laser systems hold a nonnegligible position on the laser market. These lasers have many applications especially in science and medicine. Their advantage in comparison with other systems is the nearly perfect beam quality of continuous duty lasers.
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
265
50 351.1 nm 363.8 nm
-1
[W m ]
Ar III
-1
[W m ]
5
333.6 nm Ar III 334.4 nm 335.8 nm
2
305.4 nm Ar III 302.4 nm 300.2 nm
-1
10
350.7 nm Kr III 356.4 nm
312.4 nm Kr III 323.9 nm 337.4 nm
2
1 100
Max.output power per unit length fL
Max.output power per unit length fL
-1
20
200
500
1000
-1
jR [A cm ] Fig. 3.4.10. Maximum UV laser output power versus jR of Ar III and Kr III laser.
1
0.5
0.2
0.1 100
Ar III 275.4 nm
200
-1
jR [A cm ]
500
Fig. 3.4.11. Maximum UV laser output in the short-wavelength range of the Ar III laser versus jR.
3.4.4 Helium metal ion lasers 3.4.4.1 Excitation mechanism Many metal ion laser transitions can be excited by charge-transfer (Duffendack) reactions [29Duf] (3.4.30) and Penning ionization [32Pen, 34Pen] (3.4.31): He+ + M → He + M+ ∗ ,
(3.4.30)
Hem + M → He + M+ ∗ + e .
(3.4.31)
The Duffendack-process is resonant, typical energy intervals are 0.1 . . . 0.4 eV for energy-level coincidence. The Penning-process is nonresonant, since the liberated electron can remove the excess energy. Noble gases like He and Ne have metastable states (e.g. Hem ) and ions of high energy that is sufficient to supply ionization and excitation energy of many metals like Hg, Zn, Cd, Se, Te, etc. The continuous He–Cd laser is the most successful of all metal ion lasers, an ultraviolet/blue companion to the He–Ne laser. Laser oscillation on the blue line was first obtained in 1966 by Silfvast et al. [66Sil], continuous laser operation in 1968, and in 1969 the first continuous UV laser operation also by Silfvast [68Sil, 69Sil, 69Gol]. Between 1969 and 1976 He–Cd+ lasers provided the shortest cw wavelength (325 nm) of any laser type. The operation conditions and power-limiting processes are representative to all continuous lasers with metal-noble-gas low-pressure arc columns. Figure 3.4.12 shows the energy-level diagram of He–Cd+ . The upper laser levels of the Cd II 441.6 nm and Cd II 325 nm transitions have relatively long decay time constants, so large population densities can be realized by cascade transitions of Landolt-B¨ ornstein New Series VIII/1B1
3.4.4 Helium metal ion lasers
J 3/2 1/2
3
2 S1
160 2 6s S1/2 J ~ 3/2 t 285 ns 2 0 5s2 PJ 5/2 140
18
t~ 810 ns 16
14
J 3/2 1/2
325.0 nm 2 0
5p PJ
0
441.6 nm
120
t ~ 2.19 ns t~ 5.07 ns + 2
8.99
3
Energy E [eV]
2 0
6p PJ
-1
1
2 S0 20
180
Cadmium
Helium
22
[Ref. p. 272
Energy E [10 cm ]
266
Cd 5s S1/2
Cd
100 72.54
0
Fig. 3.4.12. Energy-level diagram of He–Cd+ .
higher-lying Cd II levels. The dominant laser pump process in He–Cd glow discharges is Penningionization of Cd. The Duffendack process is also possible. The He ionization energy of 24.5 eV is nearly fitted to many energy levels of Cd II. The excitation process by the Penning reaction has the same limitation as in He–Ne lasers: the quenching of metastable densities by destructive electron collisions. The volume recombination of the ions in low-pressure discharges is not very probable, an advantage for the Duffendack process. The lower laser levels have lifetimes in the nanosecond range. Resonance radiation trapping blockade of these transitions to the Cd II ground state is (comparable to the Cu I laser) nearly two orders in magnitude larger than in Ar II lasers. This results in output powers of about 1 % of an Ar II laser.
3.4.4.2 Operating characteristic of the continuous He–Cd laser The active medium of a He–Cd+ laser is a low-pressure glow discharge column similar to the He–Ne laser discharge. The low operating temperature of 330 ◦ C corresponding to sufficient Cd vapor pressure makes the technology simple. Hollow cathode discharges can be used as well. A very good beam quality will result, if the glow discharge operates in the cataphoretic variant. In the cw He–Cd discharge Cd moves to the cathode region. The Cd transport rate ΓB through the bore is given by Hernqvist [72Her, 69Fen]: ΓB N0 αμ+ (U/L)
(3.4.32)
with N0 : Cd vapor density at the Cd pool near the anode, α: degree of ionization of Cd, Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
Cataphoretic containment section
Evaporator
Cataphoretic containment section
Bypass
Discharge tube 1 mm l.D. Thermionic cathode
Condenser Auxiliary anode
20
10
10
100
a
Output power f [mW]
Fig. 3.4.13. He–Cd+ recirculation laser tube.
Output power f [mW]
Output power f [mW]
Anode
Grid structure
267
200
12
10
b
Discharge current I [mA]
13
10 -3 Cd vapor density [cm ]
20
10
0
2
c
6 4 He pressure [Torr]
8
10
Fig. 3.4.14. Output power Φ of a cataphoretic 441.6 nm He–Cd+ laser, versus (a) discharge current, (b) Cd vapor density, (c) pressure (laser tube: 3.5 mm bore, 124 cm discharge length).
μ+ : Cd ion mobility in He, U : potential drop over the length L. To avoid axial pressure gradients with resulting stability and noise problems of the discharge a bypass between cathode and anode region is necessary. The cross section of the bypass must be about a factor of hundred larger than the discharge cross section (Fig. 3.4.13). A metallic grid structure in the bypass prevents electrical breakdown. Today mainly constructions with integrated recirculation geometry, symmetrical cathode positioning in the center, and two anodes are used. The smallsignal gain is typically 0.05 . . . 0.08 % cm−1 [78Mor, 75Miz1] at 441.6 nm and 0.03 . . . 0.04 % cm−1 at 325 nm. It can be increased by a factor of four by use of a single 114 Cd isotope in place of the natural isotopic mixture [74Miy, 71Gia]. Figure 3.4.14 gives operating parameters for optimum output power [78Mor]. The plasma parameters of the He–Cd arc column are investigated in different ways [75Miz1, 74Miy, 71Gia, 82Got, 75Miz2, 75Miz3]. An electron density of about 1012 cm−3 was obtained in 3-mm diameter discharges by spectroscopic measurements. The electron temperature for optimum Landolt-B¨ ornstein New Series VIII/1B1
268
3.4.5 Self-terminating metal vapor lasers
[Ref. p. 272
laser conditions is about 3.5 . . . 3.7 eV and nearly invariant in all laser discharges, i.e. the velocity distribution function of electrons is invariant for optimum laser plasma conditions. Therefore, “Boltzmann-invariant similarity laws” are applicable [69Pfa]. Resulting scaling rules agree with experiments in a first-order approximation [99Lit]: jR = 2.3 . . . 2.6 mA mm−1 , Ez R = 3 . . . 4 V , PHe R = 4 . . . 5 torr mm , PCd R = 10−3 torr mm , g0 R = 2 · 10−4 , Φ/LR = 1 . . . 3 mW cm−2 with Ez L: voltage drop, jπR2 : discharge current, PHe : He pressure, PCd : Cd pressure, g0 : smallsignal gain, Φ: output power, L: active length, R: bore radius in the mm-range. Although a lot of research and development has gone into these lasers in the past, they hardly have any more meaning in today’s laser market. Modern solid-state laser systems easily exceed their specifications.
3.4.5 Self-terminating metal vapor lasers 3.4.5.1 Excitation mechanism Self-terminating lasers are operated with pulse durations (typically 10 . . . 100 ns) shorter than the effective upper-level lifetime and above all characterized by high gains (ASE is possible), and high peak output powers. The most powerful self-terminating metal vapor lasers oscillate on transitions between resonance and metastable levels (“resonance–metastable lasers”). The three-energy-level structure with ground state, resonance level, and metastable level of Cu I terms is a typical example (Fig. 3.4.15). The rise time of the excitation pulse must be shorter than the radiative lifetime of the upper level in order to achieve inversion. A large inversion density is necessary because the gain duration is often only in the 10 ns range. So a low-Q resonator must be used to extract power under high-gain conditions. Walter et al. [66Wal1] specified the criteria for efficient laser conditions. Electron-impact pumping from the ground state favors population of lowest resonance levels. The cross sections are proportional to the oscillator strengths. On the other hand, the decay due to resonance radiation in the ground state is very fast. Therefore, resonance-radiation trapping of this transition is necessary. This is realized if the metal vapor density exceeds values of 1013 cm−3 (3.4.11). So the upper laser level decays mainly to the lower laser level. The Einstein A coefficient for the laser transition should be smaller than that for the excitation transition but larger than that of the relaxation transition. For efficient laser action in the visible spectrum, the lower laser level should lie between 0.75 eV and 2.25 eV in order to avoid thermal population by collisions, but to achieve a high quantum efficiency. The most powerful transitions belonging to the atoms Cu, Au, Ba, Pb are resonance–metastable transitions. The ideal energy-level structures for this process are those of Cu (and Au). The advantage of the simple low-lying energy levels of Cu is the very high quantum efficiency. A pulsed low-pressure discharge of metal vapor and a buffer gas (about 20 torr He or Ne) with diameters in the cm-range, current densities of several hundred A cm−2 with moderate electric fields in the order of 10 kV m−1 can provide electrons with temperatures of a few eV and a density up to 1014 cm−3 for efficient laser pumping. But a Cu-vapor pressure of 10−2 torr, corresponding Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
J 1/2 3/2 5/2
5
269
4 0
4p P J
40
2
30
-1
4p P J
3
3
Energy E [10 cm ]
9.8 ns 10.5 ns
578.2 nm
784 ns
3/2 1/2
510.6 nm
Energy E [eV]
4
370 ns
Cu
20
2 3/2 5/2
22
4s DJ
29 μs
1
67 μs
10
2
0
4s S1/2
0
Fig. 3.4.15. Energy-level diagram of the Cu I laser.
to a temperature of 1200 ◦ C is necessary to achieve sufficient trapping of the resonance radiation. Some technological difficulties resulted in the first years from this high-temperature conditions. A breakthrough in technology of Cu vapor lasers was realized in 1972, when Isaev et al. [72Isa, 73Isa] dispensed with the external furnace, and used instead waste thermal energy from the multi-kilohertz repetitions frequency discharge to heat the tube to its operating temperature of 1500 ◦ C.
3.4.5.2 Operating characteristics The fast pulsed discharge serves a dual purpose: maintenance of a sufficient, but not excessive, Cu-vapor pressure, and provision of sufficient pulse energy, to excite the Cu atoms to the upper laser level. This results in a relatively narrow range of average electric input power at which reliable operation of the laser can be achieved. Today the simplicity of the laser head (Fig. 3.4.16) and the inclusion of power-stabilizing circuits leads to a very stable output power. All Cu I laser devices operate in the self-heated regime with longitudinal low-pressure pulse discharges. Thermal insulation must be used within the gas envelope. A slow buffer-gas flow is normally used to remove impurities which are generated continuously. Figure 3.4.17 gives the typical dependence of output power Φ and green/yellow-ratio γ as a function of buffer gas and temperature of a conventional Cu I laser. The laser voltage, pulserepetition frequency, and buffer-gas pressure affect the heat balance in the laser by changing the electrical power input, i.e. the laser current is not an independent variable. Nevertheless, the specific pulse energy is over a wide range of tube bores approximately constant 5 μJ cm−1 ± 20 % [78Smi, 79Smi, 91Lew]. The green/yellow-ratio is generally 1.5. Time-averaged beam intensity profiles are uniform for laser tubes < 30 mm diameter, but display axial minima which become progressively deeper with increasing tube diameter. Without added H2 , the efficiency is about Landolt-B¨ ornstein New Series VIII/1B1
3.4.5 Self-terminating metal vapor lasers
[Ref. p. 272 40
8
Gas
Porous Al2O3
Al2O3ceramic tube
Gas
Green/ yellow-ratio g
6
Ne
30
He
Φ 4
g Ne
2
Cathode Cu droplets VitonO-ring seal
Pyrex envelope
Anode Watercooled end-flange
Fig. 3.4.16. Cu I laser tube with Mo- or Taelectrodes.
20
He
0 1300
Output power Φ [W]
270
10
1400
1500 1600 Temperature T [°C]
0 1700
Fig. 3.4.17. Green/yellow-ratio and laser output power for a conventional Cu I laser as a function of buffer gas and temperature.
1 %. The addition of about 1 % H2 to the laser gas will improve the output power and efficiency by a factor of 2, the specific pulse energy does not change. The pulse repetition frequency νmax (kHz) corresponding to maximum output power is approximately inversely proportional to the tube radius R (mm): νmax = 150/R
(1 ≤ R ≤ 30) .
(3.4.33)
νmax is mainly determined by diffusion of metastables. For larger values of R, R > 30 mm, νmax is determined by the metastables’ lifetime and approximately constant. Typical values of electric-field strength in the plasma are 100 V cm−1 , typical values of the small-signal gain of the 510.6 nm line are about 5 % cm−1 in large bore tubes [88Nay, 89Lew, 91Cou] and up to 25 % cm−1 in small bore tubes (R < 1 cm) [79Har]. Table 3.4.1 gives a summary of operating data for different Cu I laser systems. The Cu I laser is the most powerful, efficient and best-developed metal vapor laser. Commercial systems are available with output powers up to 120 W average. They have a wide field of applications in medicine, material processing and are excellent sources for pumping of dye lasers and titanium:sapphire lasers with high conversion efficiency. Related to the Cu I laser is the Au I laser. Two Au I transitions at 312.2 nm (6p2 P03/2 → 2 2 6s D5/2 ) and 627.8 nm (6p2 P01/2 → 6s2 2 D3/2 ) are analogous to the 510.6 nm and 578.2 nm lines in Cu I. The quantum efficiencies of these transitions are high: 47 % and 29 %, respectively. The Cu I laser devices with Au pieces instead of Cu pieces can be used for the Au I laser. Power supply and buffer gas are not different, the temperature for sufficient gold vapor pressure is about 200 ◦ C higher than in Cu I lasers. Average powers up to 20 W at 627.8 nm and up to 1.2 W at 312.2 nm have been reported [90Gab, 78Mar].
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
[%]
[mJ]
0.044 1.1 0.6 1.1 2.4 6.1 20 42 108 138
[kW]
∼4 ∼ 45 ∼ 30 30–40 – 120 500 280 – –
3.1 6.3 12 16 17 40 100 210 430 550
0.3 1.3 – 1.0 – 0.75 0.9 1.2 – –
Efficiency
Pulse energy
Peak power
Max. average power [W] 4.5 18 10 15 25 42 60 60 80 80
30 75 100 70 100 150 200 300 300 350
[cm]
[mm]
[W] – – – – – – – – 449 615
Active length
Tube bore
Amplifier power
– 7.2 – – – 10.5 – 20 36 69
– ∼ 350 – – – 900 – 1500 2700 2800
Peak Tube (charging) current voltage [A] [kV]
Table 3.4.1. Output power and operating conditions of self-heated Cu lasers.
– 35 – – – 50 30–60 170 80 65
70 6 20 15 7 6.5–6.7 5 5 4 4
4.5 25 – – – 15 – 23 – –
[torr] [kHz]
[ns]
[ns] – 70 – – – 80 – 80 60 40
Ne pressure
Rep. rate
Pulse duration
Current rise time
[91Vor] [94Wit] [91Lew] [77Isa] [96Wit] [95Hog] [89Lew] [94Kim] [99Lit] [99Lit]
Ref.
Ref. p. 272] 3.4 Ion lasers and metal vapor lasers 271
272
References for 3.4
References for 3.4 21Kle
Klein, O., Rosseland, S.: Z. Phys. 4 (1921) 46.
29Duf 29Lan
Duffendack, O.S., et al.: Phys. Rev. 34 (1929) 1132. Langmuir, I., Tonks, T.: Phys. Rev. 34 (1929) 876.
32Pen
Penning, F.M.: Z. Phys. 7 (1932) 454.
34Pen
Penning, F.M.: Physica 1 (1934) 763.
51Hol
Holstein, T.: Phys. Rev. 83 (1951) 1159.
54All
Allen, J.E., Thonemann, P.C.: Proc. Phys. Soc. (London) B 67 (1954) 768.
62Rab
Rabinowitz, P., Jacobs, S., Gould, G.: Appl. Opt. 1 (1962) 513.
63Rid
Ridgen, J.D., White, A.D.: Nature (London) 198 (1963) 774.
64Bel 64Bri 64Ger
Bell, W.E.: Appl. Phys. Lett. 4 (1964) 34. Bridges, W.B.: Appl. Phys. Lett. 4 (1964) 128. Gerritson, H.J., Goedertier, P.V.: J. Appl. Phys. 35 (1964) 3060.
65Lab
Labuda, E.F., Gordon, E.I., Miller, R.C.: IEEE J. Quantum Electron. 1 (1965) 273.
66Bri 66Paa 66Rud 66Sil 66Wal1 66Wal2
Bridges, W.B., Chester, A.N.: IEEE J. Quantum Electron. 1 (1966) 66. Paananen, R.A.: Appl. Phys. Lett. 9 (1966) 34. Rudko, R.L., et al.: Appl. Phys. Lett. 9 (1966) 41. Silfvast, W.T., Fowles, G.R., Hopkins, B.D.: Appl. Phys. Lett. 8 (1966) 318. Walter, W.T., Piltch, M., Solimene, N., Gould, G.: Bull. Am. Phys. Soc. 11 (1966) 113. Walter, W.T., Solimene, N., Piltch, M., Gould, G.: IEEE J. Quantum Electron. 2 (1966) 474.
67Bei 67Boe 67Gor
Beigman, I.L., et al.: JETP Lett. (English Transl.) 6 (1967) 919. Boersch, H., et al.: Phys. Lett. A 24 (1967) 695. Gorog, I., Sprong, F.W.: RCA Rev. 28 (1967) 38.
68Che 68Her 68Sil
Chester, A.N.: Phys. Rev. 169 (1968) 172. Herziger, G., Seelig, W.: Z. Phys. 215 (1968) 437. Silfvast, W.T.: Appl. Phys. Lett. 13 (1968) 169.
69And 69Fen 69Gol 69Her 69Pfa 69Sil
Anderson, D., et al.: Proc. IX-th. Intern. Conf. On Phenomena in Ionized Gases, 1969, p. 142. Fendley jr., J.R., Gorog, I., Hernqvist, K.G., Sun, C.: RCA Rev. 30 (1969) 422. Goldsborough, J.P.: IEEE J. Quantum Electron. 5 (1969) 133. Herziger, G., Seelig, W.: Z. Phys. 219 (1969) 5. Pfau, S., Rutscher, A., Wojaczek, K.: Beitr. Plasmaphys. 9 (1969) 333. Silfvast, W.T.: Appl. Phys. Lett. 15 (1969) 23.
70Boe
Boersch, H., Boscher, J., Hoder, D., Schafer, G.: Phys. Lett. A 31 (1970) 188.
71Bri
Bridges, W.B., Chester, A.N., Halsted, A.S., Parker, J.V.: Proc. IEEE 59 (1971) 728. Landolt-B¨ ornstein New Series VIII/1B1
References for 3.4
273
71Gia
Giallorenzi, T.G., Ahmed, S.A.: IEEE J. Quantum Electron. 7 (1971) 11.
72Her 72Isa 72Kit
Hernqvist, K.: IEEE J. Quantum Electron. 8 (1972) 740. Isaev, A.A., et al.: JETP Lett. (English Transl.) 16 (1972) 27. Kitaeva, V.F., et al.: Sov. J. Quantum Electron. (English Transl.) 1 (1972) 134.
73Alf 73Her 73Isa
Alferov, G.N., et al.: JETP Lett. (English Transl.) 18 (1973) 369. Herziger, G., Liithi, H.R., Seelig, W.: Z. Phys. 264 (1973) 61. Isaev, A.A., et al.: Instr. Exp. Techn. 16 (1973) 228.
74Aki 74Ban 74Miy
Akirvata, O.S., et al.: Sov. J. Quantum Electron. (English Transl.) 3 (1974) 519. Banse, K., L¨ uthi, H.R., Seelig, W.H.: Appl. Phys. 4 (1974) 141. Miyazaki, K., et al.: Jpn. J. Appl. Phys. 13 (1974) 1066.
75Dav 75Lue 75Miz1 75Miz2 75Miz3
Davis, C.C., King, T.A.: Advances in Quantum Electronics, New York: Academic Press, 1975. L¨ uthi, H.R., Seelig, W.: Appl. Phys. 6 (1975) 261. Mizeraczyk, J.K.: IEEE J. Quantum Electron. 11 (1975) 218. Mizeraczyk, J.K.: J. Appl. Phys. 46 (1975) 1847. Mizeraczyk, J.K.: Rep. Symp. Optics Quantum Electron. 9 (1975).
76Bur 76Lue1 76Lue2
Burkhard, P., et al.: Opt. Commun. 18 (1976) 485. L¨ uthi, H.R., et al.: IEEE J. Quantum Electron. 12 (1976) 317. L¨ uthi, H.R., et al.: Z. Angew. Math. Phys. 27 (1976) 101.
77Isa 77Lue1 77Lue2
Isaev, A.A., et al.: Sov. J. Quantum Electron. (English Transl.) 7 (1977) 253. L¨ uthi, H.R., et al.: IEEE J. Quantum Electron. 13 (1977) 404. L¨ uthi, H.R., Seelig, W.H.: J. Appl. Phys. 48 (1977) 4922.
78Ban 78Lue 78Mar 78Mor 78Smi
Banse, K.H.: Dissertation, Universit¨ at Bern, 1978. L¨ uthi, H.R., Seelig, W.H.: High-Power-Lasers and Applications, Kompa, K.L., Walther, H. (eds.), Berlin, Heidelberg, New York: Springer-Verlag, 1978, p. 119. Markova, S.V., et al.: Sov. J. Quantum Electron. (English Transl.) 8 (1978) 904. Mori, M., et al.: IEEE J. Quantum Electron. 14 (1978) 427. Smilanski, I., Kerman, A., Levin, L.A., Erez, G.: Opt. Commun. 25 (1978) 79.
79Har 79Smi
Hargrove, R.S., Grove, R., Kan, T.: IEEE J. Quantum Electron. 15 (1979) 1228. Smilanski, I., Erez, G., Kerman, A., Levin, L.A..: Opt. Commun. 30 (1979) 70.
81Got
Goto, T., et al.: J. Phys. D 14 (1981) 575.
82Got
Goto, T., Sakurai, T.: J. Phys. D 15 (1982) 2413.
84See
Seelig, W.: Proc. SPIE 455 (1984) 2.
86Apo
Apolonskii, A.A., et al.: Sov. J. Quantum Electron. (English Transl.) 13 (1986) 1004.
88Nay
Naylor, G.A., Lewis, R.R., Kearsley, A.J.: Gas Laser Technology; Proc. SPIE 894 (1988) 110.
89Alf
Alferov, G. N., et al.: Sov. J. Quantum Electron. (English Transl.) 16 (1989) 945.
Landolt-B¨ ornstein New Series VIII/1B1
274
References for 3.4
89Lew
Lewis, R.R., Maldonada, G., Webb, C.E.: Metal Vapour, Deep Blue and Ultraviolet Lasers; Proc. SPIE 1041 (1989) 54.
90Gab
Gabay, S., Hen, I., Lando, M.: High-Power Gas Lasers; Proc. SPIE 1225 (1990) 260.
91Cou 91Lew 91Vor
Coutts, D.W., et al.: CLEO91, Tech. Dig., Opt. Soc. Am., 1991, p. 518. Lewis, R.R.: Opt. Quantum Electron. 23 (1991) 493. Vorobev, V.B., et al.: Sov. J. Quantum Electron. (English Transl.) 21 (1991) 1067.
94Kim 94Wit
Kimura, H., et al.: J. Nucl. Sci. Technol. 31 (1994) 34. Withfordet, M.J., Brown, D.J.W., Piper, J.A.: Opt. Quantum Electron. 26 (1994) 1089.
95Hog
Hogan, G.P., Webb, C.E.: Opt. Commun. 117 (1995) 570.
96Wit
Withford, M.J., et al.: IQEC96, Techn. Dig. Opt. Soc. Am. (1996) 238.
99Lit
Little, C.E.: Metal Vapour Lasers, New York: Wiley, 1999.
00Bri
Bridges, W.B.: IEEE J. Sel. Topics Quantum Electron. 6 (2000) 885.
03Don
Donin, V.I., Ivanov, V.A., Pickalov, V.V., Yakovin, D.V.: J. Phys. D 36 (2003) 2366.
04LFW
Laser Focus World 40 (2004) 49.
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
255
3.4 Ion lasers and metal vapor lasers W. Seelig
3.4.1 Introduction Since the first ion laser was built in 1964 [64Bel, 00Bri], several hundreds ion laser transitions in the visible and near UV spectral range have been reported [66Bri]. Generation of these ion transitions requires low-pressure arc discharges containing noble gases or metal vapors to provide electron densities exceeding 1013 cm−3 . The corresponding high threshold current densities for ion laser excitation of more than 100 A cm−2 mostly permit only quasi-cw pulsed mode operation. The spectral range of ion lasers is the largest of all lasers, down to the X-ray region if high-Z ions are considered. Although the pump power densities increase rapidly with the laser frequency and other excitation methods must be used, some similarities to visible-range ion lasers are present. This review is restricted to classical visible and near-ultraviolet ion lasers. These are commercial systems and, in particular, noble gas ion lasers with high continuous power levels. Historically ion lasers and metal vapor lasers are closely related. The first metal vapor laser was the optically pumped cw Cs laser. [62Rab]. Difficulties with alkali metals and high temperatures have stimulated the search of other potential laser media, e.g. Hg with well-established lamp technology. So the first gas discharge metal vapor laser was a Hg I laser [63Rid]. The first gas ion laser invented by Bell [64Bel] also used mercury, the first laser with doubly ionized Hg was demonstrated by Gerritson and Goedetier [64Ger]. More important was the discovery of the continuous 488 nm Ar ion laser action in Ar–Hg-mixture discharges by Bridges et al [64Bri]. The He–Hg+ laser inspired Fowler and Silfvast to the search for new laser transitions in other He–metal discharges. A result was the continuous He–Cd+ laser, a successful commercial metal vapor laser [66Sil]. The discovery of the Cu I and Au I laser, another type of metal vapor laser, by Walter et al. [66Wal1, 66Wal2] in 1965 has started the very successful development of self-terminating resonancemetastable metal vapor lasers with repetitively pulsed metal–noble-gas low-pressure discharges. The Cu I laser is the most powerful, efficient, and best developed metal vapor laser. Oscillating on the Cu I transitions at 510.6 nm and 578.2 nm wavelength, average output powers of up to 500 W have been demonstrated from oscillators. Commercial lasers are available with output powers of up to 120 W at an efficiency of 1 %. Typical laser pulses have 10 . . . 100 ns in duration at pulse repetition rates of up to 200 kHz with peak powers of up to several hundred kW. Different metal vapor lasers are the subjects for a few thousand contributions in the scientific literature. In a comprehensive book C.E. Little [99Lit] gives a current review. This contribution is concentrated on commercially available laser systems. Therefore, the last part is restricted to the copper vapor laser, representing the class of self-terminating metal vapor high-power lasers.
Landolt-B¨ ornstein New Series VIII/1B1
256
3.4.2 Properties of gas discharge laser media
[Ref. p. 272
3.4.2 Properties of gas discharge laser media The capability of materials to amplify light of a specific wavelength if two excited levels are inversely populated, is characterized by the small-signal gain g0 . To establish population inversion, spontaneous emission losses must be compensated by a pumping mechanism. For this balance the necessary pump power density for the laser threshold P (e.g. g0 = 10−2 cm−1 ) can be estimated (Fig. 3.4.1). Here η is the fluorescence efficiency which – for most laser media – is in the percent range [84See]. 10 7
S [W cm-2 ]
10 5
10 3
10 1
10-1 10
1000 100 Laser wavelength l [nm]
Fig. 3.4.1. Threshold energy current density S = P η/g0 versus laser wavelength λ (Dopplerbroadened gas laser transitions).
There are two remarkable items resulting from these considerations: 1. P increases with more than λ−4 for short wavelengths, i.e. generation of short-wavelength laser radiation requires active media of high power density. 2. The pump power density threshold for many gas lasers is by orders of magnitude lower than it is for solid-state or dye lasers because of the narrow fluorescence line width. This is of advantage for continuous operation. Here only laser transitions in the visible and UV spectral range of atoms or ions excited in lowpressure gas discharges are considered. The lines are Doppler-broadened, and the λ−4 -dependence of the threshold energy density is realized: ΔνD ηP > 5 · 10−22 , g0 λ3 √ Δ ν D = v¯ ln 2/λ0 , v¯ = 8 kT /mπ S=
(3.4.1) (3.4.2)
with Δ ν D : Doppler width, T : gas temperature, m: atomic mass, k: Boltzmann constant. In the gas discharge the electron gas transforms the input energy into excitation energy of the laser levels. The pumping process by electron collisions is limited by its inverse destructive process of inversion due to electron collisions of second kind. Using the relation of Klein–Rosseland [21Kle]
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
-3
Electron density ne [cm ]
10
3.4 Ion lasers and metal vapor lasers
257
20
Ù
ne
1017 1014 Ú
ne h g0 L
1011 10 8 1
100 10 Laser wavelength l [nm]
1000
Fig. 3.4.2. Electron-density region of laserrelevant plasma.
σ21 ve g1 ω = exp , σ12 ve g2 kTe
(3.4.3)
a condition for the electron temperature Te in the plasma results. σ12 , σ21 are the cross sections of electrons interacting with the laser atoms, g1 , g2 are the statistical weights of the lower (1) and upper (2) state, respectively. ve is the electron velocity, and ω = 2π/λ. Usually the difference between the lifetimes is about one order of magnitude or less, and from (3.4.3) results: kTe ≥ ω .
(3.4.4)
kTe /me /2L (L: active length) gives the lowest necessary
ˇ e = 0.4 g0 L/ηλ5/2 . ne > n
(3.4.5)
Equation (3.4.1) and P < 3ne kTe electron density n ˇ e for laser action:
Fluorescence quenching of the laser radiation dominates if ne > A21 / σ−2 ve . Using the maximum possible value of the destruction cross section by electron collisions σ−2 ve ∼ = π2 2 /me 2π me kTe , A21 = f21 · 2e20 ω 2 /4π ε0 c3
(3.4.6)
(3.4.7) (3.4.8)
with A21 : Einstein coefficient, f21 : oscillator strength, ω: frequency of the laser transition, me : electron mass yields the inequation: ne < n ˆe ∼ = 103 /λ5/2 .
(3.4.9)
n ˆ e : highest electron density for laser action. kT ≥ hω and (3.4.5), (3.4.9) give the region of laserrelevant plasmas (Fig. 3.4.2). These results are valid in a wide range of laser wavelengths from the visible to the XUVspectrum. Especially the power limits of self-terminating pulse lasers can be estimated using (3.4.9). Landolt-B¨ ornstein New Series VIII/1B1
258
3.4.2 Properties of gas discharge laser media
[Ref. p. 272
Quasi-cw or continuously operating lasers have more restrictive conditions given by bottle necks in their laser mechanism which lead to an increased lifetime of the lower laser level. In the shortwavelength regime radiation trapping is important. The ensemble average value of the radiative decay time τ1 of the lower laser level is characterized by the escape factor F , were τ10 is the rad. lifetime of the single atom: 1/τ1 = F/τ10 .
(3.4.10)
F can be calculated using for instance the theory of Holstein [51Hol], but the theory is not applicable to values of F > 1/4. For large F -values which are of interest for lasers the simpler approximation τ1 = τ10 + g1 λ310 RN/4π2 v¯ gN
(3.4.11)
gives good results [78Ban]. N is the ground-state density, gN its statistical weight, R the radius of the active medium, v¯ the thermal velocity, and λ10 the wavelength of the escaped radiation from the lower laser level to the ground state. Based on this relation, and on stationary rate equations of the lower-laser-level population inequalities for the maximum laser output power and conditions for the ground-state densities of laser atoms/ions can be estimated. The population density of the lower laser level N1 is given by N1 g2 τ 1 ρ g2 N2 N1 N2 − N1 = 1− (3.4.12) − − P1 < P L = B21 ω g1 τ1 τ2 τ1 g1 τ2 with ρ: energy density of the radiation field, g2 , g1 : statistical weights, N2 : population density of the upper laser level, N2 > g2 N1 /g1 , τ2 , τ1 : time constants of the upper and lower laser level, respectively, P1 : pumping rate into the lower laser level, P2 : pumping rate into the upper laser level, B21 : Einstein coefficient of stimulated emission. For a closed cycle of the process with a time constant τN it is necessary that v. N = (P1 + P2 )τN = PΣ τN > PΣ R/¯
(3.4.13)
For a three-level laser process results with (3.4.11): g2 τ10 g2 λ310 R2 PΣ − P L R2 < PΣ R2 1 − g1 τ2 gN 4 π2 τ2 v¯2 and P L < PΣ
1−
g2 τ10 g2 λ310 RN − g1 τ2 gN 4 π2 τ2 v¯
(3.4.14)
.
(3.4.15)
P L · ω is the laser output power per volume unit. Equation (3.4.15) gives upper limits of the ground-state density of atoms or ions, respectively. The right term of (3.4.14) becomes maximal for 1 g1 τ10 + τ2 (3.4.16) τ1 = 2 g2 and an equation for the specific output power ΦL of the laser results: ΦL = π R2 P L ω < π2
gN τ2 kT ω . g2 m λ310
(3.4.17) Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
259
Equation (3.4.17) is also valid for a four-level laser process. λ10 is always the wavelength corresponding to the energy gap between ground state and lower laser level. From (3.4.17) results: If only ion levels are involved in the cw laser process then T represents the ion temperature. For atom lasers T is the neutral gas temperature. In a powerful laser discharge the ion temperatures are up to two orders of magnitude higher compared to the neutral gas temperatures. Furthermore, the distances between the ion energy levels are larger compared to the atomic levels due to the stronger binding of the lightning electron, so for ions λ10 can be smaller than for atoms of the same gas. So the maximum laser output power of cw ion lasers can be more than two orders of magnitude higher compared to cw atom lasers.
3.4.3 Noble gas ion lasers 3.4.3.1 Excitation mechanism Noble gas ion lasers are powerful continuous sources of coherent radiation in the visible and nearUV spectrum. High-power radiation of several ten watts has been generated continuously from many ionic transitions excited in highly ionized low-pressure arc discharges [66Paa, 71Bri, 69Her, 70Boe, 74Aki, 76Lue1, 76Bur, 77Lue1, 73Alf, 68Her, 86Apo]. Among these, the argon ion laser with continuous emission up to 0.5 kW in the visible is the most prominent. The behavior of the Ar II 4p–4s transitions turns out to be typical for most of the ion laser transitions in noble gases and metal vapors, respectively. In theoretical and experimental investigations [68Her, 69Her] the Ar II laser has therefore been studied as a model for continuous ion lasers in general. The energy levels of the argon ion contributing to the laser process are the excited level groups Ar II 4p (upper laser level), and Ar II 4s, Ar II 3d next to the ion ground state Ar II 3s2 3p4 3p. Figure 3.4.3 shows a generalized energy level diagram for the Ar II 4p–4s laser transitions. From quantum-mechanical selection rules the Ar II 4s–3p is an allowed transition while the Ar II 4p–3p transition is forbidden, so that radiative decay of the 4p to the ion ground state is of the type 500 nm
70 nm
Ar II 4p −→ Ar II 4s −→ Ar II 3p . The 4p decay time exceeding that of the 4s by an order of magnitude, consequently the selection rules and the high decay rate of the 4s term automatically insure a population inversion of strongly allowed transitions of the type 4p → 4s in argon, provided that the supply rate of excited 4p and 4s ions is of the same magnitude. This means, incident radiation in the 500 nm region will be amplified. In steady-state gas discharges with average electron energies of a few eV stepwise excitation will consequently dominate over all other excitation processes: e + A+ → e + A+ ∗ .
(3.4.18)
This has in fact be verified by theoretical modeling in agreement with a number of experiments performed with noble-gas lasers [68Her, 67Boe, 67Bei, 67Gor, 65Lab, 66Rud]. In the case of predominant stepwise excitation the number of lasing atoms PL generated per unit time in the unit volume of the active medium rises quadratically with the electron density ne , and the output power per unit length Φ may be written as Φ ∝ R2 PL = f (kTe )R2 n2e , Landolt-B¨ ornstein New Series VIII/1B1
(3.4.19)
260
3.4.3 Noble gas ion lasers
Energy E [eV]
t ~7.5 ns t~ 9.1 ns 33.0 32.9 32.8
284 267
2
4s P
16.0 15.9 15.8 15.7
285
1/2
266
3/2
t~ 0.36 ns ~ 72 nm
265
-1
35.2
286
457.9 nm 476.5 nm 496.5 nm 488.0 nm 514.5 nm
3
4p D
287
Energy E [10 cm ]
4 0
288
3/2 1/2 3/2 5/2 1/2 3/2 5/2 7/2
⎫ ⎬ ⎭
4p P
4p2D0
⎫ ⎬ ⎭
35.4
2 0
1/2 ⎫ ⎬ ⎭
35.6
289
4p2S0 ⎫ ⎬ ⎭
35.8
[Ref. p. 272
264 129
1/2 +
5
Ar 3p
128
2 0
P
3/2
127 126
0
Ar
0
Fig. 3.4.3. Generalized energy level diagram for the Ar II 4p–4s laser transitions.
if quenching of inversion is neglected. Maximum pumping rates PL for Ar II laser levels have been calculated [68Her, 75Lue] to occur for neutral gas densities N according to N R = const. = 3 · 1014 (cm−2 ) .
(3.4.20)
Low-pressure arc discharges with a mean electron energy of about kTe = 4 eV satisfy this condition. “Boltzmann-invariant similarity laws” [69Pfa] for the electron distribution function in optimized laser plasmas are the consequence. Substituting (3.4.20) into (3.4.19) the maximum power per unit length can be written as Φ ∝ (ne /N )2 ∝ (ne R)2 ,
(3.4.21)
x = ne /N is about the degree of ionization. The output power of ion lasers is limited for two reasons that set an upper limit to both discharge parameters x and kTe : 1. The processes leading to an inversion density are quenched a) by collisional depopulation of the upper laser level and b) by radiation trapping that limits the decay of the lower laser level [75Lue]. 2. The range of parameters favorable for high inversion densities may not be achieved in stable low-pressure arc discharges [71Bri]. The effects that quench the inversion are well known in the case of Ar II lasers and have been described quantitatively [75Lue]. According to (3.4.19), collisional depopulation of the upper laser level by electrons sets an upper limit for ne . Hence (3.4.21) Φ ∝ R2 ,
(3.4.22)
and a large tube radius should be used for high-power generation. Radiation trapping of the lowerstate decay depends on the optical thickness k0 · R of the 70-nm VUV resonance radiation, where Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
k0 = 7 · 10−14 ne · (kTi )−1/2
261 (3.4.23)
with k0 : absorption coefficient, Ti : ion temperature. An upper limit for k0 R results, and Φ ∝ (kTi )1/2 .
(3.4.24)
So high ion temperatures must be achieved in the laser plasma, large R values are helpful, but kTi < kTe sets an upper limit. Different experiments confirm the following relations for the temperatures in the Ar ion laser plasma [73Her]: Ti = Ti0 + 0.90 (jR) , Ta = Ta0 + 0.75 (jR)
(3.4.25)
with Ti0 = 2800 K, Ta0 = 1500 K, 15 < jR (A cm−1 ) < 150, j: current density.
3.4.3.2 Operating characteristics Continuous ion lasers are sophisticated sealed off devices. Their operation conditions are close to the destruction limits of the tube material. More than 99.8 % of the input energy heats the tube walls with energy flux densities of 1 kW cm−2 . Due to radial ion currents up to 10 A cm−2 with ion energies > 20 eV rapid sputtering occurs for the most wall materials. The discharge density of 1015 cm−3 requires Ultra-High Vacuum (UHV) cleanness (without any vapor impurities). Furthermore, discharge instabilities (e.g. [03Don]) can avoid good operation conditions.
3.4.3.2.1 Neutral gas depletion A stationary low-pressure arc can only be stable if the ion wall current is equal or smaller than the back flow of neutral gas from the tube wall into the plasma volume. The comparison between the radial current density of ions and neutral atoms gives 0.55 ne (kTe /m)1/2 = N (kTa /2πm)1/2 ,
(3.4.26)
where Ta is the temperature of the neutral atoms and m is the atom mass. Equation (3.4.26) is independent of the discharge diameter and of the discharge gas. It can be used to calculate the macroscopic parameter of the stability limit. The parameter jR and pR allow a geometricindependent representation [77Lue1]. Figure 3.4.4 shows the plasma parameter kTe versus ne R for stable Ar II laser arc discharges (ΔN ∝ g0 ).
Landolt-B¨ ornstein New Series VIII/1B1
262
3.4.3 Noble gas ion lasers
[Ref. p. 272
7.5
Plasma parameter kTe [eV]
Unstable discharge
5.0
Stable discharge ΔN ≥ 0 2.5
ΔN<0
0 1
2
5 -2 13 ne R [10 cm ]
10
20
Fig. 3.4.4. Plasma parameter kTe versus ne R for stable Ar II laser arc discharges (ΔN ∝ g0 ).
3.4.3.2.2 Axial gas pumping Axial gas pumping creates density gradients between the cathode and the anode [68Che]. The gas pumping in ion laser plasmas is due to the balance of axial momentum: In the plasma column electrons and ions gain equal but opposite momentum from the electric field. In a first approximation only the momentum of electrons can be transmitted to the neutral gas, the momentum of ions is transmitted to the wall. In the low-pressure discharges the radial potential distribution is reflecting nearly all electrons, whereas the ions are accelerated towards the wall [29Lan, 76Lue2]. As a result, a pressure gradient occurs in direction to the anode. This gradient can be reduced by connecting anode and cathode vessels with a bypass. For an Ar laser plasma the following relation is found by a first approximation [77Lue2]: j = 6 · 105 (R1 /R)4 (x/L1 ) (Δp/p)
(3.4.27)
with R1 : radius of the (external) bypass tube, L1 : length of the (external) bypass tube, p: filling pressure, x: degree of ionization. In general, a sufficient bypass should have a cross section which is one order of magnitude larger than the discharge cross section.
3.4.3.2.3 Transition regions Equation (3.4.26) suggests that neutral gas depletion sets a general upper limit to stable ion laser discharges. In a real discharge device, however, other current limiting effects are to be expected, which are due to axial density gradients and due to space-charge layers [71Bri]. A comparison of axial current density with neutral current density due to thermal remotion leads in a first approximation [69And] to N (kTa /2 π m)1/2 ≥ 2(me /m)1/2 · j .
(3.4.28)
This effect can be overcome by the design of the discharge tube ends [71Bri] in connection with magnetic fields. Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
263
3.4.3.2.4 Magnetic fields Magnetic fields have in most cases a positive effect on the ion laser plasma. Instabilities are results of mismatching to the discharge geometry or of the self-magnetic field of the discharge current. Axial magnetic fields are used to reduce sputter effects, and for stabilization of the arc column. Such fields mainly influence the electrons. The reduction of their radial mobility by the magnetic field leads to a decrease of the radial electric field, especially to a reduction of the negative wall potential, and therefore of the ion impact energy. The quenching of the radial ion current sets a limit for the magnetic field strength Bz [74Ban]: Bz R 1.5 (V s/m) .
(3.4.29)
Axial magnetic fields are indispensable for arc-stabilization in modern ion laser tube structures. During a long period of development all these problems have been solved. Modern commercial ion laser devices use copper–tungsten disc discharge tubes with integrated bypass, axial magnetic fields to stabilize the arc discharge and prevent sputtering damage. The use of tungsten in the central part is necessary. This metal has the highest sputter threshold energy and UHV-capabilities. Figure 3.4.5 shows a schematic cross section of the W–Cu discharge tube structure. Figure 3.4.6 shows a commercial ion laser tube construction. Cooled magnet
Magnet
Anode
Water Ceramic envelope Copper
Heated cathode Water cooling
Tungsten disk Bore Gas reservoir
Gas return holes Ceramic ring Brewster window Fig. 3.4.5. Schematic cross section of the W–Cu discharge tube structure.
Fig. 3.4.6. Commercial ion laser tube construction.
3.4.3.2.5 Summary of operation parameters The operation parameters of Ar II/Ar III lasers are summarized in Figs. 3.4.7–3.4.11 using the generalized scaling parameters [73Her, 77Lue1, 78Lue]. The results of the Ar laser are transferable to other ion lasers with relatively small modifications. Furthermore of commercial interest is Kr with lines in the red part of the spectrum. The following commercial lasers are usually available: Ar II: Output power up to 30 W, 10 lines in the range 454.5 . . . 528.7 nm with 40 % output power in 488 nm and in 514.5 nm too; efficiency 1 ◦/◦◦ . Landolt-B¨ ornstein New Series VIII/1B1
264
3.4.3 Noble gas ion lasers Doppler width DnD [GHz] 3
4
6
[Ref. p. 272
9 -1
[W m ]
200 12
Max.output power per unit length fL
-1
-1
Small-signal gain g0 [% cm ]
1.0
0.5
0
50
100
150 -1
jR [A cm ] Fig. 3.4.7. Small-signal gain of the 488 nm Ar II line of a high-power laser (R = 0.6 cm) versus product of radius and mean current density jR.
100 50 +
Ar visible 10 5 ++
Ar UV 1
20
50
100 -1 jR [A cm ]
200
Fig. 3.4.8. Maximum output power of the Ar II/Ar III laser (all lines) per unit length versus product of radius and mean current density jR.
1
^
Ez R [ V ]
2
0
0
200
100 -1
jR [A cm ]
300
Fig. 3.4.9. Product of axial field strength and radius Ez R versus jR for optimum laser operation.
Ar III: Output power up to 5 W, 2 lines, 50 % on 363.7 nm and 50 % on 351 nm. Kr II: Output power up to 20 W, 13 lines in the range 406.7 . . . 799.3 nm; efficiency 1 ◦/◦◦ . More details, other wavelengths, and the actual state of the art are summarized in Laser Focus World [04LFW]. For about twenty years basic research of continuous (low-Z) ion lasers is well established. Some results are applicable to new XUV high-Z ion lasers. By means of continuous ion lasers a series of new research fields have been opened in the past. Until now Ar/Kr ion laser systems hold a nonnegligible position on the laser market. These lasers have many applications especially in science and medicine. Their advantage in comparison with other systems is the nearly perfect beam quality of continuous duty lasers.
Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
265
50 351.1 nm 363.8 nm
-1
[W m ]
Ar III
-1
[W m ]
5
333.6 nm Ar III 334.4 nm 335.8 nm
2
305.4 nm Ar III 302.4 nm 300.2 nm
-1
10
350.7 nm Kr III 356.4 nm
312.4 nm Kr III 323.9 nm 337.4 nm
2
1 100
Max.output power per unit length fL
Max.output power per unit length fL
-1
20
200
500
1000
-1
jR [A cm ] Fig. 3.4.10. Maximum UV laser output power versus jR of Ar III and Kr III laser.
1
0.5
0.2
0.1 100
Ar III 275.4 nm
200
-1
jR [A cm ]
500
Fig. 3.4.11. Maximum UV laser output in the short-wavelength range of the Ar III laser versus jR.
3.4.4 Helium metal ion lasers 3.4.4.1 Excitation mechanism Many metal ion laser transitions can be excited by charge-transfer (Duffendack) reactions [29Duf] (3.4.30) and Penning ionization [32Pen, 34Pen] (3.4.31): He+ + M → He + M+ ∗ ,
(3.4.30)
Hem + M → He + M+ ∗ + e .
(3.4.31)
The Duffendack-process is resonant, typical energy intervals are 0.1 . . . 0.4 eV for energy-level coincidence. The Penning-process is nonresonant, since the liberated electron can remove the excess energy. Noble gases like He and Ne have metastable states (e.g. Hem ) and ions of high energy that is sufficient to supply ionization and excitation energy of many metals like Hg, Zn, Cd, Se, Te, etc. The continuous He–Cd laser is the most successful of all metal ion lasers, an ultraviolet/blue companion to the He–Ne laser. Laser oscillation on the blue line was first obtained in 1966 by Silfvast et al. [66Sil], continuous laser operation in 1968, and in 1969 the first continuous UV laser operation also by Silfvast [68Sil, 69Sil, 69Gol]. Between 1969 and 1976 He–Cd+ lasers provided the shortest cw wavelength (325 nm) of any laser type. The operation conditions and power-limiting processes are representative to all continuous lasers with metal-noble-gas low-pressure arc columns. Figure 3.4.12 shows the energy-level diagram of He–Cd+ . The upper laser levels of the Cd II 441.6 nm and Cd II 325 nm transitions have relatively long decay time constants, so large population densities can be realized by cascade transitions of Landolt-B¨ ornstein New Series VIII/1B1
3.4.4 Helium metal ion lasers
J 3/2 1/2
3
2 S1
160 2 6s S1/2 J ~ 3/2 t 285 ns 2 0 5s2 PJ 5/2 140
18
t~ 810 ns 16
14
J 3/2 1/2
325.0 nm 2 0
5p PJ
0
441.6 nm
120
t ~ 2.19 ns t~ 5.07 ns + 2
8.99
3
Energy E [eV]
2 0
6p PJ
-1
1
2 S0 20
180
Cadmium
Helium
22
[Ref. p. 272
Energy E [10 cm ]
266
Cd 5s S1/2
Cd
100 72.54
0
Fig. 3.4.12. Energy-level diagram of He–Cd+ .
higher-lying Cd II levels. The dominant laser pump process in He–Cd glow discharges is Penningionization of Cd. The Duffendack process is also possible. The He ionization energy of 24.5 eV is nearly fitted to many energy levels of Cd II. The excitation process by the Penning reaction has the same limitation as in He–Ne lasers: the quenching of metastable densities by destructive electron collisions. The volume recombination of the ions in low-pressure discharges is not very probable, an advantage for the Duffendack process. The lower laser levels have lifetimes in the nanosecond range. Resonance radiation trapping blockade of these transitions to the Cd II ground state is (comparable to the Cu I laser) nearly two orders in magnitude larger than in Ar II lasers. This results in output powers of about 1 % of an Ar II laser.
3.4.4.2 Operating characteristic of the continuous He–Cd laser The active medium of a He–Cd+ laser is a low-pressure glow discharge column similar to the He–Ne laser discharge. The low operating temperature of 330 ◦ C corresponding to sufficient Cd vapor pressure makes the technology simple. Hollow cathode discharges can be used as well. A very good beam quality will result, if the glow discharge operates in the cataphoretic variant. In the cw He–Cd discharge Cd moves to the cathode region. The Cd transport rate ΓB through the bore is given by Hernqvist [72Her, 69Fen]: ΓB N0 αμ+ (U/L)
(3.4.32)
with N0 : Cd vapor density at the Cd pool near the anode, α: degree of ionization of Cd, Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
Cataphoretic containment section
Evaporator
Cataphoretic containment section
Bypass
Discharge tube 1 mm l.D. Thermionic cathode
Condenser Auxiliary anode
20
10
10
100
a
Output power f [mW]
Fig. 3.4.13. He–Cd+ recirculation laser tube.
Output power f [mW]
Output power f [mW]
Anode
Grid structure
267
200
12
10
b
Discharge current I [mA]
13
10 -3 Cd vapor density [cm ]
20
10
0
2
c
6 4 He pressure [Torr]
8
10
Fig. 3.4.14. Output power Φ of a cataphoretic 441.6 nm He–Cd+ laser, versus (a) discharge current, (b) Cd vapor density, (c) pressure (laser tube: 3.5 mm bore, 124 cm discharge length).
μ+ : Cd ion mobility in He, U : potential drop over the length L. To avoid axial pressure gradients with resulting stability and noise problems of the discharge a bypass between cathode and anode region is necessary. The cross section of the bypass must be about a factor of hundred larger than the discharge cross section (Fig. 3.4.13). A metallic grid structure in the bypass prevents electrical breakdown. Today mainly constructions with integrated recirculation geometry, symmetrical cathode positioning in the center, and two anodes are used. The smallsignal gain is typically 0.05 . . . 0.08 % cm−1 [78Mor, 75Miz1] at 441.6 nm and 0.03 . . . 0.04 % cm−1 at 325 nm. It can be increased by a factor of four by use of a single 114 Cd isotope in place of the natural isotopic mixture [74Miy, 71Gia]. Figure 3.4.14 gives operating parameters for optimum output power [78Mor]. The plasma parameters of the He–Cd arc column are investigated in different ways [75Miz1, 74Miy, 71Gia, 82Got, 75Miz2, 75Miz3]. An electron density of about 1012 cm−3 was obtained in 3-mm diameter discharges by spectroscopic measurements. The electron temperature for optimum Landolt-B¨ ornstein New Series VIII/1B1
268
3.4.5 Self-terminating metal vapor lasers
[Ref. p. 272
laser conditions is about 3.5 . . . 3.7 eV and nearly invariant in all laser discharges, i.e. the velocity distribution function of electrons is invariant for optimum laser plasma conditions. Therefore, “Boltzmann-invariant similarity laws” are applicable [69Pfa]. Resulting scaling rules agree with experiments in a first-order approximation [99Lit]: jR = 2.3 . . . 2.6 mA mm−1 , Ez R = 3 . . . 4 V , PHe R = 4 . . . 5 torr mm , PCd R = 10−3 torr mm , g0 R = 2 · 10−4 , Φ/LR = 1 . . . 3 mW cm−2 with Ez L: voltage drop, jπR2 : discharge current, PHe : He pressure, PCd : Cd pressure, g0 : smallsignal gain, Φ: output power, L: active length, R: bore radius in the mm-range. Although a lot of research and development has gone into these lasers in the past, they hardly have any more meaning in today’s laser market. Modern solid-state laser systems easily exceed their specifications.
3.4.5 Self-terminating metal vapor lasers 3.4.5.1 Excitation mechanism Self-terminating lasers are operated with pulse durations (typically 10 . . . 100 ns) shorter than the effective upper-level lifetime and above all characterized by high gains (ASE is possible), and high peak output powers. The most powerful self-terminating metal vapor lasers oscillate on transitions between resonance and metastable levels (“resonance–metastable lasers”). The three-energy-level structure with ground state, resonance level, and metastable level of Cu I terms is a typical example (Fig. 3.4.15). The rise time of the excitation pulse must be shorter than the radiative lifetime of the upper level in order to achieve inversion. A large inversion density is necessary because the gain duration is often only in the 10 ns range. So a low-Q resonator must be used to extract power under high-gain conditions. Walter et al. [66Wal1] specified the criteria for efficient laser conditions. Electron-impact pumping from the ground state favors population of lowest resonance levels. The cross sections are proportional to the oscillator strengths. On the other hand, the decay due to resonance radiation in the ground state is very fast. Therefore, resonance-radiation trapping of this transition is necessary. This is realized if the metal vapor density exceeds values of 1013 cm−3 (3.4.11). So the upper laser level decays mainly to the lower laser level. The Einstein A coefficient for the laser transition should be smaller than that for the excitation transition but larger than that of the relaxation transition. For efficient laser action in the visible spectrum, the lower laser level should lie between 0.75 eV and 2.25 eV in order to avoid thermal population by collisions, but to achieve a high quantum efficiency. The most powerful transitions belonging to the atoms Cu, Au, Ba, Pb are resonance–metastable transitions. The ideal energy-level structures for this process are those of Cu (and Au). The advantage of the simple low-lying energy levels of Cu is the very high quantum efficiency. A pulsed low-pressure discharge of metal vapor and a buffer gas (about 20 torr He or Ne) with diameters in the cm-range, current densities of several hundred A cm−2 with moderate electric fields in the order of 10 kV m−1 can provide electrons with temperatures of a few eV and a density up to 1014 cm−3 for efficient laser pumping. But a Cu-vapor pressure of 10−2 torr, corresponding Landolt-B¨ ornstein New Series VIII/1B1
Ref. p. 272]
3.4 Ion lasers and metal vapor lasers
J 1/2 3/2 5/2
5
269
4 0
4p P J
40
2
30
-1
4p P J
3
3
Energy E [10 cm ]
9.8 ns 10.5 ns
578.2 nm
784 ns
3/2 1/2
510.6 nm
Energy E [eV]
4
370 ns
Cu
20
2 3/2 5/2
22
4s DJ
29 μs
1
67 μs
10
2
0
4s S1/2
0
Fig. 3.4.15. Energy-level diagram of the Cu I laser.
to a temperature of 1200 ◦ C is necessary to achieve sufficient trapping of the resonance radiation. Some technological difficulties resulted in the first years from this high-temperature conditions. A breakthrough in technology of Cu vapor lasers was realized in 1972, when Isaev et al. [72Isa, 73Isa] dispensed with the external furnace, and used instead waste thermal energy from the multi-kilohertz repetitions frequency discharge to heat the tube to its operating temperature of 1500 ◦ C.
3.4.5.2 Operating characteristics The fast pulsed discharge serves a dual purpose: maintenance of a sufficient, but not excessive, Cu-vapor pressure, and provision of sufficient pulse energy, to excite the Cu atoms to the upper laser level. This results in a relatively narrow range of average electric input power at which reliable operation of the laser can be achieved. Today the simplicity of the laser head (Fig. 3.4.16) and the inclusion of power-stabilizing circuits leads to a very stable output power. All Cu I laser devices operate in the self-heated regime with longitudinal low-pressure pulse discharges. Thermal insulation must be used within the gas envelope. A slow buffer-gas flow is normally used to remove impurities which are generated continuously. Figure 3.4.17 gives the typical dependence of output power Φ and green/yellow-ratio γ as a function of buffer gas and temperature of a conventional Cu I laser. The laser voltage, pulserepetition frequency, and buffer-gas pressure affect the heat balance in the laser by changing the electrical power input, i.e. the laser current is not an independent variable. Nevertheless, the specific pulse energy is over a wide range of tube bores approximately constant 5 μJ cm−1 ± 20 % [78Smi, 79Smi, 91Lew]. The green/yellow-ratio is generally 1.5. Time-averaged beam intensity profiles are uniform for laser tubes < 30 mm diameter, but display axial minima which become progressively deeper with increasing tube diameter. Without added H2 , the efficiency is about Landolt-B¨ ornstein New Series VIII/1B1
3.4.5 Self-terminating metal vapor lasers
[Ref. p. 272 40
8
Gas
Porous Al2O3
Al2O3ceramic tube
Gas
Green/ yellow-ratio g
6
Ne
30
He
Φ 4
g Ne
2
Cathode Cu droplets VitonO-ring seal
Pyrex envelope
Anode Watercooled end-flange
Fig. 3.4.16. Cu I laser tube with Mo- or Taelectrodes.
20
He
0 1300
Output power Φ [W]
270
10
1400
1500 1600 Temperature T [°C]
0 1700
Fig. 3.4.17. Green/yellow-ratio and laser output power for a conventional Cu I laser as a function of buffer gas and temperature.
1 %. The addition of about 1 % H2 to the laser gas will improve the output power and efficiency by a factor of 2, the specific pulse energy does not change. The pulse repetition frequency νmax (kHz) corresponding to maximum output power is approximately inversely proportional to the tube radius R (mm): νmax = 150/R
(1 ≤ R ≤ 30) .
(3.4.33)
νmax is mainly determined by diffusion of metastables. For larger values of R, R > 30 mm, νmax is determined by the metastables’ lifetime and approximately constant. Typical values of electric-field strength in the plasma are 100 V cm−1 , typical values of the small-signal gain of the 510.6 nm line are about 5 % cm−1 in large bore tubes [88Nay, 89Lew, 91Cou] and up to 25 % cm−1 in small bore tubes (R < 1 cm) [79Har]. Table 3.4.1 gives a summary of operating data for different Cu I laser systems. The Cu I laser is the most powerful, efficient and best-developed metal vapor laser. Commercial systems are available with output powers up to 120 W average. They have a wide field of applications in medicine, material processing and are excellent sources for pumping of dye lasers and titanium:sapphire lasers with high conversion efficiency. Related to the Cu I laser is the Au I laser. Two Au I transitions at 312.2 nm (6p2 P03/2 → 2 2 6s D5/2 ) and 627.8 nm (6p2 P01/2 → 6s2 2 D3/2 ) are analogous to the 510.6 nm and 578.2 nm lines in Cu I. The quantum efficiencies of these transitions are high: 47 % and 29 %, respectively. The Cu I laser devices with Au pieces instead of Cu pieces can be used for the Au I laser. Power supply and buffer gas are not different, the temperature for sufficient gold vapor pressure is about 200 ◦ C higher than in Cu I lasers. Average powers up to 20 W at 627.8 nm and up to 1.2 W at 312.2 nm have been reported [90Gab, 78Mar].
Landolt-B¨ ornstein New Series VIII/1B1
Landolt-B¨ ornstein New Series VIII/1B1
[%]
[mJ]
0.044 1.1 0.6 1.1 2.4 6.1 20 42 108 138
[kW]
∼4 ∼ 45 ∼ 30 30–40 – 120 500 280 – –
3.1 6.3 12 16 17 40 100 210 430 550
0.3 1.3 – 1.0 – 0.75 0.9 1.2 – –
Efficiency
Pulse energy
Peak power
Max. average power [W] 4.5 18 10 15 25 42 60 60 80 80
30 75 100 70 100 150 200 300 300 350
[cm]
[mm]
[W] – – – – – – – – 449 615
Active length
Tube bore
Amplifier power
– 7.2 – – – 10.5 – 20 36 69
– ∼ 350 – – – 900 – 1500 2700 2800
Peak Tube (charging) current voltage [A] [kV]
Table 3.4.1. Output power and operating conditions of self-heated Cu lasers.
– 35 – – – 50 30–60 170 80 65
70 6 20 15 7 6.5–6.7 5 5 4 4
4.5 25 – – – 15 – 23 – –
[torr] [kHz]
[ns]
[ns] – 70 – – – 80 – 80 60 40
Ne pressure
Rep. rate
Pulse duration
Current rise time
[91Vor] [94Wit] [91Lew] [77Isa] [96Wit] [95Hog] [89Lew] [94Kim] [99Lit] [99Lit]
Ref.
Ref. p. 272] 3.4 Ion lasers and metal vapor lasers 271
272
References for 3.4
References for 3.4 21Kle
Klein, O., Rosseland, S.: Z. Phys. 4 (1921) 46.
29Duf 29Lan
Duffendack, O.S., et al.: Phys. Rev. 34 (1929) 1132. Langmuir, I., Tonks, T.: Phys. Rev. 34 (1929) 876.
32Pen
Penning, F.M.: Z. Phys. 7 (1932) 454.
34Pen
Penning, F.M.: Physica 1 (1934) 763.
51Hol
Holstein, T.: Phys. Rev. 83 (1951) 1159.
54All
Allen, J.E., Thonemann, P.C.: Proc. Phys. Soc. (London) B 67 (1954) 768.
62Rab
Rabinowitz, P., Jacobs, S., Gould, G.: Appl. Opt. 1 (1962) 513.
63Rid
Ridgen, J.D., White, A.D.: Nature (London) 198 (1963) 774.
64Bel 64Bri 64Ger
Bell, W.E.: Appl. Phys. Lett. 4 (1964) 34. Bridges, W.B.: Appl. Phys. Lett. 4 (1964) 128. Gerritson, H.J., Goedertier, P.V.: J. Appl. Phys. 35 (1964) 3060.
65Lab
Labuda, E.F., Gordon, E.I., Miller, R.C.: IEEE J. Quantum Electron. 1 (1965) 273.
66Bri 66Paa 66Rud 66Sil 66Wal1 66Wal2
Bridges, W.B., Chester, A.N.: IEEE J. Quantum Electron. 1 (1966) 66. Paananen, R.A.: Appl. Phys. Lett. 9 (1966) 34. Rudko, R.L., et al.: Appl. Phys. Lett. 9 (1966) 41. Silfvast, W.T., Fowles, G.R., Hopkins, B.D.: Appl. Phys. Lett. 8 (1966) 318. Walter, W.T., Piltch, M., Solimene, N., Gould, G.: Bull. Am. Phys. Soc. 11 (1966) 113. Walter, W.T., Solimene, N., Piltch, M., Gould, G.: IEEE J. Quantum Electron. 2 (1966) 474.
67Bei 67Boe 67Gor
Beigman, I.L., et al.: JETP Lett. (English Transl.) 6 (1967) 919. Boersch, H., et al.: Phys. Lett. A 24 (1967) 695. Gorog, I., Sprong, F.W.: RCA Rev. 28 (1967) 38.
68Che 68Her 68Sil
Chester, A.N.: Phys. Rev. 169 (1968) 172. Herziger, G., Seelig, W.: Z. Phys. 215 (1968) 437. Silfvast, W.T.: Appl. Phys. Lett. 13 (1968) 169.
69And 69Fen 69Gol 69Her 69Pfa 69Sil
Anderson, D., et al.: Proc. IX-th. Intern. Conf. On Phenomena in Ionized Gases, 1969, p. 142. Fendley jr., J.R., Gorog, I., Hernqvist, K.G., Sun, C.: RCA Rev. 30 (1969) 422. Goldsborough, J.P.: IEEE J. Quantum Electron. 5 (1969) 133. Herziger, G., Seelig, W.: Z. Phys. 219 (1969) 5. Pfau, S., Rutscher, A., Wojaczek, K.: Beitr. Plasmaphys. 9 (1969) 333. Silfvast, W.T.: Appl. Phys. Lett. 15 (1969) 23.
70Boe
Boersch, H., Boscher, J., Hoder, D., Schafer, G.: Phys. Lett. A 31 (1970) 188.
71Bri
Bridges, W.B., Chester, A.N., Halsted, A.S., Parker, J.V.: Proc. IEEE 59 (1971) 728. Landolt-B¨ ornstein New Series VIII/1B1
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71Gia
Giallorenzi, T.G., Ahmed, S.A.: IEEE J. Quantum Electron. 7 (1971) 11.
72Her 72Isa 72Kit
Hernqvist, K.: IEEE J. Quantum Electron. 8 (1972) 740. Isaev, A.A., et al.: JETP Lett. (English Transl.) 16 (1972) 27. Kitaeva, V.F., et al.: Sov. J. Quantum Electron. (English Transl.) 1 (1972) 134.
73Alf 73Her 73Isa
Alferov, G.N., et al.: JETP Lett. (English Transl.) 18 (1973) 369. Herziger, G., Liithi, H.R., Seelig, W.: Z. Phys. 264 (1973) 61. Isaev, A.A., et al.: Instr. Exp. Techn. 16 (1973) 228.
74Aki 74Ban 74Miy
Akirvata, O.S., et al.: Sov. J. Quantum Electron. (English Transl.) 3 (1974) 519. Banse, K., L¨ uthi, H.R., Seelig, W.H.: Appl. Phys. 4 (1974) 141. Miyazaki, K., et al.: Jpn. J. Appl. Phys. 13 (1974) 1066.
75Dav 75Lue 75Miz1 75Miz2 75Miz3
Davis, C.C., King, T.A.: Advances in Quantum Electronics, New York: Academic Press, 1975. L¨ uthi, H.R., Seelig, W.: Appl. Phys. 6 (1975) 261. Mizeraczyk, J.K.: IEEE J. Quantum Electron. 11 (1975) 218. Mizeraczyk, J.K.: J. Appl. Phys. 46 (1975) 1847. Mizeraczyk, J.K.: Rep. Symp. Optics Quantum Electron. 9 (1975).
76Bur 76Lue1 76Lue2
Burkhard, P., et al.: Opt. Commun. 18 (1976) 485. L¨ uthi, H.R., et al.: IEEE J. Quantum Electron. 12 (1976) 317. L¨ uthi, H.R., et al.: Z. Angew. Math. Phys. 27 (1976) 101.
77Isa 77Lue1 77Lue2
Isaev, A.A., et al.: Sov. J. Quantum Electron. (English Transl.) 7 (1977) 253. L¨ uthi, H.R., et al.: IEEE J. Quantum Electron. 13 (1977) 404. L¨ uthi, H.R., Seelig, W.H.: J. Appl. Phys. 48 (1977) 4922.
78Ban 78Lue 78Mar 78Mor 78Smi
Banse, K.H.: Dissertation, Universit¨ at Bern, 1978. L¨ uthi, H.R., Seelig, W.H.: High-Power-Lasers and Applications, Kompa, K.L., Walther, H. (eds.), Berlin, Heidelberg, New York: Springer-Verlag, 1978, p. 119. Markova, S.V., et al.: Sov. J. Quantum Electron. (English Transl.) 8 (1978) 904. Mori, M., et al.: IEEE J. Quantum Electron. 14 (1978) 427. Smilanski, I., Kerman, A., Levin, L.A., Erez, G.: Opt. Commun. 25 (1978) 79.
79Har 79Smi
Hargrove, R.S., Grove, R., Kan, T.: IEEE J. Quantum Electron. 15 (1979) 1228. Smilanski, I., Erez, G., Kerman, A., Levin, L.A..: Opt. Commun. 30 (1979) 70.
81Got
Goto, T., et al.: J. Phys. D 14 (1981) 575.
82Got
Goto, T., Sakurai, T.: J. Phys. D 15 (1982) 2413.
84See
Seelig, W.: Proc. SPIE 455 (1984) 2.
86Apo
Apolonskii, A.A., et al.: Sov. J. Quantum Electron. (English Transl.) 13 (1986) 1004.
88Nay
Naylor, G.A., Lewis, R.R., Kearsley, A.J.: Gas Laser Technology; Proc. SPIE 894 (1988) 110.
89Alf
Alferov, G. N., et al.: Sov. J. Quantum Electron. (English Transl.) 16 (1989) 945.
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89Lew
Lewis, R.R., Maldonada, G., Webb, C.E.: Metal Vapour, Deep Blue and Ultraviolet Lasers; Proc. SPIE 1041 (1989) 54.
90Gab
Gabay, S., Hen, I., Lando, M.: High-Power Gas Lasers; Proc. SPIE 1225 (1990) 260.
91Cou 91Lew 91Vor
Coutts, D.W., et al.: CLEO91, Tech. Dig., Opt. Soc. Am., 1991, p. 518. Lewis, R.R.: Opt. Quantum Electron. 23 (1991) 493. Vorobev, V.B., et al.: Sov. J. Quantum Electron. (English Transl.) 21 (1991) 1067.
94Kim 94Wit
Kimura, H., et al.: J. Nucl. Sci. Technol. 31 (1994) 34. Withfordet, M.J., Brown, D.J.W., Piper, J.A.: Opt. Quantum Electron. 26 (1994) 1089.
95Hog
Hogan, G.P., Webb, C.E.: Opt. Commun. 117 (1995) 570.
96Wit
Withford, M.J., et al.: IQEC96, Techn. Dig. Opt. Soc. Am. (1996) 238.
99Lit
Little, C.E.: Metal Vapour Lasers, New York: Wiley, 1999.
00Bri
Bridges, W.B.: IEEE J. Sel. Topics Quantum Electron. 6 (2000) 885.
03Don
Donin, V.I., Ivanov, V.A., Pickalov, V.V., Yakovin, D.V.: J. Phys. D 36 (2003) 2366.
04LFW
Laser Focus World 40 (2004) 49.
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3.5 Excimer lasers U. Sowada
3.5.1 Introduction A molecule with a dissociative lower laser state is called “excimer”, if it consists of two atoms of the same kind. In the case of dissimilar atoms it is called “exciplex”. These words are derived from excited-state dimer or excited-state complex, i.e. they denote a molecule in a bound, excited state. At present all lasers using stimulated emission with this type of molecular species are called excimer lasers, regardless whether they are based on an excited-state complex or excited-state dimer. Excimers and exciplexes are particularly promising for laser action, because population inversion is readily achieved, once a few molecules are present. Fast dissociation of the lower laser state excludes the process of induced absorption, a decisive photon loss mechanism in normal two-state systems. In order to guarantee unrestricted molecular formation and dissociation reactions, the laser active medium of an excimer laser needs to be in the gaseous state. The output of excimer lasers is decisively influenced by chemical reactions among the many short-lived intermediates following the pumping process. Diatomic excimers often contain at least one rare-gas atom, which due to its chemical inertness is a promising candidate to have a dissociative ground state. The lowest excited electronic state of a rare-gas atom produces a species with a single electron in the outermost shell, resembling an alkali metal. These elements are known to form stable compounds with halogen atoms, since halogens lack just one electron. Therefore, the most obvious candidates for excimer lasers are the rare-gas monohalides.
3.5.2 Wavelengths and stimulated emission cross sections 3.5.2.1 Rare-gas halogen excimers 3.5.2.1.1 Rare-gas monohalides Table 3.5.1 displays the wavelengths of rare-gas monohalide excimers. Several different wavelengths have been observed, depending upon upper and lower state in the transition. For the B-X-transitions we note the following tendency: The lighter the rare-gas atom, the shorter is the wavelength λ of the transition. The dependence with regard to the mass of the halogen is reversed: The lighter the halogen, the longer is the wavelength λ. The fluorescence line widths are small (Δ λ is about 2 nm), i.e. the transitions are best represented by one of the graphs in Fig. 3.5.1b or c. The C-A-transitions are spectroscopically ten times wider (about 25 nm full width at half maximum), thus are represented by the scheme in Fig. 3.5.1a. As in the case of the B-X-transitions, increasing the mass of the rare gas will increase the wavelength, increasing the
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[Ref. p. 285
Table 3.5.1. Wavelengths observed in rare-gas monohalide excimer lasers. Reference
108 193 175 249 222 206 351 308 282 253
[77Ric] [76Hof] [77Way] [76Tel2] [76Mur2] [75Gol] [76Tel3] [76Tel1] [76Tel2] [76Tel2]
C-A-transition λ [nm]
Reference
275 240 222 460 345 300 265
[84Rho] [84Rho] [84Rho] [84Rho] [84Rho] [84Rho] [84Rho]
Energy E
Energy E
NeF∗ ArF∗ ArCl∗ KrF∗ KrCl∗ KrBr∗ XeF∗ XeCl∗ XeBr∗ XeI∗
B-X-transition λ [nm]
a
Internuclear separation
Internuclear separation
Energy E
b
Internuclear separation
c
Fig. 3.5.1. Transitions from an upper bound molecular state to a state with shallow minimum in the potential energy of the ground state. Depending upon the relative positions of the minima the bandwidth of the transition will be either spectrally broad (a) or spectrally narrow (b), (c), as indicated by the variation in length of the three arrows.
mass of the halogen will decrease it. The C-A-transition of XeF∗ has been reported to show an electrical to optical efficiency of roughly 0.1 %, output energy 100 J/(m3 atm), when pumped with an electron beam [83Nig]. The product of cross section σ for stimulated transition and lifetime τ for spontaneous decay is related to the transition wavelength λ and the bandwidth Δ λ by (3.5.1) [66Len]: σ×τ =
1 × 4π
ln (2) π
1/2 ×
λ4 . c Δλ
(3.5.1)
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The width of the band Δ λ is meant to be observed in fluorescence; c is the speed of light. The predictions and experimental results for the B-X-transitions in the two most important excimers KrF∗ and XeCl∗ are given in Table 3.5.2. The values of the cross section σ for a stimulated C-Atransition will be smaller by about a factor of 10, since the width of the band Δ λ is about ten times greater. Table 3.5.2. Cross sections for stimulated transition in KrF∗ and XeCl∗ (B-X-transition). σ·τ [m2 · ns]
τ (expt.) [ns]
KrF∗
2.4 × 10−28
XeCl∗
5.6 × 10−28
9 [76Nak, 77Bur] 7 [66Cal] 11 [82Mae]
σ [10−20 m2 ]
σ (expt.) [10−20 m2 ]
2.7 3.5
4.0 ± 0.4 [84Sza]
5.1
2.5 [81Lev]
Of the experimentally determined stimulated transition cross sections (last column of Table 3.5.2) only that one of [84Sza] appears to be accurate, since it has been measured with a short enough probe pulse to avoid repopulation of the upper laser state.
3.5.2.1.2 Polyatomic rare-gas halogen excimers Two different families of triatomic rare-gas halogen excimers have been studied, first the type where two similar rare-gas atoms are bound to a halogen atom, and second the type where all three atoms are different. In Table 3.5.3 the wavelengths and the reported band widths as observed in fluorescence are listed. Where no number is given, the width is not reported in the literature. The last column contains the reported (however, theoretical) cross sections for stimulated emission (3.5.1) [84Rho, p. 202]. Table 3.5.3. Triatomic rare-gas halides, wavelengths and cross sections for stimulated transition.
Ar2 F∗ Ar2 Cl∗ Kr2 F∗ Kr2 Cl∗ Kr2 Br∗ Xe2 F∗ Xe2 Cl∗ Xe2 Br∗ Xe2 I∗ ArKrF∗ ArKrCl∗ KrXeCl∗ KrXeBr∗ KrXeI∗
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Wavelength λ [nm]
Width of the band Δλ [nm]
Cross section σ [10−22 m2 ]
285 245 420 325 318 610 490 440 375 305 270 370 330 260
50 30 70 30
0.95
130 80 60
14.05 4.56 2.65
70 50 80 50 80
3.28
278
3.5.3 Chemical reactions in the discharge
[Ref. p. 285
3.5.2.2 Rare-gas excimers Since the positively charged dimer ions of the rare gases are stable, it is reasonable to investigate the pure rare-gas dimers. Table 3.5.4 gives the wavelengths as observed in fluorescence or laser experiments. Table 3.5.4. Excimers in the pure rare gases.
Ar∗2 Xe∗2
Wavelength λ [nm]
Reference
126 172
[79Bra] [76Lor]
In the homonuclear rare-gas excimers two different electronic states with different radiative lifetimes can be distinguished: 1 Σu , 3 Σu [76Lor]. As a function of gas pressure laser power has been found to display a maximum at 20 atm [73Hof, 73Wal]. At high density of the excimer states a reaction may occur between excimers with the result of deexcitation. Counterproductive to laser action is the short wavelength which except for Xe∗2 appears to exclude amplification by stimulated emission, since photoionization of the excimer seems to have a larger cross section.
3.5.2.3 Halogen excimers Even though halogens have a stable molecular ground state, they are interesting candidates to be used in excimer lasers. The normal ground state has electronic Σ symmetry. The lowest Π state is metastable, and transitions in the Π-system are useful for this purpose. Particularly fascinating is the F∗2 -excimer because of its short wavelength. The bandwidths of the halogen-excimers are small (ca. 2 nm). In Table 3.5.5 the wavelengths of the homonuclear halogen excimers are listed. Table 3.5.5. Wavelengths of the homonuclear halogen excimers.
F∗2 Br∗2 I∗2
Wavelength λ [nm]
Reference
158 293 342
[77Ric] [76Ewi, 76Mur1] [75Egg, 77Bur, 76Hay]
3.5.3 Chemical reactions in the discharge Understanding the chemical reactions in the gas mixture and the role of the many intermediates is very important in computer modeling. Even the apparently simple gas mixtures with only three components in a normal discharge-pumped excimer laser exhibit a large number of possible reactions, because on the nanosecond time scale many short-lived, reactive species are formed. If numerical calculations of the behavior during discharge are attempted, all possible reaction paths
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need to be included. As a result, optimal gas mixtures can be proposed, and temporal aspects of the beam can be related to the reactions. As examples for important excimer laser systems, two gas mixtures are considered, the first one containing helium (He), xenon (Xe), and hydrochloric acid (HCl), the second one argon (Ar), krypton (Kr), and fluorine (F2 ). HCl must be used as a halogen donor instead of Cl2 , because Cl2 is strongly absorbing light, in contrast to F2 . In chemical reactions the variation in time of the concentration of the reaction product P is proportional to the rate constant k and the product of the single concentrations of the reactants R. If we have n equal reactants R reacting to form the product P , we get (3.5.2): d n [P ] = k × [R] . dt
(3.5.2)
The square brackets here denote concentrations with unit cm−3 . If we have dissimilar reactants R1 , R2 , . . . , Rn , (3.5.2) reads instead: d [P ] = k × [R1 ] × [R2 ] × . . . × [Rn ] . dt
(3.5.3)
The proportionality constant k is called the reaction rate constant. It has the unit s−1 (for n = 1), cm3 s−1 (for n = 2), cm6 s−1 (for n = 3), and so on. The reaction with n = 1 is called “first order”, with n = 2 it is “second order”. Reactions described by (3.5.2) or (3.5.3) are called “nth order”. The value of a chemical rate constant k depends upon the energy of the molecules, here expressed by the gas temperature Tg , in case of electron reactions on electron energy, expressed by electron temperature Te . In this compilation these two temperatures are assumed to be given in electron volts. The positive ion of xenon is denoted Xe+ , the excited state Xe∗ , the next higher excited state Xe∗ (p). The symbol “e” is used for a free, kinetic electron, HCl(v) means vibrationally excited, XeCl(X) denotes the excited electronic molecular state. In Table 3.5.6 reactions in the gas mixture containing He, Xe, and HCl, following discharge pumping are listed. The process of stimulated emission with subsequent ground-state dissociation (No. 38) is decisive for laser action. Reactions with first-order kinetic behavior occur only rarely in Table 3.5.6 (e.g. the spontaneous radiative decay of the excimer molecule, reaction No. 37). Most common is a second-order kinetic reaction (e.g. No. 1). Third-order reactions need to be included, too (e.g. No. 18). Photon absorption reactions (Nos. 38 through 42) are better described with cross sections than rate constants. Next to the ionic recombination reaction (No. 21), there are 4 more reactions leading to the excimer XeCl∗ (Nos. 22, 24, 25, 27). The ingredients required in these 5 reactions have to be formed first, e.g. by dissociative electron attachment to HCl (No. 16). If the electron attachment rate to HCl is too high, not enough electrons may be present to sustain the discharge through impact ionization (Nos. 1 and 11). This is the reason why the concentration of HCl must be kept very low. Reaction rates of the excimer XeCl∗ , which may occur before stimulated emission, must be kept low enough, too (Nos. 28 through 37). The negative halogen ion is a very important ingredient, since it is one of the partners in creating the excimer molecule (No. 21). Reactions of this ion, which reduce its concentration in the discharge, will reduce the laser power. Due to the short wavelength of the photon field in the resonator, electron photodetachment becomes a possible reaction (No. 42). It has been discovered [89Osb], however, that electron photodetachment has a positive effect on the discharge, since it restores free electrons to sustain the discharge and produce more electrons and positive rare-gas ions (reaction No. 1). It is illustrative to add another table (Table 3.5.7) with the reactions occurring in a gas mixture containing argon (Ar), krypton (Kr), and fluorine (F2 ) [84Rho, pp. 131–132]. The relevant excimer molecule to be formed is KrF∗ . Landolt-B¨ ornstein New Series VIII/1B1
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[Ref. p. 285
Table 3.5.6. Reactions in the gas mixture containing He, Xe, and HCl, following discharge pumping. No.
Reaction
Cross section σ [cm2 ] or reaction rate constant k ([s−1 ] or [cm3 s−1 ] or [cm6 s−1 ])
Reference
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
e + Xe → Xe+ + 2e e + Xe → Xe∗ + e e + Xe → Xe∗ (p) + e e + Xe∗ → Xe+ + 2e e + Xe∗ (p) → Xe+ + 2e ∗ e + Xe+ 2 → Xe + Xe + e + Xe2 → Xe∗ (p) + Xe Xe∗ + Xe∗ → Xe+ + Xe + e Xe∗ (p) → Xe∗ + hν e + Xe∗ → Xe∗ (p) + e e + He → He+ + 2e e + He → He∗ + e e + He∗ → He+ + 2e e + HCl → HCl(v) + e e + HCl → H + Cl + e e + HCl → H + Cl− e + HCl(v) → H + Cl− Xe+ + Xe + Xe → Xe+ 2 + Xe Xe+ + Xe + He → Xe+ 2 + He He+ + He + He → He+ 2 + He Xe+ + Cl− → XeCl∗ − ∗ Xe+ 2 + Cl → XeCl + Xe ∗ Xe + HCl → Xe + H + Cl Xe∗ (p) + HCl → XeCl∗ + H Xe∗ + HCl(v) → XeCl∗ + H Xe∗ + HCl(v) → Xe + H + Cl Xe∗ (p) + HCl(v) → XeCl∗ + H XeCl∗ + HCl → Xe + HCl + Cl XeCl∗ + HCl(v) → Xe + HCl + Cl XeCl∗ + Xe → 2Xe + Cl XeCl∗ + He → He + Xe + Cl XeCl∗ + 2He → 2He + Xe + Cl XeCl∗ + Xe + He → 2Xe + He + Cl XeCl∗ + 2Xe → 3Xe + Cl XeCl∗ + e → Xe + Cl + e XeCl∗ + Xe + He → Xe∗2 + Cl + He XeCl∗ → XeCl(X) + hν XeCl∗ + hν → Xe + Cl + 2hν + Xe+ 2 + hν → Xe + Xe Xe∗ + hν → Xe+ + e Xe∗ (p) + hν → Xe+ + e Cl− + hν → Cl∗ + e ∗ He+ 2 + e → He + He + hν + He2 + e → He∗2 + hν ∗ He+ 2 + He + e → He + 2He + He2 + He + e → He∗2 + He + hν ∗ He+ 2 + 2e → He + He + e + He2 + 2e → He∗2 + e
k1 = 6.05 × 10−8 × Tg0.72 × exp(−21.98/Te ) k2 = 1.2 × 10−8 × Tg0.72 × exp(−8.36/Te ) k3 = 6.08 × 10−8 × Tg0.72 × exp(−15.42/Te ) k4 = 7.85 × 10−8 × Tg0.71 × exp(−3.77/Te ) k5 = 2.15 × 10−7 × Tg0.72 × exp(−2.4/Te ) k6 = 2 × 10−7 × Te−0.5 k7 = 2 × 10−5 × Te−0.5 k8 = 5 × 10−10 k9 = 1.5 × 107 k10 = 1.1 × 10−6 × Tg0.79 × exp(−1.37/Te ) k11 = 2.9 × 10−9 × Tg0.72 × exp(−51.96/Te ) k12 = 1.96 × 10−9 × Tg0.72 × exp(−36.87/Te ) k13 = 3.73 × 10−8 × Tg0.72 × exp(−4.7/Te ) k14 = 2.4 × 10−8 × Te−0.5 k15 = 2 × 10−9 k16 = 3 × 10−10 × Te−1.5 k17 = 2 × 10−8 k18 = 2.5 × 10−31 k19 = 1.1 × 10−31 k20 = 6.5 × 10−32 k21 = 2 × 10−6 × (Tg /0.026)−2.5 k22 = 2 × 10−6 × (Tg /0.026)−2.5 k23 = 5.6 × 10−10 k24 = 5.6 × 10−10 k25 = 6 × 10−11 k26 = 5 × 10−10 k27 = 5.6 × 10−10 k28 = 1.4 × 10−9 k29 = 7.7 × 10−10 k30 = 3.2 × 10−11 k31 = 10−12 k32 = 5 × 10−32 k33 = 1.5 × 10−31 k34 = 7.3 × 10−31 k35 = 3 × 10−7 k36 = 1.5 × 10−31 k37 = 9.3 × 107 σ38 = 2.5 × 10−16 σ39 = 2.5 × 10−17 σ40 = 6 × 10−20 σ41 = 10−18 σ42 = 2.1 × 10−17 k43 = 3.5 × 10−10 × (0.026/Te ) k44 = 1 × 10−10 × (0.026/Te ) k45 = 3.5 × 10−27 × (0.026/Te ) k46 = 1 × 10−27 × (0.026/Te ) k47 = 2.8 × 10−20 × (0026/Te )4 k48 = 8 × 10−21 × (0.026/Te )4
[82Shu] [81Lev] [82Shu] [81Lev, 82Shu] [81Lev] [79Bra] [79Bra] [81Lev] [81Lev] [81Lev] [82Shu] [82Shu] [82Shu] [82Shu] [81Dem] [80Nig] [80Nig] [81Lev] [79Bra] [81Miz] [80Bar] [80Bar] [81Lev] [81Lev] [81Lev] [81Lev] [81Lev] [82Mae] [82Mae] [82Mae] [82Mae] [81Miz] [81Miz] [79Bra] [81Lev] [80Bor] [82Mae] [81Lev] [81Lev] [82Mae] [81Lev] [81Lev] [81Miz] [81Miz] [81Miz] [81Miz] [81Miz] [81Miz] Landolt-B¨ ornstein New Series VIII/1B1
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Table 3.5.7. Reactions in the gas mixture containing Ar, Kr, and F2 , following discharge pumping. No.
Reaction
Cross section σ [cm2 ] or reaction rate constant k ([s−1 ] or [cm3 s−1 ] or [cm6 s−1 ])
Reference
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
Kr∗ + F2 → KrF∗ + F ArF∗ + Kr → KrF∗ + Ar Kr+ + F− → KrF∗ Ar∗ + F2 → ArF∗ + F Ar+ + F− → ArF∗ Kr∗ (p) + F2 → KrF∗ + F Ar∗ (p) + F2 → ArF∗ + F − ∗ Kr+ 2 + F → KrF + Kr + − ∗ Ar2 + F → ArF + Ar ArKr+ + F− → KrF∗ + Ar ArKr∗ + F2 → KrF∗ + Ar + F KrF∗ + Kr → 2Kr + F KrF∗ + Ar → Kr + Ar + F KrF∗ + 2Ar → ArKrF∗ + Ar ArF∗ + 2Ar → Ar2 F∗ + Ar Kr + ArKrF∗ → Kr2 F∗ + Ar Ar + ArKrF∗ → Ar2 F∗ + Kr KrF∗ + Kr + Ar → Kr2 F∗ + Ar ArKrF∗ + F2 → Ar + Kr + F + F2 Kr∗2 + F2 → Kr2 F∗ + F Kr∗2 + F → KrF∗ + Kr Kr2 F∗ + F2 → 2Kr + F + F2 Ar∗2 + F2 → Ar2 F∗ + F Ar∗2 + F → ArF∗ + Ar Ar2 F∗ + F2 → 2Ar + F + F2 Ar2 F∗ + Kr → ArKrF∗ + Ar ArKr∗ + Kr∗ → Kr∗2 + Ar Kr∗ + 2Ar → ArKr∗ + Ar Ar∗ + Kr + Ar → ArKr∗ + Ar Kr∗ + Kr + Ar → Kr∗2 + Ar Ar∗ + 2Ar → Ar∗2 + Ar Ar∗ + Kr → Kr∗ + Ar Ar∗2 + Kr → Kr∗ + 2Ar Ar+ + 2Ar → Ar+ 2 + Ar + Ar+ + Kr → Kr + 2Ar 2 + Ar + Kr + Ar → ArKr+ + Ar Kr+ + 2Ar → ArKr+ + Ar ArKr+ + F− → ArKrF∗ ArKr+ + Kr → Kr+ 2 + Ar ArKr+ + e → Kr∗ (p) + Ar Kr+ + 2Kr → Kr+ 2 + Kr Ar+ + Kr → Kr+ + Ar
k1 = 8.1 × 10−10 k2 = 3 × 10−10 k3 = 1 × 10−6 k4 = 8.5 × 10−10 k5 = 1 × 10−6 k6 = 8.1 × 10−10 k7 = 8.5 × 10−10 k8 = 1 × 10−6 k9 = 1 × 10−6 k10 = 1 × 10−6 k11 = 6 × 10−10 k12 = 2 × 10−11 k13 = 0 k14 = 8 × 10−32 k15 = 5 × 10−32 k16 = 2 × 10−11 k17 = 2 × 10−11 k18 = 6.5 × 10−31 k19 = 1 × 10−9 k20 = 3 × 10−10 k21 = 3 × 10−10 k22 = 1 × 10−9 k23 = 2.5 × 10−10 k24 = 3 × 10−10 k25 = 1 × 10−9 k26 = 1 × 10−10 k27 = 1 × 10−10 k28 = 1 × 10−32 k29 = 1 × 10−32 k30 = 1 × 10−32 k31 = 1.14 × 10−32 k32 = 6 × 10−12 k33 = 4 × 10−10 k34 = 2.5 × 10−31 k35 = 7.5 × 10−10 k36 = 1 × 10−31 k37 = 1 × 10−31 k38 = 1 × 10−6 k39 = 3.2 × 10−10 k40 = 1 × 10−7 k41 = 2.5 × 10−31 k42 = 3 × 10−11
[76Nak] [76Nak, 77Man] [77Man, 78Bar] [76Nak] [78Bar] [76Nak] [76Nak] [76Nak, 78Bar, 76Jac1] [76Nak, 78Bar, 76Jac1] [79Bra] (estimated) [76Nak] [76Nak] [79Bra] (estimated) [77Man, 77Shu] [76Nak] [77Man] [77Man] [78Rok] [76Nak] [76Nak] [76Nak] [76Nak] [76Nak] [76Nak] [76Nak] [76Nak] [76Nak] [76Nak] [76Nak] [76Nak] [76Nak] [73Pip, 76Nak] [77Man] [70McD] [70Boh] [78Lac] [79Bra] (estimated) [79Bra] (estimated) [79Bra] (estimated) [79Bra] (estimated) [70McD] [70Boh] (continued)
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3.5.3 Chemical reactions in the discharge
[Ref. p. 285
Table 3.5.7 continued. No.
Reaction
Cross section σ [cm2 ] or reaction rate constant k ([s−1 ] or [cm3 s−1 ] or [cm6 s−1 ])
Reference
43 44 45
Kr+ + Kr + Ar → Kr+ 2 + Ar F + F + M → F2 + M F2 + e → F− + F
46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82
Kr + e → Kr∗ + e Kr∗ + e → Kr∗ (p) + e Kr + e → Kr+ + 2e Kr∗ + e → Kr+ + 2e Kr∗ (p) + e → Kr∗ + e Kr∗ + e → Kr + e Kr∗ (p) + e → Kr+ + 2e Ar + e → Ar∗ + e Ar∗ + e → Ar∗ (p) + e Ar + e → Ar+ + 2e Ar∗ + e → Ar+ + 2e Ar∗ (p) + e → Ar∗ + e Ar∗ + e → Ar + e Ar∗ (p) + e → Ar+ + 2e ∗ Kr+ 2 + e → Kr (p) + Kr ∗ ∗ Ar2 + e → Ar (p) + Ar F2 + e → 2F + e F + e → F− KrF∗ → Kr + F + hν ArF∗ → Ar + F + hν Kr∗2 → 2Kr + hν Ar∗2 → 2Ar + hν Kr2 F∗ → 2Kr + F + hν Ar2 F∗ → 2Ar + F + hν ArKr∗ → Ar + Kr + hν ArKrF∗ → Ar + Kr + F + hν F2 + hν → 2F F− + hν → F + e + Kr+ 2 + hν → Kr + Kr + + Ar2 + hν → Ar + Ar Ar∗ (p) + hν → Ar+ + e Kr∗ (p) + hν → Kr+ + e Ar∗ + hν → Ar+ + e Kr∗ + hν → Kr+ + e Kr2 F∗ + hν → products Ar2 F∗ + hν → products KrF∗ + hν → Kr + F + 2hν
k43 = 2.5 × 10−31 k44 = 1 × 10−33 k45 = 1.1 × 10−9 k45 = 1 × 10−8 k46 = 4.1 × 10−11 k47 = 6.4 × 10−7 k48 = 1.5 × 10−15 k49 = 4.8 × 10−8 k50 = 8 × 10−7 k51 = 8 × 10−11 k52 = 1.8 × 10−7 k53 = 2.8 × 10−12 k54 = 6.6 × 10−7 k55 = 1.4 × 10−19 k56 = 2.8 × 10−8 k57 = 9 × 10−7 k58 = 5.4 × 10−12 k59 = 1.9 × 10−7 k60 = 1.1 × 10−7 k61 = 7.7 × 10−8 k62 = 3 × 10−10 k63 = 1 × 10−12 k64 = 1.5 × 108 k65 = 2.5 × 108 k66 = 3.3 × 106 k67 = 3.8 × 106 k68 = 6.7 × 107 k69 = 2 × 108 k70 = 3 × 106 k71 = 5 × 107 σ72 = 1.2 × 10−20 σ73 = 5 × 10−18 σ74 = 1.5 × 10−17 σ75 = 1 × 10−17 σ76 = 2.3 × 10−18 σ77 = 4.5 × 10−18 σ78 = 1 × 10−19 σ79 = 3.2 × 10−20 σ80 = 5 × 10−18 σ81 = 1 × 10−18 σ82 = 4.0 × 10−16
[77Man, 76Jac2] [79Bra] (estimated) [77Man, 77Che] [82Cha] [69Sha, 75Egg, 76Jac2] [76Jac1] [65Rap, 72Pet] [65Vri] [76Jac1] [69Sha, 75Egg, 76Jac2] [65Vri] [69Sha, 75Egg, 76Jac2] [76Jac1] [65Rap, 72Pet] [65Vri] [76Jac1] [69Sha, 75Egg, 76Jac2] [65Vri] [65Rap, 69Sha, 70Boh] [65Rap, 69Sha, 70Boh] [79Bra] (estimated) [79Bra] (estimated) [76Nak, 76Dun] [76Dun] [76Nak] [76Nak] [76Nak] [76Nak] [76Nak] [76Nak] [66Cal] [71Man] [78Mic] [78Mic] [79Bra] (estimated) [79Bra] (estimated) [79Bra] (estimated) [79Bra] (estimated) [79Bra] (estimated) [79Bra] (estimated) [84Sza]
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283
All important information concerning discharge behavior or gain as a function of time can be extracted from this data, if the coupled differential equations are solved and the rate constants properly applied. This second set of data in Table 3.5.7 appears to be more accurate than the one in the previous table, Table 3.5.6, because there is an even larger number of reaction pathways considered. Again we have electron reactions, including impact ionization (Nos. 48, 49, 50, 55, 56, 59) or attachment (Nos. 45 and 63). Radiation emission (Nos. 64 through 71) and absorption reactions (Nos. 72 through 82) are also included. Predictions of this scheme may in spite of this higher level of completeness be less reliable, however, since the reaction rate constants in Table 3.5.7 regarding KrF∗ /Ar do not contain an energy dependence like the data for the XeCl∗ /He in Table 3.5.6. Electron reactions are very strongly dependent on electron energy, and neglecting this will not allow to understand the consequences of increasing or decreasing the electric-field strength which produces the discharge. Heating effects of the plasma by the electric discharge will increase the kinetic energy of the atoms and molecules, which cannot be without influence on molecular reactions. But it is not possible for each of the many reactions to extract reliable data from the literature on the energy dependence of the rate constants. It is very instructive to compare the rate constants for dissociative electron attachment to the halogen molecule in Table 3.5.6 (No. 16) with that in Table 3.5.7 (No. 45). Even though literature data vary (probably due to the strong effect of electron energy), attachment to F2 seems to be faster than to HCl by a factor of 10. This is the principal reason for the different behavior of the discharge in excimer lasers. As a consequence, gas mixtures containing F2 will tend to arc rather than sustain a homogeneous glow discharge, while those containing HCl are less critical in this aspect. The data in Table 3.5.6 and Table 3.5.7 reveal another important tendency, which is of relevance to discharge stability. Argon atoms have a larger rate to be ionized by electron impact than helium (No. 55 in Table 3.5.7 compared to No. 13 in Table 3.5.6). This is quite natural, since the ionization energy is lower for the heavier noble gas. Glow discharges are most stable when the gas is at low pressure, i.e. localized discharge instabilities are less likely to form. At the high pressures present in excimer lasers, the lighter rare gas is better suited to be the buffer gas, because it will not favor rapid electron density changes. Due to the relatively high photon energies of the laser transition in these excimer lasers we need to consider photodetachment, i.e. liberation of electrons from negative ions by photon absorption (No. 73 in Table 3.5.7). It is an important reaction because of two reasons: first, it is a photon loss mechanism, and second, it is a mechanism to deliver electrons for further sustaining the discharge. For photodetachment from F− theoretical predictions [67Rob, 74Ish, 78Res, 83Clo, 87Rad] and experimental results [71Man, 88Wan] show good agreement. A value of σ = 6 × 10−22 m2 applies for photon energies just at threshold of 3.45 eV, which corresponds to a photon wavelength of 360 nm. Increasing the photon energy will reduce the cross section proportionally. Photodetachment will transform a lot of the still existing negative halogen ions into halogen atoms plus free electrons. Electron attachment will follow and transform the free electrons again into negative ions, however with a delay of a few nanoseconds. It may be argued that the observed slow recovery (2.5 ns for XeCl∗ [82Cor] and 4 ns for KrF∗ [84Sza]) of the upper laser state after depletion by an intense pulse of light is due to this effect.
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3.5.4 Beam properties
[Ref. p. 285
3.5.4 Beam properties 3.5.4.1 Pulse energy and pulse duration The first excimer lasers have been pumped by a high-power electron beam [75Sea, 84Rho]. This is technically difficult. Pumping by a transverse high-voltage discharge like in normal TEA-lasers (TEA: Transverse Electrical discharge in gas at Atmospheric pressure) is a cheaper and more reliable method, and it is used successfully in all commercial lasers. Technological reasons restrict the useful pumped volume to several 100 cm3 , and the output energies of rare-gas monohalide excimers are usually in the range 0.1 . . . 1 J [86Pum]. Higher values for the pumped volume are possible by increasing the cross section with the aid of X-ray preionization [87Cir]. This way multi-Joule pulse energy values have been created. The high gas pressures produce significant technical problems for longitudinally pumped excimer lasers [86Eic]. High-power microwaves have been shown to be applicable, too [91Kli]. Pulse duration in most cases is approximately 10 . . . 100 ns. Realization of longer pulses is restricted to XeCl∗ [87Klo]. Short pulses can be made by injecting a short pulse of the correct wavelength, as obtained from a dye laser, and using the tube of the excimer laser as a single-pass amplifier [84Sza].
3.5.4.2 Output power High average output powers with excimer lasers scale with total gas pressure [85Ern], with repetition frequency and with pulse energy. Local safety regulations pose limits on the gas pressure, especially in large-volume lasers. The product of pressure (above atmospheric) and volume should not exceed 200 bar-liters to keep potential energy low enough; otherwise regular pressure-vessel testings become necessary for commercial systems. At high pulse repetition frequencies, which are capable of exciting standing acoustic waves in the laser gas (above about 1 kHz), the output power shows a decrease due to a disturbance of discharge homogeneity [80Fah, 85Mat, 86Fon]. High pulse energies are achieved by increasing the size of the pumped volume. The output energy for the excimer system XeCl∗ is about 1000 J/(m3 bar). It appears as an optimal system, because the seed electrons from the pre-ionization do not disappear too quickly by attachment (cf. reactions No. 45 in Table 3.5.7 and No. 16 in Table 3.5.6). The effect of electron attachment must not be too strong, otherwise it will be almost impossible to achieve a homogeneous gas discharge, which is a necessity for homogeneous production of excited states. In order to have favorable competition with spontaneous decay, resonator roundtrip time must not be made much longer than a few ns. Therefore, attempts to increase the pulse energy aim at a larger cross section of the discharge [82Wat, 85Cha]. Preionization quality becomes an important prerequisite [81Her, 86Tay]. If pulsed high-power X-rays are used [86Osb], the transition from glow discharge to arc discharge sets the limits to output efficiency (defined as output pulse energy divided through the electrical energy deposited in the discharge), which usually stays below 2 %. With the prepulse-technique a value for the efficiency of 4.2 % has been reported [83Lon].
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References for 3.5
285
References for 3.5 65Rap 65Vri
Rapp, D., Englander-Golden, P.: J. Chem. Phys. 43 (1965) 1464. Vriens, L.: Physica 31 (1965) 395.
66Cal 66Len
Calvert, J.G., Pitts, J.N.: Photochemistry, New York: Wiley and Sons, 1966. Lengyel, B.A.: Introduction to Laser Physics, New York: Wiley and Sons, 1966.
67Rob
Robinson, E.J., Geltmann, S.: Phys. Rev. 153 (1967) 4.
69Sha
Shaper, M., Scheibner, H.: Beitr. Plasmaphys. 9 (1969) 45.
70Boh
Bohme, D.K., Adams, N.G., Muselman, M., Donkin, D.B., Ferguson, E.E.: J. Chem. Phys. 52 (1970) 5094. McDaniel, E.W., Ermak, V., Dalgarno, A., Ferguson, E.E., Friedman, L.: Ion-Molecule Reactions, New York: Wiley Interscience, 1970.
70McD
71Man
Mandl, A.: Phys. Rev. A 3 (1971) 251.
72Pet
Peterson, L.R., Allen jr., J.E.: J. Chem. Phys. 56 (1972) 6068.
73Hof 73Pip 73Wal
Hoff, P.W., Swingle, V.C., Rhodes, C.K.: Opt. Commun. 8 (1973) 128. Piper, L.G., Velazco, J.E., Setser, D.W.: J. Chem. Phys. 59 (1973) 3323. Wallace, S.C., Hodgson, R.T., Dreyfus, R.W.: Appl. Phys. Lett. 23 (1973) 672.
74Ish
Ishihara, T., Foster, T.C.: Phys. Rev. A 9 (1974) 2350.
75Egg 75Gol 75Sea
Eggarter, E.: J. Chem. Phys. 62 (1975) 833. Golde, M.F.: J. Mol. Spectrosc. 58 (1975) 261. Searles, S.K., Hart, G.A.: Appl. Phys. Lett. 27 (1975) 243.
76Dun 76Ewi 76Hay 76Hof 76Jac1 76Jac2 76Lor 76Mur1 76Mur2 76Nak
Dunning, T.H., Hay, P.J.: Appl. Phys. Lett. 28 (1976) 649. Ewing, J.J., Jacob, J.H., Magnano, J.A., Brown, H.A.: Appl. Phys. Lett. 28 (1976) 656. Hays, A.K., Hoffmann, J.M., Tysone, G.C.: Chem. Phys. Lett. 39 (1976) 353. Hoffman, J.M., Hays, A.K., Tisone, G.C.: Appl. Phys. Lett. 28 (1976) 538. Jacob, J.H., Mangano, J.A.: Appl. Phys. Lett. 28 (1976) 724. Jacob, J.H., Mangano, J.A.: Appl. Phys. Lett. 29 (1976) 467. Lorents, D.C.: Physica C 82 (1976) 16. Murray, J.R., Swingle, J.C., Turner jr., C.E.: Appl. Phys. Lett. 28 (1976) 538. Murray, J.R., Powell, H.T.: Appl. Phys. Lett. 29 (1976) 252. Nakano, H.H., Hill, R.M., Lorents, D.C., Huestis, D.L., McCusker, M.V.: SRI (Stanford Research Institute) Report MP-76-99, 1976. Tellinghuisen, J., Hoffman, J.M., Tisone, G.C., Hays, A.K.: J. Chem. Phys. 64 (1976) 2484. Tellinghuisen, J., Hays, A.K., Hoffman, J.M., Tisone, G.C.: J. Chem. Phys. 65 (1976) 4473. Tellinghuisen, J., Tisone, G.C., Hoffman, J.M., Hays, A.K.: J. Chem. Phys. 64 (1976) 4796.
76Tel1 76Tel2 76Tel3
77Bur 77Che
Burnham, R., Searles, S.K.: J. Chem. Phys. 67 (1977) 5967. Chen, H., Center, R.E., Trainor, D.W., Fyfe, W.I.: Appl. Phys. Lett. 30 (1977) 99.
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286 77Man 77Ric 77Shu 77Way
References for 3.5 Mangano, J.A., Jacob, J.H., Rokni, M., Hawryluk, A.M.: Appl. Phys. Lett. 31 (1977) 26. Rice, J.: 7th Winter Colloquium on High Power Visible Lasers, Park City, Utah, 1977. Shui, V.H.: Appl. Phys. Lett. 31 (1977) 50. Waynant, R.W.: Appl. Phys. Lett. 30 (1977) 234.
78Bar 78Lac 78Mic 78Res 78Rok
Bardsley, J.N.: Appl. Phys. Lett. 32 (1978) 76. Lacina, W.B., Cohn, D.B.: Appl. Phys. Lett. 32 (1978) 106. Michels, H.H., Hobbs, R.H., Wright, L.A.: Int. J. Quantum Chem. 12 (1978) 257. Rescigno, T.N., Bender, C.F., McKoy, B.V.: Phys. Rev. A 17 (1978) 645. Rokni, M., Mangano, J.A., Jacob, J.H., Hsia, J.C.: IEEE J. Quantum Electron. 14 (1978) 464.
79Bra
Brau, Ch.A.: in: Excimer Lasers, Topics in Applied Physics, Vol. 30, Rhodes, Ch.K. (ed.), Berlin, Heidelberg, New York: Springer-Verlag, 1979, p. 87.
80Bar 80Bor
Bardsley, J.N., Wadehra, M.: Chem. Phys. Lett. 72 (1980) 477. Borisov, V.M., Vysika˘ılo, F.I., Mamonov, S.G., Napartovich, A.P., Stepanov, Yu.Yu.: Sov. J. Quantum Electron. (English Transl.) 10 (1980) 333. Fahlen, T.S.: IEEE J. Quantum Electron. 16 (1980) 1260. Nighan, W.L., Brown, R.T.: Appl. Phys. Lett. 36 (1980) 498.
80Fah 80Nig 81Dem
81Her 81Lev 81Miz
82Cha 82Cor 82Mae 82Shu 82Wat
Dem’yanov, A.V., Dyatko, N.A., Kochetov, I.V., Napartovich, A.P., Pal, A.F., Pevgov, V.G., Perevoznov, A.F., Persiantsev, I.G., Starostin, A.N.: Sov. J. Plasma Phys. (English Transl.) 7 (1981) 768. Herziger, G., Wollermann-Windgasse, R., Banse, K.H.: Appl. Phys. 24 (1981) 267. Levin, L.A., Moody, S.E., Klostermann, E.L., Center, R.E., Ewing, J.J.: IEEE J. Quantum Electron. 17 (1981) 2282. Mizunami, T., Maeda, M., Uchino, O., Shimomura, O., Miyazoe, Y.: Rev. Laser Eng. (Reza Kenkyu) 9 (1981) 512. Chantry, P.J.: Applied Atomic Collision Physics Vol. 3, New York: Academic Press, 1982, p. 53. Corkum, P.B., Taylor, R.S.: IEEE J. Quantum Electron. 18 (1982) 1962. Maeda, M., Takahashi, T., Mizunami, T., Miyazoe, Y.: Jpn. J. Appl. Phys. Part 1 21 (1982) 1161. Shuaibov, A.K., Shevera, V.S., Gerts, S.Yu., Malinin, A.I.: Izv. Vyssh. Uchebn. Zaved. Fiz. 8 (1982) 121. Watanabe, S., Endoh, A.: Appl. Phys. Lett. 41 (1982) 799.
83Clo 83Lon 83Nig
Clodius, W.B., Stehman, R.M., Woo, S.B.: Phys. Rev. A 27 (1983) 333. Long, W.H., Plummer, M.J., Stappaerts, E.A.: Appl. Phys. Lett. 43 (1983) 735. Nighan, W.L., Nachshon, Y., Tittel, F.K., Wilson jr., W.L.: Appl. Phys. Lett. 42 (1983) 1006.
84Rho
Rhodes, Ch.K. (ed.): Excimer Lasers, Topics in Applied Physics, Vol. 30, 2nd ed., New York: Springer-Verlag, 1984. Szatmari, S., Sch¨ afer, F.P.: Appl. Phys. B 33 (1984) 219.
84Sza 85Cha
Champagne, L.F., Dudas, A.J., Feldman, B.J.: CLEO 85, Book of Abstracts, THQ3, 1985, p. 230.
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References for 3.5 85Ern 85Mat
86Eic 86Fon 86Osb 86Pum 86Tay 87Cir
287
Ernst, G.J, Nieuwenhuis, A.B.M., Abramski, K.M.: IEEE J. Quantum Electron. 21 (1985) 1127. Matera, M., Buffa, R., Burlamacchi, P., Fini, L., Salimbeni, R.: Rev. Sci. Instrum. 56 (1985) 205. Eichler, H.J., Hamisch, H., Nagel, B., Schmid, W.: Laser 85 – Optoelectronics in Engineering, Waidelich, W. (ed.), Berlin: Springer-Verlag, 1986, p. 15. Fontaine, B.L., Forestier, B.M., Sentis, M.L., Gevaudan, A.: CLEO 86, Book of Abstracts, WK29, 1986, p. 192. Osborne, M.R., Hutchinson, M H.R.: Appl. Phys. Lett. 49 (1986) 7. Pummer, H.: Laser 85 – Optoelectronics in Engineering, Waidelich, W. (ed.), Berlin: Springer-Verlag, 1986, p. 3. Taylor, R.S.: Appl. Phys. B 41 (1986) 1.
87Rad
Cirkel, H.-J., Baumgartl, R., Bette, W., Friede, D., M¨ uller, R.: Laser 87 – Optoelectronics in Engineering, Waidelich, W. (ed.), Berlin: Springer-Verlag, 1987, p. 16. Klopotek, P., Brinkmann, U., Oesterlin, P., M¨ uckenheim, W.: Laser 87 – Optoelectronics in Engineering, Waidelich, W. (ed.), Berlin: Springer-Verlag, 1987, p. 12. Radojevic, V., Kelly, H.P., Johnson, W.R.: Phys. Rev. A 38 (1987) 2117.
88Wan
Wang, W.C., Lee, L.C.: J. Phys. D 21 (1988) 675.
89Osb
Osborne, M.R., Winfield, R.J., Green, J.M.: J. Appl. Phys. 65 (1989) 5242.
91Kli
Klingenberg, H.H., Gekat, F.: Appl. Phys. B 54 (1991) 205.
87Klo
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3.6 Gasdynamical lasers, chemical lasers
289
3.6 Gasdynamical lasers, chemical lasers M. Hugenschmidt
3.6.1 Introduction, historical background The following review gives a survey on gasdynamic lasers and chemical lasers, concerning the basic methods and systems applied for the generation of high-intensity optical radiation. Conventional and unconventional techniques were investigated in the past, combustion-driven or electrical discharge heated high-pressure and high-temperature equilibrium gas mixtures, combined with fastflow (subsonic or supersonic) gasdynamic processes, as well as direct chemical excitation, either ignited optically, electrically or purely by chemical reactions. In any case chemical primary energy proves to provide a high specific energy density storage capability. As compared to the first generation of electrically excited gas lasers or electro-optically pumped (dielectric) solid-state lasers, these revolutionary gasdynamic and chemical laser principles and concepts allowed to progress rapidly from low energies or low average powers, respectively, to energies or intensities which are orders of magnitude higher. As a consequence, most energetic and compact laser systems were set up. The first vibrational nonequilibrium in fast flow was already demonstrated in 1946 by Kantrowitz [46Kan] who used gasdynamic methods to determine vibrational relaxation times. Their use for inversion production was suggested by Basov and Oraevskii and by Konyukhov and Prokhorov [63Bas, 66Kon]. A survey of the early gasdynamic laser activities which were successfully operated at the Avco-Averett Research Laboratory was given by Gerry [70Ger]. The rapid developments which will be discussed more in detail in the following sections are based on various principles which are schematically summarized in Table 3.6.1. Table 3.6.1. Basic principles involved in gasdynamic and chemical laser research. Type of laser
Process involved
Typical candidates
GasDynamic Lasers (GDL) Electric Discharge Lasers (EDL) Chemical Lasers (CL)
Thermal heating + gasdynamics Discharge + flow (+ downstream mixing) Discharge- or flashlamp-initiated chemical reactions, pure chemical processes
CO, CO2 lasers CO, CO2 lasers HF, DF, HCl, CO or I lasers
It should be pointed out, however, that besides the above specifically assigned groups of GasDynamic Lasers (GDL), Electric Discharge Lasers (EDL) and Chemical Lasers (CL), various combinations of these systems or techniques have been successfully developed and tested, in order to achieve improved excitation, flow and/or mixing conditions (subsonic, supersonic, premixed, downstream mixed, etc.).
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3.6.2 Gasdynamic lasers (GDLs)
[Ref. p. 333
3.6.2 Gasdynamic lasers (GDLs) 3.6.2.1 Conventional combustion-driven GDLs The GDL concept belongs to the promising ideas allowing to create extremely high-power continuous-wave (cw) or quasi-cw laser light sources. Numerous experimental and theoretical studies were carried out and a large variety of demonstrators were built. Optimization was obtained both by means of numerical modeling and by parametric experimental investigations. It should be mentioned, however, that considerable progress towards high intensities was achieved in the meantime in other fields of laser physics as well. As a consequence, these developments led to a decreasing interest in gasdynamic devices. Accordingly, many of the exciting ideas have been more or less given up since the early eighties. The aim of the present chapter is to include the important achievements and to point out the remarkable steps and milestones which have not only contributed to these particular types of lasers, but also to many other developments in the modern fields of laser physics and nonlinear optics. For the group of gasdynamic or chemical lasers, a renaissance, such as in the case of the solid-state lasers, has not been observed and may not to be expected in the near future. Nevertheless, new and interesting technical applications were suggested more recently, using laser systems based on these principles. According to recent publications of Apollonov et al. and discussions, powerful GDL- or CL-technologies could in fact provide efficient solutions to meet specific scientific or industrial high-power requirements [98Apo].
3.6.2.1.1 Population inversion due to gasdynamic processes As described in numerous publications, the basic principle of gasdynamic lasers is schematically shown in Fig. 3.6.1. Starting from an appropriate high-pressure, high-temperature reservoir of gas mixtures in local thermodynamic equilibrium, an efficient population inversion is obtained in a supersonically expanding flow through a suitably designed convergent–divergent nozzle or through a nozzle array. Efficient operation was achieved with gas mixtures comprising CO2 , N2 , including additionally smaller concentrations of H2 O-vapor or helium. It should be mentioned, however, that by the use of diatomic molecules, for example CO or HCl, other gas mixing concepts were also investigated. These combinations also allowed laser action in various IR-spectral ranges to be successfully demonstrated. Concerning a more detailed description of the various early steps, the subsequent fast developments and the state of the art finally achieved, reference is made to the literature, for example Anderson or Cassady [74And, 76And1, 80Cas]. The following discussion refers first to CO2 -gasdynamic lasers for which most important achievements were obtained by the revolutionary concept of using a supersonic expansion flow to create population inversion and optical gain. Primary energies may be provided by burning suitably chosen Combustion chamber
Laser cavity
Nozzle blades Laser beam
Diffusor
Fig. 3.6.1. Simplified schematic representation of a conventional gasdynamic laser, according to Monsler and Greenberg [71Mon].
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-1
Energy E [10 cm ]
0
(00 1)
291
(1)
1
2
(03 0)
0
(01 0)
0
(10 0)
(0200)
1
1
(01 0) 0
0
0
(00 0) n3
⎬
⎫
⎭
CO2- vibrational modes
(0) n
0
(00 0)
⎫ ⎬ ⎭
(00 0) n2
⎫ ⎬ ⎭
(00 0) n1
N2
H2O
Fig. 3.6.2. Schematic CO2 laser energy level diagram of the lower vibrational state groups of CO2 , N2 and H2 O.
fuel–oxidizer combinations, designed both to provide the chemical mixture and to fulfill optimized thermodynamic reservoir conditions. Detailed calculations of the gasdynamic laser performance were carried out by many authors. Different shapes of supersonic nozzle configurations were designed and experimentally studied by using various gas mixtures and initial reservoir conditions. By the application of these techniques, most of the input energy is initially stored in the lowest vibrationally excited state of nitrogen. These N2 (v = 1) energy levels are almost in resonance with the (000 1)-state of the CO2 asymmetric stretching mode. One single vibrational temperature has therefore frequently been used in the literature as a reasonable first approximation, in order to characterize the population densities of these two level groups. A simplified energy level diagram of the lower-lying vibrational states of the CO2 -, N2 - and H2 O-molecules is given in Fig. 3.6.2. For the sake of clearness, the rotational sublevels, in which each vibrational state is split up and which are characterized by rotational quantum numbers J, are not included in this schematic representation. The collisional energy transfer rates are determined by Translational–Vibrational (T–V) processes, as well as by intermolecular and intramolecular Vibrational–Vibrational (V–V) transitions of all molecular ensembles involved. As the upper (000 1) laser level of CO2 is only 18 cm−1 out of resonance with respect to the (v = 1)-level of N2 , the pumping reactions are basically determined by collisions with these vibrationally excited nitrogen molecules. The resulting CO2 -population in the upper laser asymmetric stretching mode ν3 can therefore be described by a local Boltzmann distribution with a temperature Tvib (000 1). Due to the fast gasdynamic expansion, this temperature decays only slowly (much slower than the translational temperature) and freezes downstream of the nozzle throat to an almost constant value which is found experimentally and confirmed numerically. As a further simplification in modeling, the lower-lying symmetric stretching modes ν1 (100 0) and bending modes ν2 (020 0) of CO2 are also frequently described by one single (lowerstate vibrational) temperature, termed Tvib (100 0) or Tvib (020 0). This is justified, as the energy levels of both groups are also rather close together. The depopulation of these two lower-state levels is basically provided by collisions with H2 O (or He). Due to the shorter relaxation time constants of the populations N (100 0) and N (020 0), their corresponding vibrational temperatures tend to follow closely the more rapidly decreasing translation temperature. At some point downstream of the nozzle, therefore, such a non-equilibrium expansion provides population densities of the upper vibrational group levels which are higher than those of the lower ones. As a consequence, the generated population inversion provides a high optical gain for the extraction of high-power laser radiation. As both the upper (000 1)- and, for example, the lower (100 0)- or (020 0)-states are split off in rotational levels (described by rotational quantum numbers J for the upper and J for the lower vibrational groups), optical gain is achievable if the rotational level population densities fulfill the so-called partial inversion conditions which are described by the following relation: N (000 1, J ) > N (100 0, J)
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(3.6.1)
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3.6.2 Gasdynamic lasers (GDLs)
[Ref. p. 333
Accordingly, stimulated emission is produced even if the total population densities (giving the sum over all rotational sublevels) of the upper vibrational group do not exceed the lower vibrational level population: N (000 1) < N (100 0) or N (000 1) < N (020 0), respectively. As a result, population inversion and gain increasingly build up downstream along the flow direction. Laser power is then extractable by the use of a suitably adapted optical cavity, perpendicularly arranged with respect to the flow direction. Typically, small-signal gain values of the order of 1 % per cm or slightly below were experimentally found and theoretically confirmed for these first-generation conventional gasdynamic laser devices.
3.6.2.1.2 GDL fuels and energy requirements Conventional CO2 -GDLs, based on combustion-driven schemes have matured rapidly. The first generation simply burned CO either in oxygen or in air. N2 was mixed with the combustion products and H2 or other hydrocarbons, such as CH4 , were added to yield the required partial pressure of H2 O-vapor (which was also frequently replaced most efficiently by He). The following reactions have to be taken into account: CO +
1 O2 ⇒ CO2 ; 2
H2 +
1 O2 ⇒ H2 O 2
or
CH4 + O2 ⇒ 2 H2 O + C .
(3.6.2)
Combustions of this type thus allowed the mixture ratios of (CO2 : N2 : H2 O) to be tailored appropriately within certain limits. Increasing CO2 -concentration was found to be favorable for high-gain media. Similar considerations also hold for other types of fuel–oxidizer combinations. For this firstgeneration gasdynamic lasers, it turned out that reservoir temperatures and plenum pressures, as well as resulting gas mixture ratios were not independent parameters; they were strongly interrelated, so that they could not be set arbitrarily for optimizational purposes. In order to achieve higher reservoir temperatures, other possible fuel–oxidizer combinations were investigated as well. N2 O, for example, was found to be a more efficient oxidizer than O2 . Furthermore, some hydrocarbons, such as C6 H6 , proved to provide more energetic fuels than CO. In this case, successful operation was obtained by using combustions of stoichiometric mixtures, such as described by the following reactions: C6 H6 + 15 N2 O ⇒ 6 CO2 + 3 H2 O + 15 N2
or C6 H6 + 51 N2 O ⇒ 6 CO2 + 3 H2 O + 18 O2 + 51 N2 .
(3.6.3)
The second of the two reactions, shown in (3.6.2), has to be taken into account in the case of high oxygen contents. It turned out that, among all the fuel–oxidizer combinations studied so far, benzene and nitrous oxide allowed the highest reservoir temperatures (of approximately 1800 K) to be achieved. With C6 H6 –N2 O–hydrocarbon-reactions, about five times higher specific energies were demonstrated (with values up to 22 kJ/kg), as compared to specific energies, typically of about 4.4 kJ/kg, based on reactions of oxygen with carbon monoxide. Lasers of this more efficient type were therefore termed “conventional gasdynamic lasers of the second generation”. In order to further increase the reservoir temperatures to values beyond 3000 K (up to 4000 K, basically limited by the dissociation of N2 ), further efforts were undertaken, for example by downstream mixing technologies which will be discussed more in detail in the following sections, or even by mixing CO2 -reaction products with preheated nitrogen. According to numerical simulations and detailed modeling, these techniques were considered to provide further promising aspects for possible third-generation gasdynamic laser developments. Both by numerical modeling of kinetic rate equations and by experimental tests of various laboratory devices, significant progress was achieved within a few years. For parametric studies, special aerodynamic facilities were adapted or developed. Even shock tubes were used, as they provided versatile, highly flexible tools for establishing various thermodynamic flow conditions, at
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least quasi-continuously during some ms. Powerful systems were set up which had been reasonably well understood. Numerical predictions were tested, to yield comparison between theory and experiment, especially for advanced fuel combinations. According to a recent paper of Boreisho and Trofimovich [97Bor], the most important features of gasdynamic lasers can be summarized as follows: – Specific energies of 10 up to 15 J/g were achieved, for special fuel components, such as N2 O, C2 N2 , etc., as compared to 6 . . . 8 J/g, if lower-cost gas mixtures are used. – Due to optimized flow conditions, high optical uniformity of the gain media and consequently high laser beam quality, close to the diffraction limit were reported for multi-pass unstable resonators. – Gasdynamic lasers may be conceived as very compact devices, values of power per unit volume of more than 100 kW/m3 are reported in the literature. – The excellent scalability of devices was demonstrated both by experimental results and by sophisticated numerical modeling.
3.6.2.1.3 Numerical modeling and simulations Fundamental methods were developed and were described in the literature worldwide by many research groups. Sophisticated codes were set up and applied in numerical modeling gasdynamic lasers (such as for example by Anderson, Glowaiki, Baev, Stricker, Rabzcuk and others [71Glo, 76Bae, 76Str2, 84Rab]. Only a few basic results will be resumed and briefly discussed. In most cases, vibrational nonequilibrium flows are approximated by Boltzmann distributions inside the different vibrational levels which are each characterized by specific vibrational temperatures. The complex vibrational kinetics, due to mutual interactions and collisions, first requires a description by a set of appropriate rate equations. The model, for example, deduced and used by Munjee and by other scientists, takes into account the specific energies E12 of the combined CO2 (ν1 and ν2 )-modes, the specific energy E3 of the ν3 -mode of CO2 and the specific energy E4 of the lowest N2 vibrational mode [72Mun]. If for simplicity, the various sublevel groups are denoted by the subscript i, the vibrational energies Ei and population distribution densities Ni are expressed by the following relations: Θi R · Θi Θi Ei = 1 − exp − . (3.6.4) and Ni = N · exp i exp(Θi /Ti ) − 1 Ti Ti R denotes the specific gas constant and Ti the corresponding vibrational temperatures, whereas the values Θi are defined by hνi /k , with the frequency νi , the Planck constant h and the Boltzmann constant k. The temporal changes dE12 /dt, dE3 /dt and dE4 /dt describe the vibrational energy transfer rates. These depend on the transition probabilities of the Translational–Vibrational (T-V) processes and on the corresponding Vibrational–Vibrational (V–V) processes. The transition probabilities themselves depend on temperatures and collision frequencies which are functions both on pressure and temperature. A comprehensive overview, comprising more detailed derivations of these vibrational rate equations, of the various models and simplifications with detailed quotations of references is given, for example by J.D. Anderson [76And1]. In summary the vibrational rate equations for multimode gas lasers have to be developed in order to describe the time behavior of the nonequilibrium vibrational energies or vibrational temperatures, respectively. For the calculation of gasdynamic laser performances, the rate equations established for dE12 /dt, dE3 /dt and dE4 /dt (according to the notation of Anderson) have to be resolved simultaneously with the governing gasdynamic flow equations (continuity, momentum, energy, state). A brief r´esum´e will be given in the following under the simplifying assumption of a three-temperaturelevel model, as mentioned above. If ρ denotes the density, u the velocity, T the temperature, p the pressure and A(x) the cross-sectional area of the nozzle as a function of x in the flow direction, these unsteady conservation equations for one-dimensional flows are given by the following relations: Landolt-B¨ ornstein New Series VIII/1B1
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continuity:
1 ∂(ρuA) ∂ρ =− · , ∂t A ∂x
(3.6.5)
momentum:
∂u 1 ∂p ∂u , =− · +u ∂t ρ ∂x ∂x
(3.6.6)
energy:
∂E p ∂u ∂ ln A ∂E =− +u +u , ∂t ρ ∂x ∂x ∂x
(3.6.7)
∂E12 ∂E12 = w˙ 12 (ρ, T, qi ) − u , ∂t ∂x ∂E3 ∂E3 = w˙ 3 (ρ, T, qi ) − u , ∂t ∂x ∂E4 ∂E4 = w˙ 4 (ρ, T, qi ) − u , ∂t ∂x
(3.6.8)
p=ρ·R·T .
(3.6.9)
rate equations:
equation of state:
The specific energies per unit mass, denoted by Ei , are related to the ith vibrational energy levels (or group of levels). w˙ i is the internal production rate of Ei due to the T–V- and V–V-collisional processes. The calculation starts with fixed equilibrium reservoir conditions (p0 , T0 , ρ0 ) which for the considered flows vary rapidly along the nozzle axis x. In one-dimensional approximation the lateral variations are neglected. The temporal changes of the thermodynamic quantities ρ, p, T , u, E, etc., are then directly obtained from the set of equations shown above. For simplicity, these quantities will be expressed by g in the following discussion and their temporal changes by ∂g/∂t . The required dependencies on x are then calculated by properly assuming a number of equally spaced grid points (or by several sets of different, in each interval equally spaced grid points). They may be obtained for example, from central finite differences, such as defined by the following relationships: ∂g g(x + Δx) − g(x − Δx) = , ∂x 2 · Δx
g(x + Δx) − 2g(x) + g(x − Δx) ∂2g = , 2 ∂x (Δx)2
(3.6.10)
which are subsequently introduced in the above given quasi-one-dimensional, unsteady conservation equations to yield (∂g/∂t)t . If Taylor series expansions up to the third term are used to calculate the subsequent flow variables at time (t + Δt) g(t + Δt) ≈ g(t) + (∂g/∂t)t Δt + (∂ 2 g/∂t2 )t (Δt2 /2) ,
(3.6.11)
the second derivatives (∂ 2 g/∂t2 )t additionally have to be considered. These are obtained by temporally differentiating the equations above. By this procedure, however, mixed derivatives (∂ 2 g/∂t∂x) also have to be retained; the latter are deduced from an additional differentiation of the above equations with respect to x. In other approximations (∂g/∂t) has simply been replaced by average values in the corresponding time intervals, whereas the third term of the Taylor series has been neglected: g(t + Δt) ≈ g(t) + (∂g/∂t)average Δt .
(3.6.12)
This results in a considerable simplification of the computer programming and in a reduction of the execution time. Both numerical approximation techniques were shown by comparison to similarly provide quite acceptable results.
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3.6.2.1.4 Population densities and small-signal gain achieved in gasdynamic lasers As the upper CO2 laser levels are almost in resonance (18 cm−1 ) with the N2 (v = 1)-level, their temperatures can be considered to be in local thermodynamic equilibrium, which can be expressed by Tvib II = T4 ≈ T3 . This relation, however, is only valid with good approximation as long as no optical power is extracted from the flow. By additionally introducing T12 ≈ Tvib I , the rate equations are reduced to two equations for Evib I and Evib II . Starting from equilibrium translation temperatures (Evib I )eq and (Evib II )eq , the relaxation rates, according to the harmonic oscillator approach are given by w˙ I =
1 eq dEvib I = [Evib I − Evib I ] , dt τI
w˙ II =
1 dEvib II = [E eq − Evib II ] . dt τII vib II
(3.6.13)
The relaxation rates τI and τII , of course, are average values. They depend on the gas mixtures, on detailed partial pressures and on mutual collisions, such as between: CO2 –CO2 , CO2 –N2 , CO2 – H2 O (or CO2 –He), N2 –N2 and N2 –H2 O (or N2 –He), see [76And1]. These relations, for a given gas mixture and for an initial plenum pressure and temperature condition, then allow the steady-state vibrational temperature distributions Tvib I and Tvib II throughout the nozzle along the flow to be determined. Furthermore, these results allow to calculate the population inversion and the smallsignal gain to be expected for specific conditions in order to yield comparison with experimental results. For the P(20)-line, for instance, the following relation was shown to provide a useful description: −234 λ2 45.6 G0 = · exp . (3.6.14) N (000 1) − N (100 0) · 4 · π · τ21 · νc T T It should be pointed out, however, that N (000 1) and N (100 0) in the equation above refer to population densities of specific rotational states J and J within the vibrational level groups for which the allowed quantum mechanical (ΔJ = J − J)-transition rules hold. In order to demonstrate the powerful tool of numerical simulation, a few results, summarized in Fig. 3.6.3, will briefly be discussed. These graphs were obtained numerically by Anderson for a wedge-shaped nozzle in the case of an initial reservoir condition of 10 bar and 1500 K. He needed up to several thousand time steps for these calculations to obtain the steady-state non-equilibrium distributions. As can be seen, the vibrational temperature Tvib II of the (000 1) upper level relaxes much slower downstream than both the translation temperature Ttrans and the lower-level vibrational temperature Tvib I , corresponding to the v1 (100 0)- and v2 (020 0)-modes. From these temperatures the population densities are determined, by assuming local Boltzmann distributions within each subgroup of the modes I and II. The upper and lower laser level population densities N (000 1) and N (100 0) of an initial density NCO2 of CO2 -molecules are then described by the following relations: 18
10 -3
N [cm ]
Tvib (0001)
1.2
3
T [10 K ]
1.6
Tvib (10 0, 02 0) 0
0.8 0.4
0
Ttrans
0.0 0 1.0 2.0 Distance along the nozzle [cm]
17
10
16
10
N (0001) N (1000, 0200)
0 1.0 2.0 Distance along the nozzle [cm]
Fig. 3.6.3. Steady-state vibrational temperatures and translation temperatures (Tvib , Ttrans ), as well as population densities N versus distance along the nozzle. (10 % CO2 , 1 % H2 O and 89 % N2 ; Aex /Ath = 24) according to Anderson [76And1]. Landolt-B¨ ornstein New Series VIII/1B1
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3.6.2 Gasdynamic lasers (GDLs) N (000 1) = NCO2 ·
exp [Θ3 /Tvib II ] Q
and N (100 0) = NCO2 ·
[Ref. p. 333 exp [Θ1 /Tvib I ] , Q
(3.6.15)
the partition function Q being defined by −1
Q = [1 − exp(−Θ1 /Tvib I )]
−2
· [1 − exp(−Θ2 /Tvib I )]
−1
· [1 − exp(−Θ3 /Tvib II )]
.
(3.6.16)
Again, the Θi were used as abbreviations for hνi /k. The population densities as a function of the distance from the wedge nozzle throat are shown in the right-hand side of Fig. 3.6.3. Apparently, the population inversion (N001 –N100 ) starts to build up already at a distance of a few mm from the throat under these conditions, developing to a substantial inversion further downstream. Detailed numerical computation showed that uncoupling the gasdynamic flowfield from the vibrational relaxation processes greatly simplified such type of calculations. This was done by calculating first the (frozen) equilibrium nozzle flow, followed by the solution of the vibrational rate equations. The results obtained, however, revealed that some of the flow parameters were severely affected by this simplifying technique, in particular also the translation temperature, so that significant errors could be introduced. In fact, a more accurate calculation of the population inversion and of the small-signal gain requires a detailed analysis, as described above, which fully takes into account the coupling between the gasdynamic flow and all the nonequilibrium relaxation processes. Furthermore, it should be pointed out that in this approximation the really existing rotational structure within the vibrational levels was not taken into account.
3.6.2.1.5 Power extraction In the following, the same notations for Evib I and Tvib I have been used to express the energy and vibrational temperature of the combined lower level v1 (100 0)- and v2 (020 0)-modes of CO2 . Correspondingly, Evib II and Tvib II describe the combination of the v3 -mode which is related to the upper state CO2 (000 1) and the nitrogen first vibrationally excited level N2 (v = 1). With the same simplifications as above, the necessary condition for laser energy to be extracted from such a gasdynamic flow is that N (000 1) exceeds N (100 0) or N (020 0), respectively. If it is additionally assumed that Evib I stays almost constant, the following relationship is obtained from (3.6.15): N −Θ1 −Θ3 N (100 0) − N (000 1) = 0 = CO2 · exp , − 0 Q Tvib Tvib I II which yields Θ1 Θ3 ≈ , 0 Tvib T vib I II
(3.6.17)
0 in which Tvib II denotes the temperature for which the population inversion goes through zero. These assumptions yield quite reasonable results for first estimations of the upper limit of power extraction 0 for a given device. Tvib II > Tvib II defines the necessary condition for laser power extraction. From Fig. 3.6.3 it can be seen that typically Tvib I > Ttrans . If in the limiting case, however, Tvib I is 0 assumed to approach Ttrans , the above equations can be approximated by the relationship Tvib II = (θ3 /θ1 ) · Ttrans = 0.409 · Ttrans , in which, of course, the detailed vibrational–rotational structure of the spectral emission has again not been taken into account. The factor 0.409 corresponds to the quantum efficiency for the 10.6 μm P(20)-transition. As a consequence, the maximum energy Emax to be extracted is determined by the relation 0 Emax = 0.409 · Evib II (Tvib II ) − Evib II (Tvib (3.6.18) II ) .
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A more accurate calculation, however, requires numerical solutions of the nonequilibrium supersonic flow. This is done by additionally taking into account the radiative transfer equation dIν /ds = Gν · Iν . The actual gain Gν takes into account the local depopulation of N2 and CO2 (000 1) and the population of CO2 (100 0), ds is measured in the direction of the radiative intensity Iν which is perpendicular to the flow. In the case of laser power extraction, the energy conservation equation has to be extended by an additional term QR which denotes the energy per unit mass related to the intensity Iν by QR = Gν Iν /ρ , so that (3.6.7) has then to be replaced by: ∂ ln A ∂E ∂E p ∂u +u +u − QR . (3.6.19) =− ∂t ρ ∂x ∂x ∂x The continuity and momentum equations remain unchanged; however, the rate equations which provide the laser radiative transitions also have to be changed accordingly. Subsequent numerical treatments, of course, require more detailed definitions of the nozzle geometry, such as: – the area ratio of nozzle entrance to nozzle throat and – the area ratio of nozzle exit (determined by the optical cavity height) to the nozzle throat. For details, the reader again is referred to the literature, for example to the comprehensive overview given by Anderson [76And1], which additionally includes many of the most important original publications and contributions to these topics.
3.6.2.1.6 Simplified calculation of small-signal gain, analytical approximations As indicated in the previous section, detailed numerical calculations were performed by many authors, for example Taylor, Bitterman, Christiansen, Russel, Herzberg, Mitra, Fiebig, Oggiano, Saunders [69Tay, 75Chr, 76Mit, 76Ogg, 76Sau], to cite only a few ones. Various approaches were used and published in the past to solve Navier–Stokes equations and rate equations by taking into account most important physical processes. Sophisticated nonequilibrium computer programs were set up and solved for various nozzle configurations to determine the small-signal gains under specific conditions. These simulations allowed to obtain more accurate values of the laser power to be extracted from a given device. Moreover, the calculations could easily be adapted to experimental facilities in order to obtain specific data, scalable for higher-power-level laser systems. However, for practical applications Anderson and coworkers therefore made a considerable effort to develop more simplified engineering correlations [76And2]. By comparison with results of complex numerical codes, approximate relationships were deduced allowing to obtain valuable and easy-to-handle predictions about GCL (GCL: Gasdynamic and Chemical Lasers) performances. This holds particularly for the small-signal gain G0 for which McManus [76McM] gave the following analytical expression: G0 = K0 {1 − 0.875[(1 − Q1) + (1 − Q2) + (1 − Q3)]} − Q4 .
(3.6.20)
The values K0 and Q1, Q2, Q3 and Q4 are determined by rather simple relationships. Their definitions are put together in Table 3.6.2. It is interesting to note, that these few, rather simple equations allow to take into account all important parameters, the initial gas-mixture composition (mole fractions %C2 O, %H2 O, %N2 ), the reservoir stagnation pressures P0 and temperatures T0 and the flow conditions which are additionally defined by the expansion nozzle shapes and sizes (hth and Aex /Ath ). As shown by McManus, excellent results were obtained for a large range of operation conditions, if Aex /Ath < 53, if additionally 0.5 < %H2 O < 30, %C2 O < 30 and P0 hth < 3. It was further shown by McManus that almost all practically interesting cases are covered by these approximations which are, therefore, considered to greatly facilitate the engineering tasks in experimental GDL-system design. Landolt-B¨ ornstein New Series VIII/1B1
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Table 3.6.2. Values K0 , Q1, Q2, Q3, Q4 required to determine the small-signal gain G0 according to (3.6.20). K0 = 1.484 exp
2 Aex − 53.037 /1532.3 Ath
with Aex = nozzle exit area to throat area ratio Ath Q1 = 0.025 Tx2.673 exp[−0.2475 Tx ] Q2 = 2.75 sin Cx exp[−Cx /1.171] with Cx =
%CO2 π , 40 + 11 AF
%CO2 = mole fractions of CO2 [%], 2 Aex AF = − 19.75 /30.25, Ath Tx = [T0 /(1.0 − 0.15 AF − 470.0)] /100.0 Q3 = 0.8 (H2 O1 + 1)0.65 exp −0.245 H2 O1 with
1
H2 O = (%H2 O − CA)
% CO2 CA − 24 3.3
(1.05 − 0.35 AF ) + 1.65,
%H2 O = mole fraction of H2 O [%], CA = 2.25 − 2.0 exp[−%CO2 /10.0], %CO2 + %H2 O + %N2 = 1 Q4 = 0.1655 exp
2 Aex − 39.15 /170.72 (P0 hth )3/2 Ath
with hth = throat height [cm]
The influence, for example, of additional H2 in CO2 -GDL on the small-signal gain was experimentally studied in shock tube experiments and compared with theoretically expected values by Novikov et al. [84Nov]. In these investigations gain coefficients G0 of 0.5 to 0.7 m−1 were reported. Remarkable contributions to the development of gasdynamic CO2 lasers were also given by Meinzer at the UTRC East Hartford. For example, the paper presented during the 3rd International GCL Conference at Marseille in 1980 [80Mei] gave an overview of the advanced state of the art already achieved at that time.
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3.6.2.1.7 Specific experimental investigations, realization of pulsed laser systems Among the many studies which led to powerful experimental demonstrators, reference should be made at least to one of the more recent GDL-concepts which was reported and summarized by Itaya [97Ita] during the Edinburgh GCL-Conference in 1996. In these investigations, methane–air combustions were successfully driven up to high pressures over 1 MPa. This refers to experiments conducted in an unstable flame propagation combustor. The theoretical analysis includes effects of high concentrations of water on the CO2 (000 1)–(100 0) transitions. The results showed that inversion can be generated and sustained in methane–air combustions at a stoichiometric ratio in gas flows which are accelerated up to Mach 5. From the experimentally measured gain values of more than 0.7 % per cm, IR laser powers up to 2.5 kW were expected to be extractable from a 30 cm path length optical cavity. Combustions of the gas mixture may be ignited by electrical sparks, causing the flames to propagate upstream until they are blown off close to the gas inlets and pushed out by the unburnt gas. The ignitions are then repeated periodically to provide high average power levels. The expansion occurred adiabatically through a supersonic nozzle (with a throat height of 1 mm, a width of 10 mm and a ratio A/A∗ of 25), in order to obtain the high Mach numbers of 5 or above.
3.6.2.1.8 Optical cavity design Power extraction from large volumes with high-quality transverse mode distributions requires a specific, unstable cavity design. A large variety of configurations, specially adapted to the high power densities of GCLs were therefore developed, investigated and optimized. A most simple, but frequently used, confocal configuration is schematically shown on the left side of Fig. 3.6.4. In this case, ring-shaped spatial near-field intensity distributions with diameters D1 and D2 are obtained which can be shown to be transformed to Gaussian distributions in the far field. Rather simple relationships which are useful for engineering purposes were deduced to describe the resulting unstable cavity beam characteristics. The round trip geometric magnification M = D1 /D2 , for example in the case of a positive-branch confocal resonator is related to the cavity length L and to the radii of curvature R1 and R2 of the two mirrors. These values define the two g-parameters g1 = 1 − L/R1 and g2 = 1 − L/R2 . The dependencies of these g-parameters and of the resulting fractional output coupling δ on M within the spherical wave approximation are then given by: g-parameters: fractional output coupling:
g1 = (M + 1)/2 , g2 = (M + 1)/2M ; δ = (M 2 − 1)/M 2 .
(3.6.21)
As was shown, the beam quality is improved by increasing M , whereas higher coupling efficiencies need lower M -factors. For more details, particularly related to the specific requirements of highpower gasdynamic lasers, reference is made to the literature, for example Siegman, or Christiansen [74Sie, 80Chr].
Supersonic aerodynamic window concept
R1
L
R2 D2 D1
Unstable optical cavity design
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Fig. 3.6.4. Basic design of an unstable confocal laser cavity configuration, including a schematic representation of an aerodynamic window design (cavity length L, radii of curvature of concave or convex mirrors, respectively: R1 , R2 ).
300
3.6.2 Gasdynamic lasers (GDLs)
[Ref. p. 333
For the extremely high power levels, typically achieved in gasdynamic lasers, bulk IR-windows (Ge, ZnSe, KCl, etc.) proved to be not capable to withstand the thermal loading without damage. As demonstrated both theoretically and experimentally the severe window problems were solved by using suitably adapted aerodynamic windows. Various alternative solutions were discussed and introduced. A comprehensive survey, related to gasdynamic laser design is given by Reilly [85Rei]. Detailed studies, of course, were carried out worldwide in laser laboratories related to this field of research. As a typical example, a specific approach – as investigated by Wildermuth and coworkers [87Wil] at the DLR-Institute of Technical Physics at Stuttgart – is schematically represented in the right-hand side of Fig. 3.6.4.
3.6.2.2 Downstream mixing GDLs Unfortunately, efficiencies of conventional GDLs were found to be rather low, typically of the order of one percent or less. Numerous concepts were therefore developed for scaling purposes, in order to improve the specific power capability. This was achieved by some promising techniques in which supersonically expanding higher-temperature N2 -streams were mixed with lower-temperature jets of CO2 and He (or H2 O) which were injected from a separate nozzle or nozzle system. As a consequence, initial plenum pressures, temperatures and flow velocities could be adjusted separately for each component. Initial stagnation temperatures of N2 up to 4000 K were used. This is almost twice as high as the dissociation temperature of CO2 (a noticeable dissociation of CO2 has already to be taken into account slightly above 2300 K). As a consequence, the vibrational energy increased significantly with increasing temperature. Furthermore, the relaxation time of pure N2 is considerably shorter than the relaxation for (N2 –CO2 –H2 O)-mixtures. A higher percentage of “quasi-frozen” vibrational energy can thus be stored during the expansion. By using different nozzle configurations, an independent optimization of the flow velocities and, as a consequence, of the downstream mixing volume was achieved as well. The improved potential of downstream mixing lasers – with respect to a substantial increase of the specific laser power by about an order of magnitude – was already suggested and shown by Bronfin et al. [70Bro]. In the idealized case of quasi-instantaneous mixing, maximum specific energies of more than 300 kJ/lb were estimated to be extractable. These values are an order of magnitude higher than those achieved with conventional GDLs. Numerically and experimentally, both concepts of laminar and turbulent mixing were taken into account. Difficulties were faced, however, concerning shock waves, disturbing the optical homogeneity of the flows and concerning additional heating effects in the mixing zones which both increase the translation temperature and thus reduce the overall gain. By computational fluid-dynamic analysis (solution of Navier– Stokes equations by means of time-dependent finite difference techniques) for tangential mixing flows, Anderson obtained (in spite of the above-mentioned restrictions) encouraging small-signal gain values of more than 6 % per cm, which are about six times higher than the values reported at that time for conventional GDLs. It is interesting to note that a similar or an almost identical computational analysis has been applied for modeling both the non-conventional gasdynamic lasers and the supersonic diffusion chemical lasers, for example HF lasers, which will be discussed in the following. The gas flow mixing concept which allows to improve substantially the efficiency of thermally excited gasdynamic CO2 lasers was studied successfully, in US, in Europe, for example in France and in Germany, or in Russia. Reference should be made at least to a few papers, e.g. Borghi, Carrega, Charpenel, Taran, or Croshko et al. [73Bor, 75Cro]. In Germany, interesting experimental investigations, related to downstream mixing concepts, were also carried out at DLR Stuttgart by Hoffmann et al. [76Hof]. These authors used arc-heated nitrogen at temperatures up to 3000 K and pressures of about 5 bar to yield Mach numbers of 3.5 to 4.5. Their basic interest was to study Landolt-B¨ ornstein New Series VIII/1B1
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various mixing nozzle configurations for the injection of cold CO2 and He for scaling purposes. Gain values of 3.05 % per cm were reported and specific energies of almost 10 kJ/kg. These values were achieved in a small device (3.5 cm of active length only), in spite of the relatively large influence of boundary layers which was found to introduce significant vibrational energy losses. In larger systems, such boundary layer effects are certainly less stringent, so that considerably higher gains and specific energies are in fact to be expected from devices based on these techniques. It is evident, of course, that a strong competition developed in the past years between the conventional GDLs and the various types of advanced downstream mixing GDLs, such as those discussed above. Similarly, a strong competition developed also with respect to other laser concepts, such as those provided by Electric Discharge Lasers (EDLs) and especially also by purely chemically excited lasers, both of which will be discussed more in detail in the following sections.
3.6.2.3 Gasdynamic CO2 laser by detonation of solid explosives Work was performed by Gabai et al. at the Hebrew University in Jerusalem [72Gab]. These authors used stoichiometrically mixed chemicals cyanuric triazide (C3 N12 ) and hexonitroethane (C2 (NO2 )6 ). Upon explosion, these delivered a mixture of CO2 : N2 = 35 % : 65 % which was certainly not an optimized ratio, but quite reasonable to start with: 4 C3 N12 + 3 C2 (NO2 )6 ⇒ 18 CO2 + 33 N2
(−2480 kcal/mole) .
(3.6.22)
The additionally required proportion of water was provided by adding hydrogen containing compounds, such as NH4 NO3 . The reaction is highly exothermic. Experimental studies were supported by the development of a computer simulation model. After the detonation, the initially solid materials produced all gases expanding through nozzles as in well-known combustion-driven devices. The nozzle expansion ratio A/A∗ was chosen to be 22. The feasibility of lasing was clearly demonstrated by the authors. However, no further publications on possible improvements, optimizations, or on similarly working solid-state explosion devices have been presented in the open literature. It cannot be excluded that other unavoidable by-products led to a serious quenching of the stimulated emission processes, thus inhibiting the originally expected high specific power density levels to be attained.
3.6.3 Fast-flow electric discharge lasers (EDL) 3.6.3.1 Electrically excited fast-flow or gasdynamic CO lasers CO lasers present some major advantages concerning high efficiencies and high power levels to be achieved. Depending upon the excitation mechanisms involved, stimulated emission may start from various vibrational level groups. Boltzmann rotational temperature distributions determine the rotational–vibrational number densities. Thus, depopulation of any of the upper vibrational levels automatically provides an increase in population and a contribution towards building up the inversion of the next lower lying level groups. Some of the related lower rotational–vibrational levels of the two-atomic CO-molecules are schematically shown in Fig. 3.6.5. Cascade processes, due to these multiple rotational–vibrational transitions, thus provide the observed line emission, in a spectral range from about 4.8 μm to more than 5.5 μm. A typical, experimentally measured spectrum is represented in Fig. 3.6.6 where the intensities are given in arbitrary units. Landolt-B¨ ornstein New Series VIII/1B1
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etc.
P32(8)
Q32(7) R32(6)
hn1- DE32 v =2
-1
Energy E [cm ]
5000 4000 P21(9)
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3000
v =1
2000 P10(10)
hn1
1000
-3
Number density n [arb. units, in cm ] Fig. 3.6.5. Schematic representation of the lower part of the CO laser energy level diagram and related vibrational–rotational population distributions.
Intensities of emitted lines I ( l) [arb. units]
v =3
6000
4.9
5.0
5.1 5.2 5.3 5.4 Wavelength l [mm]
5.5
Fig. 3.6.6. Typical CO laser spectral line emission, as observed in the case of an rf-excited, gasdynamically cooled multi-kW system, according to Schellhorn and v. B¨ ulow [95Sch].
Concerning the reaction kinetics, extensive theoretical studies in the case of subsonic-flow transverse-discharge CO lasers were carried out by many research groups, such as for example by M. Iyoda [85Iyo, 87Iyo]. Based on the combination of a multi-vibration level model with a one-dimensional flow model and a plane-parallel cavity model, these authors took into account 300 different V–R–T-processes for CO–M and N2 –M collisions (collision partner M), as well as 7500 V–V processes for CO–CO, CO–N2 , N2 –N2 . The objective of this computer simulation was to investigate the scalability, to evaluate the feasibility of closed cycle operation and to optimize parameters (such as initial pressures, partial densities, and temperatures) with respect to existing experimental devices. These studies were aimed at developing highly efficient lasers for industrial applications. As CO lasers belong to the attractive groups of molecular laser systems, physical models were also developed for lasers to be operated gasdynamically, i.e. under supersonic flow conditions. An interesting analytical approach was published by Khizhnyak et al. [85Khi]. Based on the diffusion approximation, which describes the vibrational relaxation of anharmonic molecules under highly non-equilibrium flow conditions, the approach was adopted to analyze the gas dynamic regimes of the CO-population inversion dynamics. Furthermore, both extended theoretical studies and detailed experimental investigations of electrically excited gasdynamic CO lasers were performed in many countries and laser laboratories around the world. In Germany for example, important contributions were provided by Bohn, Maisenh¨ alder and coworkers at DLR Stuttgart. Rather small-scale devices allowed in first steps, interesting experimental results to be obtained, especially concerning the specific energies. Values of more than 50 kJ/kg were reported. These systems were shown to be scalable towards higher power. Multi-kW power levels were reached in simple, rugged and compact devices. The specific energies attained by Maisenh¨ alder [76Mai] were higher than those previously published by Brunet and Mabru [75Bru] or by Rich et al. [75Ric]. These authors reported values of 21 kJ/kg and 32 kJ/kg, respectively. Landolt-B¨ ornstein New Series VIII/1B1
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Powersupply Multipass (unstable) optical cavity Nozzle
RFdischarge 13.6 MHz
Supersonic flow into vacuum vessel
Laser beam
Fig. 3.6.7. Operation principle of electrically excited, gasdynamically cooled multi-kW CO laser [95Sch].
Fig. 3.6.8. Laboratory view of multi-kW gasdynamic CO laser at ISL Saint-Louis (developed by DLR Stuttgart).
Different types of excitation schemes were suggested, analyzed by numerical modeling and investigated experimentally prior to final optimization. Various electrical energy sources were used as well for this purpose, such as dc-, rf-, microwave- or even electron-beam sustained discharges. The basic components and set-up of an experimental device, developed at DLR Stuttgart by H. v. B¨ ulow and coworkers, comprising an rf-generator to provide the electrical input energy, is schematically shown in Fig. 3.6.7. A photograph of the resulting laser system hardware based on this configuration is given in Fig. 3.6.8. This laser, as set up at DLR, was finally delivered to the German-French Research Institute, ISL, Saint-Louis for final optimization and practical applications in the field of laser material processing. During these investigations, this CO laser has proven to be a versatile tool which has been in use for many years for laser target effect investigations. In blow-down configuration, quasi-continuous multiline operation with IR-optical powers up to 6 kW was achieved. For specific industrial applications, of course, lasers of this type should preferably be operated as supersonic flow gas transport systems in a closed cycle loop. This, however, would require a more powerful pumping and gas handling system. Great efforts towards an industrialization of CO lasers were made during years in many countries. A 3-kW system operational at room temperature, for example, was reported by McNaught and Wlodarczyk in 1996 [97McN]. As already pointed out, stable CO laser discharges providing high efficiencies and specific output energies were predicted for e-beam sustained discharges by Monson, more than 20 years ago [76Mon]. This was confirmed in a quite recent publication. To conclude, reference should be made to some interesting results, reported in 1996 and published in 1997 by Dymshits and Alexandrov [97Dym]. Based on the experimental realization of a multi-hundred-kW CO laser system, these studies refer both to analytical and numerical calculations, concerning new laser configurations and concepts, in which supersonic flows and electron-beam sustained discharge excitation were successfully combined. Theoretical results were discussed and related to the feasibility of new experimental systems with IR-optical powers up to several tens of MW which are interesting for many new types of technological applications.
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3.6.3.2 Electrical discharge excited gasdynamic CO2 lasers Great effort was also made in order to improve the performance characteristics of fast-flow highpower CO2 lasers. Numerous specific electrical excitation techniques were investigated, in combination with various types of subsonic or supersonic gasdynamic flow conditions. The use of radiofrequency- or microwave-discharges was found to provide considerable advantages as compared to the use of dc-discharges. Preference was therefore given to these excitation techniques for several reasons. They were found to be less sensitive to the growth of instabilities emanating from the electrodes. Thermally, electrodes were less loaded; consequently, lower cooling requirements were needed. Due to the positive current voltage characteristics, rf-discharges do not require Ohmic discharge stabilization (in contrast to dc-discharges which cause additional losses). Fundamental studies were performed at DLR Stuttgart by Schock and H¨ ugel. With an rf-driving power source of 13 kW at a frequency of 6 MHz, efficiencies within a range of 13 to 20 % were achieved under subsonic gas flow conditions [84Sch3]. Based on their experience with carbon monoxide lasers, these authors demonstrated that rf-excitation may be well adapted to CO2 laser systems, not only for small-scale experiments or for waveguide lasers, but also for pumping larger-volume laser devices, which was important with respect to their scalability. Further studies at DLR, carried out by Schall and coworkers covered the supersonic flow regime as well [84Sch1]. In this case, microwave discharges were used. Vibrational energy in these experiments was provided by a 2.34 GHz microwave generator with an electrical power up to 4.75 kW. Gain measurements at various distances from the nozzle throat allowed to determine experimentally the optical optimum resonator position which depends both upon the laser gas composition and mass flow rates. Nozzle area ratios were changed in these parametric studies from 9 to 35, by accordingly varying the throat heights. It was shown that microwave discharge techniques, such as those originally conceived for supersonically flowing CO lasers, could be successfully adapted as well in order to operate gasdynamically expanding CO2 lasers most efficiently. Further high-power CO2 laser developments, based on original concepts of electrical excitation schemes, were carried out, both in order to increase the specific power output and to improve beam quality. These concepts include combinations of all different kinds of electrical discharges, either with subsonic or with supersonic gas flows. In France, a successful operation was conducted for example by the Marcoussis laboratories CGE research group, already early in the seventies [84Duc]. These developments led to the so-called “LEDA” laser devices (Lasers `a excitation Electrique et a D´etente Adiabatique) with which power levels of several tens, even up to above several hundreds ` of kW were achieved. In these lasers, the electrical excitation scheme was combined with the downstream mixing concept, such as already discussed above. Pure nitrogen, simply flowing through longitudinal dc-electrical discharge tubes, was heated up and vibrationally excited. A large number of individual tubes, placed in parallel, closely spaced and electrically connected in parallel to a dcpower supply, allowed to adapt the specific energy input and the nitrogen-gas throughput to almost any specific requirements. Close to the discharge tube exits, the nitrogen was flown through an array of converging, diverging nozzles. CO2 and He were injected there, either through orifices or a secondary row of nozzles for turbulent mixing with the vibrationally excited nitrogen. The basic principle is schematically shown in the left part of Fig. 3.6.9. The supersonically expanding flow was characterized by a rapidly decreasing translational temperature. In contrast, the almost frozen N2 vibrational temperature allowed an efficient collisional energy transfer to the CO2 -molecules which was favorably used to build up high population inversions. As was shown by measurements of the c2n structure index constants (which characterizes the turbulence profile), homogeneous optical refractive index distributions were achieved by Duchet, Cran¸con et Solmon in the optical cavity region [84Duc]. As a consequence of the mixing, the LEDA technique was basically developed for quasi-continuous operation in blow-down systems. Closed-loop operation could have been possible; however, it would have required a complex gas recovering, treatment and clean-up system. The
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N2
He, CO2
Gas-feed
Gas-feed
To vacuum vessel
Laser cavity
Electrical powersupply
Resistively loaded discharge circuit
305
CO2-,He injector nozzle-array
Lasercavity Laser beam
Flow tube to vacuum vessel
Fig. 3.6.9. Basic LEDA operation principle and laboratory view of the ISL multi-kW LEDA system (as developed by CGE Laboratory, Cilas/FRANCE).
right-hand side of Fig. 3.6.9 shows a photograph of a multi-kW laser of this type. This laser has been conceived by the CILAS CGE-group at Marcoussis, according to special ISL requirements and was used at Saint-Louis as a high-power 10.6 μm laser source for target effect studies by Joeckl´e, Gautier, Stern and coworkers. Powers of more than 7 kW were extracted from a short active-medium length inside the cavity of 30 cm. The time duration of laser emission (typically several tens of seconds) was determined by the volume of the gas reservoir (located outside the laboratory). This vacuum chamber was connected to the laser head through the exhaust tube which can be recognized on the right-hand side of Fig. 3.6.9.
3.6.3.3 Miscellaneous Further possibilities in mixing electric-discharge gasdynamic lasers were investigated and reported, for example by Stregack and coworkers [76Str1]. These authors showed that new coherent sources might be developed, based on molecular transitions which cannot easily be excited by electron collisions. Use was made of the fact that vibrational energy can also be efficiently transferred to the lasing molecules by molecular collisions in turbulent mixing fast flows. As known, this principle of near-resonance collisional energy transfer has been favorably used in any type of conventional electrical discharge CO2 lasers. Similar mechanisms were therefore examined to vibrationally excite other molecules, such as N2 O, CS2 or C2 H2 . This led to a new class of cw lasers to which the energy is collisionally transferred, not only from N2 , but also from CO, H2 or D2 . The following reactions, in particular (H2 –CO2 ), (D2 –CO2 ), (N2 –N2 O), (CO–N2 O), (D2 –N2 O), (CO–C2 H2 ) and (CO–CS2 ), have been investigated. The authors showed (at least in small-scale, low-power experiments) that combined electrical-discharge gasdynamic lasers using supersonic flows and turbulent mixing in fact open new possibilities in laser research, especially concerning investigations of new transitions which cannot preferentially be excited by direct electron impact.
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3.6.4 Chemical lasers As compared to the various types of lasers discussed in the previous sections, chemical lasers are based on a different principle which makes use of the fact that part of the chemical reaction enthalpy may be directly transferred to vibrational–rotational levels and extracted by stimulated emission from one or more reaction products as coherent optical radiation. Basic mechanisms are discussed for example by Polanyi [65Pol]. Important developments concern electrically pulsed chemical lasers (for example, by Batovskij et al. or by Basov et al.) [69Bat, 69Bas1]. The same holds for cw supersonic flow (basically HF or DF) diffusion lasers as first developed by Spencer et al. [69Spe]. Special interest is also related to pure chemical lasers without any electrical input, such as those studied in the case of chemical transfer lasers, for example by Cool and coworkers, which will be discussed more in detail in a separate subsection (Sect. 3.6.4.3.5). The overall energy released by chemical reactions is typically distributed over a large number of translational, rotational and vibrational states of the resulting excited molecules. In thermodynamic equilibrium, population densities are described by Boltzmann distributions. In transient processes, however, thermodynamic equilibrium distributions are usually more rapidly established for translational and rotational than for vibrational energy levels. As a consequence, population inversion in chemically excited lasers is preferentially achieved for levels involving vibrational–rotational transitions.
3.6.4.1 Fundamental processes, vibrational, rotational and translational temperatures The growth of an incident intensity Iν in a simplified two-level model is defined by the following differential equation which describes the frequency-dependent growth of intensity of a plane wave propagating along the x-axis: dIν dν = αν Iν dν . dx
(3.6.23)
The gain coefficient αν is related to the population densities by the following equation: ln 2 BV ,J →V,J gJ · · NV ,J − NV,J . αν = 2 · hν0 π c ΔνD gJ
(3.6.24)
NV ,J and NV,J denote the densities in the vibrational–rotational states of energies EV ,J and EV,J , respectively. Each state is characterized by a corresponding pair of quantum numbers (V , J ) and (V, J), as well as by statistical weights gJ and gJ . As rotational degeneracy has to be taken into account, gJ is defined by the relation gJ = 2J + 1. h denotes the Planck constant, ν0 the central frequency, ΔνD the line width (due to Doppler broadening or pressure broadening) and BV ,J →V,J the Einstein coefficient of the considered transition. The above relation shows that the following condition has to be fulfilled NV ,J NV,J > , gJ gJ
(3.6.25)
in order to obtain positive αν -values. Negative absorption means that waves are amplified and oscillation builds up, if feedback is provided by a suitably adapted optical cavity. In many realistic cases, almost identical rotational and vibrational temperatures can be assumed which, however, differ from the translational temperatures: Trot ≈ Tvib = Ttrans . The population densities are then given by the corresponding temperatures
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NV −E0 (J) = gJ · · exp ZR kTrot
N −E0 (V ) with NV = gJ · . · exp ZV kTvib
307
(3.6.26)
ZR and ZV denote the corresponding rotational and vibrational partition functions. As can be seen from these relations, inversion is only established if chemical reactions, concerning the ratio of rotational temperature Trot to vibrational temperature Tvib , fulfill the following condition: Trot E0 (J ) − E0 (J) ≤ . Tvib E0 (V ) − E0 (V )
(3.6.27)
Efficient lasing due to total inversion is only achieved if the population of the upper vibrational level V (including all rotational J -substates) exceeds the lower-state V -vibrational-level population. NV = NV ,J > NV = NV,J . (3.6.28) It has to be reminded, however, that laser emission may more easily be observed for vibrational– rotational transitions in the case of partial inversion (in spite of the fact that NV < NV ), if the inversion conditions NV ,J > NV,J are achieved for individual states.
3.6.4.2 Specific reactions and operation principles of chemical lasers As mentioned above, most of the molecular reaction products due to the exothermal processes are vibrationally excited. These excited states are indicated in the following by the superscript “+ ”. Exceptions are the photochemically generated iodine atoms, for example formed by photodissociation of specific materials, such as trifluoromethyl-iodide, CF3 I. In this particular case, electronically excited iodine atoms were generated, for which high zero power amplification coefficients were found. They are indicated by “ ∗ ”. Some of the most important types of chemical reactions that were successfully used in the past for chemical laser concepts, according to Kompa, are put together in Table 3.6.3 [70Kom]. Table 3.6.3. Basic chemical reactions used for laser investigations. Processes involved
Examples of typical reactions
Photodissociation Photoelimination Elimination (in electrical discharges) Excited energy transfer Abstraction Chain reactions
CF3 I + hν → I∗ + CF3 CH2 CHF + hν → HF+ + C2 H2 CF3 CH3 → HF+ + CF2 CH2 (1 Δ) O2 + I → (2 P1/2 ) I + O2 Cl + HI → HCl+ + I F + H2 → HF+ + H
The processes involved comprise dissociation or elimination, either by photons or by electrons in electrical discharges, by vibrational energy transfer due to molecular collisions or by other bimolecular collisional exchange reactions. Basic efforts in the past were related to following topics: – theoretical chemical kinetic studies, calculations and experimental measurements of rate constants, of collisional transfer rate constants, excitation cross-sections, relaxation processes or spontaneous emission probabilities; – exploration and research of new chemical systems (For fluorine–hydrogen reactions for example, a large number of different H2 and F2 sources were investigated. The same holds for the various techniques concerning the ignition of chemical reactions, according to various schemes. Nonself-sustained reactions were taken into account, but especially also chain reactions, as these latter were most promising, due to their highly efficient potential.); Landolt-B¨ ornstein New Series VIII/1B1
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– development of scalable laser devices (The conception and design of systems in the past concerned particularly HF and DF lasers (involving for example the use of H2 , D2 , F2 , SF6 or N2 F4 ) which found greatest interest during many years. Presently, however, the main interest has shifted towards new, even more promising developments in the field of chemical oxygen iodine lasers.). Some important types of chemical lasers are schematically listed in Table 3.6.4 and will briefly be discussed in the following. (R refers to alkyl-groups and is used as abbreviation, for CH3 , C2 H5 , C3 H7 , etc.). Table 3.6.4. List of basic chemical laser reactions, wavelengths and typical excitation methods. Typical gas mixtures CF3 I Cl2 –H2 O2 –KOH–I H2 /D2 –Cl2 HI–Cl2 CS2 –O2 H2 or RH–F2 RH–SF6 CH3 I + CF3 I CH3 I + N2 F4 UF6 /MoF6 + H2 D2 –F2 CO + O2 (+ CO2 ) Cl2 + HI (+ CO2 ) HN3 + CO2 H2 /D2 + F2 + CO2
Emitting species 2
I ( P1/2 ) I (2 P1/2 ) HCl+ / DCl+ HCl+ CO+ HF+ HF+ HF+ HF+ HF+ DF+ 0 CO+ 2 (00 1) + CO2 (000 1) 0 CO+ 2 (00 1) + CO2 (000 1)
Wavelength ranges
Excitation or initiation methods
1.315 μm 1.315 μm 3.5 . . . 4.1 μm 3.5 . . . 4.1 μm 4.7 . . . 5.6 μm 2.6 . . . 3.1 μm 2.6 . . . 3.1 μm 2.6 . . . 3.1 μm 2.6 . . . 3.1 μm 2.6 . . . 3.1 μm 3.6 . . . 4.1 μm 9.2 . . . 10.8 μm 9.2 . . . 10.8 μm 9.2 . . . 10.8 μm 9.2 . . . 10.8 μm
flash photolysis O2 (1 Δ) excitation energy transfer flash photolysis discharge / flash photolysis flash photolysis discharge / flash photolysis discharge / flash photolysis flash photolysis flash photolysis flash photolysis discharge / flash photolysis combustion flash photolysis flash photolysis (hν) excitation energy transfer
An interesting overview of reactions and quotations, corresponding to the state of the art which was already achieved in 1973, was put together and published by Wiswall and coworkers [73Wis].
3.6.4.3 Discussion and evaluation of chemical laser systems 3.6.4.3.1 Iodine lasers 3.6.4.3.1.1 Pulsed systems, photolytically initiated iodine lasers (PIL) It is interesting to note that electronically excited atomic-transition iodine lasers which were first achieved through photodissociation by Kasper and Pimentel [64Kas], are characterized by extremely high amplification coefficients at 1.315 μm of more than 100 dB/m. These lasers (see Table 3.6.4) which are operational only pulsewise make use of the magnetic dipole transition between the I (2 P1/2 )- and the I (2 P3/2 )-states. Extremely high power iodine laser sources were successfully developed and operated by Hohla, Kompa, Brederlow, Baumhacker, Witkowski and coworkers in the Max-Planck Institute for Quantum Optics, MPQ at Garching [72Hoh, 73Hoh, 88Bau, 95Bre]. Lasers of this type for some time were also considered to be useful candidates for the laser fusion research. By UV-pumping of alcyliodine (C3 F7 I), diluted in argon or other buffer gases, output energies of more than 2 kJ were reported. The “Asterix-IV” MOPA experiments (Master-Oscillator Power-Amplifier), for example, allowed nearly diffraction-limited beams to be achieved with maximum peak-power extraction of Landolt-B¨ ornstein New Series VIII/1B1
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5 TW. Typical pulse durations were ranging from 0.2 to 5 ns. Calculations based on these experimental results showed that lasers of this type provide the capability to scale up to still higher output energies and to shorter pulse durations which correspondingly both increase the accessible range of peak powers. Elaborate systems such as those mentioned above, of course, need utmost sophisticated technologies. As a consequence, they represent complex, expensive and large-volume devices. Further pumping schemes have therefore been investigated extensively, basically aimed at obtaining less expensive, smaller sized, less primary energy consuming and more compact high-energy iodine lasers. As High Explosives (HE) can store huge amounts of specific energy, up to several MJ/kg, efforts have been undertaken to make use of these chemical energy resources which may be rapidly released upon detonation. The use of high-explosive charges for iodine laser pumping has therefore been investigated to feed the pumping source, for example, at Los Alamos since the early 1980s. Two different schemes were investigated and reported by C.R. Jones [95Jon]: 1. In a first series of experiments, explosion-driven shock waves through gases were used. These were well known to provide intense optical radiation, characterized by plasma temperatures in the range of 25.000 to 35.000 K. These temperatures are usually even higher than those of xenon flashlamps or ablating-wall flashlamps. By using the emission of high-explosive shocked argon (basically the spectral range in the UV around 280 nm), Jones achieved laser energies up to 1 kJ by using a laser cell, 17 cm in diameter and 94 cm in length, filled with 20 torr of C3 F7 I and 580 torr of Ar. 2. In a second approach, thin metal films (1 μm aluminum) were exploded by megampere-level current pulses from explosive-driven magnetic flux compression generators. Laser energies were estimated in these experiments to be of the order of 0.4 kJ in the case of a 5 cm diameter laser cell filled with 50 torr C3 F7 I and 100 torr Ar. The laser tube was located parallel to the 48-cm-long exploding cylindrical metal film discharge at a distance of 11 cm. Further results related to more specific systems or optimization have not been reported so far. According to Jones, the main purpose of the experiments cited above was to demonstrate the feasibility and to evaluate the scaling potential of explosively driven pulsed iodine laser devices.
3.6.4.3.1.2 Continuous-wave iodine lasers (COIL) Concerning continuous-wave (cw) iodine laser sources, a real breakthrough was achieved by using the COIL technology (Chemical Oxygen Iodine Lasers). Most efficient pumping schemes were developed after the first realizations and publications by McDermott et al. [78McD, 84McD] in 1978 by various research groups. Rosenwaks in Israel, for example, showed as early as in 1982 that very compact systems could be designed due to the high efficiencies. The first Japanese COIL was reported in 1983. However, the greatest continuous efforts were especially undertaken by the Air Force Laboratories research group in US. The mechanism is based on chemically produced energy, intermediately stored in the O2 (1 Δ)-state of oxygen molecules, which is produced by the following reaction: Cl2 + H2 O2 + 2 KOH ⇒ (1 Δ) O2 + 2 KCl + 2 H2 O .
(3.6.29)
Gaseous Cl2 is mixed with liquid-phase H2 O2 and KOH resulting in H2 O, solid-state KCl and singlet-delta excited oxygen (1 Δ) O2 . By downstream mixing of iodine, part of this energy can be transferred to the iodine atoms in the flow. High efficiencies were achieved, as the O2 (1 Δ)-state is almost in resonance with the upper-laser-level electronically excited I (2 P1/2 )-state from which the lasing transition occurs to the lower I (2 P3/2 )-level: O2 (1 Δ) + I ⇒ I (2 P1/2 )
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(3.6.30)
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[Ref. p. 333
The COIL belongs to today’s most important high-power lasers, see for example Truesdell and Lamberson [92Tru] or Bohn [92Boh]. All real high-power COIL systems realized so far are operated in the continuous-wave mode. This also holds for the High-Energy Airborne COIL-demonstrator ABL YAL 1A which is designed for being integrated in a modified Boeing 747-400F freighter aircraft which is currently in progress [02Lam]. It should be mentioned, however, that the Zeeman splitting of the iodine lasing line, already studied in 1968 by Kidder et al., can actually be used to increase the energy-storage capability [68Gre1]. Progress towards high-average-power pulsed multi-kW systems has been reported [00Hag] during the Laser Ablation-2000 conference at Santa Fe. As a consequence a temporal modulation or repetitively a pulsed mode of operation is feasible, which can provide an increase of energy by the application of gain-switching techniques. Due to the particular importance of COIL-systems, details about the actual state of the art will not further be discussed in the present chapter. These topics will be the subject of a special chapter, Chap. 3.7, devoted to present recent developments and achievements of COIL lasers.
3.6.4.3.2 HCl and HBr lasers 3.6.4.3.2.1 Pulsed HCl lasers and HBr laser studies The first real chemical laser, discovered by Kasper and Pimentel in 1965, was an HCl-explosion laser [65Kas]. The authors were investigating flash-photolytically initiated hydrogen-chlorine explosions, according to the reaction schemes listed in Table 3.6.5. Table 3.6.5. Basic chemical reactions in HCl-explosion laser. Cl2 + hν Cl + H2 H + Cl2
⇒ ⇒ ⇒
2 Cl HCl + H HCl+ + Cl
(ΔE = +1 kcal/mole) (ΔE = −45 kcal/mole)
As can be expected, the second of the reactions above yields only nearly thermoneutral, nonexcited HCl. Experimentally, laser action was thereby found to develop basically due to transitions in the v(2 ⇒ 1)-band. The spectral emission of HCl lasers is centered around 3.6 to 3.9 μm. According to flash photoionization (e.g. Corneil and Pimentel) the first HCl- or DCl-lasers were operated in the pulsed mode [68Cor]. Further investigations were related to reaction between Clatoms and HI-molecules. Cl-atoms were generated by Airey through flash photolysis [67Air] or by Moore through pulsed electrical discharges [68Moo]: Cl + HI ⇒ HCl + I (ΔE = −32 kcal/mole) .
(3.6.31)
The use of electron-beam-controlled discharges for HCl laser concepts, for example, was theoretically considered by United Aircraft Research Laboratories researchers early in the seventies. A few years later, in 1979, Ameur and coworkers in France used simple multi-pin TE-discharges (as known from CO2 lasers) to initiate (H2 + Cl)-reactions at low-pressure regimes. In spite of the small energies, typically of the order of several hundreds of mJ, their results enabled them to compare experimental and theoretical data, as obtained with a computer simulation model in which both the multiline emission and the influence of wavelength-selective gratings in the resonator for single-line emission could be included [79Ame]. Laser action in HBr due to pulsed electrical discharges was first reported by Deutsch [67Deu1]. Further studies were carried out by Wood, or by Toyoda and coworkers [80Toy] who used Transversely Excited discharges (TE) between solid bar electrodes and pin cathodes. In these experiments the Br-gas was flown through Teflon or glass pipes. Gaseous Br, evaporated from a reservoir, was
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mixed with H2 , He, and Ar prior to entering the laser tube. Exhaust gas passed through a molecular sheave and liquid nitrogen trap. In the case of multiline emission, the output spectrally consists of P-lines, ranging from P10 (4) at λ = 4.017 μm to P43 (7) at λ = 4.608 μm. 3.6.4.3.2.2 Continuous-wave laser excitation Continuous-wave HCl laser emission was already demonstrated early in 1967. Anlauf et al. [67Anl] succeeded in maintaining continuously vibrational population inversion. Besides the abovementioned exothermic (H+Cl2 )-process, they also investigated the vibrational population inversion of (H + Br2 )-reactions. Continuous-wave HCl laser emission was also reported in 1970 by Cool, Stephens and Shirley [70Coo1] who used a longitudinal rf-discharge to produce atomic Cl for the subsequent reactions with hydrogen. Furthermore, cw laser excitation was achieved, due to the reaction of Cl-atoms with hydrogen halides. This chemical process has already been discussed above, concerning the pulsed mode of laser operation. Accordingly, the reaction of Cl-atoms with HI-molecules (which is also included in Table 3.6.3 and Table 3.6.4) was similarly used for cwHCl lasers. For this reaction to occur, premixed hydrogen-iodide and molecular chlorine has to be used. Partial dissociation of Cl2 was also conveniently achieved by flash photolysis, allowing the chemical reactions not to develop explosion-like as in the case of a real chain reaction. In similar experiments, Glaze et al. [71Gla1] achieved partial dissociation of Cl2 with He admixed by means of a 21 MHz high-frequency discharge.
3.6.4.3.2.3 Numerical analysis Some interesting theoretical results which were already published by Igoshin in 1979 [79Igo] should at least briefly be mentioned, as far as these are related to HCl laser emission. Igoshin’s detailed numerical analysis was based on the (ClF+H2 )-reaction. He showed that emission could be obtained not only from excited HCl+ , but also simultaneously from HF+ -molecules (which will be considered more in detail in Sect. 3.6.4.3.4). He developed a kinetic model including detailed information on temperature-dependent rate constants. Initiation was started first by the dissociation of ClF, according to the reaction: ClF ⇒ Cl+F. Igoshin then considered the subsequently developing chain reactions, the first involving F- and H-atoms. The second chain was related to Cl- and H-atoms, the third chain referred to collisions between Cl and F whereas the fourth chain reaction finally was related to processes between Cl- and H-atoms, similarly as in the second case, but followed by processes like H + Cl2 ⇒ HCl + Cl. He showed that stimulated HF laser emission (2.7 μm to 2.9 μm) is preferably observed for H2 –ClF-mixtures with low content of H2 , whereas maximum HCl laser energy output (in the range of 3.3 μm to 4 μm) is achievable for hydrogen-rich mixtures.
3.6.4.3.3 CO lasers As already mentioned in Sect. 3.6.3.1 on “Electrically excited fast-flow or gasdynamic lasers” CO lasers provide interesting infrared high-power laser sources with an emission spectrum from slightly below up to above 5 μm. Powerful laser concepts were realized by means of chemical energy transfer, by using the CS2 and O2 , as cited in Table 3.6.4 above. Detailed models have been established, such as for example by Guenoche and Sedes who calculated the population of each vibrational level of the CO-molecules to be expected behind a normal shock wave propagating in CS2 –O2 – Ar-mixtures [80Gue]. Numerical programs of this type were also used to determine the influence of the vibrational–vibrational exchange reactions as well as the vibrational–translational transfer rates.
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3.6.4.3.3.1 Pulsed CO lasers Pulsed chemical lasers may usually convert a considerable part (up to above 10 %) of their chemical enthalpy into coherent optical radiation. They require, however, electrical input energy in order to initiate the chemical reaction either by flash photolysis or some type of electrical discharges. Pulsed CO laser emission, due to photolytically excited CS2 –O2 -mixtures was first reported in 1966 by Pollack [66Pol1, 66Pol2]. Reactions were initiated optically by flashlamps, giving rise to multiline radiation of more than 30 lines in the 5 μm spectral range. For typical partial pressures of 1 torr CS2 , 1 torr O2 with 150 torr He as buffer gas, laser emission was observed above an electrical input energy threshold of 200 J. In CS2 -O2 -mixtures, the following reactions were discussed as candidates to possibly provide vibration–rotationally excited CO-molecules. In a first step CS-, SO- and O-radicals are formed as dissociation products, induced by flash photolytical processes: CS2 + hν ⇒ CS + S
O2 + S ⇒ SO + O .
followed by
(3.6.32)
Vibrational–rotational excitation of CO is subsequently generated by the following reactions of these CS-, SO- and O-radicals: SO + CS ⇒ CO+ + S2 ;
O + CS2 ⇒ CO+ + S2 ;
O + CS ⇒ CO+ + S .
(3.6.33)
Detailed spectroscopic investigations were carried out by many groups, such as for example by Gregg and Thomas [68Gre2] who found and published 270 new laser lines as early as in 1968. These authors assigned a large number of rotational P-branch and R-branch lines according to transitions between vibrational levels 1 → 0, 2 → 1, etc., up to 16 → 15. Further observations were reported by Arnold and Kimbell [69Arn]. As possible mechanisms, this group considered the chemical reactions 1 to 10 which are listed in Table 3.6.6, including the corresponding enthalpies. Experimentally, Arnold et al. observed pulsed CO emission in flowing CS2 –O2 -mixture with various inert buffer gases (He, N2 , or air) at low pressures of a few torr. Proper excitation was achieved by electrical sparks. Typical pulse durations were of the order of several tens of μs. Spectrally, a range between 5.0 and 5.3 μm was covered in these experiments which could be attributed to P-lines of the v = (13 → 12, 12 → 11, 11 → 10, 10 → 9, 9 → 8, 8 → 7, 7 → 6 and 6 → 5) vibrational–rotational transitions. From their experimental results, Arnold and Kimbell concluded that the reactions 1 and 2 in a first step belong to the most important processes for the Table 3.6.6. Chemical reactions related to CO lasers [69Arn, 72Sua, 76Ros]. No.
Chemical reaction
[69Arn]
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
CS2 + hν O + CS2 O + CS2 O + CS2 CS + SO O + OCS O + CS O2 + CS OCS + O2 O2 + S O + NO2 S + NO2 SO + O2 SO + SO SO + SO CS2 + S
• • • • • • • • • •
⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒
CS + S CS + SO OCS + S CO+ + S2 CO+ + S2 CO+ + SO CO+ + S CO+ + SO CO+ + SO2 SO + O NO + O2 NO + SO SO2 + O SO2 + S S2 O2 CS + S2
flash photolysis or discharge 23 kcal/mole 53 kcal/mole 82 kcal/mole 59 kcal/mole 51 kcal/mole 81 kcal/mole 87 kcal/mole 64 kcal/mole 6 kcal/mole
[72Sua] •
[76Ros] • •
• (75 kcal/mole) • (81 kcal/mole)
•
• • • • • • •
• •
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production of CS. These radicals were needed in the subsequent steps for the generation of the population inversion in CO for which they claimed reaction 7: (O + CS ⇒ CO+ + S) and reaction 8: (O2 + CS ⇒ CO+ + SO) to be mainly responsible. In a different approach, chemical reactions were considered by Suart, Dawson and Kimbell both experimentally and theoretically using a computer simulation program. Concerning details, such as the rate constants, the reader is referred to their paper [72Sua]. These authors, in contrast, concluded that the vibrationally excited CO+ may be basically generated by the reaction 7 shown in Table 3.6.6: (CS + O ⇒ CO+ + S), followed by the subsequent reaction 10: (S + O2 ⇒ SO + O). This second reaction is required, in order to support the atomic oxygen production rate of the chain which competes with the simultaneously occurring oxygen consuming reactions. A few minor discrepancies, found in these papers concerning the enthalpies are also indicated in Table 3.6.6. Further investigations on pulsed CO lasers based on a CS2 –NO2 -reaction were carried out and published by Rosenwaks in 1976 [76Ros]. Starting from flash-photolytically initiated CS2 and NO2 , he achieved the initial production of the required CS- and O-radicals simultaneously in a single step, as compared to the 2-step process in the case of the first known (CS2 + O2 )-mixtures. These chemical reactions have additionally been included in Table 3.6.6. The key role was considered by Rosenwaks also to be determined by the reaction 7: (O + CS ⇒ CO+ + S) with CS-radicals generated by flash photolysis according to the reaction 1: (CS2 + hν ⇒ CS + S) while O-atoms were provided by reaction 10: (S + O2 ⇒ SO + O). 3.6.4.3.3.2 Continuous-wave CO lasers In the paper of Suart et al., cited above, the authors considered not only pulsed but also cw CO laser systems. In their first experiments, an O2 –He mixture was flown through a 2.45 GHz microwave cavity, to partially dissociate O2 to O atoms. CS2 or CS2 –CO mixtures were then introduced by a radial array of holes downstream of the oxygen–helium flow. Of course, different configurations, slits and nozzles were developed in the past for this injection and mixing technique. As compared to the longitudinal gas-flow configurations, power could be increased by using transverse excitation schemes and mixing geometries and by the addition of cold CO, such as for example published by Jeffers and Wiswall [70Jef]. The underlying basic chemical reactions O + CS2 ⇒ CS + SO and O + CS ⇒ CO+ + S have already been cited as reactions 2 and 7 in Table 3.6.6. Higher specific output energies were achieved by using active nitrogen, N-atoms together with O2 + CS2 . The N-atoms were generated in a condensed discharge, mixed with the injected CS2 and O2 and exhausted by a vacuum pump. The individual flow rates were optimized by Hirose et al. [73Hir]. The authors set up numerical models to describe this kind of reactions. Theoretical results were found to be in good agreement with experimental data. Various reactions were discussed, whereby preference was given to the schemes shown in Table 3.6.7. Interesting features were also reported by the developments of continuous-wave free-burning chemical flame lasers, such as by the combustion of CS2 /O2 at low pressures, for example by Foster and Kimbell [70Fos], or by Djeu et al. [71Dje]. After ignition, a self-sustaining flame allowed to build up inversion in the reaction zone, from which laser emission was extracted by means of a suitably adapted optical cavity. The self-sustaining system must officially have involved branching Table 3.6.7. Chemical cw CO laser reactions. N + CS2 NS + N S + O2 O + CS2 CS + O N+ 2 + CS2
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chain reactions to maintain a steady-state concentration of those intermediates which are lost by so-called termination reaction or by diffusion out of the flame. Optical gain was achieved in COvibration–rotation transitions P(12)–P(14) in the bands 10 → 9, 9 → 8 and 8 → 7. The following four reactions were estimated by the authors to describe the branching reactions of low-pressure CS2 –O2 -flame systems: CS2 + O ⇒ (k1 ) CS + SO ;
SO + O2 ⇒ (k2 ) SO2 + O ;
S + O2 ⇒ (k4 ) SO + O .
CS + O ⇒ (k3 ) CO+ + S ; (3.6.34)
For details related to the experimental device, or concerning the rate constants k1 to k4 , the reader is referred to the literature, e.g. Pilloff, Searles and Djeu [71Pil]. At first sight, their simplicity made such flame lasers appealing. High specific power densities, however, were not achieved so far so that practical and powerful laser devices did not seem feasible.
3.6.4.3.4 HF, DF lasers Similar experiments to those with flash-photolytically initiated hydrogen-chlorine explosions which were carried out by replacing chlorine by fluorine led to the discovery of the HF lasers. As early as in 1967, Deutsch reported on molecular laser action in hydrogen-halides and deuterium-halides as well [67Deu1]. He listed and identified a large number of rotational lines of lower vibrational transitions which were observed in chemical reactions, initiated by pulsed electrical discharges. He studied a large variety of commercial freons, such as CF4 , CBrF3 , CClF3 , CClF2 , either with H2 or with D2 . Laser emission was also found by replacing H2 by CH4 or CH3 Cl. The basic mechanisms in these various schemes, for example in the case of hydrogen, were determined by chemical reactions which provided the pumping energy sources for this group of lasers. The reactions involved were all found to be exothermic which may even lead to chain-reaction developments. According to the values of the enthalpies which are shown in Table 3.6.8, higher vibrational levels (v) were excited and inverted by the so-called hot reactions, as compared to those, observed in the case of the so-called cold reactions. Table 3.6.8. Basic HF laser pumping schemes. F + H2 F + CH4 F2 + H
⇒ ⇒ ⇒
HF+ + H HF+ + CH3 HF+ + F
ΔE = −31.8 kcal/mole ΔE = −31.6 kcal/mole ΔE = −97.9 kcal/mole
(cold reaction, v typically < 4) (hot reaction, v typically up to 10)
The enthalpies ΔE (−31.8, −31.6 and −97.9 kcal/mole) were determined by measuring the released specific reaction energies from which the activation energies have been deduced. Similar considerations hold for DF lasers in which energy is supplied by the corresponding (F + D2 )- and (F2 + D)-processes. Spectrally, HF lasers were found to emit in a large range between 2.76 and 2.91 μm for which, unfortunately, the atmosphere is strongly absorbing. However, by replacing hydrogen by the isotope deuterium the wavelengths are shifted towards a range between 3.67 and 3.89 μm for which excellent atmospheric transmission characteristics hold.
3.6.4.3.4.1 Pulsed HF, DF lasers As already mentioned, most chemical laser devices require electrical energy in order to initiate the processes. Pulsed HF- or DF-laser chemical reactions were ignited both by flash photolysis and by different kinds of electrical discharges. Accordingly, a large variety of experimental facilities were developed and optimized for particular needs. Difficulties were overcome by directly mixing Landolt-B¨ ornstein New Series VIII/1B1
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H2 and F2 and by controlling chemical chain reactions, for example by means of buffer gases. Safe handling of F2 –H2 -mixtures is required, in order to obtain controllable and stable chemical reactions without self-ignition. This was shown, at least in small-scale experiments, to be achievable by using He-diluents, at least in a limited range of pressures up to a few tens of torr.
3.6.4.3.4.1.1 Flash-photolytically initiated reactions As already mentioned, reactions of H2 –F2 –He-mixtures were successfully ignited by flash photolysis. However, specific laser energies proved to be low, as compared to the electrical energies required for the optical ignition of the reactions. In small-scale experiments, typical IR-optical energies in the mJ-range were reported, such as for example by Hess [71Hes], which, however, required flashlamp energies of several hundreds of J. Nevertheless, it was demonstrated that mixtures under these conditions could be safely manipulated and did not undergo uncontrolled prereactions between H2 and F2 . Similar chain-reaction results were confirmed by Suchard and coworkers [71Suc, 73Suc]. Concerning a comparison between experimental results and numerical modeling, reference is made to the publication of Suchard and Sutton [74Suc1]. A different type of photolytic initiation was suggested by Watanabe who successfully investigated chemical HF, DF laser action ignited by radiation, generated by Teflon-surface sparks which provide a higher UV radiative efficiency than commercial Xe-flashlamps. Specific energies of 11 J/l were obtained for HF and 4.2 J/l for DF [80Wat]. A fast mixing procedure was applied in these studies by the injection of H2 /Ar and F2 /Ar/O2 to prevent a prereaction or premature ignition of the H2 /F2 gases used. Interesting experimental results were also obtained and reported, using UF6 , WF6 , SbF5 , XeF4 or other molecules as fluorine atom sources. Detailed studies were carried out, for example by Kompa, Parker, Pimentel, Kasper and many others [67Kom, 68Kom, 69Kom, 68Par, 69Par]. Early results concerning UF6 were already published in 1967. Other molecules, such as MoF6 in particular, were extensively investigated by Chester and Hess [73Che, 72Hes]. In these measurements, for example, it was found that MoF6 could not only be used as a fluorine donor, but also as a stabilizer for F2 –H2 –He mixtures, prior to triggering flashlamps or other electrical circuits for discharge ignition. Additionally, this MoF6 -admixture allowed to considerably increase the chemical efficiency up to above 12 % (as compared to values typically below the 1 % range). As a consequence, such an admixture correspondingly led to a marked increase of the pulsed output energy. Some of the basic reactions which were taken into account in the case of UF6 as fluorine donor are summarized in Table 3.6.9. Ea denotes the activation energy to be supplied for initiation. Table 3.6.9. Flashlamp-pumped HF laser reaction based on UF6 . UF6 + hν F + H2 H + UF6 H + UF5
⇒ ⇒ ⇒ ⇒
UF5 + F HF + H HF + UF5 HF + UF4
ΔE = −32 kcal/mole ΔE = −46 kcal/mole
(Ea = 1.7 kcal/mole) (Ea unknown)
Pulsed HF laser emission was achieved by Klimek and Berry [73Kli] in their experiments, carried out with formyl-fluoride (HFCO). The authors analyzed in detail the photochemistry and spectroscopy of flash-photolytically initiated HFCO. Some of the important basic processes are summarized in Table 3.6.10, also including some important subsequent reactions and reaction products which have to be considered as well in this particular case. These processes are termed photoelimination reactions, as several bonds of the formyl-fluoride molecules are broken up by the photochemical processes, in contrast to photodissociation effects in which only single chemical bonds of the reactants are ruptured.
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Table 3.6.10. HF laser reaction due to photolysis of HFCO. HFCO + hν ⇒
HFCO∗ + (electronic and vibrational excitation) ⇒ HF+ + CO HFCO∗ + ⇒ H + FCO HFCO∗ + ⇒ F + HCO and F + HFCO ⇒ HF+ + FCO
For the generation of powerful HF laser pulses, further chemical reactions were studied by Gross and coworkers [68Gro], such as those between F2 O and H. Starting initially from gas mixtures containing molecular hydrogen, atomic species have to be provided in a first step. This is achieved for example by using fluorine atoms which are easily generated by partial dissociation of any of the known fluorine donor molecules (e.g. CF4 , CBrF3 , CClF3 , CClF2 ). Hydrogen atoms are then produced according to the well-known exothermal process (F + H2 ⇒ HF + H). The subsequent exothermic reaction between H and F2 O produces both OF and vibrationally excited HF+ . Furthermore, the OF radicals may undergo secondary processes with molecular hydrogen, according to OF + H2 ⇒ HOF + H, so that the exothermic reactions between H, HOF and OF listed in Table 3.6.11 have to be retained as well. As can be seen, even the secondary processes involved contribute to yield vibrationally excited HF+ lasing molecules. Table 3.6.11. Chemical HF laser reaction scheme in the case of F2 O and H. H + F2 O ⇒
OF + HF+ OF + H2 ⇒ HOF + H HOF + H ⇒ HF+ + OH H + OF ⇒ HF+ + O
The photoelimination technique, published in the literature which was studied for example by Berry and Pimentel [68Ber, 69Ber] represents an other interesting scheme for the efficient generation of pulsed HF or DF laser radiation. By reactions between the radicals CH3 and CF3 for example, vibrationally excited 1,1,1-trifluoroethane is generated, from which an energy of the order of 60 to 80 kcal/mole is obtained by elimination of HF. This energy is distributed between the reaction products and consequently, a considerable part is also available to vibrationally excite HF: + CH3 + CF3 ⇒ CH3 CF+ 3 ⇒ CH2 CF2 + HF .
(3.6.35)
Similar considerations hold for DF+ . Experimentally, mixtures of CH3 I (or CD3 I) and CF3 I were photolyzed with xenon flashlamps. Both in the case of hydrogen and deuterium, these mechanisms were shown to work quite efficiently. Lasing was demonstrated for v (1 ⇒ 0 and 2 ⇒ 1) transitions. It should be mentioned, that the same mechanism of photoelimination was also successfully applied to hydrogen chloride, starting from chloroethylenes. Further systems of so-called abstraction-elimination HF lasers, as reported by Padrick and Pimentel were based on the photolytically initiated reaction of tetrafluorohydrazine N2 F4 , either with CH4 or with methyl-iodide CH3 I. In both cases Ar was used as buffer gas [71Pad, 72Pad]. The mechanisms were attributed to both HF-abstraction and -elimination reactions from chemically activated CH3 NF+ 2 . In the N2 F4 –CH4 processes the authors showed that both N2 F4 and the flashphotolyzed dissociation products NF2 were capable of efficiently furnishing F-atoms which initiate laser emission by H-atom abstraction. In the N2 F4 –CH3 I reactions HF+ is basically formed by elimination, according to the steps indicated in Table 3.6.12. First CH3 is photolytically generated. Its subsequent reaction with N2 F4 allows the formation of excited CH3 NF+ 2 from which the lasing HF-molecules are produced in the third step, again by elimination reactions. Landolt-B¨ ornstein New Series VIII/1B1
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Table 3.6.12. HF laser chemical reactions, according to Padrick et al. [71Pad]. CH3 I + hν CH3 + N2 F4 CH3 NF+ 2
⇒ ⇒ ⇒
CH3 + I∗ CH3 NF+ 2 + NF2 HCN + 2 HF+
3.6.4.3.4.1.2 Discharge-initiated pulsed HF, DF lasers As already mentioned, successful pulsed laser action was also achieved in electrical discharges, both by the use of longitudinal and transverse electrode configurations. Reliabilities and efficiencies were demonstrated for years. An improved stability of laser gas mixtures with respect to unwanted prereactions in the case of fluorine with hydrogen or deuterium, respectively, by preventing chain reactions from building up explosively, was reported by Whittier and Kerber [74Whi]. These authors used successfully an additional premixing technique by the injection of O2 in a cold trap (84 K) together with F2 and He prior to the mixing with H2 . Numerous research programs were aimed at investigating more stable experimental conditions for safety reasons. Specific molecules were taken into account, from which fluorine could be detached, even in spite of lower efficiencies to be expected. Longitudinal electric discharges were first used. Experiments, for example carried out by Deutsch, date back to 1967 [67Deu2, 71Deu]. Ultee, a few years later, in 1970, extended his investigations to a larger variety of different gas mixtures. These comprised fluorine containing hydrocarbons, such as CH2 F2 , CHF3 , CH2 ClF or fluoro-compounds (for example CClF3 or SF6 ) together with hydrogen or hydrogen containing compounds (e.g. CH4 ). Longitudinal electrical discharges proved to be well suited for the initiation of such a type of chemical reactions [70Ult]. Experimentally, gain coefficients were measured by Ultee up to 1 cm−1 , which he confirmed theoretically by calculations. Longitudinal discharges were also optimized by Deutsch in early experiments [74Deu]. He demonstrated optimized performance characteristics by using H2 –C2 F6 –He laser gas mixtures. Depending on gas flow rates, pulse repetition rates were raised to several tens of Hz. After the advent of the first Transversely Excited Atmospheric pressure (TEA) CO2 lasers by Dumanchin and Beaulieu [69Dum, 70Bea], subsequent electrical discharge HF, DF laser experiments were also performed by making use of the more promising transverse electrical discharges. With such transversely excited HF or DF lasers, Deutsch achieved uniformly distributed gain values of 76 dB/m for HF lasers and 39 dB/m for DF lasers which were high, as compared to the values of 36 dB/m (HF) and 19 dB/m (DF) measured by Kompa et al. in the case of flash-initiated (H2 or D2 ) / UF6 reactions. Additionally, CHFCl2 and CHF2 Cl were successfully used in pulsed discharges. These two candidates belong to the group of fluorine-containing hydrocarbons already discussed above. Further reactions of NF3 , either with H2 or with C2 H6 , were investigated by Lin [71Lin]. In his experiments emphasis was placed on the evaluation of the spectral output of laser radiation in order to improve the knowledge of underlying mechanisms. In an effort to obtain higher specific energies by using transverse electrical discharges, Green and Lin investigated reactions of both N2 F4 and NF3 as fluorine sources. They further worked with various hydrogen sources HX, from which the required atomic hydrogen was produced by partial dissociation according to one of the techniques already cited above, whereas He was introduced as a buffer gas [71Gre]. The possible reactions listed in Table 3.6.13 were analyzed with respect to an optimization of the specific energy. From the knowledge of the high specific energies and the fact that spectrally only vibrational– rotational transitions 1 ⇒ 0, 2 ⇒ 1 up to 3 ⇒ 2 were experimentally observed in discharge-initiated HF lasers of this type, it was concluded that the excitation mechanism in both cases was basically determined by the atomic fluorine production rate which leads subsequently to the following, lower energetic process of population inversion: F + HX ⇒ HF+ + X
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Table 3.6.13. Chemical reactions using NF3 - or N2 F4 -fluorine donors. NF3 -HX-case
H + NF3 ⇒ HF+ + NF2 H + NF2 ⇒ HF+ + NF 2 NF ⇒ N2 + 2 F
N2 F4 -HX-case
H + N2 F4 ⇒ HF+ + N2 F2 + F H + N2 F2 ⇒ HF+ + N2 + F
−77 kcal/mole −65 kcal/mole −82 kcal/mole −78 kcal/mole −118 kcal/mole
Table 3.6.14. Exothermicities ΔE of chemical reactions between various fluorine sources and hydrogencontaining compounds HX. Fluorine sources: F2 ; SF6 ; CHFCl2 ; CHF2 Cl; NF3 ; N2 F4 . Reaction: F + HX. X
HX
Reaction: F + HX
ΔE [kcal/mole]
H CH3 C2 H5 Cl Br
H2 CH4 C2 H6 HCl HBr
F + H2 F + CH4 F + C2 H6 F + HCl F + HBr
−31.7 −31.9 −37.8 −32.8 −48.3
Depending on X, the enthalpies ΔE are of the order of −32 to −48 kcal/mole. Various combinations of fluorine sources and hydrogen-containing compounds are listed in Table 3.6.14. The basic mechanisms consist, in a first step, in partially dissociating fluorine, in order to allow the chemical reactions to be started with the additional species according to their individual exothermicities. In many laboratory devices fluorine was replaced for safety reasons by SF6 to prevent the chainreaction mode of operation. The energies required for partial dissociation of these molecules were provided by electron collisions in electrical (non-self-sustained or self-sustained) discharges, such as for example also by longitudinal or transverse discharge schemes: SF6 + e ⇒ F + SF5 + e .
(3.6.37)
Of course, higher-order dissociation products, such as SF4 and F2 , were generated as well and contributed to the overall laser performance. Subsequent chemical energy transfer in these configurations was mainly provided by the so-called cold reaction of atomic fluorine with hydrogen (F + H2 ⇒ HF+ + H), or by (F + D2 ⇒ DF+ + D) in the case of deuterium, for which the same considerations hold. Experiments of this type were carried out for example by Wenzel and Arnold in 1972 [72Wen]. These authors used a double-discharge-initiated configuration both in SF6 –H2 and in SF6 –C4 H10 . However, electrical efficiencies (η = 0.6 %) were rather poor. The same holds for the specific energies which were found to be of the order of 300 mJ/l. In the same year, improved values (η = 4 %) and pulse energies of more than 10 Joule were demonstrated by Kompa, Pummer and coworkers at the Max Planck Institute at Garching [73Pum]. Rather uniform discharges in low-pressure SF6 –H2 mixtures were obtained in these experiments with a resistively decoupled multi-pin cathode array and a flat anode. Experimental studies were also performed at ISL during that time, by using UV-preionized transverse electrical discharges both for the generation of pulsed HF- and DF-laser radiation with energies up to several tens of J. High optical gain was achieved with the chosen discharge technique, both in the HF- and DF-mode of operation, so that the laser cavity had to be carefully designed to avoid a decrease in population inversion due to Amplified Spontaneous Emission (ASE). Experiments were performed with ethylene (C2 H4 ), ethane (C2 H6 ), propylene (C3 H6 ), propane (C3 H8 ), cyclopropane (C3 H6 ), isobutylene (C4 H8 ), butane (C4 H10 ), acetylene (C2 H2 ), etc. For the HF laser operation, best yields were found by replacing H2 by propane (C3 H8 ). Improved HF laser efficiency, due to the replacement of H2 by other hydrocarbons, was known and confirmed by other authors as well. Unfortunately, deuterized carbon species were not commercially available. DF laser energies, Landolt-B¨ ornstein New Series VIII/1B1
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Fig. 3.6.10. Laboratory view of the transversely excited UV-preionized pulsed HF/DF laser, developed at ISL. The lower photograph reveals performance tests of the preionization surface spark array, mounted behind the mesh grid cathode inside the laser head, after removal of the two side walls, supporting the (Ernst-profile) anodes.
as compared to HF laser energies under the same electrical discharge conditions, were therefore found to be approximately 40 % lower. A laboratory view of the HF/DF-multigas laser, developed at ISL, is shown in Fig. 3.6.10. This laser used UV-preionized uniform discharges, fed by a highvoltage Marx generator. An inside view of the opened laser head allows the surface spark array behind the two mesh grid cathodes and the Ernst-profile anodes to be seen in the lower part of Fig. 3.6.10. Pulse energies of more than 20 J in the HF-mode and up to 15 J in the DF-mode (by simply replacing propane by deuterium) allowed interesting laser–target effect studies to be performed with this pulsed chemical laser device in the two wavelength ranges, centered both around 2.7 μm and 3.7 μm. Further pulsed HF chemical laser technologies were published more recently which, for example, made use of X-ray preionization sources. Interesting contributions were also provided by a French group at Laserdot/Aerospatiale, for example by Prigent, Huguet, Lacour and Brunet [92Pri]. This laser was operated with SF6 –C2 H6 –Ne at 110 torr. X-ray pulses of about 4 J with pulse durations of 30 ns were generated by a corona plasma cathode. Laser pulse energies of 1 J were obtained with this facility. The rather poor performance was attributed to the long X-ray pulse duration which prevents higher electron densities from being achieved for a more efficient preionization and more uniform discharge. Some almost exotic approaches have even suggested to use water as hydrogen source. Laser discharges were ignited in (F2 –H2 O–He)-mixtures at low pressures of a few torr. Excited species were generated according to the following reaction F + H2 O ⇒ HF+ + OH (−18.26 kcal/mole) which, however, proved to be rather inefficient.
3.6.4.3.4.1.3 Repetitively pulsed HF, DF lasers As pointed out by Hao-Lin Chen, Daugherty and Fyfe [75Che], multipulse operation of (H2 /F2 )chain-reaction lasers was also shown to be feasible, in spite of the rather poor chemical stability of (F2 + H2 )-mixtures against preignition. In their experimental device, stable flame speeds were achieved by admixture of O2 and He, without ultrasonically propagating detonation waves. Lasing action and performance characteristics at 10 pps (pulses per second) and energy densities of 10 J/(l atm) were demonstrated. Design-limited repetition rates were expected up to more than 100 pps.
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Capacitor banc Anode Cathode Highvoltage power supply
Heat exchanger Chemical trap
[Ref. p. 333
Blower
Fig. 3.6.11. Repetitively pulsed HF/DF chemical laser. Schematic design of an experimental kW-class laser demonstrator device (Brunet, Mabru and Vannier, Laserdot, A´erospatiale, France [92Bru]).
Using supersonic flows, a special type of pulsed HF laser was also operated at higher repetition rates by Chuchem and Rosenwaks [84Chu]. Their discharges were run in (SF6 –H2 )- as well as in (NF3 –N2 )-flames. Pre-ignition and detonation were excluded if the gas flow velocity exceeded the fluorine/hydrogen flame propagation velocity. With premixed (oxygen inhibited) diluted gas mixtures the system could then be operated without suffering detonation problems. These conditions could be met in supersonic gas flows which were efficiently used, so that the device was even run at repetition rates up to several tens of kHz. Various other laser systems, pumped by transverse electrical discharges, both for the generation of single pulses and for higher-repetition-rate pulse bursts with high average powers, were set up. Based on thyratron-switched discharges in (SF6 –C3 H8 )-mixtures, repetition rates up to 1.1 kHz were achieved by Jacobson et al. [73Jac]. Further developments were carried out, for example in France, especially in the field of DF lasers. Remarkable energies per pulse of the order of 10 J and pulse repetition rates of 100 pps were demonstrated by Brunet and coworkers. These authors showed the feasibility of average power levels in the kW-range and scalability to even higher intensities [92Bru]. The basic experimental set-up and operation principle can be seen in Fig. 3.6.11. Electrical efficiencies were reported to be of the order of several percent. Lasers of this type were engineered as compact devices which were found to be scalable towards higher average powers. It should be pointed out that the values in the kW-range achieved so far, do not represent an upper physical limit at all.
3.6.4.3.4.2 Continuous-wave HF or DF lasers Hurle and Hertzberg were the first to suggest the use of nonequilibrium convective flows to produce continuous-wave laser action [65Hur]. The simplest case is realized by directly using suitably diluted, partially dissociated fluorine, expanded through nozzles and mixed with hydrogen or deuterium.
3.6.4.3.4.2.1 Diffusion type of chemical cw HF, DF lasers Devices based on this principle, such as developed by Spencer and coworkers [70Spe1] were termed diffusion chemical lasers. Their operation is based on the rapid diffusion of a fuel (H2 or D2 ) into a fast-flowing gas stream containing fluorine atoms as an oxidant. According to the so-called cold reactions (H2 + F) or (D2 + F) already mentioned above, vibrational transitions of these lasers are mainly restricted to lower vibrational values v, typically smaller than 2 to 3. An important technique for the generation of atomic fluorine is based on a high-frequency discharge in diluent-
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rich (He–F2 )-mixtures, capable of providing partial F2 -dissociation. The gas stream follows a rapid expansion through a water-cooled nozzle bank. Subsequent mixing with hydrogen or deuterium is achieved by injection of these gases in this fast, but subsonic flow, close to the nozzle exit plane. Glaze and Linford operated a system using various types of rf-sources, upstream of the nozzle array, at 21 MHz [71Gla2] and at 8 MHz, respectively [73Gla]. These authors aimed at determining performance characteristics e.g. the spectral power distribution and achievable small-signal gain coefficients. Laser-excited fluorescence measurements were used by Fried et al. [73Fri] to provide valuable information on vibrational relaxation rates of HF+ due to collisions with molecular species typically used in HF lasers, such as N2 , SF6 and F2 and to give a basic physical insight into the temperature dependencies of the rate constants in a large range from 295 K to 730 K. For fundamental research studies shock tube experiments were carried out, both to dissociate fluorine and to establish well-defined thermodynamic conditions, for example in a reflected shock. Subsequent expansion through a nozzle or nozzle array provides gas dynamically fast (even supersonic) flows which allow for a homogeneous mixing of all reactants including diluents. Airey and McKay [69Air] used their shock tube facility to successfully establish a steady-state inversion, high enough to sustain quasi-cw laser action. Atomic fluorine was generated in a reflected shock, according to the scheme described above, prior to a supersonic expansion through a twodimensional Mach-4 nozzle. Close to the nozzle or nozzle array exit, HCl was additionally injected (Mach 2) from a reservoir. The cooling by the supersonic expansion provides an increased gain and efficiency, as rotational and translational temperatures are almost in thermodynamic equilibrium (due to their short relaxation times), in contrast to the vibrational temperature. In the supersonic mixing zone, cw laser action was achieved, due to the following reaction: F + HCl ⇒ HF+ + Cl
(−32 kcal/mole) .
(3.6.38)
By such experiments, it was found that in laser systems of this type, partial inversion, rather than total inversion most likely, played the dominant role. Of course, the time duration of the laser action was limited by the flow time of the shock tunnel. In many other cw laser experimental investigations, F2 was also replaced by the less dangerous fluorine containing species such as SF6 or by other molecules which even allow an easier handling, as in the case of the pulsed lasers discussed in the previous section: – Hinchen and Banas, for example, studied dc-discharges in N2 –He–SF6 in order to provide the required F-atoms [70Hin]. As a fuel, they injected downstream H2 or D2 through small holes in a movable support tube in order to uniformly mix the atomic fluorine with the other species. The chemical processes of the (F + H2 )- or (F + D2 )-reactions occurred slightly upstream of the optical cavity. – Bertrand et al. used a surfatron microwave discharge, fed by a 915 MHz magnetron, to partially dissociate SF6 (mixed with rare gas), prior to the injection of H2 or D2 . These authors realized a compact small device which proved to be suitable for fundamental research applications [79Ber]. – To overcome difficulties due to turbulences in mixing processes resulting in non-stationary gain distributions, Buczek and coworkers [70Buc] used premixed flows of SF6 , He and H2 (or D2 respectively) which were first considered only in the case of pulsed laser systems. Continuouswave laser operation was achieved by magnetic crossfield stabilization of the dc-discharges perpendicular to the flow direction. These electrical discharges were located upstream of the subsonic gas flow, parallel to the optical cavity. Many other systems, of course, were studied as well. It should be mentioned, however, that only rather low output powers were usually achieved with such types of dc- or rf-driven discharge flow lasers. Anyway, such small-scale experiments proved to be important for obtaining fundamental knowledge of the underlying physical processes and scalability. Moreover, even these lower-power lasers allowed to be used as versatile coherent radiation sources for various diagnostic purposes, such as for example for infrared spectroscopic investigations.
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Anode
N2+F+S
N2+F+S
Free jet
Cathodes Optically active region
H2
H2+F +
N2+F+S
H2 Archeater
[Ref. p. 333
HF +H H2
Laser beam
Fig. 3.6.12. Schematic representation of an electrical arc-driven cw HF/DF laser, according to Spencer and coworkers [70Spe2, 71Mir, 72Spe, 73Cho].
However, the basic interest in most of the studies cited above was to make more efficient use of the large amount of chemically stored energy, in order to achieve real high-power laser radiation. Supersonic diffusion laser systems using HF were pioneered by Spencer, Mirels and coworkers [70Spe2, 71Mir, 72Spe, 73Cho]. These authors achieved important steps. Power levels were increased from several hundreds of W first to finally rapidly exceed the multi-kW cw-power range. In the first experiments, electrical arc burners were used to heat up atmospheric-pressure nitrogen. Temperatures, even after mixing with SF6 , were found to be still as high as thousands of K (e.g. 2500 K). As a result, SF6 was highly dissociated (which was confirmed by the formation of SF5 + F and of higher dissociation products). Again supersonic expansion was realized by means of a nozzle (or a nozzle array). In the same way as in the shock tube experiments, translational and rotational temperatures were cooled down in the supersonic free jets, almost to room temperature. H2 or D2 was finally mixed into this rapidly expanding flow by diffusion, after injection through orifices of perforated tubes or through separate rows of injector nozzles. The operation principle, according to the experiments carried out by Spencer and coworkers, is schematically shown in Fig. 3.6.12. The experimentally determined ratio of extracted laser powers in the HF- or DF-mode of operation, respectively, was 1 : 0.7. This corresponds to conversion efficiencies of 12 % or 8 %, respectively. For many years, great effort was put into the investigation of various excitation schemes, even by using volatile inorganic fluorides or bromides to improve photochemical yields. An interesting comparison between H2 and HBr used as fuels in cw HF lasers was made by Cummings, Dube and Witte [74Cum]. Their fluorine atoms were also generated by an electrical arc in SF6 . As compared to the exothermicity of the (F + H2 )-reaction ΔE = −32 kcal/mole, the higher value ΔE = −47 kcal/mole of the (F + HBr)-process seemed promising at first sight: F + HBr ⇒ HF+ + Br
(−47 kcal/mole) .
(3.6.39)
The hot mixture with He as a diluent was subsequently expanded through a nozzle array (36 twodimensional supersonic nozzles of area ratio 15.5) to rapidly cool down the translational temperature of the flow. The individual nozzles were separated by slits, through which H2 (or HBr for comparison) could be sonically injected. In fact, higher-order vibrational transitions were observed; however, optical power extraction was found to be lower than in the case of the (F + H2 )-reaction which the authors attributed to stronger vibrational deactivation processes. Various other techniques were tested in order to improve the mixing, for example by Manfriani et al. who used the trip-jet arrangements in which small amounts of inert gases were injected normal to the flow upstream of the cavity [84Man]. As an example, an arc-driven supersonic cw HF laser based on this principle was also investigated and developed by A. Sontag and R. Joeckl´e at ISL, Saint-Louis. Figure 3.6.13 shows a laboratory view of this device which was conceived for laser power levels in the kW-range [92Son]. The main emphasis in these studies was not to develop conceptionally a completely new device, Landolt-B¨ ornstein New Series VIII/1B1
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Fig. 3.6.13. Arc-driven supersonic cw chemical laser, as realized by A. Sontag and R. Joeckl´e (ISL) [92Son].
but to develop non-commercialized tools which were favorably used in those days for fundamental parametric investigations of laser-target-effect studies. For cw diffusion-type chemical HF- or DF-lasers detailed numerical models were developed, for example by Hofland, King and Mirels. These authors developed numerical codes providing solutions for laminar diffusion-controlled combustion of initially separated fuels and oxidizers. In a flame sheet model including collisional phenomena, they took into account that both emission and absorption compete with depopulational effects. Closed-form solutions were obtained, showing the dependencies of saturated laser performance on experimental parameters, such as on gas transport properties, on relative pumping rates and on cross-sections for vibrational deactivation. For details again, reference is made to the literature [72Kin, 72Hof1, 72Hof2]. Another numerical two-dimensional model of supersonic mixing HF laser was suggested by Kewley. This model took into account realistic chemistry, as well as time-averaged chemical production rates of each species, both in laminar and in turbulent flows [76Kew]. In stationary HF or DF lasers, rotational equilibrium was found not to be fully accomplished. This can explain some discrepancies between experimentally measured and calculated spectra. Detailed numerical solutions of complete and reduced Navier–Stokes equations for supersonic chemical flow modeling with respect to cw HF lasers were given by Baev and Golovichev [84Bae]. These authors were using the “RICE”-method, as developed by Rivard et al. [75Riv]. A computer program “SPEED” was set up at Los Alamos National Laboratory which was aimed to determine the behavior of multicomponent chemical flows at arbitrary speeds. An interesting, less time-consuming approach was chosen and published by R. Schmitt [84Sch2]. The code he developed allowed the calculation of laminar and turbulent mixing of two supersonic flows (fuel and oxidizer) taking into account lateral pressure gradients, chemical reactions and vibrational relaxation. The model was validated by comparison with more detailed finite-difference Navier–Stokes calculations of Kothari et al. [77Kot].
3.6.4.3.4.2.2 Chain-reaction lasers So far, mainly HF/DF lasers based on the so-called “cold” (F + H2 )- or (F + D2 )-reactions have been discussed, which were considered for some time to be the leaders among continuous-wave chemical lasers. In the chain-reaction case, however, the more energetic, so-called “hot” (H + F2 )or (D + F2 )-processes were included as well. Chain-reaction excitation was observed for example by Rosen [73Ros], Cummings et al. [75Cum], Meinzer and coworkers [79Mei] and others, either under subsonic or supersonic flow conditions. Initiation was achieved by various types of discharges, such
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as by microwave discharges or by arc discharges as well. Laser effects of (H2 –F2 )-chain reactions were extensively studied, for example, by Gastaud, Brunet and coworkers [80Gas2]. These authors used nickel mass heaters to partially dissociate F2 . Fuel–oxidizer mixing was accomplished by the use of an array of supersonic nozzles. Laser action from higher vibrational bands 5 → 4 and 4 → 3 was demonstrated. The highest specific laser output power achieved at that time was reported to be 280 kJ per kg of F2 . Chain-reaction lasers were also realized purely chemically without any external electrical sources. Lvov, Stepanov and Shcheglov [84Lvo], for example, considered theoretically two schemes for autonomous chain-reaction chemical cw HF lasers, a combustion model and an initiation model by means of a standing detonation wave. This second approach was already suggested by Basov and Oraevskii. In this case, auxiliary reactions such as NO + F2 ⇒ NOF + F
(3.6.40)
have to be additionally taken into account. According to Lvov, this requires a uniform mixing of (F2 –H2 –NO–He) as reacting gases in a cold supersonic flow in which pre-reactions are negligible. The sudden combustion is then initiated, after passing through a nearly normal stationary shock wave, built up close to the exit of a second supersonic expansion nozzle bank.
3.6.4.3.4.2.3 Combustion-driven chemical lasers Combustor concepts proved to be of utmost importance for the generation of fluorine atoms. The advantage of this type of lasers is that optical power, generated by combustion is independent of an electrical power supply. The expanded gases, however, have to be removed quickly from the system. As diffusors cannot fully recover the low pressure in the lasing zone, of the order of several tens of torr up to the atmospheric pressure of the outside world, some electrical power is needed anyway to operate the pumps. A certain disadvantage of combustion-driven devices consists in the fact that continuous, recirculated flows are impossible and that a practicable tankage, according to the run time has therefore to be provided. Systems were developed and strongly investigated by many research groups. L.E. Wilson [80Wil] at Kirtland Airforce Base, for example, studied combustion-driven chemical DF lasers. His interest particularly concerned the study of processes based on the reaction of F2 or NF3 with C2 H4 or with other hydrocarbon fuels. In his experiments D2 was injected into the supersonically expanding, Fatoms containing flow, immediately after the combustor chamber exit nozzle bank. In this zone, fuel and oxidizers are mixed for an efficient production of the DF as lasing molecules. Diluents, such as He, N2 , etc., but also other reaction products were found to have a large influence on the laser power to be extracted from such a device. Typical specific powers in smaller-scale experiments (nevertheless in the range of several kW) were of the order of 45 to 90 kJ/kg. The laser performance of combustion-driven chemical lasers was also extensively studied in Europe, such as for example: – by a German group of the DLR at Stuttgart-Lampoldshausen. Studies by Willi Bohn and coworkers were mainly related to experiments by the realization of devices for specific applications with respect to scalability. Basic studies referred both to technological optimization of systems and to improvements of spectral emission characteristics [84Mas], beam qualities or specific power densities; – successful fundamental research programs were also set up by French groups (ONERA and especially also at the Marcoussis CGE-Laboratories providing significant contributions and progress in technology, as achieved by Brunet, Voignier, Gastaud, and Regnier and of course other coworkers as well [80Voi, 80Gas1], see for example Fig. 3.6.14. Important research goals of these authors were to optimize the fluorine atom production and to minimize HF and or other deactivator molecule concentrations. These species are unavoidably Landolt-B¨ ornstein New Series VIII/1B1
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H2O
D2 D2 F2 +He
D2 D2
F2 +He
D2
D2 D 2
Fig. 3.6.14. Typical chemical DF-laser nozzle configurations, according to Gastaud et al. [80Gas1].
produced in any type of combustor device. Parametric investigations were also carried out, to compare reactions of F2 or NF3 with different fuels (H2 , C2 H4 and H2 S) combined either with He or N2 as diluents. Continued efforts in cw HF laser research and development, however, were primarily made in US, as well as in Russia. Many of the US program activities were sponsored by the Defense Advanced Research Project Agency (DARPA) and by the Ballistic Missile Defense Organization (BMDO). Their primary objective was to demonstrate the multi-megawatt-class power capability in combination with excellent beam quality. Additionally, new technologies were intended to be validated for space-based applications. In the early seventies already, sophisticated technologies were therefore developed (many of them were subject to classification). Some of the activities, however, such as part of those, for example, related to the “ALPHA” high-power chemical laser program, have been made available in the open literature. In the case of the ALPHA program, a quasi-cw megawatt-class hydrogen-fluoride laser was developed, which first lased in 1989 and which was noticeably improved in 1990 in subsequent tests [95Ack]. This demonstrator used a large, highly mass efficient nozzle array in cylindrical geometry through which the reacting mixture flowed radially outwards, accelerated to supersonic velocities. Atomic fluorine F (and molecular nitrogen N2 ) was provided by a combustor in the central part of the device, due to the reaction of NF3 with D2 , with He as a diluent. This supersonically expanding flow passes through a secondary wedge, across the primary nozzles which inject the hydrogen fuel H2 . The annularly shaped active gain medium is then formed by the mutual reactions between the H2 - and F-streams which provided the excited HF-molecules. Multi-megawatt power extraction in this device was achieved by using a specially developed high extraction decentered annular ring resonator. The system was integrated at the TRW Capistrano Test Site and was operated successfully as one of the most sophisticated and highest-power laser systems of the US in those years.
3.6.4.3.5 Transfer chemical lasers Vibrationally excited molecules, especially hydrogen halides, experience collisional deactivation losses which usually compete with stimulated emission. Reactions of this type were therefore strongly investigated in the past. The Transfer Chemical Lasers (TCLs) make use of this particular property. The v-v-coupling of specific molecules such as DF+ with the CO2 allows the upper (000 1) laser level to be populated. By suitably introducing CO2 -admixtures, a large amount of the chemically generated DF vibrational energy was in fact shown to be vibrationally transferred to the admixed molecules which allows to improve the overall energy storage capability of such laser systems. In the case of DF+ , it was found that an efficient near-resonance transfer of vibrational energy can be easily used to create population inversion in CO2 . In a vibrational energy transfer laser of this type, the following reactions were therefore to be considered: DF(v) + CO2 (000 0) ⇒ DF(v − 1) + CO2 (000 1) .
(3.6.41)
The required vibrationally excited DF+ -molecules were generated arbitrarily, according to the various techniques, described and discussed in the preceding chapters, both in the pulsed and in the continuous-wave mode of operation. The basic principles, concepts and achievements during Landolt-B¨ ornstein New Series VIII/1B1
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the first several years after their first realization were summarized in an overview paper by Cool in 1973 [73Coo] which consequently covered the state of the art at that time. Cool included not only the above mentioned (DF+ –CO2 )-reactions but also (HF+ –CO2 )-processes. However, due to the different energetic levels of HF, as compared to DF, the vibrational excitation transfer to CO2 was less efficient from HF+ than from DF+ . Additionally, Cool and coworkers considered capabilities provided by the introduction of further hydrogen halides. These included vibrational energy transfer reactions in (HCl+ –CO2 )- and (HBr+ –CO2 )-mixtures. 3.6.4.3.5.1 Pulsed transfer chemical (TCL) CO2 lasers Efficient energy transfer processes, in particular to CO2 were investigated and demonstrated by several research groups. As mentioned above, different techniques were used in pulsed chemical transfer lasers to first vibrationally excite specific molecules (mainly DF) by means of chemical reactions. These include the initiation of the reactions by – flash photolysis and/or by – suitably preionized (UV, electron beam, X-ray) electrical discharges. Purely chemical reactions without electrical energy for ignition were also suggested and studied, of course, and will be included in the following discussion.
3.6.4.3.5.1.1 Energy transfer from vibrationally excited nitrogen In 1969, Basov et al. [69Bas2] studied explosions of (HN3 + CO2 )-mixtures. The decomposition of HN3 was triggered photolytically by xenon flashlamps. The rapidly developing reactions were branched, according to the steps indicated in Table 3.6.15. Table 3.6.15. Branched reactions in flashlamp-pumped pulsed chemical transfer lasers using HN3 . HN3 + hν HN + HN3 0 N+ 2 (v = 1) + CO2 (00 0) CO2 (000 1) + n · hν0
⇒ ⇒ ⇒ ⇒
HN + N2 2 H + 2 N+ 2 N2 (v = 0) + CO2 (000 1) CO2 (100 0/020 0) + (n + 1) · hν0
It was found in fact that most of the vibrational energy of nitrogen is efficiently transferred to the CO2 -molecules, similarly as in the well-known case of electrically excited CO2 lasers. It should be mentioned that the HN3 -molecules were directly produced in the experimental set-up by the reaction between sodium acid and sulfuric acid.
3.6.4.3.5.1.2 Energy transfer from vibrationally excited hydrogen halides Gross and coworkers [69Gro] already reported in 1969 on a successful demonstration of chemically pumped, pulsed CO2 lasers, using vibrationally excited DF+ . DF+ was generated by flashphotolyzed (F2 O + D2 )-mixtures, according to the following reactions: F2 O + D + hν ⇒ DF+ + OF ;
F2 O + H + hν ⇒ HF+ + OF ,
(3.6.42)
which, similarly, were already discussed and summarized in Table 3.6.11. Typical laser pulse durations were 20 μs. DF laser emission was found to be immediately quenched by the addition of CO2 . Landolt-B¨ ornstein New Series VIII/1B1
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In fact, the energy was efficiently transferred to the CO2 -molecules. Maximum energies per pulse were obtained at pressures of 25 to 45 torr for gas mixture ratios of pH2 : pF2 O : pCO2 = 1 : 1 : 1 . Detailed investigations on the HF and DF laser emission spectra in the case of (H2 + F2 )-, or (D2 + F2 )-reactions were also carried out by Basov et al. [71Bas1]. The experiments (allowing the various bands and transitions to be determined, both in the cases of the HF and DF lasers), were carried out by using electrical pulse discharge initiation. Due to the high vibrational band transitions, it was concluded that both the so-called “cold” and “hot” processes contributed to the overall energy extraction. Concerning the energy-transfer processes between DF- and CO2 molecules, the reactions were ignited by flash photolysis. Pulse energies were found to depend strongly on the initial concentrations of the D2 -, F2 - and CO2 -molecules. The rate constants were determined by an analysis of the oscillation delay times with respect to the initiating flashlamp pulses. They were found to be (1.5 ± 0.5) · 10−12 cm3 s−1 . This value is comparable to that of the HCl- and CO2 -energy-transfer processes. Most interesting measurements were also reported by Poehler et al. [72Poe]. These authors worked with stable D2 –F2 –CO2 -mixtures, diluted in He, cooled down to −60 K. Their reactions were also initiated with flashlamps. In these experiments, TCL laser energies of 5 J were extracted with peak powers of 200 kW. Similarly, direct chain reactions of D2 and F2 were studied by Wilson and Stephenson [72Wil]. With suitably chosen diluents (nitrogen), these authors succeeded in stabilizing gas mixtures near or slightly above atmospheric pressure, being above the second explosion limit. In small-scale experiments they managed to safely fill a laser chamber and to precisely trigger the ignition of the reaction optically, by means of flashlamps. They found that both the cold (F + H2 )- and hot (H + F2 )-reactions contributed to the observed DF laser output energies. Moreover, after insertion of CO2 , stable CO2 –F2 –D2 -mixtures were also obtained. This stability allowed vibrational energy transfer from DF+ to CO2 which was found to already take place during the explosion. Similar DF chain-reaction experiments were also carried out by Suchard et al. [72Suc, 74Suc2]. With a 290 cm3 reaction chamber, they achieved energies of 2.8 J with a CO2 : F2 : D2 : He = 8 : 1 : 0.33 : 10 mole ratio. The corresponding chemical efficiencies were measured to be higher than 5 %. Both experimental studies and theoretical calculations were performed on similar devices by Poehler and coworkers [73Poe]. Their investigations referred to high-pressure pulsed transfer CO2 lasers, supported by chemical, flash-initiated chain reactions. Output energies of several J, a smallsignal gain coefficient of 3 m−1 and chemical efficiencies up to above 3 % were reported by these authors. Concerning kinetic modeling and computer simulation, the reader is referred to the literature, for example to the paper of Kerber, Cohen and Emanuel [73Ker]. These authors conscientiously reviewed published data, both concerning theoretically calculated and experimentally determined rate constants which they introduced into theoretical models. The rate constants govern the basic DF–CO2 -processes, as well as the CO2 (000 1)-collisional deactivation by molecular or atomic species, such as by DF, D and F. They showed that laser performance simulations are most sensitively dependent on the precision of these rate coefficients. Further studies of the vibrational relaxation of molecules, such as vibrationally excited HF, CO and NO in the v = 1 level group, were determined experimentally by Green and Hancock by using a line-tunable pulsed chemical HF laser [73Gre]. Their measuring device allowed them to determine with high accuracy the rates at which O2 , CO or NO quench, for example HF (v = 1). 3.6.4.3.5.2 Continuous-wave DF–CO2 transfer chemical lasers After the first experiments with pulsed transfer chemical DF–CO2 lasers, carried out, as cited above by Gross, emphasis of research since about 1970 was focused on cw DF–CO2 laser devices. The experimentally observed, remarkably strong coupling between DF and CO2 was an unexpected result which at first was not explicable in terms of the first-order perturbation theory commonly used at Landolt-B¨ ornstein New Series VIII/1B1
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3.6.4 Chemical lasers
[Ref. p. 333
that time. Most developments were therefore motivated by the concept of direct cw conversion of chemical energy into electromagnetic infrared radiation energy.
3.6.4.3.5.2.1 Subsonic continuous-wave DF–CO2 transfer chemical laser Two classes of lasers may be considered separately: first, lasers that need electrical energy for the initiation of the chemical reactions and second lasers which are not dependent on any kind of electrical power input.
Primary dissociation by means of electrical energy sources The first (DF–CO2 ) and (HF–CO2 ) continuous-wave transfer chemical lasers were described by Cool, Falk and Stephens in 1969 [69Coo1]. They suggested a two-stage energy transfer mechanism in order to explain the pumping of CO2 which similarly had also been observed in experiments carried out with HCl–CO2 and DF–CO2 . In these studies, they used various combinations of chemical reactions to create HCl+ , HF+ or DF+ , such as shown in Table 3.6.16. Table 3.6.16. CO2 -pumping by a two-stage energy transfer mechanism. HCl+
HF+
DF+
Cl + HI ⇒ HCl+ + I Cl2 + H ⇒ HCl+ + Cl
F + H2 ⇒ HF+ + H F2 + H ⇒ HF+ + F F + HI ⇒ HF+ + I
F + D2 ⇒ DF+ + D F2 + D ⇒ DF+ + F F + DI ⇒ DF+ + I
A primary flow of He with either partially dissociated chlorine, fluorine, hydrogen or deuterium was injected into the main flow tube. Partial dissociation was accomplished by means of an rfdischarge in a side arm. Further downstream, a secondary flow of CO2 , either with Cl, HI, DI, F2 , H2 or D2 , was introduced and mixed to create the excited species (HF+ , DF+ or HCl+ ) for an efficient transfer of the chemically produced vibrational energy to achieve inversion of the CO2 molecules. It should be mentioned that Cool and Stephens [70Coo2] even extended this technique to studies of HBr–CO2 lasers. Other reactions were considered in detail by Bin-Nun and Rokni [74Bin]. These authors obtained cw-CO2 laser operation by using nitric oxide (NO) together with nitrogen atoms: NO + N ⇒ N+ 2 +O
(−75 kcal/mole) ,
(3.6.43)
which allowed to create excited nitrogen molecules. The subsequent vibrational energy transfer which populates the upper laser level occurs similarly, as described above. Experimentally (in contrast to Brunet’s NO–F2 -reaction), the production of excited atomic nitrogen in the (N2 –He)flow required an external energy source. Partial dissociation of N2 and excitation of the N-atoms were achieved by Bin-Nun et al. by using a 2.45 GHz microwave discharge. CO2 was finally added downstream of the discharge region, as well as the required NO.
Primary dissociation processes by chemical reactions A most important progress towards cw DF–CO2 or HF–CO2 Transfer Chemical Lasers (TCLs) was attained by Cool and coworkers [69Coo2, 70Coo3]. They investigated new schemes, using purely chemical means in which no external electrical energy sources were required (except pumping Landolt-B¨ ornstein New Series VIII/1B1
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facilities). Significant power levels were achieved in such systems, simply by mixing commercially available bottled gases in subsonic flows. The production of vibrationally excited DF+ for example was achieved by using the exothermic (NO + F2 )-reactions listed in Table 3.6.17 to provide atomic fluorine which is required to initiate the so-called “cold” reactions. Table 3.6.17. (NO + F2 )-reactions for atomic fluorine generation. F2 + NO F + D2 D + F2 DF(v = n) + CO2 (000 0)
⇒ ⇒ ⇒ ⇒
NOF + F DF+ + D DF+ + F DF(v = n − 1) + CO2 (000 1)
−18 kcal/mole (primary active centers) −31.7 kcal/mole −98 kcal/mole
CO2 in these experiments was injected into subsonic flows through rows of tubes with small orifices. As compared to the originally assumed 2-stage processes allowing to populate the (000 1)levels of CO2 , it seemed in the case of DF–CO2 that direct transfer is presumably responsible for the most efficient laser pumping. The same processes were also studied by Basov et al. [71Bas2] who used a similar longitudinal flow mixing configuration and priming active centers, provided by the auxiliary chemical (F2 + NO)-reaction to initiate the chain reactions. Furthermore, extensive studies were successfully carried out by Brunet and Mabru [71Bru]. The reacting components in their experiments were injected from a central (F2 + He)-stream and mixed with laterally injected NO, D2 , and CO2 . The optical cavity, in contrast to the longitudinal configurations cited above, was transverse to the flow direction. In both cases, the achieved power levels were of the order of a few watts (2.1 W in the case of Basov and 19 W in the paper of Brunet and coworkers). Based on their experience and previous experimental results, Cool, Shirley and Stephens set up a fast (but still subsonic) flow system, transverse to the optical axis which allowed significant improvements and power levels up to 160 W [70Coo4]. They reported detailed measurements on unsaturated gain coefficients, saturation parameters and rotation–vibration state populations for relevant CO2 laser P- and Q-branch transitions. A most extensive study was also performed and published by Falk [71Fal]. With his device he achieved in 1971 powers of 560 W which were the highest values reported at that time. Figure 3.6.15 shows a schematic sketch of the fundamental operation principle as used by Cool, Shirley and Stephens. A premixed flow of He-diluted fluorine was injected at the upstream end by a first array of injectors. In a second row, premixed NO and CO2 were additionally introduced to allow the auxiliary atomic fluorine generation reaction to take place immediately. Due to the subsequent D2 -injection, chain reactions generate the required vibrationally excited DF+ -molecules which transfer most of their vibrational energy to the upper CO2 laser levels. The conclusion of Cool and coworkers based on these preliminary results was that considerable higher power levels are to be expected by further improvements of system design parameters and especially also by using chemical reactions in supersonic flows. For a cavity static pressure (identical to the exhaust pressure) of 16 torr, chemical efficiencies of 4.6 % were achieved, as well as saturation intensities of 143 W/cm2 , an unsaturated gain of 3.3 m−1 and specific energies of 25 kJ/lb.
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3.6.4 Chemical lasers (F2+ He)injector
D2 injector
[Ref. p. 333
Multipass optical cavity
Exhaust to cold trap and vacuum pump
Fig. 3.6.15. Purely chemically excited continuous-wave (DF–CO2 ) transfer chemical laser (according to Cool, Shirley and Stephens) [70Coo4].
N2 purged mirror box Laser beam
(CO2+ NO)-injector
3.6.4.3.5.2.2 Supersonic cw DF–CO2 transfer chemical laser As compared to gasdynamic lasers, in which inversion is also created purely by chemical means (such as those available in high-pressure bottled gases) and by supersonic gasdynamic expansion, TCL devices generated population inversion by nonequilibrium energy release due to selective chemical processes. The basic principle of a supersonic transfer chemical DF–CO2 laser, as suggested by Cool, is shown in Fig. 3.6.16. D2-injector (CO2+ He)injector
(F2+ He)injector
CO combustor O2+ He
Optical cavity
Diffusor exhaust to ambient pressure
Expansion nozzle array
Laser beam
Fig. 3.6.16. Purely chemically excited continuous-wave supersonic DF–CO2 transfer chemical laser (according to Cool et al. [73Coo]).
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Cools basic idea was to create operating-pressure conditions in the optical cavity section, so that a direct exhaust to atmospheric pressure should be possible without any electrical pumping requirements. As a consequence, flow parameters were chosen to be quite similar to those of already existing GDLs. Part of the required CO2 (of the order of 50 %) was obtained by combustion of CO with O2 (with He as diluent). Premixed F2 , He and CO2 was separately injected downstream of the CO-combustor zone. Stagnation conditions of the combined fast flow were about 1400 K and 15 bar which caused partial dissociation of the injected F2 . Further downstream, this flow was accelerated through an array of supersonic nozzles. Immediately upstream of the nozzle, D2 was injected by a multiple array of small sonic orifices. Basic uniform mixing was achieved after expansion to closely Mach number four at the nozzle exits, near the cavity. Rotational temperatures in the reaction zone of the optical cavity decreased to 400 K with static pressures of the order of about 0.1 atm. According to numerical calculations, specific energies were expected to be 20 kJ/lb, which was slightly lower than in the subsonic case in spite of a fourfold higher cavity pressure. However, as an interesting feature it should be pointed out that the saturation intensity was increased by almost an order of magnitude from 143 W/cm2 to 1300 W/cm2 , which showed that supersonic DF–CO2 chemical transfer laser concepts offer potential advantages for large-scale high-power generation. Further experiments both in the subsonic and supersonic regimes were carried out by Tregay and coworkers at the Bell Aerospace Company. Concerning a detailed description of the IRIS-1 and IRIS-2 facilities reference is made to the literature [75Tre]. Both the oxidizer F2 diluted with He and the fuel NO with CO2 were premixed prior to being injected in the precombustor which was designed to achieve a near steady-state reaction of the F2 and NO molecules. Atomic fluorine was generated by means of the reaction F2 + NO ⇒ FNO + F, according to (3.6.40). The deuterium injection was finally accomplished downstream by a range of nozzle arrays either with sonic or supersonic orifices, respectively, to generate the vibrationally excited DF+ . Due to the presence of CO2 , the vibrational energy of DF+ was almost resonantly transferred to excite ground-state CO2 -molecules in order to achieve population inversion and high-power CO2 laser emission. Optical power was extracted from a cavity with an optical gain path of 76 cm in length. With IRIS-1 in the subsonic regime powers of 15 kW were attained. The published power values of the modified supersonic IRIS-2 version were found to be slightly lower. This was explained by the fact that the supersonic nozzle height in these experiments was smaller than the optical cavity height so that only a restricted part of the optically available volume contributed to the laser emission. From chemoluminescence measurements (3 ≤ v ≤ 11), it was concluded that DF+ -production must have been largely provided by chain reactions.
3.6.4.3.6 Miscellaneous 3.6.4.3.6.1 Pulsed NO laser NO laser emission was observed on over sixty lines in the range between 5.85 μm and 6.3 μm. Experiments were reported by Giuliano and Hess [67Giu] who achieved efficiently vibrational– rotational excitation of NO-molecules by using flash-photolyzed nitrosyl chloride (NOCl). Mixtures of NOCl and He were used, typically at pressures between 50 and 125 mbar. It was found that the addition of Cl2 had no quenching effect (in contrast to the addition of NO). It even proved to be advantageous, as it allowed to achieve a reduction of the He-content and consequently an enhancement of the chemical reversibility for repeated operation. A major motivation for these investigations was that such systems might be interesting for solar pumping schemes which were shown to be feasible, due to the broad absorption spectrum of nitrosyl chloride from the far UV up to 650 nm [66Pol3]. In Table 3.6.18 NO + Cl2 -reactions for NO laser concepts are listed.
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Table 3.6.18. NO + Cl2 -reactions for NO laser concepts. 2 NO + Cl2 ⇒ 2 NOCl NOCl + hν ⇒ NO+ + Cl NOCl + Cl ⇒ NO + Cl2
3.6.5 Concluding remarks For many years gasdynamic and chemical laser concepts were capable of providing the only feasible technologies for achieving both high-energy and high-power coherent radiation sources with nearly diffraction-limited optical beam quality. This is still true today, at least for all types of applications that need laser intensities close to, or even above hundreds of kW. In competition, performance characteristics of high-power solid-state lasers and diode lasers will certainly continue to evolve, if extrapolated from the values achieved in the meantime. However, further progress of solid-state laser technology concerning power extraction is expected to be restricted, both for technical and economical reasons, to the range of medium energy levels or power levels, respectively. In contrast, the development of the various classes of gasdynamic and chemical lasers, summarized in the present chapter was strongly motivated by the need to explore reliable, inexpensive, light-weight, modular pumping energy sources to be most efficiently used for the generation of coherent radiation in various spectral ranges up to the highest energy and power levels. Activities were strongly supported by numerous applications in fundamental research and in industrial processing techniques, as well as by defense-related and space applications. New concepts were therefore investigated both experimentally and theoretically. Smaller-sized systems were first set up in many laboratories to demonstrate feasibility and to evaluate scalability towards larger power scale devices. Based on these results, real high-power demonstrators have been conceived which open new perspectives to satisfy industrial and economic requirements. Lasers have been conceived both to run continuously and temporally modulated (for example in the repetitively pulsed mode) in order to provide tools with power levels largely exceeding tens to hundreds of kW, either cw or averaged. Such tools are of great interest, as they open new fields in mechanical engineering, in material processing and in particular also in many environmental tasks that need safe handling of high energy densities which are interacting with any kind of material. Such applications may include the removal of debris, reliable and remote handling of contaminated components, even of parts of buildings, for example of nuclear power plants, etc. According to recent estimates, the already existing need for affordable high-power laser devices will increase in the future for which GCL, EDL or CL high-power devices will provide appropriate candidates for economical solutions.
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Anderson jr., J.D.: AIAA J. 12 (1974) 1699. Bin-Nun, E., Rokni, M.: IEEE J. Quantum Electron. 10 (1974) 89. Cummings, J.C., Dube, M.C., Witte, A.B.: Appl. Phys. Lett. 25 (1974) 89. Deutsch, T.F.: IEEE J. Quantum Electron. 10 (1974) 84. Siegman, A.E.: Appl. Opt. 13 (1974) 353. Suchard, S.N., Sutton, D.G.: IEEE J. Quantum Electron. 10 (1974) 490. Suchard, S.N.: IEEE J. Quantum Electron. 10 (1974) 87. Whittier, J.S., Kerber, R.L.: IEEE J. Quantum Electron. 10 (1974) 844.
75Bru 75Che 75Chr 75Cro 75Cum 75Ric 75Riv 75Tre
Brunet, W.L., Mabru, M.: J. Appl. Phys. 46 (1975) 7. Chen, H.L., Daugherty, J.D., Fyfe, W.: IEEE J. Quantum Electron. 11 (1975) 648. Christiansen, H., Russel, D.A., Hertzberg, A.: Annu. Rev. Fluid Mech. 7 (1975) 115. Croshko, V.N., Fomin, N.A., Soloukhin, N.A.: Acta Astron. 2 (1975) 929. Cummings, J.C., Dube, C.M.: IEEE J. Quantum Electron. 11 (1975) 712. Rich, J.W., Bergman, R.C., Lordi, J.A.: AIAA J. 13 (1975) 1. Rivard, C., Farmer, O.A., Butler, T.D.: LASL-Report LA-5812, 1975. Tregay, G.W., Drexhage, M.G., Wood, L.M., Andrysiak, S.J.: IEEE J. Quantum Electron. 11 (1975) 672.
76And1
Anderson jr., J.D.: Gasdynamic Lasers – An Introduction, New York: Academic Press (ISBN 0-12-056950-7), 1976. Anderson jr., J.D.: Proc. 1st Int. Symposium on Gasdynamic and Chemical Lasers 1976, Fiebig, M., H¨ ugel, H. (eds.), K¨ oln-Portz: DFVLR-Press, 1976, p. 1. Baev, V.K., Golovich, V.I.: Proc. 1st Int. Symposium on Gasdynamic and Chemical Lasers 1976, Fiebig, M., H¨ ugel, H. (eds.), K¨ oln-Portz: DFVLR-Press, 1976, p. 111.
73Che 73Cho 73Coo 73Fri 73Gla 73Gre 73Hir 73Hoh 73Jac 73Ker 73Kli 73Poe 73Pum
76And2 76Bae
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76Kew 76Mai 76McM 76Mit 76Mon 76Ogg
76Ros 76Sau 76Str1
76Str2
References for 3.6 Hoffmann, P., H¨ ugel, H., Schall, R.: Proc. 1st Int. Symposium on Gasdynamic and Chemical Lasers 1976, Fiebig, M., H¨ ugel, H. (eds.), K¨ oln-Portz: DFVLR-Press, 1976, p. 171. Kewley, D.J.: Proc. 1st Int. Symposium on Gasdynamic and Chemical Lasers 1976, Fiebig, M., H¨ ugel, H. (eds.), K¨ oln-Portz: DFVLR-Press, 1976, p. 212. Maisenh¨ alder, F.: Proc. 1st Int. Symposium on Gasdynamic and Chemical Lasers 1976, Fiebig, M., H¨ ugel, H. (eds.), K¨ oln-Portz: DFVLR-Press, 1976, p. 279. McManus, J.E.: M.S. Thesis, Dept. of Aerospace Engineering, University of Maryland, 1976. Mitra, N.K., Fiebig, M.: Proc. 1st Int. Symposium on Gasdynamic and Chemical Lasers 1976, Fiebig, M., H¨ ugel, H. (eds.), K¨ oln-Portz: DFVLR-Press, 1976, p. 298. Monson, D.J.: AIAA J. 14 (1976) 614. Oggiano, M.S., Onorato, M., Pandolfi, M.: Proc. 1st Int. Symposium on Gasdynamic and Chemical Lasers 1976, Fiebig, M., H¨ ugel, H. (eds.), K¨ oln-Portz: DFVLR-Press, 1976, p. 341. Rosenwaks, S.: Proc. 1st Int. Symposium on Gasdynamic and Chemical Lasers 1976, Fiebig, M., H¨ ugel, H. (eds.), K¨ oln-Portz: DFVLR-Press, 1976, p. 441. Saunders, C., Otten, L.J.: Proc. 1st Int. Symposium on Gasdynamic and Chemical Lasers 1976, Fiebig, M., H¨ ugel, H. (eds.), K¨ oln-Portz: DFVLR-Press, 1976, p. 448. Stregack, J.A., Wexler, B.L., Watt, W.S.: Proc. 1st Int. Symposium on Gasdynamic and Chemical Lasers 1976, Fiebig, M., H¨ ugel, H. (eds.), K¨ oln-Portz: DFVLR-Press, 1976, p. 520. Stricker, J., Waichman, K., Manheimer-Timnat, Y.: Proc. 1st Int. Symposium on Gasdynamic and Chemical Lasers 1976, Fiebig, M., H¨ ugel, H. (eds.), K¨ oln-Portz: DFVLRPress, 1976, p. 535.
77Kot
Kothari, A.P., Anderson, J.D., Jones, E.: AIAA J. 13 (1977) 92.
78McD
McDermott, W.E., Pchelkin, N.R., Benard, D.J., Bousek, R.R.: Appl. Phys. Lett. 32 (1978) 469.
79Ame
Ameur, Y., Delaporte, T., Menard J., Menard-Bourcin, F.: J. Appl. Phys. 50 (1979) 6648. Bertrand, L., Monchalin, J.P., Pitre, R., Meyer, M.L., Gagn´e, J.M., Moisan, M.: Rev. Sci. Instrum. 50 (1979) 708. Igoshin, V.I.: Sov. J. Quantum Electron. (English Transl.) 9 (1979) 315. Meinzer, R.A., Hall, R.J., Dobbs, G.M.: Proc. 2nd Int. Symposium on Gas-Flow and Chemical Lasers 1978, Wendt, J.F. (ed.), Hemisphere Publishing Corporation, 1979, p. 269.
79Ber 79Igo 79Mei
80Cas 80Chr 80Gas1
80Gas2 80Gue 80Mei
Cassady, P.E.: J. Energy 4 (1980) 145. Christiansen, W.R.: Proc. 3rd Int. Symposium on Gas-Flow and Chemical Lasers 1980, Journal de Physique, Suppl´ement Colloque (ISBN 2-902731-23-X), 1980, p. 371. Gastaud, M., Voignier, F., Bousselet, P., Regnier, P.: Proc. 3rd Int. Symposium on Gas-Flow and Chemical Lasers 1980, Journal de Physique, Suppl´ement Colloque (ISBN 2-902731-23-X), 1980, p. 263. Gastaud, M., Brunet, H., Voignier, F., Bousselet, P.: Experimental study of a continuous wave HF chain reaction laser, private communication, 1980. Guenoche, H., Sedes, C.: Marseille, private communication, 1980. Meinzer, R.A.: Proc. 3rd Int. Symposium on Gas-Flow and Chemical Lasers 1980, Journal de Physique, Suppl´ement Colloque (ISBN 2-902731-23-X), 1980, p. 155.
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References for 3.6 80Toy
80Voi 80Wat
80Wil
84Bae 84Chu 84Duc
84Lvo
84Man
84Mas 84McD 84Nov
84Rab 84Sch1
84Sch2 84Sch3
85Iyo 85Khi
85Rei
87Iyo
337
Toyoda, K., Osada, H., Namba, S.: Proc. 3rd Int. Symposium on Gas-Flow and Chemical Lasers 1980, Journal de Physique, Suppl´ement Colloque (ISBN 2-902731-23-X), 1980, p. 251 . Voignier, F., Regnier, P.: Proc. 3rd Int. Symposium on Gas-Flow and Chemical Lasers 1980, Journal de Physique, Suppl´ement Colloque (ISBN 2-902731-23-X), 1980, p. 45. Watanabe, K., Sato, Y., Lee, C.H., Obara, M., Fujioka, T.: Proc. 3rd Int. Symposium on Gas-Flow and Chemical Lasers 1980, Journal de Physique, Suppl´ement Colloque (ISBN 2-902731-23-X), 1980, p. 243. Wilson, L.E.: Proc. 3rd Int. Symposium on Gas-Flow and Chemical Lasers 1980, Journal de Physique, Suppl´ement Colloque (ISBN 2-902731-23-X), 1980, p. 1. Baev, V.K., Golovichev, V.I.: Proc. 4th Int. Symposium on Gas-Flow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 111. Chuchem, D., Rosenwaks, S.: Proc. 4th Int. Symposium on Gas-Flow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 121. Duchet, M., Crancon, J.P., Solmon, J.: Proc. 4th Int. Symposium on Gas-Flow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 227. Lvov, V.I., Stepanov, A.A., Shcheglov, V.A.: Proc. 4th Int. Symposium on Gas-Flow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 471. Manfriani, L., Sandfird, J., Carbonaro, M.: Proc. 4th Int. Symposium on Gas-Flow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 141. Massig, J.H.: Proc. 4th Int. Symposium on Gas-Flow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 149. McDermott, W.E.: Proc. 4th Int. Symposium on Gas-Flow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 69. Novikov, S.S., Doroshenko, V.M., Kudriavtsev, N.N.: Proc. 4th Int. Symposium on GasFlow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 577. Rabczuk, G.: Proc. 4th Int. Symposium on Gas-Flow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 595. Schall, W., Hoffmann, P., H¨ ugel, H., Schock, W.: Proc. 4th Int. Symposium on Gas-Flow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 301. Schmitt, R.: Proc. 4th Int. Symposium on Gas-Flow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 165. Schock, W., H¨ ugel, H.: Proc. 4th Int. Symposium on Gas-Flow and Chemical Lasers 1982, Onorato, M. (ed.), New York, London: Plenum Press, 1984, p. 435. Iyoda, M., Hori, M., Sato, S., Fujioka, T.: Proc. 5th Int. Symposium on Gas-Flow and Chemical Lasers 1984, Kaye, A.S., Walker, A.C. (eds.), Adam Hilger Ltd., 1985, p. 41. Khizhnyak, S.M., Soloukin, R.I., Zhdanok, S.A.: Proc. 5th Int. Symposium on Gas-Flow and Chemical Lasers 1984, Kaye, A.S., Walker, A.C. (eds.), Adam Hilger Ltd., 1985, p. 397. Reilly, J.: Proc. 5th Int. Symposium on Gas-Flow and Chemical Lasers 1984, Kaye, A.S., Walker, A.C. (eds.), Adam Hilger Ltd., 1985, p. 337. Iyoda, M., Terunuma, K., Sato, S., Fujioka, T.: Proc. 6th Int. Symposium on Gas-Flow and Chemical Lasers 1986, Rosenwaks, S. (ed.), Berlin, Heidelberg, New York: SpringerVerlag, 1987, p. 225.
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References for 3.6
87Wil
Wildermuth, E., Giesen, A., H¨ ugel, H.: Proc. 6th Int. Symposium on Gas-Flow and Chemical Lasers 1986, Rosenwaks, S. (ed.), Berlin, Heidelberg, New York: SpringerVerlag, 1987, p. 96.
88Bau
Baumhacker, H., Brederlow, G., Chen, Ch., Fill, E., Krause, H., Volk, R., Witte, K.J.: Jahrbuch Laser, Kohler, H. (ed.), Essen: Vulkan Verlag, 1988, p. 46.
92Boh
Bohn, W.: Proc. 9th Int. Symposium on Gas-Flow and Chemical Lasers 1992, Fotokapis, C., Kalpouzos, C., Papazoglou, T. (eds.); Proc. SPIE 1810 (1992) 468. Brunet, H., Mabru, M., Vannier, C.: Proc. 9th Int. Symposium on Gas-Flow and Chemical Lasers 1992, Fotokapis, C., Kalpouzos, C., Papazoglou, T. (eds.); Proc. SPIE 1810 (1992) 273. Prigent, P., Huguet, M., Lacour, B., Brunet, H.: Proc. 9th Int. Symposium on Gas-Flow and Chemical Lasers 1992, Fotokapis, C., Kalpouzos, C., Papazoglou, T. (eds.); Proc. SPIE 1810 (1992) 290. Sontag, A., Joeckl´e, R.: Proc. 9th Int. Symposium on Gas-Flow and Chemical Lasers 1992, Fotokapis, C., Kalpouzos, C., Papazoglou, T. (eds.); Proc. SPIE 1810 (1992) 286. Truesdell, K.A., Lamberson, S.E.: Proc. 9th Int. Symposium on Gas-Flow and Chemical Lasers 1992, Fotokapis, C., Kalpouzos, C., Papazoglou, T. (eds.); Proc. SPIE 1810 (1992) 476.
92Bru
92Pri
92Son 92Tru
95Ack
95Bre
95Jon 95Sch
97Bor
97Dym
97Ita
97McN
98Apo
Ackermann, R., Callaham, D., Cordi, A., Lurie, H., Thomson, M.: Proc. 10th Int. Symposium on Gas-Flow and Chemical Lasers 1994, Bohn, W., H¨ ugel, H. (eds.); Proc. SPIE 2502 (1995) 358. Brederlow, G., Baumhacker, H., Fill, E., Volk, R., Witkowski, S., Witte, K.J.: Proc. 10th Int. Symposium on Gas-Flow and Chemical Lasers 1994, Bohn, W., H¨ ugel, H. (eds.); Proc. SPIE 2502 (1995) 351. Jones, C.R.: Proc. 10th Int. Symposium on Gas-Flow and Chemical Lasers 1994, Bohn, W., H¨ ugel, H. (eds.); Proc. SPIE 2502 (1995) 344. Schellhorn, M., v. B¨ ulow, H.: Proc. 10th Int. Symposium on Gas-Flow and Chemical Lasers 1994, Bohn, W., H¨ ugel, H. (eds.); Proc. SPIE 2502 (1995) 63. Boreisho, A.S., Trofimovich, A.G.: Proc. 11th Int. Symposium on Gas-Flow and Chemical Lasers and High Power Laser Conference 1996, Baker, H.J. (ed.), ISBN 0-8194-25079; Proc. SPIE 3092 (1997) 456. Dymshits, B.M., Alexandrov, B.S.: Proc. of the 11th Int. Symposium on Gas-Flow and Chemical Lasers and High Power Laser Conference 1996, Hall, D.R., Baker, H. (eds.), ISBN 0-8194-2507-9; Proc. SPIE 3092 (1997) 448. Itaya, Y., Kawamura, Y., Kobayashi, N., Takami, Ch., Hasatani, M.: Proc. 11th Int. Symposium on Gas-Flow and Chemical Lasers and High Power Laser Conference 1996, Baker, H.J. (ed.), ISBN 0-8194-2507-9; Proc. SPIE 3092 (1997) 452. McNaught, W.G., Wlodarczyk G.: Proc. 11th Int. Symposium on Gas-Flow and Chemical Lasers and High Power Laser Conference 1996, Baker, H.J. (ed.), ISBN 0-8194-25079; Proc. SPIE 3092 (1997) 452. Apollonov, V.V., Drosdov, P.A., Favorsky, O.N., Foefilaktov, V.A., Ikonnikov, V.K., Kuznetzov, A.B., Maliavine, V.P., Prokhorov, A.M., Suzdaltsev, A.G., Vagin, Y.S.: Proc. Int. Symposium on High Power Laser Ablation 1998, Phipps, C.R. (ed.); Proc. SPIE 3343 (1998) 97.
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339
00Hag
Hager, G.D., Anderson, B.T., Kendrick, K.R., Tate, R.F., Helms, C.A., Adler, R.J., Fischer, C.H., Brown, A.J., Pummer, D.N.: Proc. Int. Symp. High Power Laser Ablation 2000, Phipps, C.R. (ed.); Proc. SPIE 4065 (2000) 646.
02Lam
Lamberson, S.E.: Proc.Int. Symposium on High Power Laser Ablation 2002, Phipps, C.R. (ed.); Proc. SPIE 4760 (2002) 25.
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341
3.7 Iodine lasers ´nek K. Rohlena, J. Bera
3.7.1 Principles of operation The principle of iodine lasers was discovered by a pure serendipity fairly early in the laser history [64Kas]. The laser transition proceeds between the two levels of the atomic iodine ground state fine structure doublet I(52 P1/2 ) → I(52 P3/2 ) + hν (1.315 μm) . The population inversion between these two levels can be achieved in two fundamental ways: 1. photolytically by the photodissociation [61Rau] of a suitable fluorinated iodide such as CF3 I, i–C3 F7 I, n–C3 F7 I, etc. by the UV light around 270 nm, 2. chemically by a resonant energy transfer between the excited molecular oxygen molecule O2 (1 Δg ) and the atomic iodine. The excited oxygen is currently mostly produced chemically by a decomposition of hydrogen peroxide H2 O2 in a chilled basic solution by the chlorine Cl2 . The photodissociation lasers are characterized by a high amplification and a low saturation energy. They rank among a class of high-power lasers such as Nd:glass, CO2 and excimer. They are mostly operated in a single-shot short-pulse regime and are usually used in a laser plasma or inertial fusion research. The largest of them is the 12 channel 30 kJ Iskra V in Russian Federal Nuclear Centre, VNIIEF Arzamas 16 – Sarov, Russia, generating a short 250 ps pulse [96Kir, 91Ann], which is a thermonuclear grade system; somewhat smaller was the 8 beam 1 kJ Iskra IV [80Kor]. A singlebeam Asterix IV at MPQ, Garching, Germany, achieved 0.8 kJ in 400 ps pulses and 2.1 kJ in a pulse several ns long [96Bau, 95Bau, 91Bau, 83Bre]. This laser, which is also distinguished by its excellent beam quality, was moved to Prague, Czech Republic, where it became operational in the year 2000 in a newly established research centre PALS (Prague Asterix Laser System) [01Jun]. Its predecessor in Prague a smaller Perun at the Institute of Physics, produced 40 J in 300 ps (focused 500 ps) [92Ber] and it is now being rebuilt to a hybrid system SOFIA with a tunable solid-state oscillator for pumping an OPCPA (Optical Parametric Chirped Pulse Amplification) chain to generate ultrashort pulses. A remarkable repetitive (0.5 Hz) free-running system at the USAF Research Laboratory, Kirtland Air Force Base, NM, USA (further Kirtland AFB), operated with pulses of 70 J 8–12 μs long [95Sch]. The chemical systems (COIL: Chemical Oxygen Iodine Laser) based on a flow of laser medium through a resonator are either continuous or repetitively pulsed. The first successful device was reported in [78McD]. Nowadays, they are mostly developed for special technological or military tasks. They operate either in a subsonic or a supersonic regime. The supersonic RADICL (Research And Development Iodine Chemical Laser) system at Kirtland AFB [96Hag] gave 34 kW of cw power. If magnetically switched the same system produced pulses 35.5 μs long (leading peak ∼ 1 μs), peak power 38 kW, average power 5.6 kW and the repetition rate 500 Hz [93Hag3], the magnetically assisted mode-synchronized laser generated pulses of 2.1 ns at the repetition rate 43.6 MHz and peak power 2.5 kW (at a lower Cl2 consumption) [96Phi]. The system has been closed and its successor the Airborn Laser System is being developed for the anti-missile defense Landolt-B¨ ornstein New Series VIII/1B1
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3.7.2 Laser transition cross-section
[Ref. p. 351
[01Lam]. At the Kawasaki HI Ltd. company, Japan, the cw power 5 kW of their COIL experimental device was increased to 8.8 kW [96Fuj], also in Japan Miki Pulley Co. Ltd., Kanagawa, operate a system at 5.5 kW [04Tei], Institute of Chemical Physics, Dalian, China, runs a system of 3.7 kW [96Sun, 00San], at the DLR Institute of Technical Physics in Stuttgart, Germany, the system of 2.5– 5 kW [96Han] has since been upgraded to 10 kW [05Han], a system at the Ben Gurion University at Beer Sheva, Israel, had 60 W [95Eli], now it performs at 0.7 kW [05Ros]. A subsonic system in the Institute of Physics, Prague, Czech Republic, attained 50–100 W in a continuous regime [91Sch] and was also operated in a repetitive (1.3–4 kHz, 250 W peak power) magnetically switched regime [94Sch], now a supersonic upgrade renders 0.5 kW cw power [04Spa]. An experimental system at the Lebedev Institute branch, Samara, Russia, had originally 170 W, now it reaches 770 W of cw power [96Nik, 05Nik], elsewhere in Russia, the Russian Federal Nuclear Centre, VNIIEF Arzamas 16 – Sarov, Russia, operate a chemical iodine laser system at 3.4 kW [05Vys] and a large cw system of 13.5 kW was recently reported by a joint team of Voenmekh Baltic State Technical University and Laser Systems Ltd. at St. Petersburg [05Bor]. At the Korea Atomic Energy Research Institute, Taejon, Korea, a system of 2.2 kW is in operation [00Kwo], another system in India, Delhi, gives 5 kW [03Tya]. An important progress has equally been achieved in a sophisticated 3D modelling of the mixing process of the injected iodine into the flow of excited oxygen with a buffer gas (N2 , He) in the supersonic case [97Mad, 97Mas, 99Mad, 00Der, 05Jir]. A good survey embracing also advanced technological aspects of COIL is to be found in [04Bar]. Interesting is also a hybrid system at the Lebedev Institute, Troitsk, [84Bas, 86Bas, 95Vag, 96Paz] combining the photodissociation and chemical pumping, which gives 15–40 μs pulses of 1.8 J at 60 Hz. Generally speaking, the photodissociation systems operate with a large gain close to saturation and a relatively broad luminescence line overlapping due to a strong collisional broadening several hyperfine transitions of the atomic iodine I(52 P1/2 ) → I(52 P3/2 ). The chemical systems have a much lower gain and the luminescence line is usually very narrow with a Doppler broadening of just a single hyperfine transition 3–4.
3.7.2 Laser transition cross-section The transition is of magnetic dipole type with a fairly long natural life time e.g. [83Bre] gives τI (2 P1/2 ) = 0.13 s, earlier estimates are somewhat longer [79Hoh], see also [81Fil] for a discussion. The nuclear spin of 127 I is 5/2, the upper J = 1/2 level is thus split in 2 (F = 2, 3) and the lower J = 3/2 in 4 sublevels (F = 1–4) of the hyperfine structure, between which altogether 6 transitions are allowed (selection rule |F − F | ≤ 1, F + F ≥ 1), listed in Table 3.7.1. Table 3.7.1. Characteristics of the hyperfine transitions I(2 P1/2 ; F ) → I(2 P3/2 ; F ). Trans. F → F
k [cm−1 ]
λ [μm]
AF F [s−1 ] [81Sch]
%
AF F [s−1 ] [71Der]
2–3 2–2 2–1 3–4 3–3 3–2
7602.6202 7602.6858 7602.7105 7603.1385 7603.2794 7603.3450
1.315336 1.315325 1.315320 1.315246 1.315222 1.315211
1.76 2.20 1.69 3.67 1.54 0.44
13 16.2 12.5 37.5 16.2 4.6
2.4 3.1 2.4 5.1 2.2 0.6
5.65
100
7.90
Summary
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Ref. p. 351]
3.7 Iodine lasers
343
The wavenumber k and wavelength λ are taken from [80Eng], the rest of the table was constructed by averaging the summary values of the laser transition Einstein coefficient A = 1 are degeneracy factors of the upper hyperfine levels, gF = 2F + 1, gF AF F (gF F,F gu g ) given by [72Zue] and [71Der] (A = 5.65 s−1 , i.e. τI(2 P1/2 ) = 0.18 s) using then gu = F F the relative values of [71Der] (shown in the 5th column %)1 . This is a procedure applied in [81Sch]. The absolute values of [71Der] are given in the last column for a comparison (A = 7.9 s−1 , τI(2 P1/2 ) = 0.13 s). The maximum stimulated emission cross-section can at a very low pressure for the strongest transition 3 → 4 be estimated as2 [84Zag, 86Zag, 95Car] √ Δ ν √ln 2 Δ ν 2 ln 2 7 λ2 A34 ln 2 c c σ3→4 (max) = Erfc exp 2 12 4 π3/2 Δ νD Δ νD Δ νD x 2 (Erfc(x) = 1 − √2π 0 d t e−t ). For somewhat higher pressures ≥ 30 mbar in the collisionalbroadening domain the maximum stimulated emission cross-section for the dominating 3 → 4 transition if given as [83Bre] σ3→4 (max) =
7 λ2 A34 , 12 4 π2 Δ νc
for intermediate pressures (lower levels F = 1–4 mixing) 7 λ2 F A3F σ3→(2,3,4) (max) = , 12 4 π2 Δ νc and for still higher pressures (both the upper F = 2, 3 and the lower F = 1–4 levels mixing) 5 7 λ2 ( 12 F A2F + 12 F A3F ) . σ(2,3)→(1,2,3,4) (max) = 2 4 π Δ νc The numerator bracket is now the summary Einstein coefficient A (last row of Table 3.7.1), Δ νD = √ 1.48 × 107 T [Hz] is the Doppler line FWHM (e.g. for T = 300 K: Δ νD = 250 MHz), Δ νc is the collisional width Δ νc = αi pi , i
pi [torr] is the partial pressure of the i-th component, the pressure-broadening coefficients αi [MHz/torr] are given by Table 3.7.2. A very detailed information on the line wavelengths and widths can be found in [81Sch] and the pressure-dependent line profiles are given in [76Fus]. The hyperfine level scheme of the atomic iodine is very sensitive to the superimposed external magnetic field due to Zeeman effect. This can be used, especially in the case of COIL, with advantage for frequency tuning [91Kel, 93Hag1, 93Hag2] and gain control, magnetic switching [93Hag3, 94Sch] and even a power stabilization [98Sug]. 1
The partial Einstein coefficients AF F are defined as AF F =
2
1 4ω 3 gF 3c3
MF ,MF
|JF MF |
−e ˆ + 2S)|J ˆ F MF |2 . (L 2mc
Their relative values (column %) correspond to the factors Q(IJF ; IJ F ) calculated from Table 75 in [63Sob]. The stimulated emission cross-section is defined in analogy with [81Hop] (Appendix B), but the averaging is done over the upper levels. The inversion population density is thus derived as (nu − ggul nl ) where nu,l are the total number densities of the upper and lower laser level as populated by the photodissociation and gu,l are the full statistical weights (summary degeneracy factors) of the upper and the lower level. For the iodine laser transition gu = 12 and gl = 24.
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3.7.3 Iodine photodissociation lasers
[Ref. p. 351
Table 3.7.2. Pressure-broadening coefficients of the I(2 P1/2 ) → I(2 P3/2 ) transition. Comp.
α [MHz/torr]
Ref.
i–C3 F7 I n–C3 F7 I O2 Ar CO2 N2
9.3 10.4 6–7 5.1 7.2 5.1
[78Bab, 83Bre] [78Bab, 83Bre] [84Zag, 81Sch] [84Zag, 75Pad] [84Zag, 75Pad] [84Zag, 75Pad]
3.7.3 Iodine photodissociation lasers The pumping light for the photodissociation lasers can be provided by a variety of sources. The highest efficiency in production of useful photons would have a black body at ∼ 14 kK [80Gib], but such a radiator would also produce an excess in harder photons, which would split other bonds in the alkyliodide molecules. This is particularly evident when using still a hotter source, such as an explosion shockwave (20–35 kK). A short list of pumping radiation sources follows: – special Xe flash tubes with a short (10 μs) [77Kam, 80Kor, 81Bak, 91Aba, 96Bau] or a long (∼ 300 μs) pumping pulse [80Zue, 61Rau, 83Her, 84Ska, 87Sti, 92Ber], – open discharge in the laser mixture itself initiated either by a wire explosion [79Bas] or a gliding discharge [77Bev, 80Kor], – shock wave released by an explosive [92Arz], – sun light [83Zal, 86DeY, 86Hwa], – others: excimer emission including lasers [82Fil] and spontaneous radiation [76Swi], arcs [70Gen] etc. Alkyliodides are chosen as parent molecules for the iodine production, since the yield f of the iodine atoms in the upper laser level 52 P1/2 is usually very high. So for i–C3 F7 I: f 90 %, for n–C3 F7 I: f (97 ± 2) %. The pumping radiation in the useful band 250–290 nm is for the current lamps emitted with the 5–8 % efficiency, dependent on the temperature of the Xe plasma in the lamps, which in combination with the quantum yield ∼ 20 % and the loss of the pumping radiation ∼ 50 % is limiting the efficiency of the photodissociation lasers to well below 1 %.
3.7.3.1 Pumping kinetics of the iodine photodissociation laser The absorption cross-section of the alkyliodides can be best fitted [82Kru] by a line-shape function 2
σabs (max) a 1 1 σabs (λ) = exp −b − λ λ a determining the production rate of the excited iodine RI + hνpump (∼ 270 nm) → R + I(2 P1/2 ) , σpump = f × σabs , which is for the radical R = i–C3 F7 : σabs (max) = 6.3 × 10−19 cm2 , a = 2.75 × 102 nm, b = 0.901 × 107 nm2 , f ∼ 90 % [82Kru]; for R = n–C3 F7 : σabs (max) = 7.8 × 10−19 cm2 , a = 2.71 × 102 nm, b = 0.891 × 107 nm2 , f = (97 ± 2) % [82Kru, 83Sme, 83Coh], both with the energy loss for the dissociation plus excitation −3.24 eV. Landolt-B¨ ornstein New Series VIII/1B1
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Table 3.7.3. Selected rate constants for the iodine photodissociation laser for R = i–C3 F7 and, alternatively, following immediately bellow the same reaction with R = n–C3 F7 3,4 (for some reactions two alternative rates with the corresponding references are given). Reaction3
Rate4
2
Ref. −17
I( P1/2 ) + RI → I + RI (R = n–C3 F7 ) I(2 P1/2 ) + I2 → I + I2
(2.7 ± 0.3) × 10 (1.7 ± 0.2) × 10−16 3 × 10−11 9.9 × 10−12 10−32.423 × f1 (T ) 10−31.244 × f2 (T ) 10−29.437 × f3 (T ) 10(−11±0.4) × f4 (T ) 2.5 × 10−11 1.0277 × 10−10 exp (−401.4/T ) (1.9 ± 0.3) × 10−12 5.2 × 10−17 ∼ 10−19 (2.40 ± 0.07) × 10−17 (1.2 ± 0.3) × 10−13 (2.9 ± 0.5) × 10−33 × f5 (T ) (2.2 ± 0.4) × 10−33 × f6 (T ) (2.9 ± 0.5) × 10−35 × f5 (T ) 3.8 × 10−31 10−31.437 × f3 (T ) (2.9 ± 0.4) × 10−16 (4 ± 1) × 10−33 × f7 (T ) (2 ± 1) × 10−13 (2 ± 1) × 10−13 (3 ± 1) × 10−11 (7 ± 1) × 10−12 (5 ± 1) × 10−13 1.38 × 10−12 10(15.5±0.3) × f8 (T )
2 I + He → I2 + He 2 I + SF6 → I2 + SF6 2 I + I2 → 2 I2 I + RI → R + I2 I(2 P1/2 ) + O2 → I + O2 (1 Δ g ) I(2 P1/2 ) + H2 O → I + H2 O I(2 P1/2 ) + N2 → I + N2 I(2 P1/2 ) + He → I + He I(2 P1/2 ) + SF6 → I + SF6 R + I2 → RI + I 2 I + RI → I2 + RI (R = n–C3 F7 ) I + I(2 P1/2 ) + RI → I2 + RI (R = n–C3 F7 ) I + I(2 P1/2 ) + I2 → 2 I2 I(2 P1/2 ) + R2 → I + R2 2 I + R 2 → I2 + R 2 I(2 P1/2 ) + R → RI (R = n–C3 F7 ) I + R → RI (R = n–C3 F7 ) 2 R → R2 (R = n–C3 F7 ) RI → R + I
[78Dob, 91Sko1] [78Dob] [78Gri, 96Sko] [72Dea, 75Bur] [84Coh] [84Coh] [84Coh] [91Sko2, 96Sko] [72Der2, 72Dea, 75Bur] [95Car] [78Gri] [72Dea, 75Bur] [95Sko] [67Hus] [91Sko2, 96Sko] [79Sko, 96Sko] [91Sko1] [95Sko] [74Kuz, 75Bev] [95Sko] [78Dob, 91Sko1] [74Dym, 91Sko1] [73Kuz, 78Kuz, 96Sko]5 [96Sko]5 [96Sko]5 [73Kuz, 78Kuz] [86Sko, 91Sko1]5 [69Zal, 70Zal, 74Bel2, 75Bev, 75Zal] [91Sko1]
2
f1 (T ) = (300/T )1.716 × 100.944×log (T /300) ; f2 (T ) = (300/T )2.59 ; 2 f3 (T ) = (300/T )5.844 × 102.163×log (T /300) ; f4 (T ) = exp [−(6550 ± 300)/T ] ; f5 (T ) = exp [(1360 ± 200)/T ] ; f6 (T ) = exp [(1130 ± 90)/T ]; f7 (T ) = exp [(1310 ± 100)/T ] ; f8 (T ) = exp [−(24450 ± 450)/T ] .
Analogically RI + hνpump (∼ 270 nm) → R + I σpump = (1 − f )σabs with the energy loss −2.3 eV for the dissociation only (hereafter I means always the ground state of atomic iodine I(2 P3/2 )). A rich data thesaurus for the iodine photodissociation laser is summarized in [82Kru]. Reliable values for other iodides can be found in [96Sko]. In Table 3.7.3 3,4,5 selected rate constants for the iodine photodissociation laser are given. 3 4 5
I, O2 , . . . always mean the atoms and molecules in the ground state, e.g. I(2 P3/2 ) or O2 (3 Σ− g ), . . . Dimension for dissociation (pyrolysis) is s−1 , for a dual reaction cm3 s−1 , for a triple one cm6 s−1 ; logarithm is base 10. For T = 300–460 K.
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3.7.4 Chemical oxygen iodine laser (COIL)
[Ref. p. 351
Since the molecular iodine I2 is an efficient quencher of the upper laser level its photolytic dissociation is to be equally considered in the kinetic scheme especially for the case of a long pumping pulse. The absorption line shape can be approximated by ε a σabs (λ) = σabs (max) exp − − b , λ where for the case of dissociation plus excitation, I2 + hν(∼ 500 nm) → I + I(2 P1/2 ) , σabs (max) = 2.7 × 10−18 cm2 (λ = 525.8 nm), ε = 1.596, a = 6335 nm, b = 12.047 and the energy loss −2.5 eV [73Tel, 81Pra, 88Roh]. Similarly, for the dissociation only, I2 + hν(∼ 500 nm) → 2 I , σabs (max) = 8.2 × 10−19 cm2 (λ = 493.3 nm), ε = 2, a = 4720 nm, b = 9.569 with the energy loss −1.6 eV [81Pra, 88Roh].
3.7.4 Chemical oxygen iodine laser (COIL) The Chemical Oxygen Iodine Laser (COIL) is the only chemical laser known working on an electronic transition. Its pumping mechanism, which was discovered by [72Der2], consists in a resonant energy transfer reaction between the excited singlet oxygen molecule O2 (1 Δ g ) and the atomic iodine. An energy difference between the O2 (1 Δ g ) and I(2 P1/2 ) of just 0.034 eV has a temperature equivalent of only 402 K, which ensures an efficient pumping of the upper laser level once the atomic iodine is available [72Der1]: O2 (1 Δ g ) + I ↔ O2 + I(2 P1/2 ) . The reverse rate constant of the transfer equals kforw /Kequil , where the rate constant of the forward 3 −1 reaction kforw = 2.3 × 10−8 /T cm3 s−1 [95Eli], or, alternatively, (7.6 ± 2.5) × 10−11 T /300 cm s 3 402 as given by [96Kul], and the constant of chemical equilibrium Kequil = 4 exp T [86Bas, 96Yur]. In the absence of quenching the minimum concentration of the singlet oxygen ensuring a positive energy flow from oxygen to iodine in a mixture is given by the inequality [O2 (1 Δ g )] 1 ≥ . [O2 ] + [O2 (1 Δ g )] 1 + 2Kequil The systems mostly have a perpendicular resonator into which a singlet oxygen flow from a chemical Singlet Oxygen Generator (SOG) is introduced and prior to reaching the active zone iodine vapor is injected together with a suitable carrier gas, such as Ar or He. The molecular iodine I2 must first be dissociated I2 + n O2 (1 Δ g ) → 2 I + n O2 and only then it can be excited to participate in the lasing process. The value of n is estimated to be n ∼ 4–7. The exact mechanism of the dissociation, which in principle must be stepwise, has not yet been clarified in detail, see [01Kom] for a discussion. Another alternative way involving electronically excited I2 and vibrationally excited O2 was recently considered in [06Azy]. A decisive progress has been achieved by the arrival of supersonic COIL systems. The dynamic cooling of the expansion zone, which is used for lasing inside the resonator, means that the equilibrium of energy exchange between I(52 P1/2 ) and O2 (1 Δ g ) is shifted in favor of iodine. Moreover, Landolt-B¨ ornstein New Series VIII/1B1
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the faster flow stretches the active zone over the whole width of the resonator and enhances the iodine feeding rate. A lower temperature also means a smaller Doppler fluorescent line broadening and thus a higher gain. This is at the cost of a more powerful vacuum pump, which must sustain the supersonic flow. In the case of the largest COIL system the pump is usually assisted by a diffuser, which may be even integrated in the iodine injection assembly [00Nik]. The supersonic flow velocity of the Mach number M ∼ 1.5–3 is reached by letting the excited oxygen leaving a generator usually with a carrier gas (He or N2 ) pass through an array of heated Laval-type nozzles composed of blades, which have in their sides orifices trough which the iodine vapor is injected in the oxygen flow, also mixed with a suitable buffer gas. The streaming and the mixing is thus a fairly complex process involving a complicated geometry and also dependent on many parameters, which has to be modeled by a 3D hydrodynamics including the reaction kinetics to achieve an optimum operation.
3.7.4.1 Generators of the excited oxygen (SOG) The singlet oxygen O2 (1 Δ g ) is a long-lived molecule with the natural life-time τO2 (1 Δ g ) = 74 min, see [99Spa] for a discussion of this value, since earlier references give a somewhat shorter lifetime. Similarly, the next higher excited state O2 (1 Σ+ = 7 s [71Kea]. The g ) has the life-time τO2 (1 Σ+ g ) excited molecules can thus be produced in a separate generator and conducted by a pipe into the resonator. The excited oxygen is generated by a decomposition of H2 O2 in a cooled basic solution (BHP: Basic Hydrogen Peroxide) of KOH (or NaOH, LiOH) by chlorine Cl2 . Usual BHP mixtures for the COIL contain H2 O2 (1–3 mol), HO− 2 (6–8 mol), diluted by water to about 50 % by weight. The summary reaction6 H2 O2 + Cl2 + 2 KOH → O2 (1 Δ g ) + 2 KCl + 2 H2 O occurs on the gas–liquid interface, more precisely in a very thin layer near the surface of the liquid of about 100 nm in thickness, out of which the excited oxygen diffuses back to the gas phase. The generators are thus differing in the way how this interface is provided. [96Yur] is citing 4 types: disk (wetted wall wading disks), aerosol, bubbler or sparger and jet. Rotating the jets leads to an improved type called the twister SOG [05Vys] and the droplet generator can also be regarded as a mutation of the jet SOG. The yield of the singlet oxygen usually lies between 40 and 80 % at a pressure of fractions to tens of torr. A very promising performance and a high pressure offers the jet generator originally developed at the Lebedev Institute at Samara, Russia, which first achieved 100 torr of pressure of excited oxygen [91Zag]. Recently, other SOG types were developed mostly, however, as clones based on the above mentioned principles. Improvements of the jet generator aim either at a removal of BHP droplets which may enter the mixing zone with the flow of the excited oxygen and subsequently reduce the laser power output by quenching the excited iodine by water, or seek to increase the surface of BHP available for the reaction. Some of them include mechanical moving parts, either rotating or vibrating. Noteworthy is the twisting aerosol flow generator driving a multikilowatt grade laser in Arzamas 16 [01Vys] or the droplet SOG feeding the Airborne Laser, likely in the MW range, which is being developed at the Kirtland AFB [01Lam]. 6
This summary reaction represents, in fact, a chain starting with a preparation of BHP solution in the first stage, which means that practically all the OH− ions in the basic solution are replaced by HO− 2 4 OH− + H2 O2 ↔ HO− 2 + H2 O , equilibrium constant 4 × 10 ,
which is followed by the reaction with gaseous Cl2 1 − Cl2 + 2 HO− 2 → O2 ( Δ g ) + 2 Cl + H2 O2 .
The last reaction again summarizes a chain of 3 reactions Landolt-B¨ ornstein New Series VIII/1B1
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3.7.4 Chemical oxygen iodine laser (COIL)
[Ref. p. 351
3.7.4.2 Pumping kinetics of the chemical oxygen-iodine laser Beside the fundamental reactions shown above there are a number of other processes going on in the mixture. Table 3.7.4 summarizes some of them, which are useful in constructing the models of COIL operation. The reaction scheme in this table was taken over from [95Per] as the simplified reaction mechanism, a less concise scheme also to be found in [95Per], is designated as the standard COIL kinetics package. Another lengthy kinetics scheme is given in [94Kul]. Table 3.7.4 is augmented by the following Table 3.7.5, which gives the hyperfine and translational7 relaxation rate constants for oxygen-iodine laser [84Zag, 93Cop1, 95Eli]. Table 3.7.4. Selected rate constants for the chemical oxygen-iodine laser (for some reactions two alternative rates with the corresponding references are given)3 . Reaction3 1
Rate4 2
O2 ( Δ g ) + I ↔ O2 + I( P1/2 )
O2 (1 Δ g ) + I2 → O2 + I2 (nvibr > 0) I(2 P1/2 ) + I2 → I + I2 (nvibr > 0) I2 (nvibr > 0) + O2 → I2 + O2 I2 (nvibr > 0) + O2 (1 Δ g ) → 2 I + O2 I2 (nvibr > 0) + H2 O → I2 + H2 O O2 (1 Δ g ) + I(2 P1/2 ) → O2 (1 Σg ) + I I(2 P1/2 ) + H2 O → I + H2 O 2 O2 (1 Δ g ) → O2 (1 Σg ) + O2 O2 (1 Σg ) + H2 O → O2 (1 Δ g ) + H2 O O2 (1 Σg ) + I2 → O2 + 2 I
Ref. −8
kforw = 2.3 × 10 /T (7.6 ± 2.5) × 10−11 × T /300 7.8 × 10−11 Kequil = 0.75 exp(402/T ) 7 × 10−15 1.6 × 10−11 exp(272/T ) 3.5 × 10−11 5 × 10−11 3 × 10−10 3 × 10−10 4 × 10−24 T 3.8 exp(700/T ) 3.8 × 10−13 exp(−390/T ) (1.9 ± 0.3) × 10−12 2 × 10−12 7 × 10−28 T 3.8 exp(700/T ) 6.7 × 10−12 4 × 10−12
[95Eli] [96Kul] [97Mad] [96Yur] [83Hei, 95Eli] [95Eli] [96Yur] [86Han, 95Eli] [95Per, 95Eli] [95Per, 95Eli] [93Cop2, 95Eli] [96Kul] [78Gri, 95Eli] [95Per] [96Kul] [80Koh, 95Eli] [72Der2, 95Eli]
Table 3.7.5. Hyperfine and translational7 relaxation rate constants for the oxygen-iodine laser [84Zag, 93Cop1, 95Eli]. Transition
Rate4
I(2 P1/2 ; F1 ) + O2 → I(2 P1/2 ; F2 ) + O2 I(2 P3/2 ; F1 ) + M → I(2 P3/2 ; F2 ) + M I(2 P1/2 ; F = 2, 3; Ekin ) + He → I(2 P1/2 ; F ; Ekin ) + He 2 2 I( P1/2 ; F = 2, 3; Ekin ) + O2 → I( P1/2 ; F ; Ekin ) + O2 I(2 P3/2 ; F = 1 . . . 4; Ekin ) + He → I(2 P3/2 ; F ; Ekin ) + He I(2 P3/2 ; F = 1 . . . 4; Ekin ) + O2 → I(2 P3/2 ; F ; Ekin ) + O2
1 × 10−10 4 × 10−10 √ 1.8 × 10−11 T 8.7 × 10−11 1.3 × 10−10 T 0.262 2.7 × 10−10
− HO− 2 + Cl2 → HOOCl + Cl , − − HO2 + HOOCl → ClO2 + H2 O2 , − 1 ClO− 2 → Cl + O2 ( Δ g ) ,
rate 4.5 × 10−14 cm3 s−1 , rate very high , rate 107 s−1 .
The first reaction of the last chain strongly releases heat and BHP has thus to be kept cool at −10 to −30◦ C [04Bar].
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3.7.4.3 All-gas chemical oxygen-iodine lasers The heterogeneous reaction on the liquid–gas interface in a conventional COIL represents a serious inconvenience limiting its practical use. Moreover, much of the energy content of the produced O2 (1 Δ g ) is spent on the dissociation of the iodine molecules. The alternative ways of overcoming this difficulty are, however, just in the experimental stage. The first one consists in injecting directly the atomic iodine rather than the molecular one. The atomic iodine is produced by a substitution of I in the gaseous HI by a halogen gas atom, either F or Cl. This, in turn, is liberated by homogeneous reactions with NO, which in the case of Cl produced by a reduction of ClO2 , are summarized in Table 3.7.6. Table 3.7.6. Reaction rates of Cl-based atomic iodine injection. Reaction
Rate4
Ref.
ClO2 + NO → NO2 + ClO ClO + NO → NO2 + Cl Cl + ClO2 → 2ClO Cl + NO2 + N2 → NO2 Cl + N2 Cl + NO2 Cl → Cl2 + NO2 ClO + NO2 + N2 → NO3 Cl + N2 Cl + Cl + N2 → Cl2 + N2 Cl + HI → I + HCl (HCl∗ ) I + I + N 2 → I2 + N 2 I + NO2 + N2 → INO2 + N2 I + INO2 → I2 + NO2
2.51 × 10−12 exp (−600/T ) 6.39 × 10−12 exp (290/T ) 3.4 × 10−11 exp (160/T ) 1.3 × 10−30 (298/T )2 5.5 × 10−12 1.75 × 10−31 exp (1150/T ) 2.38 × 10−32 exp (805/T ) 2.31 × 10−8 (298/T )4.45 exp (1500/T ) 6.15 × 10−34 (T /298)0.07 exp (894/T ) 3.02 × 10−31 298/T 8.3 × 10−11
[73Bem] [97DeM] [97DeM] [97DeM] [81Nel] [77Leu] [73Wid] [77Mei] [72Ip] [01Atk] [76Van]
Alternatively, fluorine atoms may be prepared by the method described in [76Kol] as expressed by a summary reaction F2 + NO → FNO + F with the rate constant 7 × 10−13 exp (−1150/T ) [cm3 s−1 ], they may replace Cl in the reaction with HI. Other fairly elegant way, how to make COIL a more attractive device for a daily practical use by avoiding the clumsy chemistry, is to produce the excited O2 (1 Δ g ) molecules in an electric discharge. Although a stationary, self-sustained low-pressure discharge in a pure oxygen gas is known to render a much lower yield of O2 (1 Δ g ) than the chemical reactor, typically ∼ 15 %, as obvious from an illustrative example of a microwave discharge in [84Mav], which is not enough for an efficient lasing, admixtures or a transition to a supersonic regime have improved the situation considerably. An admixture of NO into a flow of O2 with a buffer gas entering the discharge space allowed to increase the I(2 P1/2 ) luminescence [01Sch] and eventually to cross the threshold of positive gain [05Car1]. A real lasing of this Discharge Oxygen Iodine Laser (DOIL, synonyms ElectriCOIL, EOIL) has been reported [05Car2] in a supersonic regime with a high-frequency discharge as an O2 (1 Δ g ) source. 7
Dependence on the kinetic energy Ekin signifies a collision rate in the energy (velocity) space describing the shifts in the energy due to collisions and evolution of the energy distribution function. M means any component of the laser mixture.
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3.7.5 Outlook
[Ref. p. 351
3.7.5 Outlook The modern demands of inertial fusion research by lasers [95Lin] do not favor the iodine photodissociation lasers as fusion drivers. Energy in the MJ range planned for the largest Nd:glass systems under construction is not within reach of the current iodine laser systems, however large. Unless pumped by the light of the shockwave launched by a conventional explosion the pulse energy remains limited by the size of the final amplifier aperture to the kJ range. Another drawback is the natural tendency to generate in the subnanosecond region, whereas the present laser inertial fusion is based preferably on pulses several nanoseconds long. Consequently, the thermonuclear programs based on iodine lasers are being phased out and some of the systems have been closed8 . On the other hand, there are many advantages, which make iodine photodissociation lasers attractive as an instrument for non-nuclear research. These are, first of all, a reasonable frequency of shots and a very good beam quality. Also, a multipass amplifier operation is easy to implement, since a double pass of the amplified pulse is enough for an extraction of the stored energy, which is technically achievable using just passive optical elements. In combination with a phase conjugation system it is, in principle, possible to reduce the focal spot to a size comparable to the laser wavelength. The somewhat longer wavelength and the subnanosecond pulse gives the iodine laser a relative advantage over the Nd lasers when used as a driver for X-ray lasing from a linear focus. It is to be expected that in future a technique of generation of ultra-short pulses OPCPA will be implemented circumventing the inherent narrowness of the fluorescent line. Other possible upgrade may consist in using a solid-state master oscillator to feed the iodine laser chain. This might make easier a generation of pulses several nanoseconds long. Whereas the photodissociation systems are used routinely as instruments of physical research, the chemical oxygen iodine laser is still under development. Nevertheless, two important milestones have been passed: transition to supersonic systems and the invention of the jet generator of excited oxygen. A relatively small supersonic COIL fed from a tiny jet generator can yield several kilowatts in a cw operation. The power of these systems is restricted by no constraints usually encountered in a solid state and thus it might be raised high above the values characteristic of the solid-state lasers. Although the chemistry inherent in its operation likely precludes any systematic use in the industry, the high power and the possibility to use a glass fiber to channel it to a workpiece predestines the COIL systems for special tasks. A real breakthrough will, however, only be achieved if the chemical part of COIL could be avoided and the excited oxygen is supplied by some kind of gas discharge with a comparable efficiency.
Acknowledgement This contribution was written in a partial fulfilment of the project “Research Center of Laser Plasma” No. LC528 of Ministry of Education of the Czech Republic. We are also obliged to our colleagues J. Kodymov´a and V. Jir´ asek for a steady update on COIL.
8
Iskra IV was replaced by a multipass Nd beamlet system Luch. Landolt-B¨ ornstein New Series VIII/1B1
References for 3.7
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References for 3.7 61Rau
Rautian, S.G., Sobelman, I.I.: Zh. Eksp. Teor. Fiz. 41 (1961) 2018.
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Sobelman, I.I.: Vvedenie v Teoriu Atomnykh Spektrov, Mocsow: Fizmatgiz, 1963.
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Husain, D., Wiesenfeld, J.R.: Trans. Faraday Soc. 63 (1967) 1349.
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Zalesskii, V.Y., Venediktov, A.A.: Sov. Phys. JETP (English Transl.) 28 (1969) 1104.
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Bemand, P.P., Clyne, M.A.A., Watson R.T.: J. Chem. Phys. Faraday Trans. I 69 (1973) 1356. Kuznetsova, S.V., Maslov, A.I., Prishedko, V.N.: Kratkie Soobshchenia po Fizike (FIAN) 10 (1973) 13. Tellinghuisen, J.: J. Chem. Phys. 58 (1973) 2821. Widman, R.P., DeGraff, B.A.: J. Phys. Chem. 77 (1973) 1325.
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75Bev 75Bur 75Pad 75Zal
Beverly III, R.E.: Opt. Commun. 15 (1975) 204. Burde, D.H., McFarlane, R.A., Wiesenfeld, J.R.: Chem. Phys. Lett. 32 (1975) 296. Padrick, T.D., Palmer, R.E.: J. Chem. Phys. 62 (1975) 3350. Zaleskii, V.Y.: Sov. J. Quantum Electron. (English Transl.) 4 (1975) 1009.
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Fuß, W., Hohla, K.: Z. Naturforsch. A 31 (1976) 569. Kolb, C.E.: J. Chem. Phys. 64 (1976) 3087. Swingle, J.C., Turner, C.E., Murrag, J.R., George, E.V., Krupke, W.F.: Appl. Phys. Lett. 28 (1976) 387. Van Den Bergh, H., Troe, J.: J. Chem. Phys. 64 (1976) 736.
76Van
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79Bas 79Hoh
79Sko
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96Hag 96Han
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99Spa 00Der 00Kwo 00Nik 00San 01Atk
01Jun
01Kom 01Lam 01Sch 01Vys
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Landolt-B¨ ornstein New Series VIII/1B1
Index
357
Index
Aberration 223 Absorber mirror dispersive saturable (D-SAM) 89 semiconductor saturable (SESAM) 34, 66, 76, 88 semiconductor saturable, quantum-dot (QD-SESAM) 69 saturable 34, 36, 79, 86 Fabry–Perot, antiresonant (A-FPSA) 88 fast 82, 106 fast, model 112 mechanism 83 semiconductor 88 slow 82 Absorption anomalous 242 nonsaturable 225 self- 20 Acousto-optic modulator (AOM) 76, 79 Active mode-locking 36 Adaptive pulse compression 120 Additive pulse mode-locking (APM) 66, 91 A-FPSA (antiresonant Fabry–Perot saturable absorber) 88 AlGaAs/GaAs injection laser 72 AlGaAsSb 87 Algorithm, principal component generalized projections (PCGPA) 123 All-optical atomic clock 129 α-DFB (distributed feedback) 23 Ambipolar diffusion coefficient 186 Amplification chirped-pulse (CPA) 73, 217, 223, 245 chirped-pulse, optical-parametric (OPCPA) 341 chirped-pulse, spatially evolving (SCPA) 223 double-pass 220 multiple-pass 229, 231 nonlinear 5, 6 optical parametric 35 regenerative 8 short-pulse 230 Amplified spontaneous emission (ASE) 217 Amplifier excimer 218 Landolt-B¨ ornstein New Series VIII/1B1
off-axis pre- and power- 227 semiconductor optical (SOA) 72 Amplitude, self-, modulation (SAM) 36 Angle, Brewster 75 Anomalous absorption 242 Antimonide 87 Antiresonant Fabry–Perot saturable absorber (A-FPSA) 88 AOM (acousto-optic modulator) 76, 79 APM (additive pulse mode-locking) 66, 91 Approximation, slowly-varying-envelope 107 Ar II laser 259 Ar–Hg-mixture discharge 255 Arc discharge 195 -driven 322 stabilization 263 Array, micro-lens 21 ASE (amplified spontaneous emission) 217 Atmospheric pressure, transversely excited (TEA) CO2 laser 317 Atomic clock, all-optical 129 Attachment, electron- 284 Au I laser 255 Autocorrelation interferometric (IAC) 122 optical 121 Avalanche, electron- 192 Axial flow laser fast-flow 207 slow-flow 207 Axis fast 74 slow 74 Back-side-coated (BASIC) mirror 101 Bandwidth 215 gain 221 of the pulse 93 BASIC (back-side-coated) mirror 101 Basic hydrogen peroxide (BHP) 347 Beam electron-, excitation 177 parameter product BP P 6 BHP (basic hydrogen peroxide) 347 Birefringent fiber 92
358 Boltzmann equation 182 Boundary layer 193 BP P (beam parameter product) 6 Bragg grating 72 reflector distributed (DBR) 86, 245 saturable (SBR) 88 Breakdown voltage 194 Brewster angle 75 Brillouin scattering, stimulated 242 Broadening Doppler 175 line Doppler fluorescent 347 homogeneous 175 natural 174 pressure 175 Stark 176 Carrier envelope offset (CEO) 126 Catastrophic optical damage (COD) 20 Cavity design 76 unstable 299 Cell, Zeeman 10 CEO (carrier envelope offset) 126 Chain-reaction excitation 323 Characterization, pulse- 34 Charge space-, field 196 -transfer (Duffendack) reaction 265 Chemical excitation 179 flame laser 313 flow, supersonic 323 iodine laser, research and development (RADICL) 341 laser (CL) 289, 306, 310 diffusion-type 320, 323 oxygen iodine laser (COIL) 179, 341, 346 technology 309 reaction 279, 289 enthalpy 306 transfer laser (TCL) 325, 328, 330 DF–CO2 327 vapor deposition, metal-organic (MOVPE) 86 Chirp 93, 220 parameter 109 Chirped Gaussian pulse 109 mirror 100 double- (DCM) 100 pulse amplification (CPA) 73, 217, 223, 245 amplification, optical-parametric (OPCPA) 341
Index amplification, spatially evolving (SCPA) 223 Gaussian 109 Chlorine, hydrogen-, explosion 310, 314 CL (chemical laser) 289 Clock atomic, all-optical 129 -work, phase-locked 129 CO laser 311 pulsed 312 sealed-off 211 CO2 laser 205 fast-flow high-power 304 gas-dynamic 208 system 9 transversely excited atmospheric pressure (TEA) 317 COD (catastrophic optical damage) 20 Coefficient diffusion, ambipolar 186 Einstein 5, 173 for spontaneous emission 172 for stimulated emission 172 rate electron attachment 186 ionization 186 self-phase modulation (SPM coefficient) 107 Coherent emission 5 COIL (chemical oxygen iodine laser) 179, 341, 346 technology 309 Colliding pulse mode-locked (CPM) 33 laser 111 Collision integral 182 of second kind 9 Color-center laser 40, 88 Comb frequency 37, 126 Combustion-driven 289 scheme 292 Communication, optical 245 Compensation, dispersion 94 Compression pulse 33, 99 adaptive 120 external 35 scheme 120 temporal 215 Compressor grating 99 pair 120 prism 99 Condition, threshold- 174 Conductivity, thermal, of glasses 66 Confinement fusion, inertial (ICF) 242, 243 Confocal resonator 299 Constant, plasma dielectric 187 Landolt-B¨ ornstein New Series VIII/1B1
Index Contrast, gain- 228 Conversion efficiency 18 frequency 219 SPM-to-SAM 91 Cooling system 210 Copper vapor laser 255 Coupling, galvanic 193 CPA (chirped-pulse amplification) 73, 217, 223, 245 CPM (colliding pulse mode-locked) 33 laser 111 Cr2+ :ZnSe 68 Cr3+ :LiSAF 68 Cr3+ :LiSCAF 68 Cr3+ :LiSGaF 68 Cr:LiSAF laser 66 Cr:YAG laser 40 Cryogenic discharge 211 Cs laser 255 Cu I laser 255, 270 Cutting 13, 24 Cycle, few-, pulse 122 Damage sputtering 263 threshold 81 DBR (distributed Bragg reflector) 86, 245 DC discharge 190 DCM (double-chirped mirror) 100 Decay time, radiative 258 Density electron 184 mode 173 pump power 174, 175 Dephasing 83 Deposition, sub-micron-scale 246 Design cavity 76 resonator 14 slab 16 Detonation wave 319 Device LEDA (Lasers ` a excitation Electrique et ` a D´etente Adiabatique) 304 SESAM enhanced (E-SESAM) 89 low-field-enhancement resonant-like (LOFERS) 89 DF laser 314 emission spectrum 327 DFB (distributed feedback) 23 DFDL (distributed-feedback-dye laser) 236 Dielectric constant, plasma 187 film 87 Diffraction pattern 6 Landolt-B¨ ornstein New Series VIII/1B1
359 Diffusion chemical laser 320 coefficient, ambipolar 186 -cooled laser 207 -type chemical laser 323 Dilute nitride 87 Dimer, rare-gas 278 Diode-pumped solid-state laser 13 Dipole transition, magnetic 308 Direct electric-field reconstruction, spectral-phase interferometry for (SPIDER) 120 writing 19 Direction fast 16, 20 slow 16, 20 Directional selectivity 6, 7 Discharge arc 195 Ar–Hg-mixture 255 cryogenic 211 DC 190 electric, laser (EDL) 289 electrical 289 flow laser 321 gas 180 excitation 176 glow 190, 191, 283 high-pressure 192 -initiated HF laser 317 low-pressure metal–noble-gas 255 microwave 190, 194, 304 oxygen iodine laser (DOIL) 349 stability 283 TEA (transversely excited at atmospheric pressure) 192 laser 284 type 190 Disk, thin-, laser 66 Dispersion 92 compensation 94 negative 99 Dispersive saturable absorber mirror (D-SAM) Dissociation, photolytic 346 Distortion, phase-front 238 Distributed Bragg reflector (DBR) 86, 245 feedback (DFB) 23 feedback dye laser (DFDL) 236 Distribution function, electron 182 Maxwell 184 near-field intensity 299 DOIL (discharge oxygen iodine laser) 349 Doped solid-state laser rare-earth- 40
89
360 transition-metal- 40 Doppler broadening 175 fluorescent line broadening 347 Double-chirped mirror (DCM) 100 Double-pass amplification 220 Doubling, frequency 18 Downstream mixing laser 300 Drift velocity, electron 184 Driven arc- 322 combustion- 289 scheme 292 Dry-etching technique 246 D-SAM (dispersive saturable absorber mirror) Dual-wavelength laser 216 Duffendack charge-transfer reaction 265 process 265 Duration, pulse 33 measured 122 minimum 221 subpicosecond 219 Dye laser 33 Dynamic gain saturation 110
Index
89
E-SESAM (enhanced SESAM device) 89 Edge-emitting semiconductor diode laser 72 EDL (electric discharge laser) 289 Effect Kerr 90 soliton 114 Talbot 23 Efficiency conversion 18 extraction 225, 226 HF laser 318 quantum 173 Einstein coefficient 5, 173 for spontaneous emission 172 for stimulated emission 172 Electric discharge laser (EDL) 289 field reconstruction, direct, spectral-phase interferometry for (SPIDER) 120 Electrical discharge 289 transverse, in gas at atmospheric pressure (TEA) laser 284 ElectriCOIL see DOIL Electro-optical filamentation 20 Electron attachment 284 rate coefficient 186 avalanche 192 -beam excitation 177 density 184 distribution function 182
drift velocity 184 energy transfer frequency 183 mobility 186 momentum transfer frequency 183 reaction 283 temperature 184 Electrophoresis 196 Emission amplified-spontaneous (ASE) 217 coherent 5 spectrum DF laser 327 HF laser 327 spontaneous, Einstein coefficient for 172 stimulated, Einstein coefficient for 172 Emitter, single 9 Energy ponderomotive 243 storage time 225 transfer frequency, electron 183 Enhanced SESAM device (E-SESAM) 89 Enthalpy, chemical reaction 306 EOIL see DOIL Epitaxial structure 9 Epitaxy, molecular beam (MBE) 86 Equation Boltzmann 182 gasdynamic flow 293 Haus’s master 108, 113 formalism 102, 116 Maxwell 187 rate 5, 172, 297 vibrational 293 Er:Yb:glass 67 Escape factor 258 Etching, dry-, technique 246 Excimer amplifier 218 laser 10, 13 system 215 rare-gas monohalide 275 Excitation chain-reaction 323 chemical 179 electron-beam 177 frequency 183 gas discharge 176 gas-dynamic 178 rate 7 rotational 185 transverse 313 traveling-wave (TWE) 223 vibrational 185 Excited, transversely, atmospheric pressure (TEA) CO2 laser 317 Expansion flow, supersonic 290 Landolt-B¨ ornstein New Series VIII/1B1
Index Explosion hydrogen-chlorine 310, 314 limit 327 shockwave 344 External pulse compression 35 Extraction efficiency 225, 226 power 296 Fabry–Perot saturable absorber, antiresonant (A-FPSA) 88 Factor escape 258 M 2 74 Fast axis 74 direction 16, 20 -flow axial-flow laser 207 high-power CO2 laser 304 ignitor 243 saturable absorber 82, 106 model 112 Feedback 7 distributed (DFB) 23 Femtosecond laser 77 Fermi–Dirac statistics 84 Few-cycle pulse 122 Fiber birefringent 92 laser 92 mode-locked 73 Field ionization, optical (OFI) 243 near-, intensity distribution 299 space-charge 196 strength, reduced 188 Filamentation 35, 189, 192, 242 electro-optical 20 Film, dielectric 87 Filter, interference 22, 89 Filtering spatial 234, 239 spectral 236 Flame laser, chemical 313 Flow discharge, laser 321 fast-, high-power CO2 laser 304 gas-, longitudinal 313 gasdynamic, equation 293 supersonic chemical 323 expansion 290 nonequilibrium 297 Fluence, saturation 73 Fluorescence line width 275 Landolt-B¨ ornstein New Series VIII/1B1
361 quenching 257 Fluorescent Doppler line broadening 347 Focusability 239, 242 Focusing, self- 223, 238, 244 Formation, soliton 96 Forward transfer, laser-induced (LIFT) 247 Four-level laser process 259 Frequency comb 37 optical 126 conversion 219 doubling 18 excitation 183 ionization 183 plasma 187 repetition 284 -resolved optical gating (FROG) 123 for complete reconstruction of attosecond burst (FROG-CRAB) 123 transfer electron energy 183 electron momentum 183 Fresnel number 6 FROG (frequency-resolved optical gating) 123 -CRAB (FROG for complete reconstruction of attosecond burst) 123 Function electron distribution 182 line-shape 344 Fusion, inertial confinement (ICF) 242, 243 Gain bandwidth 221 contrast 228 saturation, dynamic 110 small-signal 206 Galvanic coupling 193 Gas discharge 180 excitation 176 -dynamic CO2 laser 208 excitation 178 laser 205 flow, longitudinal 313 mixture 279 noble, ion laser 259 raredimer 278 monohalide excimer 275 Gasdynamic flow equation 293 laser (GDL) 289 Gating, optical, frequency-resolved (FROG) Gaussian pulse, chirped 109 GDL (gasdynamic laser) 289
123
362
Index
Generalized projections algorithm, principal component (PCGPA) 123 Generation, second harmonic (SHG) 236 Generator Marx 319 singlet oxygen (SOG) 346 Gires–Tournois interferometer (GTI) 96 Glasses, thermal conductivity of 66 Glow discharge 190, 191, 283 high-pressure 192 Grating Bragg 72 compressor 99 pair 96 compressor 120 GTI (Gires–Tournois interferometer) 96 Hardening, transformation 13 Harmonic generation, second (SHG) Haus master equation 108, 113 formalism 102, 116 HCl laser 311 He –Cd laser 265 –Cd+ laser 255, 266 –Hg+ laser 255 –Ne laser 10, 265 Heat sink 16 Helium-neon laser see He–Ne laser HF laser 311, 314, 315, 322 discharge-initiated 317 efficiency 318 emission spectrum 327 HF+ molecule 311 HF/DF laser 322 Hg–Ar-mixture discharge 255 Hg I laser 255 High-power CO2 laser, fast-flow 304 diode laser (HPDL) 21 High-pressure glow discharge 192 Hole burning, spatial 77 Holography 242 Homogeneous line broadening 175 Homogenization technique 239 HPDL (high-power diode laser) 21 Hydrogen -chlorine explosion 310, 314 peroxide, basic (BHP) 347
236
IAC (interferometric autocorrelation) 122 ICF (inertial confinement fusion) 242, 243 Ignition, optical 315 Ignitor, fast 243 Impulse response 121 Incoherent superposition 22 Inertial confinement fusion (ICF) 242, 243
Instability Q-switching 119 thermal 189 Integral, collision 182 Intensity distribution, near-field 299 saturation 206 Interference filter 22, 89 Interferometer Gires–Tournois (GTI) 96 Sagnac 232 Interferometric autocorrelation (IAC) 122 Interferometry, spectral-phase, for direct electricfield reconstruction (SPIDER) 120, 124 International Telecommunication Union (ITU) 67 Inversion population 290, 295, 341 Iodine chemical laser, research and development (RADICL) 341 laser 309, 341 photolytically initiated (PIL) 308 oxygen laser, chemical (COIL) 341, 346 technology 309 oxygen laser, discharge (DOIL) 349 Ion laser 255 metal 265 noble gas 259 Ionic recombination reaction 279 Ionization frequency 183 multiphoton 243 optical field (OFI) 243 Penning 177 rate coefficient 186 ITU (International Telecommunication Union) 67 Kerr effect 90 -lens mode-locking (KLM) 34, 67, 91, 112 Kinetics reaction 302 vibrational 293 Klein–Rosseland relation 256 KLM (Kerr-lens mode-locking) 34, 67, 91, 112 Laser AlGaAs/GaAs injection 72 Ar II 259 Au I 255 chemical (CL) 289, 306, 310 diffusion-type 320, 323 chemical flame 313 chemical oxygen iodine (COIL) technology 309 CO 311 pulsed 312
179, 341, 346
Landolt-B¨ ornstein New Series VIII/1B1
Index sealed-off 211 CO2 205 fast-flow high-power 304 gas-dynamic 208 stripline 207 system 9 transversely excited at atmospheric pressure (TEA) 317 colliding pulse mode-locked (CPM) 111 color-center 40, 88 copper vapor 255 Cr:LiSAF 66 Cr:YAG 40 Cs 255 Cu I 255, 270 LEDA (Lasers ` a excitation Electrique et ` a D´etente Adiabatique) 304 DF 314 emission spectrum 327 diffusion-cooled 207 discharge flow 321 discharge oxygen iodine (DOIL) 349 distributed-feedback-dye (DFDL) 236 downstream mixing 300 dual-wavelength 216 dye 33 electric discharge (EDL) 289 excimer 10, 13 fast-flow axial-flow 207 femtosecond 77 fiber 92 mode-locked 73 gasdynamic (GDL) 205, 289 HCl 311 He–Cd 265 He–Cd+ 255, 266 He–Hg+ 255 He–Ne 10, 265 helium-neon see Laser, He–Ne HF 311, 314, 315, 322 discharge-initiated 317 efficiency 318 emission spectrum 327 HF/DF 322 Hg I 255 -induced forward transfer (LIFT) 247 iodine 309, 341 ion 255 metal ion 265 vapor 255 microchip 68 Q-switched 36 NO 331 noble gas ion 259 photodissociation 341, 344 Landolt-B¨ ornstein New Series VIII/1B1
363 photolytically initiated iodine (PIL) 308 polishing 17 process four-level 259 three-level 258 pulsed CO 312 transfer chemical (TCL) 326 transfer chemical (TCL) DF–CO2 327 Q-switched 242 research and development iodine chemical (RADICL) 341 resonance–metastable 268 ring 73 sealed-off 207, 211 self-terminating 268 pulse 257 semiconductor diode, edge-emitting 72 slow-flow axial-flow 207 solid-state 11, 40 diode-pumped 13 rare-earth-doped 40 transition-metal-doped 40 spectroscopy 33 TEA (transversely excited at atmospheric pressure) 208, 284 CO2 317 thin-disk 66 threshold 8, 256 transfer chemical (TCL) 325, 328, 330 DF–CO2 327 pulsed 326 transverse-flow 208 vertical-external-cavity surface-emitting (VECSEL) 39, 69 waveguide 207 Yb3+ :YAG, thin-disk 78 Z- 23 Layer, boundary 193 LEDA (Lasers ` a excitation Electrique et ` a D´etente Adiabatique) laser device 304 Lensing, thermal 11 Level four-, laser process 259 rotational 291 three-, laser process 258 LIFT (laser-induced forward transfer) 247 Limit explosion 327 stability 261 Line broadening Doppler fluorescent 347 homogeneous 175 natural 174
364 -shape function 344 width, fluorescence 275 Lithography 242 UV 13 Load, thermal 11 LOFERS (low-field-enhancement resonant-like SESAM device) 89 Longitudinal gas flow 313 Loss modulator 106 Low-field-enhancement resonant-like SESAM device (LOFERS) 89 Low-pressure discharge, metal–noble-gas 255 Lu2 O3 67 M 2 -factor 74 Machining, micro- 13, 244 Macroscopic polarization 83 Magnetic dipole transition 308 Marking 13 Marx generator 319 Master equation of Haus 108, 113 formalism 102, 116 Master oscillator power amplifier (MOPA) 16 Maxwell distribution 184 equation 187 MBE (molecular beam epitaxy) 86 Measured pulse duration 122 Mechanism mode-locking 38, 111 saturable absorber 83 Metal ion laser 265 –noble-gas low-pressure discharge 255 -organic chemical vapor deposition (MOVPE) 86 vapor laser 255 Metastable, resonance-, laser 268 Micro -chip laser 68 Q-switched 36 -lens array 21 -machining 13, 244 -step mirror 20, 21 Micron, subdeposition 246 structuring 244 Microscopy, X-ray 242 Microwave discharge 190, 194, 304 Minimum pulse duration 221 Mirror absorber dispersive saturable (D-SAM) 89 semiconductor saturable (SESAM) 34, 66, 76, 88 semiconductor saturable, quantum-dot (QD-SESAM) 69
Index back-side-coated (BASIC) 101 chirped 100 double- (DCM) 100 micro-step 20, 21 piezo-electric 10 Mixing, downstream, laser 300 Mixture Ar–Hg, discharge 255 gas 279 Mobility, electron 186 Mode density 173 -locked 33 colliding pulse (CPM) 33 colliding pulse (CPM) laser 111 fiber laser 73 -locking 36 active 36 additive pulse (APM) 66, 91 mechanism 38, 111 passive 36, 72, 102, 110, 112 passive, stable 119 Q-switched 33 soliton 115 matching, optimized (OMM) 74 volume, optical 11 Modulation self-amplitude (SAM) 36, 79, 85 self-phase (SPM) 90 coefficient 107 Modulator acousto-optic (AOM) 76, 79 loss 106 optical 79 Molecular beam epitaxy (MBE) 86 reaction 283 Molecule HF+ 311 Momentum transfer frequency, electron 183 Monohalide excimer, rare-gas 275 Monte-Carlo particle simulation 184 MOPA (master oscillator power amplifier) 16 MOVPE (metal-organic chemical vapor deposition) 86 Multiphoton ionization 243 Multiple-pass amplification 229, 231 Multiplexing, optical 231 Natural line broadening 174 Nd:YAG 33 Nd:YLF 33, 67 Nd:YVO4 67 Near-field intensity distribution Negative dispersion 99 Nitride, dilute 87 NO laser 331 Noble gas
299
Landolt-B¨ ornstein New Series VIII/1B1
Index ion laser 259 –metal low-pressure discharge 255 Nonequilibrium supersonic flow 297 Nonlinear amplification 5, 6 susceptibility, second-order 92 Nonsaturable absorption 225 Number, Fresnel 6 Off-axis pre- and power-amplifier 227 Offset, carrier envelope (CEO) 126 OFI (optical field ionization) 243 OMM (optimized-mode-matching) 74 OPCPA (optical parametric chirped pulse amplification) 341 OPO (optical parametric oscillator) 67 Optical amplifier, semiconductor (SOA) 72 autocorrelation 121 communication 245 field ionization (OFI) 243 frequency comb 126 gating, frequency-resolved (FROG) 123 for complete reconstruction of attosecond burst (FROG-CRAB) 123 ignition 315 mode volume 11 modulator 79 multiplexing 231 parametric amplification 35 chirped pulse amplification (OPCPA) 341 oscillator (OPO) 67 Optimized-mode-matching (OMM) 74 Oscillation, relaxation 5 Oscillator, optical parametric (OPO) 67 Oxygen iodine laser, chemical (COIL) 179, 341, 346 technology 309 iodine laser, discharge (DOIL) 349 singlet, generator (SOG) 346 Packaging 22 Pair grating 96 compressor 120 prism 99 Parameter product BP P 6 chirp 109 Particle simulation, Monte-Carlo 184 Pass double-, amplification 220 multiple-, amplification 229, 231 Passive mode-locking 36, 72, 102, 110, 112 stable 119 Pattern, diffraction 6 Landolt-B¨ ornstein New Series VIII/1B1
365 PCGPA (principal component generalized projections algorithm) 123 Penning ionization 177 process 265 Peroxide, basic hydrogen (BHP) 347 Phase front distortion 238 -locked clockwork 129 synchronization 232 transition of the second kind 8 Photodissociation 307 laser 341, 344 Photoionization 310 Photolytic dissociation 346 Photolytical process 312 Photolytically initiated iodine laser (PIL) 308 Piezo-electric mirror 10 PIL (photolytically initiated iodine laser) 308 Plasma dielectric constant 187 frequency 187 Pointing stability 234 Polarization, macroscopic 83 Polishing 13 laser 17 Ponderomotive energy 243 pressure 242 Population inversion 290, 295, 341 Power and pre-amplifier, off-axis 227 extraction 296 high-, CO2 laser, fast-flow 304 pump, density 174, 175 Pre- and power-amplifier, off-axis 227 Pressure transversely excited (TEA) CO2 laser 317 broadening 175 high-, glow discharge 192 ponderomotive 242 Principal component generalized projections algorithm (PCGPA) 123 Prism compressor 99 Process Duffendack 265 laser four-level 259 three-level 258 Penning 265 photolytical 312 translational–vibrational (T–V) 291, 293 vibrational–vibrational (V–V) 293 Product, beam parameter BP P 6
366 Projections algorithm, principal component generalized (PCGPA) 123 Pulse adaptive, compression 120 bandwidth of 93 broadening 93 characterization 34 chirped amplification (CPA) 217, 223, 245 amplification, optical-parametric (OPCPA) 341 amplification, spatially evolving (SCPA) 223 Gaussian 109 chirped, amplification (CPA) 73 compression 33, 99 external 35 duration 33 measured 122 minimum 221 subpicosecond 219 few-cycle 122 Gaussian, chirped 109 generation, stable 119 laser, self-terminating 257 mode-locking, additive (APM) 91 short, amplification 230 Pulsed CO laser 312 transfer chemical laser (TCL) 326 DF–CO2 327 Pump power density 174, 175 threshold 74 Q-switch 209 Q-switched laser 242 microchip laser 36 mode-locking 33 Q-switching 35 instability 119 QD-SESAM (quantum-dot semiconductor saturable absorber mirror) 69 Quantum-dot semiconductor saturable absorber mirror (QD-SESAM) 69 Quantum efficiency 173 Quenching fluorescence 257 Radiative decay time 258 RADICL (research and development iodine chemical laser) 341 Raman scattering 242 Rare-earth-doped solid-state laser 40 Rare-gas dimer 278 monohalide excimer 275 Rate
Index coefficient electron attachment 186 ionization 186 equation 5, 172, 297 vibrational 293 excitation 7 repetition 34 transmission 7 Reaction chain-, excitation 323 charge-transfer (Duffendack) 265 chemical 279, 289 enthalpy 306 electron 283 ionic recombination 279 kinetics 302 molecular 283 Recombination reaction, ionic 279 Recovery time 37 Reduced field strength 188 Reflector, Bragg distributed (DBR) 86, 245 saturable (SBR) 88 Regenerative amplification 8 Relation of Klein–Rosseland 256 Relaxation oscillation 5 time 83, 289 vibrational 302 Repetition frequency 284 rate 34 Research and development iodine chemical laser (RADICL) 341 Resonance–metastable laser 268 Resonator confocal 299 design 14 Response, impulse 121 Ring laser 73 Rosseland, Klein–, relation 256 Rotational excitation 185 level 291 vibrational transition 301, 306 Rovibrational transition 209 Sagnac interferometer 232 SAM (self-amplitude modulation) 36, 79, 85 Saturable absorber 34, 36, 79, 86 Fabry–Perot, antiresonant (A-FPSA) 88 fast 82, 106 fast, model 112 mechanism 83 mirror, dispersive (D-SAM) 89 semiconductor 88 Landolt-B¨ ornstein New Series VIII/1B1
Index slow 82 Bragg reflector (SBR) 88 Saturation fluence 73 gain, dynamic 110 intensity 206 SBR (saturable Bragg reflector ) 88 Sc2 O3 67 Scattering Brillouin, stimulated 242 Raman 242 SCPA (spatially evolving chirped-pulse amplification) 223 Sealed-off CO laser 211 laser 207, 211 system 205 Second harmonic generation (SHG) 236 kind collision of 9 phase transition of the 8 -order nonlinear susceptibility 92 Selectivity, directional 6, 7 Selfabsorption 20 amplitude modulation (SAM) 36, 79, 85 focusing 223, 238, 244 phase modulation (SPM) 90 coefficient 107 terminating laser 268 pulse laser 257 Semiconductor diode laser, edge-emitting 72 optical amplifier (SOA) 72 saturable absorber 88 mirror (SESAM) 34, 66, 76, 88 mirror, quantum-dot (QD-SESAM) 69 spectroscopy, ultrafast 83 SESAM (semiconductor saturable absorber mirror) 34, 66, 76, 88 device enhanced (E-SESAM) 89 low-field-enhancement resonant-like (LOFERS) 89 QD- (quantum-dot-) 69 Sesquioxide 67 SHG (second harmonic generation) 236 Shock tube 321 -wave explosion 344 Short-pulse amplification 230 Signal, small-, gain 206 Simulation Monte-Carlo particle 184 Landolt-B¨ ornstein New Series VIII/1B1
367 Single emitter 9 Singlet oxygen generator (SOG) 346 Sink, heat 16 Slab design 16 Slitting 17 Slow axis 74 direction 16, 20 -flow axial-flow laser 207 saturable absorber 82 Slowly-varying-envelope approximation 107 Small-signal gain 206 SOA (semiconductor optical amplifier) 72 SOG (singlet oxygen generator) 346 Soldering 13 Solid-state laser 11, 40 diode-pumped 13 rare-earth-doped 40 transition-metal-doped 40 Soliton effect 114 formation 96 mode-locking 115 Space-charge field 196 Spatial filtering 234, 239 hole burning 77 Spatially evolving chirped pulse amplification (SCPA) 223 Spectral filtering 236 -phase interferometry for direct electric-field reconstruction (SPIDER) 120, 124 Spectroscopy laser 33 semiconductor, ultrafast 83 X-ray 242 Spectrum, emission DF laser 327 HF laser 327 SPIDER (spectral-phase interferometry for direct electric-field reconstruction) 120, 124 Spiking time 5 SPM (self-phase modulation) 90 coefficient 107 -to-SAM (self-amplitude modulation) conversion 91 Spontaneous emission amplified (ASE) 217 Einstein coefficient for 172 Sputtering damage 263 Stability discharge 283 limit 261 pointing 234 Stabilization, arc- 263
368 Stable passive mode-locking 119 pulse generation 119 Stark broadening 176 State, vibrational 291 Statistics, Fermi–Dirac 84 Stimulated Brillouin scattering 242 emission, Einstein coefficient for 172 Storage time 230 energy- 225 Stripline CO2 laser 207 Structure, epitaxial 9 Structuring, sub-micron 244 Sub-micron -scale deposition 246 structuring 244 Subpicosecond pulse duration 219 Superposition, incoherent 22 Superradiance 5 Supersonic flow chemical 323 expansion- 290 nonequilibrium 297 Susceptibility, second-order nonlinear 92 Synchronization, phase-locked 232 System cooling 210 laser CO2 9 excimer 215 sealed-off 205 Talbot effect 23 TCL (transfer chemical laser) 325, 328, 330 DF–CO2 327 pulsed 326 TEA (transversely excited at atmospheric pressure) CO2 laser 317 discharge 192 laser 208, 284 Technique dry-etching 246 homogenization 239 Technology COIL (chemical oxygen iodine laser) 309 Temperature electron 184 vibrational 295 Temporal compression 215 Thermal conductivity of glasses 66 instability 189 lensing 11 load 11 Thin-disk laser 66 Yb3+ :YAG 78
Index Three-level laser process 258 Threshold condition 174 damage 81 laser 8, 256 pump 74 Time decay, radiative 258 recovery 37 relaxation 83 spiking 5 storage 230 energy 225 vibrational relaxation 289 Transfer charge-, reaction (Duffendack reaction) 265 chemical laser (TCL) 325, 328, 330 DF–CO2 327 pulsed 326 forward, laser-induced (LIFT) 247 frequencyelectron energy 183 electron momentum 183 Transformation hardening 13 Transition magnetic dipole 308 -metal-doped solid-state laser 40 phase-, of the second kind 8 rotational–vibrational 301, 306 rovibrational 209 vibrational–vibrational (V–V) 291 Transmission rate 7 Transverse excitation 313 -flow laser 208 Transversely excited at atmospheric pressure (TEA) CO2 laser 317 discharge 192 laser 208, 284 Traveling-wave excitation (TWE) 223 Tube, shock 321 T–V (translational–vibrational) process 291, 293 TWE (traveling-wave excitation) 223 Ultrafast semiconductor spectroscopy Unstable cavity 299 UV lithography 13
83
Vapor copper-, laser 255 metal-, laser 255 VECSEL (vertical-external-cavity surface-emitting laser) 39, 69 Velocity, electron drift 184 Vertical-external-cavity surface-emitting laser (VECSEL) 39, 69 Landolt-B¨ ornstein New Series VIII/1B1
Index Vibrational excitation 185 kinetics 293 rate equation 293 relaxation 302 time 289 –rotational transition 301, 306 state 291 temperature 295 translational– (T–V) process 291, 293 vibrational– (V–V) process 293 transition 291 Voltage, breakdown- 194 Volume, optical mode 11 V–V (vibrational–vibrational) process 293 V–V (vibrational–vibrational) transition 291
Landolt-B¨ ornstein New Series VIII/1B1
369 Wave detonation 319 traveling-, excitation (TWE) Waveguide laser 207 Wavelength, dual-, laser 216 Welding 13, 25 Writing, direct 19 X-ray microscopy 242 spectroscopy 242 Y2 O3 67 Yb3+ :YAG thin-disk laser Z-laser 23 Zeeman cell
10
78
223
