Photonics & Nanotechnology: Proceedings of the International Workshop and Conference on Icpn 2007 Pattaya, Thailand, 16-18 December 2007

Photonics & Nanotechnology

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Photonics & Nanotechnology

Proceedings of the International Workshop and Conference on ICPN 2007

Pattaya, Thailand

16 – 18 December 2007

edited by

Preecha Yupapin King Mongkut’s Institute of Technology Ladkrabang, Thailand

Prajak Saeung Department of Physics, Faculty of Science Ramkhamhaeng University, Thailand

World Scientific NEW JERSEY

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LONDON

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SINGAPORE

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TA I P E I

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Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

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PHOTONICS AND NANOTECHNOLOGY Proceedings of the International Workshop and Conference on ICPN 2007 Copyright © 2008 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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ISBN-13 978-981-277-971-7 ISBN-10 981-277-971-X

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Benjamin - Photonics and Nanotechnology.pmd1

10/31/2008, 11:50 AM

v

PREFACE

Nonlinear optical physics has been to optical engineers and scientists a very interesting subject, especially, when the nonlinear behaviors of light in optical devices generate benefits in some cases. This book is entitled ‘Photonics and Nanotechnology’, where the papers were selected by the International Conference on Photonics and Nanotechnology (ICPN) committees during the conference in the year 2007, which was held in Pattaya, Thailand, from December 16 –18, 2007. The conference was organized by the Department of Applied Physics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang (KMITL), Thailand. Twelve papers out of sixty were selected, and the extended versions were slightly different from the conference versions. All papers concern optical devices and materials, especially, the nonlinear behaviors and their benefits. The conference was partially supported by the Department of Applied Physics, Faculty of Science, KMITL, Optical Society of America (OSA), The Institute of Optical Engineering Society (SPIE), IEEE-LEOS (Thailand), National Electronics and Computer Technology Center (NECTEC), Thailand and Ch. Karnchang (Thailand). There were some keynote and invited talks involved from the United States of America, Europe and Japan. Professor Yupapin from KMITL was the general chair of the conference. He had pushed a lot of effort and contributions to make the conference a success. Finally, we expect that the proceedings volume will be useful to the optical researchers and society. Preecha P. Yupapin

CONTENTS

Preface

v

Capacitance-Voltage Characteristics of InN Quantum Dots in AlGaN/GaN Heterostructure A. Asgari and M. Afshari Bavili

1

A Comparison of Different Coherent Deep Ultraviolet Generations Using Second Harmonic Generation with the Blue Laser Diode Excitation C. Tangtrongbenjasil and K. Konaka

7

Application of Reflection-Spectrum Envelope for Sampled Gratings X. He, D.N. Wang, D. Huang and Y. Yu

18

Temperature-Dependent Photoluminescence Investigation of Narrow Well-Width InGaAs/InP Single Quantum Well W. Pecharapa, W. Techitdheera, P. Thanomngam and J. Nukeaw

24

Shooting Method Calculation of Temperature Dependence of Transition Energy for Quantum Well Structure B. Jukgoljun, W. Pecharapa and W. Techitdheera

31

Design of Optical Ring Resonator Filters for WDM Applications P. Saeung and P.P. Yupapin

35

Chaotic Signal Filtering Device Using the Series Waveguide Micro Ring Resonator P.P. Yupapin, W. Suwancharoen, S. Chaiyasoonthorn and S. Thongmee

42

An Alternative Optical Switch Using Mach Zehnder Interferometer and Two Ring Resonators P.P. Yupapin, P. Saeung and P. Chunpang

48

Entangled Photons Generation and Regeneration Using a Nonlinear Fiber Ring Resonator S. Suchat, W. Khunnam and P.P. Yupapin

52

Nonlinear Effects in Fiber Grating to Nano-Scale Measurement Resolution P. Phipithirankarn, P. Yabosdee and P.P. Yupapin

60

Quantum Chaotic Signals Generation by a Nonlinear Micro Ring Resonator C. Sripakdee, W. Suwancharoen and P.P. Yupapin

65

Investigation of Photonic Devices Pigtailing Using Laser Welding M.M.A. Fadhali

72

A Soliton Pulse in a Nonlinear Micro Ring Resonator System: Unexpected Results and Applications P.P. Yupapin, S. Pipatsart and N. Pornsuwancharoen

81

Author Index

109

1

CAPACITANCE-VOLTAGE CHARACTERISTICS OF InN QUANTUM DOTS IN AlGaN/GaN HETEROSTRUCTURE

A. ASGARI1 ,2 , M. AFSHARI BAVILI1 1 Photonics-Electronics

Group, Research Institute for Applied Physics, University of Tabriz, Tabriz 51665-163, Iran 2 School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Crawley, WA 6009, Australia E-mail: [email protected]

In this paper the capacitance-voltage characteristics of InN quantum dots embedded in AlGaN/GaN heterostructure has been studied. This work has been done for the InN quantum dots with different quantum dot size, and energy dispersion and for the AlGaN/GaN heterostructures with different Al mole fraction and number of quantum wells in different temperatures. The presence of InN quantum dot will cause Gaussian shape in capacitance-voltage characteristics approximately, where the peak of curves can evidence the position of quantum dots in the structures. Our calculation results show the Gaussian shape (or negative differential capacitance) is much higher at low temperature and for quantum dots with low energy and higher size dispersion. Keywords: AlGaN/GaN Heterostructures; InN Quantum Dots; capacitance.

1. Introduction The progress of epitaxial growth technology has been responsible for many new structures based on lowdimensional system where quantum effects were clearly observed. Self assembled systems like the quantum dots (QDs) are very important examples of this advance. Recently, considerable interest has been focused on electronic devices based on semiconductor heterostructures containing quantum dots, in which the motion of quasi-particles is quantized along all three coordinates. In order to develop the application of these devices, it is necessary to investigate the influence of quantum dot on electronic properties of these semiconductor structures.1 Capacitance spectroscopy is a highly efficient method for studying of electrical properties of these structures. Recently, several research groups reported some results about AlGaAs/GaAs heterostructures containing a layer of self-organized InAs QDs.2 But Nitride based nanostructures have significantly different properties as compared to GaAs based quantum wells and QDs. GaAs has zinc blend crystal structure, but III-V nitrides are available in both zinc blend and wurtzite crystal structure which leads to strong built in piezoelectric fields in heterostructures. This can induce red shift in GaN/AlN self-organized QDs. 3 In this paper we present the results of capacitance-voltage studies of the AlGaN/GaN heterostructures containing a layer of InN QDs. 2. Model Description Consider the modeled sample structure as Fig. 1. The capacitance of the structure is the sum of the bulk capacitance and QDs capacitance. In order to determine the capacitance, one has to know the conduction band profile and all quantized state to calculate the electron density function and Fermi energy level using self consistent solution of Schrdinger and Poisson equations. It has been done in this article using numerical Numerov’s method.4–6 To calculate the charge density in the structure, it has been assumed that the plane containing the QDs acts like an equipotential surface and also only the ground state of quantum dots has been occupied. Also, we consider the plane containing QDs and the highly doped buffer layer are near the electrostatic equilibrium.7 The capacitance in devices as Schottky device is directly related with the charge ∂Q where inside the depletion region and can be expressed by C = ∂V Q = Qbulk + QQD = qS(ND W − NQD )

(1)

2

Fig. 1.

The modeled sample structure and Schematic conduction band profile.

And S is the Schottky contact area, ND is the bulk doping density, W is the width of depletion region and equal to in the Fig. 1. Solving Poisson equation for the different applied voltage the capacitance can be obtained as:7 s S qND  Cbulk = +S (2) dSL 2(φB − V ) CQD

Z ∞    d d · D(E, V )f (E, V )dE = qS t dV 0

(3)

where  NQD D(E, V ) = √ exp −2 π∆E

E + EQD + q dt V ∆E

and f (E, V ), the Fermi-Dirac energy distribution function, is f (E, V ) = 1 + exp



1  q(E − qV ) kT

!2  

(4)

(5)

Also  is the GaN dielectric constant, t and d are the structure width as expressed in Fig. 1, φ B is the Schottky barrier high, ∆E is the energy dispersion characteristics which expresses the effects of the dots size dispersion.2 EQD is the electron level within the QDs. To calculate the QD energy levels, it has been assumed the QDs have spherical shape and the Fermi level in the dots was the same as in highly doped substrate.8 To find the CQD , the integral in Eq. (2.3) has been solved numerically. 3. Results and Discussion The device structure as shown in Fig. 1 contains an AlGaN/GaN superlattice of N quantum wells with 1.5 nm thickness of GaN and 3 nm of Alx Ga1−x N barrier width, a layer containing InN QDs, a 10 nm GaN layer between QDs layer and superlattice, and a 20 nm Si-doped GaN layer with doping density of 8 × 10 4 cm−3 . The QDs layer includes a carrier density of 6.5 × 1010 cm−2 . The Schottky contact area and barrier high is 2 × 10−7 cm2 and φB = 1.3x + 0.84 (eV), respectively, where x is the Al mole fraction in the barrier. The capacitance-voltage characteristics of these structures have been analyzed in different physical situations. For the applied voltage range from −1 to +1 V, the dominant behavior of capacitance comes from

3

Fig. 2. The variation of Capacitance of AlGaN/GaN heterostructures with InN QDs as function of applied voltage at different temperature. The number of quantum well in super lattice is n = 30 and Al mole fraction is x = 0.3.

Fig. 3. The variation of Capacitance of AlGaN/GaN heterostructures with InN QDs as function of applied voltage at T = 100 K, EQD = 80 meV and for different energy dispersion characteristic. The number of quantum well in super lattice is n = 30 and Al mole fraction is x = 0.3.

the QD capacitance. As one can see from Figs. 2, 3, and 4, the total capacitance increases with increasing of applied voltage from −1 V, due to the filling of the quantum dots, showing a peak at voltage range from V = −0.25 to 0.25. The peak broadening is due to the fluctuations in the dot sizes. If the voltage increases, the total capacitances decreases and for further increases trend to bulk capacitance because the dots are completely discharge. Figure 2 shows the variation of the capacitance as function of applied voltage at different temperature. As evident from the figure, the QD capacitance for low temperature is higher than the

4

Fig. 4. The variation of C-V characteristics of AlGaN/GaN heterostructures with InN QDs at T = 100 K, ∆E = 110 meV and for different quantum dot energy. The number of quantum well in super lattice is n = 30 and Al mole fraction is x = 0.3.

high temperatures capacitance. Also with the increasing of the temperature, the peak positions shift toward the low voltages. This is caused by the dynamical process involving the capture/emission rate of the dots. The energy dispersion characteristics, ∆E, is 110 meV and EQD is the 80 meV in these calculations. Figure 3 shows the variation of the capacitance as function of applied voltage at different energy dispersion characteristics, in T = 100 K and for dots with EQD is the 80 meV. As evident from the figure,

Fig. 5. The variation of C-V characteristics of AlGaN/GaN heterostructures with InN QDs at T = 100 K, ∆E = 110 meV, EQD = 80 meV and for different Al mole fraction. The number of quantum well in super lattice is n = 30.

5

Fig. 6. The variation of C-V characteristics of AlGaN/GaN heterostructures with InN QDs at T = 100 K, ∆E = 110 meV, EQD = 80 meV and for different number of quantum well in super lattice, the Al mole fraction is x = 0.3.

the QD capacitance for low energy dispersion characteristic is very small and total capacitance behave as bulk capacitance. With increasing the energy dispersion characteristic, the QD show a higher negative differential capacitance. In this case there is only a small change in the peak positions which shift toward the high voltages. Also, as shown in Fig. 4, the total capacitance as function of applied voltage at different QD energy level, in T = 100 K and for the quantum dots with energy dispersion characteristic of 110 meV is expressed. As evident from the figure, the QD capacitance for dots with high energy level is very small and total capacitance behaves as same as bulk capacitance. With decreasing the QD energy level, the QD capacitance shows a higher negative differential capacitance. In this case there is not any change in the peak positions along the voltage axes. To calculate the C-V characteristic in Figs. 3, 4, and 5, 30 quantum wells has been taken into account in super lattice and Al mole fraction in the barriers is x = 0.3. The effects of AlGaN/GaN heterostructures on C-V characteristics have been analyzed too. The variation of Capacitance as function of applied voltage for the structures with Al mole fraction of 0.1 to 1 in the super lattice barriers are shown in Fig. 5. As evident from the figure and Eq. (2.2), the capacitance decreases with increasing the Schottky barrier potential which varies linearly with Al mole fraction. So, for the structures with higher Al mole fraction, the quantum dots show more negative differential capacitance. Also the calculation has been done for the structures with different number of quantum well in the superlattice. Figure 6 shows the results of this calculation for the number of quantum well of n = 5, 10, 20, 30, 40, and 50. It is clearly known that with increasing the distance between the capacitor plates, the electrical capacitance decreases. So to see the quantum dot capacitance effect, it’s better to have the structures with low bulk capacitance. 4. Conclusions In summary, this paper presented a study of the capacitance-voltage characteristics in the InN quantum dots system embedded in a GaN matrix in AlGaN/GaN heterostructure. The proposed is based on the analysis of the solution of the Poisson and Schrdinger equations and in the well defined relationship between capacitance and density of sates. The calculation results shoe that the presence of InN quantum dot will cause a negative differential capacitance which can evidence the position of quantum dots in the structures. Also, our calculation results show that the negative differential capacitance is much higher at low temperature and for quantum dots with low energy and higher size dispersion.

6

References 1. 2. 3. 4. 5. 6. 7. 8.

A. A. J. Chiquito, et al., Phys. Rev. B 61, 5499 (2000). P. N. Brounkov, et al., Semiconductors. 32, 1096 (1998). A. Bagga, et al., Phys. Rev. B 68, 155331 (2003). A. Asgari, Study of transport properties of AlGaN/GaN Heterostructure, Physics Faculty, University of Tabriz, Ph.D. Thesis. , 84 (2003). A. Asgari, et al., J. Appl. Phys. 95, 1185 (2004). A. Asgari, et al., Materials Science and Engineering C 26, 898 (2006). Ph. Lelong, et al., Physica E 2, 678 (2006). C. E. Pryor, et al., Phys. Rev. B 72, 205311 (2005).

7

A COMPARISON OF DIFFERENT COHERENT DEEP ULTRAVIOLET GENERATIONS USING SECOND HARMONIC GENERATION WITH BLUE LASER DIODE EXCITATION C. TANGTRONGBENCHASIL AND K. NONAKA Department of Electronic and Photonic Systems Engineering, Frontier Engineering Course, Kochi University of Technology, Tosayamada, Kami City, Kochi Prefecture 782-8502, Japan

Nano-focus beam applications of short wavelength approximately 220 nm now play important roles in engineering and industrial sections. At present, light sources at approximately 220 nm are commercially available but large size, difficult to maintain, and expensive. Compact wavelength tunable and cost effective light sources at approximately 220 nm are required. Laser diode with sum-frequency generation methods are employed to generated the shorter wavelength approximately 220 nm. This paper presents comparison of second harmonic generation schemes using a nonlinear optic crystal and two types of laser diode, which are a 440 nm single mode blue laser diode and a 450 nm multimode Fabry-Perot blue laser diode, has potential to generate wide tunable coherent deep ultraviolet-c at approximately 220 nm. Using the blue laser diode with the sum-frequency technique, a high second harmonic power is hardly observed due to low conversion efficiency. The best performance of second harmonic generation using blue laser diode, nonlinear optic crystal, and an high-Q external cavity laser diode was observed as 1.1 µW second harmonic ultraviolet-c power at 224.45 nm ultraviolet-c wavelength and 5.75 nm ultraviolet wavelength tunability. In addition, the improvement of increasing second harmonic power approximately 220 nm and the limitation of wavelength tuning of short wavelength are also theoretically discussed in this paper.

1. Introduction Coherent short wavelength ultraviolet C (UV-C) approximately 220 nm is very useful for nano-focus beam applications such as beam lithography for very large scale integrated circuit (VLSI) and molecular spectroscopy. Excimer lasers and sum-frequency from solid state lasers, which are able to generate very high power1 but these lasers have very large bodies, complex structures, fixed wavelength, high manufacturing costs, and high maintenance costs, are conventional coherent UV sources at the short wavelength approximately 220 nm. Due to these disadvantages of excimer UV lasers and solid state UV lasers, compact, simple to fabricate, cost effective, and coherent wavelength tunable flexibility of UV sources are in demanded. One of the possible solutions is second harmonic generation (SHG) with nonlinear optic crystal and laser diode (LD). Due to advance technology in optoelectronics, small size LD can generate high optical power as 300 mW for continuous wave at 20ºC2,3. The SHG researches have been reported for 4 decades4-6. Most of SHG researches were implemented with gas laser at wavelength longer than 780 nm resulting fixed wavelength4-6. Only a few researchers reported the SHG for short wavelength approximately 220 nm, due to very low conversion efficiency, a complex setup, insufficient LD power, oscillation quality, and crystal efficiency7-10. External cavity diode laser (ECDL) with nonlinear optic crystal, that is one of the solutions for SHG researches, has been reported7-10. This paper present a performance comparison of SHG using a 440 nm single mode blue LD with a BBO nonlinear optic crystal and a 450 nm multimode Fabry-Perot blue LD with a BBO nonlinear optic crystal. The mathematical estimation of SH power and the improvement of SHG conversion efficiency are also discussed. 2. Theoretical Background Dmitriev, et al. and Mills published simple SHG mathematical estimations when uniform beam is employed4-5. However, Dmitriev, et al. and Mills’ equations are not able to estimate properly the SH power. Boyd and Kleinman

8

published a SHG mathematical model including phase mismatch factor, focal position factor, strength of focusing factor, birefringence factor, and absorption factor, that is suitable to estimate the SH power when focusing Gaussian beam is employed6. In this paper, a 440 nm fundamental single mode wavelength blue LD with a BBO nonlinear optic crystal and a 445 nm and fundamental wavelength multimode Fabry-Perot blue LD with a BBO nonlinear optic crystal were implemented to generate tunable coherent deep UV-C. The shortest usable wavelength of the BBO crystal is 205 nm, due to phase matching angle limitation of fundamental and SH waves11. Using Sellmeier’s equations4,5, operating refractive index, phase matching angle, walk-off angle, and effective conversion coefficient can be theoretically obtained. The SH output power ( P2ω ) can estimated by6, P2ω = Pω2 L

2ω 2 d eff2 k F 2 πε o noF neUV c 3

⋅

1 4ξ

ξ (1+ µ ) ξ (1+ µ )

∫

∫

e −[ β

2

(τ −τ ′ )2 + κ (τ −τ ′ ) − iσ (τ −τ ′ )]

e − i (τ ′ −τ )]

− ξ (1− µ ) − ξ (1− µ )

dτ dτ ′

(1)

where Pω is fundamental power [W], L is crystal length [m], deff is conversion efficiency, kF is fundamental wave propagation constant, ε0 is Planck’s constant = 8.854 × 10−12  VAiims  , c is light speed in free space = 3 × 108 [m s ] , noF is ordinary fundamental wave refractive index, neUV is extraordinary SH wave refractive index, b is confocal ρ 1 parameter, ξ is strength of focus = L , µ is focal position, β is birefringent parameter = ξ 2 Lk , ρ is walk off angle b

F

[radian], κ is absorption factor, and σ is phase mismatch. When σ = 0, focal position is at the center of the BBO crystal or µ = 0, and no absorption or κ = 0, the optimized SH output power ( P2ω ) can be calculated as6, 2ω 2 d eff2 k F

1 P2ω = Pω L ⋅ 2 3 πε o noF neUV c 4ξ 2

ξ ξ

e −[ β (τ −τ ′) ] ∫ ∫ e−i (τ ′−τ )] dτ dτ ′ , −ξ −ξ 2

2

(2)

β = 0 if and only if ρ = 0 that is invalid at either short fundamental wavelength as 440 nm or 445 nm. ρ are equal to 0.067 radian and 0.073 radian, at 440 nm fundamental wavelength and 445 nm fundamental wavelength, respectively. Consequently, β are equal to 13.06 radian and 14.05 radian when 100 mm focal length of focusing lens was employed for 440 nm fundamental wavelength and 445 nm fundamental wavelength, respectively. Moreover, effective focal length, which is a very important factor to optimized the SH conversion efficiency, is required to estimate but it is not included in Eq. (1) and Eq. (2). The effective focal length can be estimated by6, Leff =

πb 2

=

2π noF f wc ,

(3)

where f is operating focal length of focusing lenses and wc is beam radius of the collimated input beam. The effective focal length is directly proportional to the confocal parameter. Equation 3 implies that there is an optimum effective focal length of any arbitrary confocal parameter depending on the focal length of focusing lens. By the symmetry of focusing and defocusing with the identical focal lengths of focusing lenses, consequently the optimized crystal length is equal to 2Leff . In addition, the confocal parameter is directly proportional to the operating focal length, so longer focal length requires longer crystal length or longer SH interaction length to optimize the conversion efficiency. Figure 1 shows simulations of SH output power vs fundamental input power with various focal lengths and optimum nonlinear optic crystal lengths when confocal parameter = 0.084. Even confocal parameter is fixed; the conversion efficiency can be improved by implementing long focal length and long nonlinear optic crystal length. Moreover, it implies that long focal length requires long interaction length or long crystal length to optimize SH output power. Figure 2 shows simulations of SH output power vs fundamental input power with various confocal parameters when focal length of focusing lenses is 100 mm and nonlinear optic crystal length is 10 mm. Even focal length of focusing lens and interaction length are fixed; the conversion efficiency can be improved by constructing the higher confocal parameter system. However, if the higher value of confocal parameter is required, the optic size including lens diameter, nonlinear optic crystal length, nonlinear optic crystal crosssectional area, and optical operating distance must be enlarged.

9

Fig. 1. Simulations of SH output power vs fundamental input power with various focal length of focusing lenses and optimum nonlinear optic crystal lengths when confocal parameter = 0.084.

Fig. 2. Simulations of SH output power vs fundamental input power with various confocal parameters when focal length of focusing lenses is 100 mm and nonlinear optic crystal length is 10 mm. On the other hand, narrow wavelength tolerance or single longitudinal mode oscillation is one of requirements to realize theoretical SHG efficiency that must be enhanced. The wavelength tolerance must be control as narrow as possible by oscillation wavelength selection system e.g. grating and feedback mirror, etc12-16. If the fundamental

10

wavelength is single longitudinal mode oscillation, consequently the SH wave is also single longitudinal mode oscillation. The SH wavelength tunablility depends on the angle and position of feedback fundamental light passing through grating back to LD. The feedback angle of fundamental light must be set as close as possible to the polarization plane of LD, so that narrow single mode fundamental wavelength can be realized. To tune fundamental wavelength, the position shift with respect to the orthogonal of polarization plane must be tuned. In contrast, narrowing wavelength tolerance can cause phase mismatch. To overcome this problem, the nonlinear optic crystal angle must be properly adjusted to matching angle.

3. Coherent Deep UV-C Generation Setups and Experimental Results In this section, 3 experimental setups of coherent deep UV-C generations approximately 220 nm basing on SHG scheme are discussed. A single mode blue LD approximately 440 nm and a multimode Fabry-Perot blue LD approximately 450 nm are employed as fundamental wavelength light sources. The single mode blue LD 440 nm can provide maximum continuous fundamental wave only 60 mW. To enhance higher continuous fundamental power, the multimode Fabry-Perot blue LD 450 nm, which is able to provide up to 300 mW when LD temperature is proper controlled at 25ºC3, was implemented instead of the 440 nm single mode blue LD. The detail performance and comparison will be discussed in later section.

3.1. SHG with Feedback Grating as a Wavelength Selector Configuration The simple and compact coherent deep UV-C generation approximately 220 nm is shown in Fig. 3. The single mode blue LD approximately 440 nm was employed as fundamental light source that can provide maximum continuous fundamental wave at 60 mW. The single mode blue LD was installed in a mount that can control the LD temperature constantly and also provide a quasi-collimating beam. LD waveguide rear-end has approximately 90% high reflection (HR) coating but LD waveguide front-end has coating reducing a few percentage of reflectivity decreases the catastrophic optical damage (COD) damaging. The LD was controlled at 20ºC. The quasi-collimating beam has beam profile of the effective parallel and perpendicular beam axes are 3.5 mm and 1.5 mm, respectively. The quasi-collimating beam was focused at the center of 10 mm length BBO crystal by a 100 mm bi-convex lens. Consequently, the effective parallel and perpendicular beam waist at the focusing region are 74.68 µm and 32.01 µm, respectively. The maximum average power of the fundamental wavelength inside the cavity was 64.83 mW. Thus, a 3.45 kW/cm2 excitation is expected at around focus region. The output radiation from BBO optic crystal consisting of approximately 440 nm fundamental wavelength and approximately 220 nm SH wavelength were, consequently, collimated and reflected by a 100 mm concave mirror to obtain the similar quasi-collimating beam profile as launching from LD mount. Then, the approximately 440 nm fundamental wavelength and the approximately 220 nm SH wavelength were completely separated by prism at Brewster angle for the 440 nm fundamental wave. To stabilize and narrow wavelength tolerance, the 440 nm fundamental wave was launched to reflection grating that has 40% transmission and 60% reflection. The 40% transmission from the reflection grating was employed to monitor the fundamental wavelength tolerance. To enhance the external high-Q ECLD and to narrow the fundamental wave, the 60% reflection from the reflection grating must be fed to the same path back to the LD mount. In addition, if the fundamental wave is narrow and single mode, the SH wave would also narrow and single mode. Consequently, the conversion efficiency of narrow and single mode wave is better than wide and multimode wave. To tune the wavelength, slight adjusting the angle of the reflection grating with respect to LD polarization plane can stabilize and tune fundamental wavelength and SH wavelength. Generated UV light was measured by the photomultiplier tube with transimpedance amplifier as shown in Fig. 3. Figure 4 shows experimental results of SHG with feedback grating as the wavelength selector and examples of operating fundamental wavelength stabilities. 220-nm range deep UV-C is too close to the limiting edge of crystal matching condition and BBO crystal absorption band. Consequently, the conversion efficiency is lower than near UV wavelength. The maximum generated SH power was obtained as 0.165 µW at 218.45 nm SH wavelength when

11

Fig. 3. SHG experimental setup with internal wavelength separator.

Fig. 4. Experimental results of SHG with internal wavelength separator and examples of operating fundamental wavelength stabilities. 64.83 mW fundamental power was enhanced. The SH tunability is 1.45 nm in range of 218.45 nm – 219.9 nm. The 3-dB spectrum widths (∆λ) of 436.9 nm fundamental wave and 439.8 nm fundamental wave are 0.035 nm and 0.039 nm, respectively. In addition, the extinction ratio of 436.9 nm fundamental wave and 439.8 nm fundamental wave are 24.10 dB and 29.56 dB, respectively. The wavelength separator was located inside the SHG cavity, it caused the difficulty of minimizing phase mismatch. When operating fundamental wavelength was changed, the crystal angle must be re-tuned. In addition, the position of optical spectrum analyzer (OSA) must be re-tuned to monitor the stability of operating fundamental wavelength. Moreover, 1.45-nm narrow SH wavelength tunability wave was observed.

12

3.2. SHG with Transmission Grating as a Wavelength Selector Configuration Due to the difficulty of re-tuning of SHG cavity and OSA position in section 3.1, the wavelength separator (prism) should be located outside the SHG cavity. Because of the polarizations of fundamental wavelength and SH wavelength differ by 90º, so a 220 nm dichroic mirror was employed to separate approximately 220 nm wave and approximately 440 nm wave. In addition the feedback light in section 3.1 is only 60%, so a transmission grating and a 440 nm high reflection (HR) flat mirror were implemented as wavelength selector. In addition the transmission grating and the 440 nm HR flat mirror were also employed as an external high-Q ECDL enhancement. The transmission grating has splitting ratio of 0th order and 1st order by 5% and 95% of incident wave, respectively. The 0th order from the transmission grating was employed to monitor the stability of the operating fundamental wave. The OSA can be fixedly place to monitor the stability of the operating fundamental wave because the position of 0th order does not depend on the transmission grating angle. Adjust the angle of feedback mirror is able to tune and stabilize the operating wavelength in this setup. In addition, employing the transmission grating with the 440 nm HR feedback mirror is able to improve the Q factor of ECLD. Figure 5 shows SHG experimental setup with transmission grating as the wavelength selector configuration. In practice, the 220 nm dichroic mirror is not able to reflect only 220 nm wave but a few percentages of 440 nm wave is also reflected. To separate 220 nm wave out of 440 nm wave completely, the prism must be employed. With the similar of beam profile as in section 3.1 and the maximum average power of the fundamental wavelength inside the cavity was 64.36 mW. Thus, a 3.43 kW/cm2 excitation is expected at around focus region.

Fig. 5. SHG experimental setup with external wavelength separator. Figure 6 shows experimental results of SHG with external wavelength separator and examples of operating fundamental wavelength stabilities. The maximum generated SH power was obtained as 0.194 µW at 218.25 nm SH wavelength when 64.36 mW fundamental power was enhanced. The SH tunability is 1.85 nm in range of 218.25 nm – 220.1 nm. The 3-dB ∆λ of 436.6 nm fundamental wave, 438.2 nm fundamental wave, and 440.2 nm fundamental wave are 0.040 nm, 0.039 nm, and 0.042 nm, respectively. In addition, the extinction ratio of 436.6 nm fundamental wave, 438.2 nm fundamental wave, and 440.2 nm fundamental wave are 25.73 dB, 23.55 dB, and 29.47 dB, respectively. This configuration can be improved by enhancing higher fundamental power. Because of high-Q ECDL feed operating fundamental wave back to LD mount with similar beam profile, so SH power can also be detected in front of LD mount.

13

Fig. 6. Experimental results of SHG with external wavelength separator and examples of operating fundamental wavelength stabilities.

3.3. Symmetry SH Detection Configuration with Multimode Blue LD The enhancement of higher fundamental wave power is one of the important factors to generate high SH power, so a 450 nm multimode Fabry-Perot blue LD was employed. The 450 nm multimode Fabry-Perot blue LD is able to generate continuous power up to 300 mW when LD temperature is controlled at 25ºC3. However, the number of oscillation mode increases when the injection current increases. Multimode oscillation reduces the SHG efficiency due to narrow crystal matching tolerance. Moreover, the SHG from section 3.2 can be improved by bi-directional detection; in front of LD mount and before the transmission grating (see Fig. 7). However, to simplify the experimental setup of bi-directional detection, symmetry configuration is extremely required. Figure 7 shows symmetry SH detection configuration multimode blue LD. In this section, two 100 mm plano-convex lenses were employed to focus quasi-collimating fundamental wave from LD mount and defocus to re-collimate and to obtain similar quasi-collimating fundamental wave beam profile as launching from LD mount. The polarizations of fundamental wavelength and SH wavelength differ by 90º as mentioned in section 3.2. Two dichroic mirrors were placed before (forward detection) and after (backward detection) plano-convex lenses (see Fig. 7) to separate the 225 nm SH wave out of SHG cavity and to maintain the 450 nm fundamental wave in the SHG cavity. In practice, the reflected 225 nm wave from the dichroic mirror always contains a few percentage of the 450 nm wave, even the dichroic mirrors are exactly placed at the Brewster angle. So the reflected wavelength can be completely separated by prisms that were set to Brewster angle for the 225 nm SH wavelength transparency to obtain pure 225 nm coherent deep UV-C. With the similar of beam profile as in section 3.1 and 3.2, the maximum average power of the fundamental wave inside the cavity of multimode Fabry-Perot blue LD can be obtained 103.30 mW, due to imperfect of temperature controller. Thus, a 5.50 kW/cm2 excitation is expected at around focus region. Figure 8 shows experimental results of SHG at 448.9 nm fundamental wavelength and the variation of fundamental power vs. fundamental wavelength. The maximum generated SH power was obtained as 1.1 µW at 224.45 nm SH wavelength when 103.30 mW fundamental power was enhanced. The 1.1 µ W was the total detections of 0.67 µW forward detection and 0.34 µW backward detection. Using bi-directional detection technique, an approximately 50% of SH power was obtained at backward detection, due to surface loss and scattering from

14

Fig. 7. Symmetry configuration of SHG with external wavelength separator.

Fig. 8. Experimental results of SHG at 448.9 nm and the variation of fundamental power vs. fundamental wavelength. fundamental wave, and 455.4 nm fundamental wave were small as 0.040 nm and 0.050 nm, respectively. In addition, the average extinction ratio was approximately 25 dB. From this setup, the transmission grating was set and fixed at 60º that maximized the splitting ratio of 0th order and 1st order of transmission. Only adjusting the angle of the 440 nm HR flat mirror can tune the operating fundamental wavelength. The difference position and angle of feedback fundamental light can cause wavelength tunability and oscillation mode suppression of fundamental light of multimode Fabry-Perot blue LD. Consequently, fundamental power of nearby wavelength is decreased, due to mode suppression. In addition, the limitation of wavelength tuning range is gain profile LD waveguide. At the shortest wave and longest wave, the operating fundamental power was decreased by 2.1 dB comparing with 448.9 nm fundamental wave that has the maximum fundamental power at 103.30 mW. Consequently, the SH power at the shortest wave and longest wave in this setup were decreased as 0.6 dB comparing with 224.45 nm SH wave

15

that has the maximum generated UV power at 1.1 µW. The total SH powers of shortest wave and longest wave in this system were obtained as 0.101 µW and 0.104 µW, respectively.

4. Discussion The 3 different coherent deep UV-C generation experimental setups and experimental results were explained. Table 1 shows performance comparison of 3 experimental SHG setup. The SHG with feedback grating as a wavelength selector configuration can generate the maximum UV power only 0.165 µ W at 218.45 nm SH wavelength when 64.83 mW fundamental power was enhanced by the 440 nm single mode blue LD. The SH tunability was only 1.45 nm in range of 218.45 nm – 219.9 nm. Because of the SH wavelength tunability was too narrow as 1.45 nm, the wavelength separator (prism) should be located outside SH cavity by inserting the 220 nm dichroic mirror to reflect approximately 220 nm wave outside the SH cavity and maintain the fundamental wave inside the SH cavity. In addition, to improve the fundamental feedback power, the transmission grating, which has the extinction ratio of 5% and 95% of 0th order and 1st order, and the 440 nm HR flat mirror were employed to reduce feedback loss and to enhance high-Q ECLD. From this improvement, the maximum UV power can be generated as 0.194 µW at 218.25 nm SH wavelength when 64.36 mW fundamental power was enhanced by the 440 nm single mode blue LD. The SH tunability was improved by 0.5 nm to be 1.85 nm in range of 218.25 nm – 220.1 nm. The UV generation basing on SHG scheme can generate UV in both of forward direction that was enhanced directly from LD and backward direction that was enhanced indirectly from LD but from feedback fundamental light from the 440 nm HR flat mirror. To assure the experimental high-Q cavity symmetry for bi-directional UV detection, two of the 220 nm dichroic mirrors were employed to separate the SH wave outside the SHG cavity and maintain fundamental wave inside the SHG cavity. The maximum generated UV power was

Table 1. Performance comparison of 3 experimental SHG setups. SHG setup types

Comparison topics Type of LD

SHG with feedback grating as the wavelength selector

SHG with transmission grating as the wavelength selector

440 nm Single mode blue LD

Symmetry SH detection with multimode blue LD 450 nm multimode Fabry-Perot blue LD

Maximum enhanced fundamental power inside SHG cavity

64.83 mW

64.36 mW

103.30 mW

Maximum generated SH power

0.165 µW at 218.45 nm

0.194 µW at 218.25 nm

1.1 µW at 224.45 nm

Weak points of generated SH power

1. Too low enhanced fundamental power low

1. Difficulty of LD temperature control

2. Low confocal parameter

2. Low confocal parameter

SH wavelength tunability

1.45 nm in range of 218.45 nm – 219.9 nm

Type of wavelength selection and feedback

Only reflection grating

Transmission grating and flat mirror

Wavelength tuning technique

Adjust the angle of refection grating

Adjust only the angle of feedback mirror without adjust the angle of transmission grating

Weak point of wavelength tuning technique

Low fundamental feedback light causes difficulty in wavelength tuning

1.85 nm in range of 218.25 nm – 220.1 nm

Waveguide characteristic of single mode blue LD limits wavelength tuning

5.75 nm in range of 221.95 nm – 227.7 nm

Waveguide characteristic of multimode Fabry-Perot blue LD limits wavelength tuning

16

obtained as 1.1 µW at 224.45 nm SH wavelength when 103.30 mW fundamental power was enhanced by the 450 nm multimode Fabry-Perot blue LD. The 1.1 µW was the total detections of 0.67 µW forward detection and 0.34 µW backward detection. Using bi-directional detection technique, an approximately 50% of SH power was obtained at backward detection, due to surface loss and scattering from lenses, BBO crystal, transmission grating, and flat mirror. Using the multimode LD, the SH tunability was extremely improved by 3.9 nm to be 5.75 nm in range of 221.95 nm – 227.7 nm. On the other hand, there are 2 possibilities to improve the SHG conversion efficiency; 1) increase the enhanced fundamental power or 2) increase the confocal parameter. Increasing the enhanced fundamental power is easy method but it consumes a lot of energy whereas increasing the confocal parameter requires beam expander and beam reducer that causes enlarge optical size. To improve the wavelength tunability, the high feedback fundamental power is required to reduce wavelength tolerance and suppress nearby wavelength. By this technique, the high performance grating and high refection fundamental power are required. 5.

Conclusions

In summary, using the single mode blue LD with flexible wavelength tunable and high-Q ECLD can observed similar level of fundamental power at every tuned wavelength resulting similar level of SH generated UV power can also be obtained. In contrast, using the multimode Fabry-Perot blue LD with wide wavelength tunability and single mode oscillation high-Q ECLD cannot provide the similar level of fundamental power at every tuned wavelength. The maximum fundamental power was observed as 103.30 mW at 448.9 nm whereas the maximum fundamental power of the shortest and the longest wavelength were observed as 55 mW which was approximately 2.1 dB decreasing resulting different levels of SH generated UV power were observed which was approximately 0.6 dB difference. The experimental results of our experimental setups were well matched to the Boyd and Kleinmann model estimation. To improve the SH conversion efficiency, higher enhanced fundamental power is required but it consumes a lot of energy. Moreover, the increasing of confocal parameter and the crystal length are another possible solution. However, there is a trade-off between optic size and conversion efficiency. If the high conversion efficiency is required, the optical system size must be increased. In contrast, if the compactness is required, the conversion efficiency is low. On the other hand, the main parameters; phase matching angle, walk-off angle, and effective coefficient must be carefully controlled due to very slightly change of these parameters cause suddenly change of SH efficiency. Up to present, the best performance of wavelength tuning is implementation of the multimode Fabry-Perot blue LD with transmission grating and feedback mirror that is able to tune as wide as 5.75 nm. The limitation of wavelength tuning of this setup is from the waveguide characteristic and gain profile of the multimode Fabry-Perot blue LD. This paper showed the sufficient of wavelength tunability and compactness comparing with the conventional excimer and YAG laser. Moreover, this system has potential to focus and achieve the higher power density than bulk laser at the selected area. Acknowledgment This research was supported by JST research foundation and NICHIA Corporation foundation. References 1. 2. 3. 4.

W. L. Zhou, Y. Mori, T. Sasaki, and S. Nakai, Optics Communications 123, pp. 583-586, 1996. NICHIA Corp., “Blue Violet Laser Diode, NDHU110APAE2”. NICHIA Corp., “Fabry-Perot Multimode Blue Laser Diode, NDHB220APAT1”. V. G. Dmitriev, G. G. Gurzadyan, and D.N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Springer Series in Optical Sciences Volume 64. 5. D.L. Mills, Nonlinear Optics: Basic Concepts, 2nd edition, ed. (Springer, New York, 1998).

17

6. G. D. Boyd and D.A. Kleiman, “Parametric Interaction of Focused Gaussian Light Beam,” Journal of Applied Physics, Vol. 39, No. 8, pp 3597–3639, 1968. 7. K. Ohara, M. Sako, and K. Nonaka, “210 nm ultraviolet generation using blueviolet laser diode and BBO SHG crystal,” CLEO Pacific RIM conference, Taipei, 2003. 8. K. Ohara K. Nonaka, and P. Vesarach, “0.2 µm Deep UV Generation using 0.4 µm Blue Laser Diode with Wavelength Tunable Cavity,” CLEO Pacific RIM conference, Tokyo, 2005. 9. C. Tangtrongbenchasil, K. Ohara, T. Itagaki, P. Vesarach, and K. Nonaka, “219-nm Ultra Violet Generation Using Blue Laser Diode and External Cavity,” Japanese Journal of Applied Physics, Vol. 45, No. 8A, pp. 6315– 6316, 2006. 10. C. Tangtrongbenchasil, K. Nonaka, and K. Ohara, “220-nm Ultra Violet Generation Using an External Cavity Laser Diode with Transmission Grating,” MOC 2006, Sep. 2006, Seoul, Korea, Vol. 2, pp. 5–8. 11. CASIX Co., Ltd., “Product Catalog 2004”. 12. T. Laurila, T. Joutsenoja, R. Hernberg, and M. Kuittinen, “Tunable external-cavity diode laser at 650 nm based on a transmission diffraction grating,” Applied Op., Vol. 41, No. 27, pp. 5632–5637, 2002. 13. H. Patrick and C.E. Wieman, “Frequency stabilization of a diode laser using simultaneous optical feedback from a diffraction grating and narrowband Fabry-Perot cavity,” Rev. Sci. Instrum., Vol. 62, No. 11, pp. 2593– 2595, 1991. 14. A. Wicht, M. Rudolf, P. Huke, R. Rinjkeff, and K. Danzmann, “Grating enhanced external cavity diode laser,” Appl. Phys. B, 2003. 15. M. W. Flemming and A. Mooridian, “Spectral Characteristics of External-Cavity Controlled Semiconductor Lasers,” IEEE J. Quantum Electron, Vol. QE-17, No. 1, pp. 44–59, 1981. 16. K. Hayasaka, “Frequency stabilization of an extended-cavity violet diode laser by resonant optical feedback,” Optics Comm. 206, pp. 401–409, 2002.

18

APPLICATION OF REFLECTION SPECTRUM ENVELOP FOR SAMPLED GRATINGS XIAOYING HE1,2, D.N.WANG2*, DEXIU HUANG1 AND YONGLIN YU1 1

Wuhan National Laboratory for Optoelectrons, Huazhong University of Science and Technology, Wuhan, Hubei,430074, P.R.China 2 Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, P.R.China

Analytical expression is proposed for evaluating the performances of sampled gratings. Accuracy of this expression has been verified by simulated reflectivity spectrum with the transfer matrix method. A new technique of multiplex reflection-spectrum envelope concatenation is introduced to demonstrate a 23-channel grating with uniform characteristics in all channels. The proposed technology can densify sampled grating both in spectral channels number and in spatially physical corrugation.

1. Introduction Sampled gratings (SGs) are naturally attractive for wide applications in optical communications and optical sensor systems such as tunable semiconductor reflectors [1, 2], multi-channel dispersion compensators [3, 4], multi-channel multiplexers-demultiplexers [5], repetition rate multiplication [6], etc. Particular interests that have been shown in the performances of sampled gratings include the envelope-top flatness and 3dB envelope bandwidth of the reflection spectrum. Especially, the multi-channel gratings with broad flat-top spectrum envelopes, as tunable semiconductor reflectors, will significantly improve the performances of laser over a wide tuning range. A number of techniques proposed for this purpose, including Sinc-apodization [7], multiple-phase shift technique [8], and interleaved technique [9]. Moreover, the transfer matrix method cannot convey the relation of grating parameters and the top-flatness and width of reflection-spectrum envelope (RSE). Simulation employing transfer matrix method is a time-consuming task especially for long gratings. Therefore, it is necessary to propose an analytical expression of RSEs for conventional sampled gratings to study the impacts of grating parameters on RSEs. In this paper, an accurate analytical expression of the RSE for sampled grating is proposed and demonstrated. Based on this analytical expression, the new multiple reflection-spectrum envelope concatenation (MRSEC) technology is employed to design multi-channel gratings with broad flat-top reflection spectra. 2. Analytical Expression of Reflection-spectrum Envelope 2.1. Theory The main spectral features of sampled grating, whether photo-refractive grating or etched grating, can be derived from the modulation of the effective refractive index. The effective refractive-index profile can be governed by:

  ∞    2π neff ( z ) = n0 ,eff + δ neff ( z ) ⋅  f ( z ) ∗  δ ( z − iZ 0 ) ⋅ g ( z )   ⋅ 1 + υ cos   Λ   i =−∞   

∑

*

Corresponding author email: [email protected]

 z  , 

(1)

19

Zg Zg  1, − ≤z≤ f ( z) =  2 2 , 0 , otherwise 

(2)

L L  1, − ≤ z ≤ g (z) =  2 2, 0, otherwise

(3)

Where n0,eff is the average effective refractive index for the propagating mode, δ neff is the dc index change spatially averaged over a grating, υ is the fringe visibility of the index change, Λ is the grating period, Z0 and Zg are the sampling period and the grating pitch length in the sampling period, respectively. L is the total length of the sampled grating. The rectangular function f (z) is the sampling function of the SG without apodization, and the rectangular function g(z) is the whole grating profile function without apodization. The coupling coefficient κ(n) corresponding to the nth Fourier component in the SG is:

κ ( n) = κ 0

Zg Z0

sin c(π nZ g / Z 0 )e

iπ Z g / Z 0

.

(4)

The diffracted order n can be expressed as a function of the wavelengths λ:

n=

Z 0  2 n0 ,eff π π  − . π  λ Λ

(5)

where, Z0/π can be regarded as the diffracted numerical aperture of sampled grating, and the 2n0,eff π/λ is the wave number. Thus, due to the Fourier theory, the analytic expression for the RSEs is defined by:  2 n0 , eff 1    Zg  Zg 2n0 ,eff 1   iπ Z g  λ − Λ   Renv ( λ ) = tanh  κ 0 sin c  π ⋅ Z0  −  e ⋅ L.   Z0 Λ   λ  Z0   2

(6)

Fig. 1. Reflection spectrum and reflection-spectrum envelope of conventional sample grating. The Sinc function in Eq. (6) is related with the Fourier transform component function of the rectangular function f ( z ). From Eq. (6), it is clear that the shape of the RSEs is determined by the Sinc function related with the grating pitch length Zg, the average effective refractive index n0 ,eff and the grating period Λ. Clearly, only using Eq. (6), the basic performances of the RSEs can be analyzed accurately, and the optimal design of parameters for the SGs can be obtained as well. This will be helpful to design multi-channel gratings with broad flat-top reflection spectra.

20

2.2. Reflection-spectrum Envelope of Conventional Sampled Grating

Fig. 2. Conventional sampled grating in real space and spatial frequency β space.

Fig. 3(a). Reflection-spectrum envelope of conventional sampled grating with different sampling period and the duty cycle Zg/Z0 = 1/15.

Fig. 3(b). Reflection spectrum of conventional sampled grating with different sampling period and the duty cycle Zg/Z0 = 1/15. The RSE of the conventional sampled grating calculated by the analytical expression Eq. (6) is plotted with the dashed line in Fig. 1. The transfer matrix method is also used to verify the proposed method, simulated the reflection spectrum with the solid line. Parameters are used here as follows: n0,eff = 1.485, Λ = 521.7 nm, δ neff = 5 × 10-4, and N = 20 (the number of the sampling period). Simulation with the transfer matrix method is a time-consuming task especially for long gratings. Obviously the proposed method provides a simple and fast way to evaluate overall performances of SGs, such as the flatness and 3dB bandwidth of reflection-spectrum envelop. As shown in Fig. 1, the calculated RSE are well consistent with the reflection-peak values in reflection spectrum obtained by the transfer matrix method.

21

Fig. 4. Principle of the multiple reflection-spectrum envelope concatenation technology, (a) reflection-spectrum envelopes of conventional sampled gratings, (c) resultant reflection-spectrum envelope, (b) sub-gratings, (d) new grating structure. The spatial corrugation and reflection frequency spectrum of the conventional sampled grating have a relation analogous to the Fourier transform, which are illustrated in Fig. 2. The spatial index profile of the sampled grating in Fig. 2(e) can be composed by the mathematic operation of the four spatial index profile functions in Fig. 2(a), Fig. 2(b), Fig. 2(c), and Fig. 2(d). The reflection spectrum corresponding to the spatial frequency β in Fig. 2( j) consists of the four parts of Fig. 2(f ), Fig. 2(g), Fig. 2(h), and Fig. 2(i). From Fig. 2, it is apparent that the every reflection peak and its sidelobes are related with the Fourier transform component function of the rectangular function g ( z ), and the rough shape of the RSEs is determined by the Fourier transform function of the rectangular function f ( z ). Assuming that the length of conventional sampled grating is infinite, their sidelobes will be eliminated and the linewidth of every reflectivity peak is quite narrow. The impact of the sampling period on reflection spectrum envelope are calculated by the proposed method and the transfer matrix method respectively, and shown in Fig. 3(a) and Fig. 3(b). Obviously, Fig. 3(a) presents a clear picture of dependence of reflection spectrum envelope on the sampling period. 3. Application of Reflection-spectrum Envelope The analytical expression (Eq. (6)) of the RSE for conventional sampled gratings is based on the Fourier theory. The broad flat-top RSE can be realized by concatenating or partly overlapping a series of RSEs of conventional sampled gratings, which can be proposed as multiple reflection-spectrum envelope concatenation (MRSEC) technology. Concatenation with M = 5 RSEs of conventional sampled gratings in Fig. 4 provides an example of application of the multiple reflection-spectrum envelop concatenation technology to present a new grating structure composed by five sub-gratings, which can be called as the digital concatenated grating. The digital concatenated grating consists of a set of nonapodized M conventional sampled gratings. As shown in Fig. 4(b), the duty cycle of each conventional sampled grating is 1/M (M = 5). From Fig. 4(a), the concatenation and overlap of RSEs can supply the gap of the Sinc shape of conventional sampled gratings. Based on the Fourier theory the proposed grating structure, as shown in Fig. 4(d), can be obtained by inverse Fourier transform of the resultant RSE with a broad flat-top in Fig. 4(c). The characteristics of every RSE in Fig. 4(a) are basically uniform except the central wavelength. The spacing of the central wavelength of adjacent RSE in Fig. 4(a) keeps as a constant, which must be lower than the 3dB bandwidth of each RSE. In accordance with the RSE of Fig. 4(a), the characteristics of sub-gratings, such as sampling period, the effective refractive index and the grating pitch length must be the same except grating period in Fig. 4(b). At the interface of each adjacent grating in Fig. 4(d) the phase is zero, which is used for eliminating the unwanted phase modulation in the whole grating. The channel spacing ∆f of the digital concatenated grating, which is equal to the channel spacing of the sub-gratings, is inversely proportional to the sampling period Z0 as:

∆f =

c 2 n0 ,eff Z 0

.

(7)

where c is the velocity of light. Apart from performing broad flat-top reflection-spectrum, the MRSEC technology can also be employed to eliminate empty regions within the grating and reduce the index modulation required to preserve reflection strength.

22

In this proposed scheme, spectrum property of the digital concatenated grating composed of five sub-gratings has been simulated in Fig. 5. The simulation parameters of those gratings are n0,eff = 1.485, δ neff = 5 × 10-4, N = 10, and Z0 = 1.043 mm, respectively. The reflection-spectrum of the digital concatenated grating simulated with transfer matrix method has been plotted with black line in Fig. 5. Obviously, in Fig. 5, the reflectivity peak values of the digital concatenated gratings (black line) are consistent well with its RSE (red lines) calculated by analytical expression. It can be seen in Fig. 5 that twenty-three identical useful channels has been obtained. From Fig. 5, the envelope top of reflection spectrum has ripples, which can be introduced by sidelobes of Sinc-envelopes of each subgrating. Therefore, it is important for choosing a proper interval of central wavelengths of RSEs to obtain a broad flat-top RSE. For well design of the digital concatenated grating with the best broad flat-top envelope, we should ensure the separation between center wavelengths of adjacent conventional sampled grating be the multiple of the spacing between reflectivity peaks.

Fig. 5. Digital concatenated grating with five sub-gratings. 4. Conclusion The analytical expression of the RSE for conventional sampled grating is deduced by Fourier theory. Sidelobes can be eliminated and the linewidth of each reflectivity peak becomes quite narrow with infinite grating length. The accuracy of this expression has been verified by simulated reflectivity spectrum by use of transfer matrix method. When compared to the transfer matrix method, our proposed technology provides a simple, clear and fast way to evaluate the performance of the RSEs. A new technique of multiple reflection-spectrum envelope concatenation is introduced to increase the channel number with uniform peaks. The proposed technology can densify sampled grating both in spectral channels number and in spatially physical corrugation. An example of a 23-channel grating with uniform characteristics in all channels is demonstrated. Acknowledgments The authors undertook this work with the supports of the National Natural Science Foundation of China under Grant No. 60677024, the National High Technology Research Development Program of China under Grant No. 2006AA0320427, and Hong Kong Polytechnic University Research Grant G-U321. References 1.

2. 3.

V. Jayraman, Z-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor laser with sampled gratings”, IEEE J. Quantum Electron., Vol. 29, No. 6, pp.1824–1834, 1993. X. He, W. Li, J. Zhang, X. Huang, J. Shan, D. Huang, “Theoretical analysis of widely tunable external cavity semiconductor laser with sampled fiber grating”, Optic. Commun., Vol. 267, pp. 440–446, 2006. X. F. Chen, Y. Luo, C. C. Fan, T. Wu, and S. Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system,” IEEE Photon. Technol. Lett., Vol. 12, No. 8, pp. 1013–1015, 2000.

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4.

5. 6. 7. 8. 9.

Y. Dai, X. Chen, Y. Yao, and S. Xie, “Dispersion compensation based on sampled fiber Bragg gratings fabricated with reconstruction equivalent-chip method”, IEEE Photon, Technol. Lett., Vol. 18, No. 8, pp. 941– 943, 2006. W. H. Loh, F. Q. Zhou, and J. J. Pan, “Novel designs for sampled grating based multiplexers-demultiplexers”, Opt. Lett., Vol. 24, No. 21, pp. 1457–1459, 1999. P. Petropoulos, M. Ibsen, M. N. Zervas, and D. J. Richardson, “Generation of a 40 GHZ pulse stream by pulse multiplication with a sampled fiber Bragg grating,” Opt. Lett., Vol. 25, No. 8, pp. 521–523, Apr. 2000. M. Ibsen, M. K Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation”, IEEE Photon, Technol. Lett., Vol. 10, No. 6, pp. 842–845, 1998. H. Ishii, Y. Tohmori, Y. Yoshikuni, T. Tamamura, and Y. Kondo, “Multiple-phase-shift super structure grating DBR lasers for Broad wavelength tuning”, IEEE Photon. Technol. Lett., Vol. 5, No. 6, pp. 613–615, 1993. M. Gioannini and I. Montrosset, “Novel interleaved sampled grating mirrors for widely tunable DBR laser”, IEE Proceedings, Vol. 148, 13–18, 2001.

24

TEMPERATURE-DEPENDENT PHOTOLUMINESCENCE INVESTIGATION OF NARROW WELL-WIDTH InGaAs/InP SINGLE QUANTUM WELL

W. PECHARAPA∗ , W. TECHITHEERA, P. THANOMNGAM and J. NUKEAW KMITL Nanotechnology Research Center, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand ∗E-mail: [email protected]

The formation of In0.53 Ga0.47 As/InP single quantum well with narrow well width grown by Organometallic Vapor Phase Epitaxy is verified by photoluminescence spectroscopy. PL spectra exhibit the e(1)-hh(1) transition in the well. PL measurement was conducted at various temperatures from 15 K to 200 K in order to investigate the important temperature-dependent parameters of this structure. Important parameters such as activation energies responsible for the photoluminescence quenching and broadening mechanisms are achieved. Because of small thermal activation energy of 15.1 meV in the narrow well, carriers can escape from the well to the barrier states. The dependence of PL width on temperature revealed that Inhomogeneous mechanism is the dominant mechanism for the broadening of PL peak and homogeneous mechanism is responsible at high temperature due to electron-phonon interaction. Keywords: InGaAs/InP; single quantum well; photoluminescence.

1. Introduction Semiconductor compound materials from group III and V have gained great interest according to suitable properties for practical optoelectronic devices. Most of these devices are fabricated in form of quantum structures. In0.53 Ga0.47 As lattice-matched to InP has promised for ultrahigh speed devices utilizing the high electron mobility and high peak velocity. The band gap of 0.75 eV is good for photodetector in optical communication systems. Moreover, semiconductor injection lasers using InGaAs/InP quantum well structures can be shifted into the 1.3–1.55 µm region by change the well thickness. Therefore, high-quality interface of quantum structure device is required. Many works have devoted to study the optical properties of related structures. Band gap blue shift of InGaAs/InP multiple quantum wells(MQWs) by different dielectric film coating and annealing was observed by PL.1 The results suggested that the shift depended on the dielectric layers, annealing conditions and combination between cladding layer and dielectric layer. The effect of doping concentration variation in the InP donor layer of InGaAs/InP high-electron mobility transistor (HEMT) structures was investigated by mean of PL.2 The variation of doping concentration caused different transitions of the confined states in the wells. PL technique and secondary ion mass spectroscopy (SIMS) were conducted to determine the well widths in InGaAs/InP MQWs.3 Both techniques give good agreement in values of quantum well widths. In this work, the formation of In0.53 Ga0.47 As/InP single quantum well with narrow well width grown by Organometallic Vapor Phase Epitaxy is verified by photoluminescence spectroscopy. PL spectra exhibit the e(1)-hh(1) transition in the well. PL measurement was conducted at various temperatures from 15 K to 200 K in order to investigate the important temperature-dependent parameters of this structure. 2. Methodology Few monolayers In0.53 Ga0.47 As/InP SQWs were grown by Organometallic Vapor Phase Epitaxy (OMVPE) at low pressure. Trimethylgallium (TMGa), Trimethylindium (TMIn), AsH3 , and PH3 were used as the source gases for Ga, In, As and P respectively. 100-nm thick InP buffer layer was grown on semi-insulating InP substrate. After the gas source for In and P was suspended, InGaAs well layer was grown with thickness of 2–4 monolayers (ML) before InP cap layer with 2 nm thick was grown. The growth temperature was 600◦ C. In PL experiment, Argon ion laser with filtered wavelength of 488 nm was used as optical excitation source. The sample was cooled down from room temperature (RT) to 15 K in a cryostat. The luminescence

25

from the sample was dispersed by the monochromator and was carried out by Ge detector. The signal was amplified by a lock-in amplifier and displayed by a computer. The stepped motor of the monochromator was automatically controlled by a signal from PC via RS-232 port. 3. Results and Discussion In Fig. 1, PL spectra of all samples at 15 K exhibit clear peaks, which are attributed to the luminescence from quantum well. The solid lines represent the fitting curves of each sample. The observed PL peak of the sample with the well width of 4 ML, 3 ML, and 2 ML is at 1.079 eV, 1.151 eV, and 1.198 eV respectively. The peaks due to the n=1 excitonic transition (e(1)-hh(1)) are clearly identified. PL peak has a dramatic increase (about 40–60 meV) when the well width is decreased by only one monolayer. These features reflect the formation of the extremely thin well-width single quantum well between lattice-matched InP and InGaAs. The sample with 3 ML-well width shows the strongest intensity, implying the optimization of good formation and uniformity of the sample. Figure 2 shows temperature-dependent PL of the sample with 3 ML well width. As temperature increases from 15 K to 200 K, PL spectra are weaker and exhibit the red shift, moving to the lower photon energy. The PL peak position versus measured temperature is illustrated in Fig. 3. The PL peak of about 1.152 eV at 15 K slightly shifts to lower energy of 1.138 eV at 200 K. The red shift of about 14 meV from 15 K to 200 K is probably caused by the decrease in the band-gap energy as the temperature increases. 4 It can be deduced that the luminescence of the extremely thin or small quantum structure is almost independent of the temperature.5 Meanwhile, the PL intensity drop as temperature increases is due to the fact that when temperature increases, the photocarriers have more probability meet various types of defects and recombine non-radiatively on them5 and the small binding energy of the exciton. At higher temperature, the thermal energy is significant comparing to the binding energy of the exciton, and the exciton-phonon interaction is considerable, reflecting in weaker and broader PL spectra. The calculation of the peak observed in the PL spectra of the particular quantum well transition is done by estimating the transition energies expected for a quantum well with a given well width. The ground state energy level in the quantum well is calculated by solving one-dimensional Schr¨ odinger equation of a finite square well. In the calculation, the energy gap of InP and In0.53 Ga0.47 As are 1.35 eV and 0.73 eV respectively.6 The effective mass of electron (m∗e ) and hole (m∗hh ) for In0.53 Ga0.47 As are 0.0416m0 and 0.46m0 respectively. The band discontinuity for conduction band, ∆Ec , and valence band, ∆EV , are 0.217 eV and 0.403 eV,

Fig. 1.

PL spectra of In0.53 Ga0.47 As/InP single quantum well as a function of the well width at 15 K.

26

Fig. 2.

PL spectra of the sample with well width of 3 ML at different temperature.

Fig. 3.

PL peak position of the sample as a function of temperature.

respectively.6 The calculation shows the higher values (about 70–90 meV) than the measured values. The origin of the difference may come from the imperfection at the interface between the extremely thin layer of InGaAs and InP barrier.7 The effect of temperature on PL characteristics of the sample is thoroughly investigated. The integrated PL intensity shown by closed square and full width at half maximum (FWHM) of the PL peak shown by closed circle of the sample as a function of temperature is plotted in Fig. 4. As the temperature increases from 15 K to 80 K, The PL intensity rapidly decreases. Further increase in temperature from 80 K to 150 K causes insignificant decrease of PL intensity. Meanwhile, The FWHM of PL peak increases with increasing temperature, especially after 80 K. The temperature dependence of the integrated PL intensity of an exciton emission peak is expressed as following equation, 8,9 IP L (T ) =

I0 1 + A exp (−EA /kB T )

(1)

27

Fig. 4.

Integrated PL Intensity and FWHM of PL peak as function of temperature.

Fig. 5.

Variation of Integrated PL intensity with temperature of the sample.

where I0 is the integrated PL intensity near 0 K, A is a constant, EA is the thermal activation energy which is responsible for the quenching of PL intensity in the temperature-independent PL spectra, T is the temperature, and kB is Boltzmann constant. Figure 5 presents the integrated PL intensity of the sample. These measured values were fitted using equation (1) and shown by the solid line. The fitting curve obviously exhibits satisfactory consistence with the experimental data. From fitting curve, the thermal activation energy (EA ) of this structure of 15.1 meV is obtained. Normally, the temperature-induced quenching of luminescence in quantum well structure is caused by two mechanisms: thermal emission of charge carriers out of confined states in the well into barrier states 10 and thermal dissociation of excitons into free-electron-hole pairs.4 Because of very narrow well width, the subband energy of electron in conduction band and hole in valence band are closed to the top of the well. The confined carriers can easily escape from the quantum wells. Therefore the first quenching mechanism dominates and the small thermal activation energy can be regarded as the delocalization energy of carriers

28

in the well.4 The temperature-dependent broadening of PL spectra of this structure is also investigated. Typically, the broadening of the PL spectra in quantum well structure can be summarized as the sum of two components: a temperature-independent inhomogeneous broadening due to interface roughness, fluctuations in binding energies alloy fluctuations (Γin ), and the temperature-dependent homogeneous broadening which typically due to electron-optical phonon or exciton-phonon interactions, (Γ hom ), which is given by the following expression,11 Γhom = exp



ΓLO  . ELO +1 kB T

(2)

Note that, ΓLO is the electron-phonon or exciton-LO-phonon coupling constant and ELO is the optical phonon energy. Therefore the total broadening is the summation of inhomogeneous broadening and homogeneous broadening due to the electron-phonon interaction. Figure 6 shows the FWHM of PL spectra from the sample with 3-ML well width as a function of temperature. The solid line is the fitting curve to the measured point using equations (2). It agrees well with the experimental data. The corresponded parameters extracted from the curve fitting are obtained as follows, ΓLO = 32.0 meV, ELO = 24.5 meV, and Γin = 42.7 meV. Fitting data reveals that inhomogeneous broadening mechanism is the dominant mechanism responsible to the broadening of PL spectrum of this structure. The inhomogeneous broadening which is independent to temperature depends on several mechanisms such as well width fluctuation, donor-to-acceptor recombination and local fluctuation in the strain. 11 For this quantum structure of very narrow well, the well width fluctuation should dominates and the local fluctuation in the strain is neglected due to lattice matching between InP and In0.53 Ga0.47 As. The second part of broadening of PL spectrum is homogeneous broadening which is temperature-dependent mechanism. Figure 7 shows the homogeneous broadening of In0.53 Ga0.47 As/InP SQW as a function of temperature. The homogeneous broadening is negligible at low temperature (<40 K). At higher temperature, its value increase drastically from 0 meV to 4 meV with increasing temperature from 40 K to 150 K. At low temperature, the carriers are trapped in the well resulting in minimum variations of the binding energies of the carriers and the inhomogeneous broadening mechanism dominates. At elevated temperatures, the electronphonon interaction becomes the dominant broadening mechanism and the FWHM consequently increases with increasing temperature.

Fig. 6.

FWHM of PL spectra of the sample as a function of temperature.

29

Fig. 7.

The homogeneous broadening of In0.53 Ga0.47 As/InP SQW as a function of temperature.

4. Conclusions The photoluminescence of very thin In0.53 Ga0.47 As/InP SQWs grown by OMVPE was conducted. The PL peaks reveal the luminescence from the recombination between e(1)-hh(1) in quantum wells. The photon energy of PL peak has such good agreement to calculated results. The temperature-dependence of The PL spectra was investigated. As temperature increase, PL emission peaks become broader, weaker, and exhibit significant redshift. The thermal activation energy that affects PL intensity quenching of this structure is obtained from the plot of integrated PL intensity versus temperature. Due to small thermal activation energy in the narrow well, carriers can easily escape from the well to the barrier states resulting in the PL intensity quenching at low temperature. The broadening of PL emission peak is analyzed in terms of homogeneous and inhomogeneous broadening mechanisms. It is revealed that inhomogeneous mechanism is the dominant mechanism for the broadening of PL peak and homogeneous mechanism has significant role at high temperature due to electron-phonon interaction. Acknowledgements The authors would like to acknowledge National Nanotechnology Center for research funds and department of Applied Physics, King Mongkut’s Institute of Technology Ladkrabang for the research facilities. References 1. J. Zhao, J. Chen, Z.C. Feng, J.L. Chen, R. Liu, and G. Xu, Thin Solid Films 498, 179 (2006). 2. K. Radhakrishnan, T.H.K. Patrick, H.Q. Zheng, P.H. Zhang, S.F. Yoon, Microelectron. Eng. 51-52, 441 (2000). 3. D.N. Bose, P. Banerji, S. Bhunia, Y. Aparna, M.B. Chhetri, and B.R. Chakarborty, Appl. Surf. Sci. 158, 16 (2000). 4. Y.T. Shih, Y.L. Tsai, C.T. Yuan, C.Y. Chen, C.S. Yang, and W.C. Chou, J. Appl. Phys. 96, 7267 (2004). 5. B. lambert, A. Le Corre. V. Drouot, H.L. Haridon, and S. Loualiche, Semicond. Sci. Tech. 13, 143 (1998). 6. J. Nukeaw, R. Asaoka, Y. Fujiwara, and Y. Takeda, Thin Solid Films 334, 44 (1998). 7. J. Boherer, A. Krost, and D. Bimberg, Appl. Phys. Lett. 60, 2258 (1992). 8. M. Furis, A.N. Cartwright, J. Hwang, and W.J. Schaff, Proc. Material Research Society Symposium 2004 798, (2004).

30

9. Y.A. Chang, J.R. Chen, H.C. Kuo, Y.K. Kuo, and S.C. Wang, J. Lightwave Technol. 24, 536 (2006). 10. S. Weber, W. Limmer, K. Thonke, R. Sauer, K. Panzlaff, G. Bacher, H.P. Meier, and P. Roentgen, Phys. Rev. B. 52, 14739 (1995). 11. M. Furis, A.N. Cartwright, H. Wu, and W.J. Schaff, Proc. Material Research Society Symposium 2004 798, (2004).

31

SHOOTING METHOD CALCULATION OF TEMPERATURE DEPENDENCE OF TRANSISITION ENERGY FOR QUANTUM WELL STRUCTURE BUNJONG JUKGOLJUN Computational Physics Research Laboratory, Applied Physics Department, Faculty of Science, KMITL, Bangkok, Thailand, 10520 WISANU PECHARAPA Optical Development Research Laboratory, Applied Physics Department, Faculty of Science, KMITL, Bangkok, Thailand and KMITL Nanotechnology Research Center, KMITL, Bangkok, Thailand, 10520 WICHARN TECHITDHEERA Computational Physics Research Laboratory, Applied Physics Department, Faculty of Science, KMITL, Bangkok, Thailand, 10520 and KMITL Nanotechnology Research Center, KMITL, Bangkok, Thailand, 10520

The ground state transition energy as various temperatures of a single quantum well structure has been calculated. The numerical technique called shooting method was developed to get eigen values and eigen functions. Pässler’s model and Aspnes’s equation are adopted to calculate the energy gap(Eg) of Al0.3Ga0.7As and GaAs respectively. Our calculation has been tested by comparing the results to PL experimental data of Al0.3Ga0.7As/GaAs single quantum well. Good agreement has been found in the low temperature range (less than 40 K) and fair result has been obtained in the range of temperature higher than 40 K.

1. Introduction Quantum well devices have been extensively studied in the last decade due to their potential of producing the high performance and low energy consumption devices. In the former works [1– 4], our calculations based on an analytical solution of finite quantum well. In this work, the full numerical scheme has been developed to calculate the eigen values and eigen functions. 2. Quantum Well Structure and Temperature Dependence The model of quantum well structure we’ve used to calculation, shown below. The left and the right hand side materials are symmetric Al0.3Ga0.7As which energy gap depends on temperature through the equation after Pässler[5].

E g (T) = E g (T = 0) −

Where

p  αθ  p 2T  1 +   − 1  θ  2    

α(x) = 4.9 + 0.7x + 3.7x2 2

(10-4 eV/K)

θ = 202 + 5x + 260x

(K)

E(T = 0, x) = 1.517 + 1.23x

eV

p = 3.5 (for Al0.3Ga0.7As).

(1)

32

Eg(Al0.3Ga0.7As)

∆Ec=0.6∆Eg e1

e1-hh1 Eg(GaAs)

recombination

∆Ev=0.4∆Eg

hh1

Al0.3Ga0.7As barrier

GaAs Well

Al0.3Ga0.7As barrier

Fig. 1. The model of quantum well structure of Al0.3Ga0.7As/GaAs. In the same way, the inside material, GaAs, changes its energy gap through the equation after Aspne[6],

E g (T) = 1.519 −

5.405 x10 −4 T 2 eV. T + 204

(2)

Band offset is 0.6∆Eg and 0.4∆Eg has been accepted for conduction band and valence band, respectively (∆Eg is the energy band difference between Eg of Al0.3Ga0.7As and Eg of GaAs) at a calculated temperature. 3. The Ground State Energy Calculation by Shooting Method We had started our work by dividing the problem into two parts to calculate. The first part is in conduction band and the second one is in the valence band. The calculation scheme of the two parts are slightly different. 3.1. Calculation in Conduction Band The Schroedinger equation for a single quantum well with a constant potential depth V0 and electron effective mass m is

− ℏ2 d 2ψ + V0ψ = Eψ 2 m dx 2

(3)

We used the value of electron effective mass m = 0.067 m0 (m0 is electron mass) for GaAs well as shown in the Fig. 1. The finite difference for second order differential equation is

ψɺɺi ≈

ψ i −1 2ψ i + ψ i +1 h2

(4)

The solution of eq. (3) with the helping from eq. (4) is [7]

 2m  (δ x)2 (V0 − E ) + 2 ψ ( xi ) − ψ ( xi − δ x) 2 ℏ 

ψ ( xi + δ x) = 

(5)

33

with initial conditions

ψ(0) = 1

ψ (δ x) =

and

(6)

m (δ x)2 (V0 − E ) + 1 2 ℏ

(7)

The equation (6) and (7) are typically used as initial conditions in the shooting method to find the ground state energy Ee1. The energy E is first randomly chosen to solve the eq. (5). The value of E that satisfied the eigen value has to give the longest zero of eigen function outside the well. The calculation is performed only in a half side from x = 0 to x = L/2 due to the symmetry of well. The computer code has been developed by using the equation (5)–(7) when V0 is specified, m is known as mention above and ħ is Planck’s constant over 2π. 3.2. Calculation in Valence Band and Transition Energy The calculation in valence band is the same with the calculation in conduction band. Only the difference is the effective mass of hole (m = 0.45 m0) and band offset (equal to and 0.4∆Eg). After the calculation, we get the ground state energy in the valence band Ehh1. The transition energy is calculated from Et = Eg(GaAs) + Ee1 + Ehh1

(8)

4. Result and Discussion Our calculation of transition energy as various temperatures range from 12 K to 200 K are compared to the photoluminescence data[8]. The PL peaks shown in Fig. 2 the small peaks is clearly observed in the low temperatures range from 12 K to 40 K. Higher than 40 K small peaks and dominant peaks seem to be merged. The important thing is that, the small peaks are the peaks from ground state transition energies of the quantum well. So it’s should be careful to use this data, especially in case of the extreme precision is required. From the comparison to this PL data, we found that the calculation give the good results in the temperatures range from 12 K to 40 K. Higher than 40 K it give the fair results (see Fig. 3).

Al0.3Ga0.7As/GaAs (SQW) PL PL Intensity units) Intensity (arb. (arb.units))

12 K 15 K 20 K 40 K 60 K 80 K 100 K 120 K 140 K 160 K 180 K 200 K 220 K

1.44

1.46

1.48

1.5

1.52

1.54

1.56

1.58

Photon Energy (eV)

Photon Energy (eV)

Fig. 2. PL peaks as various temperatures. From the testing by above comparison, our calculation is usable to calculate a quantum well transition energy by full numerical scheme called shooting method. Only slightly changed some parameters or functions, we would calculate any species of quantum well and predict ground state transition energy at a given temperature.

Transition energy (eV)

34

Temperature (K)

Fig. 3. Show the comparison of our calculation with the PL data. References 1. 2.

3.

4.

5. 6. 7.

Wisanu Pecharapa, Pongladda Panyajirawut, and Prasert Kraisingdecha “Study of Al0.3Ga0.7As/GaAs Single Quantum Well Grown by Molecular Beam Epitaxy,” Private Communication. W. Techitdheera, P. Thanomngam, W. Pecharapa, J. Nukeaw, “Al0.3Ga0.7As/GaAs single quantum well transition energy calculation”, The 2nd Symposium on Mathematical, Statistical and Computer Science 2005, 19–20 February 2005, Bangkok Thailand. Bunjong Jukgoljun, Wisanu Pecharapa, Wicharn Techitdheera, Prasert Kraisingdecha, Chawarat Siriwong, Chokechai Phuttharaksa, Ekachai Chongsereecharoen, Temperature Dependent-Photoluminescence of AlGaAs/GaAs Single Quantum Well Grown by Molecular Beam Epitaxy, KMITL International Conference on Science and Applied Science 2006, 8–10 March 2006, Bangkok, Thailand. Wicharn Techitdheera, Pitiporn Thanomngam, Wisanu Pecharapa, Jiti Nukaew, Prasert Kraisingdecha, e1 – hh1 Transition Energies Calculation of Al0.3Ga0.7As/GaAs Single Quantum Well. Siam Physics Congress 2006: Frontier Research in Physics and Keys Technologies for Development, 23–25 March 2006. Bang Saen, Chonburi, Thailand. S. A. Lourenço et al., “Temperature Dependence of Optical Transitions in AlGaAs” Journal of Applied Physics, Vol. 89, No. 11, 2001. Jasprit Singh, Semiconductor Devices: An Introduction, McGraw-Hill, Singapore, 1994. Nicholas J. Giordano, Computational Physics, Prentice Hall, New Jersey, 1997.

35

DESIGN OF OPTICAL RING RESONATOR FILTERS FOR WDM APPLICATIONS S. PIPATSART, P. SAEUNG AND P. P. YUPAPIN Advanced Research Center for Photonics, Department of Applied Physics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand

In this paper, we design the ring resonator filters such as moving average (MA), autoregressive (AR) and autoregressive moving average (ARMA) filters. These filters are designed as add/drop filter, channel selection and dispersion compensator. The transfer functions of optical filters are derived using Z-transforms.

1. Introduction Optical integrated circuits and all-optical systems are very interesting subjects for high speed signal processing purposes. In photonics the optical ring resonator is most often used as a building block in a filter [1], channel add/drop [2], channel selection [3] or dispersion compensation [4] system. Recent, the demand for these devices are increasing rapidly because of deployment of systems such as the high speed dense wavelength division multiplexer (DWDM) optical fiber communication system. Filters are broadly classified into two categories: finite impulse response (FIR) and infinite impulse response (IIR) [5]. FIR filters have no feedback paths between the output and input i.e. do not rely on optical reflections. These are also referred to as moving average (MA) filters and examples are Mach-Zehnder interferometers (MZI). IIR filters inherently base on multiple reflections between the output and input. IIR filters are referred as autoregressive (AR) filters. Examples of these include fiber Bragg gratings (FBGs) and optical all-pass filter. By coupling a ring resonator inside an MZI, an autoregressive moving average (ARMA) filter can be obtained. Optimum design for the optical Filters is then the need of today. Important characteristics of Electrical and Optical Filters are similar e.g. the stop-band rejections, the pass-band gain, the pass-band width, phase delay computations etc. Given the enormous research in the field on digital filter design, optical filters can be modeled as digital filters and the theory and various optimization techniques can be used efficiently for design. Digital signal processing provides a readily available mathematical framework, the Z-transform, for the design of complex optical filters. Digital signal processing techniques are relevant to optical filters because they are linear time invariant systems that have discrete delays. A linear time-invariant system is one which behaves linearity with respect to the input and whose parameters are stationary with time. The aim of this paper is to design and simulate the filtering characteristics and applications of the following three major single stage optical filters such as MA, AR and ARMA filters to obtain a magnitude response in the frequency domain. The design algorithm is generalized so that any magnitude response can be approximated with such filters. 2. Optical Filter Designs and Z-transform In this section, we discuss the important aspects of optical filters in relation to discrete filters, and explain how Z-transforms can be used to describe optical filters as well. Two interfering waves, which are delayed with respect to one another form the filter function. The incoming signal is split into multiple paths by either wavelength division or amplitude division. Then the waves are recombined, provided they have the same polarization and the same frequency, the relative phases determine whether they interfere constructively or destructively. The phase φ is a function of the path length L and the propagation constant β = 2πne /λ where ne is the effective refractive index of the waveguide delay line by assuming to be independent of wavelength and λ is the wavelength of light. For delay line signal processing approach the unit delay is generally defined as T = Lu ne /c, where Lu is the smallest path

36

length and is called the unit delay length and c is velocity of light. The key to analyzing optical filters using Z-transforms is that each delay be an integer multiple of a unit delay length Lu . The phase is expressed as φ = pβLu where p is an integer while z−1 is the Z-transform parameter, which is defined as z −1 = exp − j β Lu . Since the delays are integer multiples or discrete values of the unit delay, the frequency response is generally periodic in nature. One period is defined as free spectral range (FSR) and for more realistic case for a delay with dispersion, FSR is given by

FSR =

1 c = T n g Lu

(1)

where ng = ne + f
( dne /df ) f is called as the group refractive index evaluated at either central frequency f o or
central wavelength λo . 2.1. A Single Stage MA Optical Filter The fundamental building block of the MA filter is the MZI shown in Fig. 1. The MZI has two inputs, two outputs and coupling coefficients designated by κ i which is the coupling factor of the i th coupler. The through and cross port transmission parameters are represented as ci = cos θ = 1 − κ i and − js = − j sin θ = − j κ . The waveguides connecting the couplers have lengths L1 and L2 . To analyze its frequency response, the unit delay is set equal to the difference in path lengths, Lu = L1 − L2 . The longer arm has a transfer function of z −1 relative to the shorter arm. A brief simplification and the assumption that κ = κ 1 = κ 2 leads to the transfer function of the MA optical filter (analogous to the MZI) as 2 2 −1 − jcs (1 + z −1 )  X 1  Y1   − s + c z =    Y  −1 c 2 − s 2 z −1  X 2   2   − jcs (1 + z )

(2)

Fig. 1. Waveguide layout of Mach-Zehnder interferometer device. 2.2. A Single Stage AR Optical Filter A single stage AR filter can be realized using a single ring resonator (SRR) with two couplers as shown in Fig. 2. It is the simplest optical waveguide filter with a single-pole response. The unit delay is equal to Lu = L1 + L2 + Lc1 + Lc 2 where Lc1 and Lc 2 are the coupling region lengths for each coupler. The feed-forward delay is the relative delay between the two paths; whereas, the feedback delay is the total feedback path length. Using c and s as before, the ring's transfer function for the drop port, Y2 is given by

H 21 ( z ) =

−1 Y2 ( z ) − κ 1κ 2 γ z = X 1 ( z ) 1 − c1 c 2 γ z −1

(3)

where γ = e−α ( L 1+ L 2 )/ 2 is the propagation loss in the common path length L1 + L2 . The common term − s1 s2 γ z −1 , is the transmission from the input to the output without the feedback path connected. Propagation once around the feedback path is given by c1c2γ z −1 . Other responses of the ring resonator for the throughput port can similarly be obtained as

H 11 ( z ) =

Y1 ( z ) c − c γ z −1 = 1 2 −1 X 1 ( z ) 1 − c1c 2γ z

(4)

37

Fig. 2. Single ring resonator with two couplers. The device can be used as a channel add/drop filter. The filter’s group delay is defined as the negative derivative of the phase of the transfer function with respect to the angular frequency as follows [4]

τn = −

{ {

} }

 Im H ( z )  ∂  tan −1  ∂ω  Re H ( z ) 

(5)

where τn is normalized to the unit delay of the waveguide, T. Thus, we obtain from (4) the relative group delay τr for the circuits of Fig. 2 is given by

τn =

τn T

=

(1 − (c1c 2 γ ) 2 ) / 2 [((c1c 2 γ ) − 1) cos(φ / 2)] 2 + [((c1c 2 γ ) + 1) sin(φ / 2)] 2

(6)

2.3. A Single Stage ARMA Optical Filter To minimize passband loss, an ARMA lattice architecture is advantageous. A special type of ARMA filter is an optical all pass filter, which ideally has a constant magnitude response shown in Fig. 3. All pass filters are widely deployed as dispersion compensation devices which have a constant transmission on the whole spectrum and a frequency dependent phase response. The optical feedback path length is L and α is the linear intensity attenuation coefficient. The single stage optical all pass filter has the following transfer function which is given by

E ou t ( z ) E in ( z )

=

c − γ z −1 1 − cγ z −1

.

(7)

where γ = e−α L / 2 is the propagation loss. The group delay time is the term which describes characteristic of all-pass filter as dispersion compensation. The normalized group delay, τn as a function of normalized angular frequency, ω for a lossless waveguide is given by

τn

x =1

=

1− c2 1 + c − 2 c cos ω 2

Fig. 3. Basic single stage optical all pass filter. The device can be used as a dispersion compensator.

(8)

38

Another ARMA filter can be obtained by coupling a ring resonator inside an MZI as shown in Fig. 4.

Fig. 4. A Mach-Zehnder interferometer with one arm loaded by a ring resonator. The device can be used as a channel selection filter. The transfer function for this architecture in the Z-domain is given by

Eou t ( z ) Ein ( z )

(c c 2

=

r

) (

)

− j ϕ +ϕ − s 2 e − jϕ t − c 2 e − jϕ r − s 2 cr e ( t r ) γ z −1

1 − cr e

− jϕ

r

γz

−1

(9)

where φ r and φ t are the phase shift of the ring and MZI, respectively. 3. Results and Discussion In the results, we first present the frequency responses of MA filter (Fig. 1) followed by corresponding results on AR and ARMA filter, respectively. Figure 5 illustrates the magnitude responses of MA filter using MZI. The MZI has an unit delay length ( Lu ) equal to 136 µ m and group refractive index is assumed to be ng = 3.5 . A special case arises for κ 1 = κ 2 = 0.5 is shown in Fig. 5(a). Both output responses have transmission minimum that are zero in this case. The influence of optical loss of the MZI with α = 5 dB/cm is shown in Fig. 5(b). The response for identical couplers with κ 1 = κ 2 = 0.55 is shown in Fig. 5(c). The null of the through port is washed out, whereas the cross port null remains zero. The MZI response for the through port in Fig. 5(d) showing the impact of the coupling ratio and we found that as κ 1, 2 decreases the null is become wash out.

Fig. 5. The magnitude responses of MA filter using MZI. Solid line: through port, dash line: cross port assuming (a) κ 1 = κ 2 = 0.5, α = 0 , (b) κ 1 = κ 2 = 0.5, α = 5 dB/cm, (c) κ 1 = κ 2 = 0.55, α = 0 and only through port (d) varying in coupling ratio.

39

The filter characteristics as shown in Fig. 6 are the simulation results of the through and drop port of the AR filter using a SRR with two couplers. The SRR has a radius equal to 136 µ m , the coupling coefficients of κ 1 = κ 2 = 0.2 and the internal loss are fully compensated ( α = 0 ). The design frequency (wavelength) f
= 193.1 THz ( λ
= c / f
= 1552.52 nm), FSR = 100 GHz and ng = 3.5. The on-off ratio is calculated and obtained to be 19 dB. The shape factor of the drop port is approximately 0.165.

Fig. 6. Frequency responses of the AR filter using a single ring resonator with two couplers, κ 1 = κ 2 = 0.2, α = 0, γ = 0, R = 136 µ m .

Fig. 7. The realization of low cross talk of the AR filter at drop port, with κ 1 = κ 2 = κ < 0.2.

Fig. 8. The relative group delay responses of RR in Fig. 2 comparing different symmetric coupling coefficients. By using the SRR filter with low coupling coefficients of κ 1 = κ 2 < 0.2, where a high on-off ratio of more than 20 dB can be realized for the drop port as shown in Fig. 7. The output intensities will be unity at resonance ( β L = 2M r π ),

40

which indicates that the resonance wavelength is fully extracted by the resonator, for identical symmetrical couplers κ1 = κ 2 , especially lossless in waveguide (α = 0) and couplers (γ = 0). The relative group delay responses of circuit in Fig. 2 is plotted in Fig. 8, assuming the circumference of ring L = 0.86 mm and using symmetric coupling coefficients κ 1,2 = κ . The relative group delay responses show a period of 100 GHz, which is the same as the FSR of ring resonator and found that as κ is decreased become sharper and steeper. The normalized group delay response of dispersion compensator as Fig. 3 is shown in Fig. 9. The parameters of circuit used for this simulation are the same as Fig. 6. The internal ring losses are assumed to be fully compensated ( α = 0 ). The normalized group delay response is periodic functions of frequency of 100 GHz, which is the same as the FSR of ring resonator and found that as κ is decreased become sharper and steeper at resonant point.

Fig. 9. Normalized group delay response of dispersion compensator with lossless as Fig. 3 comparing different coupling coefficients of κ = 0.1, 0.4 and 0.7.

Fig. 10. Relative output intensities for the ARMA filter of Fig. 4 for varying coupling coefficients of κ r = 0.1- 0.4. The frequency response of the ring resonator is used to obtain a channel selection filter by coupling the ring resonator to one arm of an MZI as shown in Fig. 4. Using κ = 0.1 couplers in the MZI and the coupling coefficients of the ring is varied for four values of κ r = 0.1- 0.4. Decreasing κ r while κ is fixed at 0.5, the responses become larger on-off ratio and sharper at resonant point as shown in Fig. 10.

4. Conclusions We have proposed the design and analysis of single stage optical filters such as MA, AR and ARMA filters in general. The transfer function models of optical filters are derived by using Z-transform analysis. The present

41

analysis has been restricted to directional coupler and waveguide that characterized by two parameters, the power coupling ratio and intensity attenuation coefficient. Results obtained have shown the potential of using such device in WDM communication system.

References 1. 2. 3. 4. 5.

A. Rostami, G. Rostami, “Full-optical realization of tunable low pass, high pass and band pass optical filters using ring resonators,” Opt. Commun. 240(3), 133–151 (2004). B. E. Little, S. T. Chu, H. A. Haus, J. S. Foresi and J.-P. Laine, “Microring Resonator Channel Dropping Filters,” IEEE J. Lightwave Technol. 15(6), 998–1005 (1997). C. K. Madsen, “Efficient architectures for exactly realizing optical filters with optimum bandpass designs,” IEEE Photonics Technol. Lett. 10(8), 1136–1138 (1998). C. K. Madsen, “Optical all-pass filters for polarization mode dispersion compensation,” Opt. Lett. 25(12), 878– 880 (2000). C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, Wiley, 1999.

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CHAOTIC SIGNALS FILTERING DEVICE USING THE SERIES WAVEGUIDE MICRO-RING RESONATORS P. P. YUPAPIN, S. CHAIYASOONTHORN AND S. THONGMEE Advanced Research Center for Photonics, Department of Applied Physics, Faculty of Science King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand

This paper proposes a system of signal security using the optic series waveguide micro ring resonator, where the chaotic noise generation and cancellation can be performed. The required communication signals can be multiplexed with the generated chaotic noise in a micro ring resonator before transmission. The required information can be recovered via optic series waveguide micro ring resonator by a specific user at the output port of the waveguide micro-ring resonator. Simulation results obtained have shown the potential of applications which is closed to the practical applications, especially, the required information can be retrieved by the specified users. The ring parameters used with the ring radii are ranged between 10–20 µm, κ1 = κ2 = 0.0225 and n2 = 2.2 × 10−15 m2/W. The simulation results obtained have shown the potential of using such a proposed device for tunable band-pass and band-stop filters, which can be used for the information security in the system by the optic series waveguide micro ring resonator.

1. Introduction Chaotic filter for communication are nonlinear effect communication and used to the scurrility communication such as the military message transmission system, the secretly message and the specially communication. Chaotic filter for communication uses a noise-like broadband chaotic waveform as carrier. The signal in fiber optic ring resonator has chaotic effect, Kerr effect, Bistability stated, Bifurcation stated and we call the nonlinear behaviors [1]. The controlling optical chaotic in nonlinear fiber optic communication using quantized and synchronized chaotic in the optical system [2]. We can be application the single waveguide micro-ring resonator on the concept of tunable filter [3], which the couple band pass Filter for WDM System [4], the Synthesis of direct-coupled resonators band pass photonic filters [5], the filter synthesis for periodically coupled micro-ring resonators [6], the synthesis of a parallel-coupled ringresonator filter [7] and the wavelength selective integrated device by vertically coupled micro-ring resonator filter [8]. However the chaotic signal and nonlinear behavior can be application of spatiotemporal communication with synchronized optical chaos [9] and the optical filter design and analysis a signal processing approach [10]. In this paper, we report: 1) the operating principle generation chaotic signal in series waveguide micro-ring resonator, 2) the simulation for filtering the band pass and band stop the message transmission, 3) Result and discussion the series waveguide micro-ring resonator and finally conclusion. 2. Chaotic Generation Consider waveguide micro ring resonator configuration is depicted in Fig. 1, which the construction a series waveguide ring resonator coupler [11], the circumference of the waveguide micro ring is L. For convenience of analysis, we assume the complex electric field at each port as shown in Fig. 1 is E(t), where Ein(t) is the incoming light field of an input port and the transmitted light field to the output port is Eout(t). While the rest of the fields E1(t) and E2(t) are the circulated fields inside the fiber ring. Here, the input light is assumed to be monochromatic with constant amplitude and random phase modulation which results in temporal coherence degradation. Hence, the input light field can be expressed as

Ein (t ) = E0 exp j ϕ0 (t ) .

(1)

43

(a)

(b) Fig. 1. A schematic diagram of (a) a micro ring resonator (b) the series micro ring resonator. The equation (2.2) is given by [1],

    2 Eout1 (t) (1−(1−γ) x )κ  =(1−γ)1−  Ein (t ) 2 2 φ (1−x 1−γ 1−κ) +4 x 1−γ 1−κ sin     2   2

Eout1 = ( Ein1 )

(2)

    2 (1−(1−γ) x )κ  (1−γ)1−  2 2 φ (1−x 1−γ 1−κ) +4 x 1−γ 1−κ sin     2  

(3)

    2 ( 1 − ( 1 −γ ) x ) κ  (1−γ)1−  2 2 φ (1−x 1−γ 1−κ) +4 x 1−γ 1−κ sin     2  

(4)

When the Eout1 = Ein2 and к1= к2;

Eout 2 (t ) =( Ein2 )

A close examination of equation (2.4) indicates that a ring resonator in the particular case to very similar to a Fabry-Perot cavity, which has an input and output mirror with a field reflectivity, 1 − к, and a fully reflecting mirror, − αL where n0 and n2 are the linear and nonlinear refractive indices, the coupling coefficient is к. Where x = exp 2 2 represents the one round-trip losses coefficient, ~φ0 = kLn0~ and φ NL = kLn2 E1 is the linear and nonlinear phase shift, k = 2π/λ is the wave propagation number in a vacuum, respectively. This nonlinear behavior investigation of light traveling in a single ring resonator (SRR) [9], where the parameters of the system were fixed to λ0 = 1.55 µm, n0 = 3.34, Aeff = 50 µm2, α = 0.5 dB/mm are the bending loss of the waveguide InGaAsP/InP [11], γ = 0.1, r1 = 12–13 µm and r2 = 15–17 µm. The coupling coefficient of the fiber coupler was fixed in this investigation to к1 = к2 = 0.0225. The nonlinear refractive indices were ranged from n2 = 2.2 × 10−15 m2/W [12], and plot 20000 iterations of round-trips inside the optical fiber ring. We assume that φL = 0 for simplicity.

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Fig. 2. Shown the chaotic output and input the micro-ring at the roundtrips 20,000 (a) 10 µm (b) 20 µm. The Fig. 2 show the chaotic behavior of waveguide micro-ring resonator of the series waveguide Fig. 2(a) the radians 10 µm have the chaotic but haven’t the band pass filter and stop band, which the Fig. 2(b) the radians 20 µm have the chaotic filter multi-range.

3. Numerical Simulation In this section, simulation results are presented to illustrate the micro-ring resonator radii 13 µm and 14 µm by show the Fig. 3 the nonlinear behavior micro-ring resonator at the round trip time 20,000. The Fig. 3(a) the radian 13 µm show to nonlinear effect have the filter phenomenon, which the Fig. 3(b) show the nonlinear effect and have range of multi-filter phenomenon.

Fig. 3. Shown the chaotic output and input the micro-ring at the roundtrips 20,000 (a) 13 µm (b) 14 µm.

Fig. 4. Shown the chaotic output and input the micro-ring at the roundtrips 20,000 (a) 16 µm (b) 17 µm.

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In Fig. 4 is the nonlinear behavior micro-ring resonator at the round trip time 20,000. The Fig. 4(a) the radians 16 µm show to nonlinear effect have the stop band filter phenomenon, which the Fig. 4(b) shown the radians 17 µm asperity to the nonlinear effect and have the multi-filter phenomenon.

4. Results

Fig. 5. Have shown the chaotic output and input the micro-ring at the roundtrips 20,000 (a) 12 µm (b) 15 µm (c) R = 12 µm series into the R = 15 µm. In the Fig. 5 shown the nonlinear effect and nonlinear behavior can be the filtering band pass filter and band stop filter to the application transmission of optical system. The Fig. 5(a) shown the nonlinear effect of band stop filter have the range of roundtrips time are 9,050–11,500 roundtrips and the two side band we call the band pass filter of roundtrips time are between 7,550–8,550 roundtrips and 11,500–12,500 roundtrips, which the Fig. 5(b) shown the nonlinear effect of band pass filter have the range of roundtrips time are 8,250–11,550 roundtrips and the side band we call the band stop filter of roundtrips time are 8,000–8,500 roundtrips, 11,500–11,800 roundtrips, Fig. 5(c) shown the nonlinear effect of band pass filter have the range of roundtrips time are 9,550–11,500 roundtrips.

Fig. 6. Shown the chaotic output and input the micro-ring at the roundtrips 20,000 (a) 16 µm (b) 17 µm (c) R = 16 µm series into the R =17 µm.

In the Fig. 6 shows the nonlinear effect and nonlinear behavior can be the band pass filter and band stop filter to the application transmission of optical system. The Fig. 6(a) shows the nonlinear effect of band stop filter have the range of roundtrips time are 9,500–10,500 roundtrips and the two side band we call the band stop filter of

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roundtrips time are between 7,550–8,550 roundtrips and 11,550–12,550 roundtrips, which the Fig. 6(b) same to the nonlinear effect of band pass filter have the range of roundtrips time are 9,000–11,000 roundtrips and the multi-side band we call the band stop filter and band pass filter. The Fig. 6(c) same to the nonlinear effect of band stop filter have the range of roundtrips time are 9,500–10,500 roundtrips. We can be change to the roundtrips are 29 × 10−12 sec/roundtrip.

Fig. 7. Shown the chaotic output and input the micro-ring at the roundtrips 20,000 (a) 16 µm (b) 17 µm (c) R = 16 µm series into the R = 17 µm and the couple coefficient K1 = K2 = 0.5. In the Figs. 7 and 8 shown the nonlinear behavior of filtering in the series micro ring resonator, which the very the couple coefficient K1 = K2 = 0.5 and K1 = K2 = 0.25 of the micro ring resonator can be selected to the band stop filter and band pass filter.

Fig. 8. Shown the chaotic output and input the micro-ring at the roundtrips 20,000 (a) 16 µm (b) 17 µm (c) R = 16 µm series into the R =17 µm and the couple coefficient K1 = K2 = 0.25.

5. Conclusion The series waveguide micro-ring resonator can be application variety benefit and multi-purposes device: such as the chaotic coding, the band pass filtering, chaotic cancellation and the packet switching. We can be future design the three series waveguide micro-ring resonator and the band-pass filter four in one packet to multiple tunable Add/Drop

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filters, which the user can be tunable to channel in the optical remote control. The information security can be send to message by used to band stop filter in the fiber optic system and the filtering chaotic coding to uses.

Acknowledgments One of the authors (W. Suwancharoen) would like to acknowledge the Rajamangala University of Technology Isan Sakon-nakon Campus, Thailand for giving him a scholarship in higher education at King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand. And S. Chaiyasoonthorn and S. Thongmee would like to acknowledge the Ramkhamheang University of Thailand for giving him a scholarship in higher education at King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand.

References 1. P. P. Yupapin and W. Suwancharoen, “Chaotic Noise Control and Cancellation using a Micro Ring Resonator Incorporating an Optical Add/Drop Multiplexer” Optics Communications, Vol. 280, pp. 345–350, 2007. 2. P. P. Yupapin, P. Saeung and W. Suwancharoen, “Coupler-loss and coupling-coefficient dependence of bistability and instability in a fiber ring resonator: nonlinear behaviors,” J. of Nonlinear Optical Physics & Materials (JNOPM). Vol. 16, pp. 1–8, 2007. 3. S. Tak Chu, B. E. Little, W. Pan, T. Kaneko and Y. Kokubun, “Cascaded micro ring resonators for crosstalk reduction and Spectrum cleanup in Add-Drop Filters” J. IEEE Photonics Technology Lett. Vol. 11, No. 11, pp. 1423–1425, 1999. 4. A. Melloni and M. Martinelli, “Synthesis of Direct-Coupled-Resonators Band pass Filter for WDM System” J. Lightwave Tech. Vol. 20, No. 2, pp. 296–303, 2002. 5. A. Melloni, M. Floridi, and M. Martinelli, “Synthesis of direct-coupled resonators band pass photonic filters,” in Proc. LEOS 2000 13th Annu. Meet., Rio Grande, Puerto Rico, Nov. 13–16, ThC4, pp. 704–705, 2000. 6. B. E. Little, S. T. Chu, J. V. Hryniewicz and P. P. Absil, “Filter synthesis for periodically coupled microring resonators,” Opt. Lett., Vol. 25, No. 5, pp. 344–346, 2000. 7. A. Melloni, “Synthesis of a parallel-coupled ring-resonator filter,” Opt. Lett., Vol. 26, No. 12, pp. 917–919, 2001. 8. Y. Kokubun, “Wavelength Selective Integrated Device by Vertically Coupled Microring Resonator Filter” Photonics Based on Wavelength Integration and Manipulation IPAP Books 2 pp. 303–316, 2005. 9. J. Garcia-Ojalvo and Rajarshi Roy, “Spatiotemporal Communication with Synchronized Optical Chaos” Physical review letters, Vol. 86, No. 22, pp. 5204–5207, 2001. 10. C. K. Madsen and J. H. Zhao, “Optical Filter Design and Analysis: A Signal Processing Approach”. New York: Wiley, 1999. 11. T. Aizawa, K. G. Ravikumar, Y. Nagasawa, T. Sekiguchi and T. Watanabe, “InGaAsP/InP MQW directional coupler switch with small and low-loss bends for fiber-array coupling”, IEEE Photonics Technology. Lett. 6, pp. 709–711, 1994. 12. D. K. Sparacin, S. J. Spector, L. C. Kimerling, “Silicon Waveguide Sidewall Smoothing by Wet Chemical Oxidation” IEEE Journal of Lightwave Technology, 23(8), pp. 2455–2461, 2005.

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AN ALTERNATIVE OPTICAL SWITCH USING MACH ZEHNDER INTERFEROMETER AND TWO RING RRSONATORS P. P. YUPAPIN AND P. SAEUBNG Advanced Research Center for Photonics, Department of Applied Physics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand P. CHUNPANG Department of Physics, Faculty of Science, Mahasarakham University, Mahasarakham 44000, Thailand

In this paper, we present an experimental investigation of all-optical switch using a symmetric Mach-Zehnder interferometer (MZI) combined with double fiber ring resonators. Here, we replace the ordinary-fiber ring resonator on one arm of MZI by a 980 nm-laser pumped erbium-doped fiber (EDF) ring resonator to form an EDFA. When adjusting the EDF pump power up we note increasing in switching power. Experimental results indicate that using MZI with double EDF ring, switching power is lowered significantly to nanowatt level in comparison with that of MZI with a single EDF ring of milliwatt level.

1. Introduction Nonlinear behaviors in optical fibers have recently received considerable attention owing to its potential application to all-optical switch (AOS) for future all-optical communication and optical computation [1–3]. However, AOS using silica-based ordinary fiber requires high switching power around few-hundred watts due to low nonlinearity in silicon material. So far, the losses in the ring of actual AOS is very large, which result in the increase of switching power, and even make the device unable switching. In order to solve this problem, two useful configurations have been reported for AOS based nonlinear fiber ring resonator. One is a silica-fiber AOS by coupling a ring resonator with one arm of a Mach–Zehnder interferometer (MZI) [2]. The other consists of fiber ring resonators with fiber directional couplers [3]. Both configurations using a pumped EDF ring acts as a nonlinear medium instead of ordinary fiber ring. Because the gain of EDF compensates all of losses and the EDF has nonlinearity stronger than that of the ordinary fiber, the switching power can be reduced down to milliwatts. In this paper, a newly propose an experimental investigation of all-optical switch using MZI and side-coupled with double fiber ring resonators. Here, we replace the ordinary-fiber ring resonator on one arm of MZI by EDF ring. We adjust a pumped EDF to control parameter of switching power of the AOS. With this configuration, the switching power can be reduced down to nanowatt level and also alternated switch between two output ports of MZI.

2. Nonlinearity Phase Response of Fiber Ring Resonator The proposed AOS using double ring resonators with one arm using EDF ring side-coupled to two arm of MZI is shown in Fig. 1. The circumferences of the two rings are L1 and L2 , and the coupling coefficients between the rings and MZI arms are set to be the same r = 0.3. It was shown in Ref. [2] that at resonance, the ring resonator introduces a phase shift of π to the lightwave propagating on the MZI arm coupled with the ring. If the wavelength of an input optical signal is coincident with the resonance peak of the system, it is dropped to the output1, whereas other signals go to the output2. In the ring, a lightwave from a laser diode (LD) at 980 nm with power P through wavelength-division multiplexing (WDM) pumps the EDF. Here, the gain of EDFA compensates the losses and controls parameters of the switch.

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Fig. 1. The experimental setup of a MZI combined with double fiber ring with one arm using EDF ring. One useful feature of a fiber ring resonator is that the original power gets to build up in the fiber ring and keeps circulating inside the ring. The buildup factor B, which is defined as the ratio of the power circulating inside the ring to the input power, is given by [2]

B=

P1 1− r 2 = P0 1+ r 2 a12 − 2 ra1 cos φ 0

(1)

where P0 is the input power, P1 is the average power inside the ring and r is the reflection coefficient of the coupler. a1 = exp(−α1 L1 / 2) and φ0 = β 1 L 1 are the single-pass field transmission and linear phase shift in the ring, respectively. α1 is the intensity attenuation coefficient, β1 is the wave propagation constant associated with the fundamental mode supported by the ring waveguide, and L1 is the circumference of the upper ring. Under conditions that the incident light is on resonance with the fiber ring and the loss is negligible (a1 = 1), the maximum value of the buildup factor Bmax = (1+ r ) / (1− r ). Thus, when r is very close to unity, the power circulating inside the fiber ring becomes very high. This power buildup can induce nonlinear effects if the ring possesses an intensitydependent nonlinear refractive index n2 that results from the third-order susceptibility ( χ (3) ) of the EDF material [2]. The nonlinear refractive index n2 can be included in the single-pass phase shift as

φ1 = φ L1 + φ NL1 ≅ β1 L1 + γ1 Leff 1 P1 ,

(2)

where Leff 1 = [1− exp(−α1 L1 )] / α1 , is the effective interaction length due to the loss and γ 1 is the nonlinearity coefficient (related to n2 by γ1 = 2 π n2 / λ Aeff , where λ is the input wavelength and A eff is the effective core area of the waveguide). φ L1 and φ NL1 are the single-pass linear and nonlinear phase shifts, respectively. In such a nonlinear case, φ0 in Eq. (1) should now be replaced by φ1 . Thus, by substituting Eq. (1) into Eq. (2), we get a transcendental equation for the single-pass phase shift as

φ1 ( P0 , φ L1 ) = φ L1 + γ 1 Leff 1

1+

r12 a12

1 − r12 P0 − 2r1a1 cos φ1 ( P0 , φ L1 )

(3)

The nonlinear response of switching device can be evaluated by the derivative of phase shift φ with respect to input power P0 . This derivative can be expressed as

8L n d φ1 d φ1 d φ0 dP1 = ≈ 1 2 F2 dP1 d φ0 dP1 dP0 πλAeff

(4)

where F is resonator finesse [2].

3. Experimental Results The experiment is setup as Fig. 1. In the device, the EDF is pumped by an LD at 980 nm to amplify the signal light at 1550 nm. Double ring fiber resonators coupled MZI by symmetrical fused couplers with reflectivity of r = 0.3.

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The MZI has a balance path lengths (i.e. ∆L = 0) while the circumferences for the upper ring is L1 = 12 m and L2 = 8 m for the lower ring. In this paper, we replace the 12 m ordinary fiber ring by a 10 m EDF for the upper ring resonator. The light beam from a tunable diode laser with a 1550 nm wavelength was launched into the system at input port. The output signal at port out1 and out2 were connected to the spectrum analyzer. In the experiment, t he maximum power is launched into the system with the power of 1 mW. The pumping laser at wavelength 980 nm was applied to the EDF ring fiber is in the range of 0–50 mW. A condition for controlling the EDF pump power is adjusted within 0–10 mW for the lower power and 11–50 mW for the higher power.

(a)

(b) Fig. 2. The output switching power with low power pumping laser (a) power output 1550 nm at port 1, and (b) output power at port 2. The output switching power of light at wavelength 1550 nm for each pump power is spliced into port 1 and 2. The corresponding switching powers for low pumping power are approximately 9 and 4.5 nW for port 1 and port 2, respectively, as shown in Fig. 2. While, the high pumping power of EDF, the switching powers are approximately 270 and 20 nW for port 1 and port 2, respectively, as shown in Fig. 3. We also found that, in order to get smaller switching power, we should use the larger reflectivity.

4. Discussion and Conclusion In conclusion, we have experimentally demonstrated the use of the MZI and double fiber ring resonators for optical switching investigation and characterization. The EDF pumping power is adjusted for low power about 0–10 mW and 11–50 mW for high power. To optimize the experimental result can be controlled by the prototype parameters

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such as the optical spectral width, optical power and coupling coefficient. We can concluded with this configuration, the switching power can be reduced down to nanowatt level and also alternated switch between two output ports of MZI.

(a)

(b) Fig. 3. The output switching power with high power pumping laser (a) power output 1550 nm at port 1, and (b) output power at port 2.

References 1. A. Bananej and C. Li, IEEE Photon. Technol. Lett., 16, pp. 2102–2104 (2004). 2. J. E. Heebner, et al., IEEE J. Quantum Electron., 40, pp. 726–730 (2004). 3. C. Li, N. Dou and P. P. Yupapin, J. Optics A: Pure and Applied Optics, 8, pp. 728–732 (2006).

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ENTANGLED PHOTONS GENERATION AND REGENERATION USING A NONLINEAR FIBER RING RESONATOR

S. SUCHAT∗ Department of Physics, Faculty of Science and Technology Thammasat University, Pathumtani 12121, Thailand ∗E-mail: [email protected] W. KHUNNAM and P. P. YUPAPIN† Advanced Research Center for Photonics, Department of Applied Physics Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang Bangkok 10520, Thailand †E-mail: [email protected]

A new technique of an entangled photon pair generation and regeneration characterization using an all fiber optic scheme is investigated. The proposed system is consisted of a fiber optic ring resonator. The Kerr nonlinearity effect in the fiber ring resonator is exploited for the generation of two independent beams. The advantage of such a system is that it requires a simple arrangement without any optical pumping part and bulky optical components. Polarized light pulse trains are launched randomly into a nonlinear fiber optic ring resonator. Where the superpositions of light pulses in a nonlinear fiber optics ring resonator are randomly occurred which is formed the entangled photon pairs. A polarization controller controls polarization states of light pulses while circulating in the ring resonator. The entangled photons are seen on the avalanche photo-detector. Then the output of the entangled photon states recovery by using a fiber ring resonator incorporating an erbium-doped fiber (EDF) has been investigated. We have shown that the weak entangled photon states can be recovered after circulating in the amplified fiber optic medium. The results obtained have shown that this system can be used to achieve the recovered polarization entangled states with the obtained high gain. The amplifying noise has also been detected and seen on the spectrum output. This is affected to the entangled photon visibility, which is discussed. Keywords: Entangled photons; quantum communication; quantum repeater; ring resonator.

1. Introduction Quantum information was theoretical well established by Bennett et al.1 The proposed scheme was also presented for quantum cryptography by the same authors.2 The area of this research is now popularly investigated in either theoretical3 or experimental works that expect to have an implemented system for wide range of application in the near future. This is the uncertainty principle of the information is occurred which can be clarified by the link between sender (Alice) and receiver (Bob), without any cheating by Eave. A single photon can be either particle or light where the case of polarized light pulse having two polarization states corresponding two spin states of a particle that is satisfied the quantum entanglement pair. The initial state of the polarized light input is randomly and the detected signal unknown due to the uncertainty principle that the initial information is loose when the output signal is measured. The applications of the phenomena are such as quantum cryptography, quantum teleportation, quantum key and quantum CODEC (code and decode) that they are popularly studied. Zellinger et al.4 have demonstrated that atom can transported by using a classical channel using a Mach-Zehnder Interferometer (MZI), where the photons in linear or circular polarization states can be formed an entanglement pairs. The quantum cryptography either by free space, wireless or optical fiber has been reported. Weinfurter et al.5 have shown that the quantum cryptography can be realized by using a single photon transmission in a light wave channel. Recently he has demonstrated that four states of polarized light can be used for quantum cryptography using such a simple arrangement. Suchat and Yupapin6 have also shown that using a classical MZI with one arm modulated by a LiNbO3 crystal can generate a single photon. Brendel et al.7 have generated pulse polarization entanglement or pulse energy time entanglement, it had made by MZI, was a delay circuit. But Takesue et al.8 have also shown the same results using Michelson interferometer, where both them having the same result. Silberhorn et al.9 report on the generation of a continuous variable entanglement using an optical fiber interferometer, where the Kerr nonlinearity in the fiber is exploited for the

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generation of two independent squeezed beams. Since the nonlinearity of optical ring resonator has shown great promise for a variety of applications including optical time delay10 and optical switching.11 The idea of the quantum repeater has been proposed for long-distance entanglement.12 This is created by distributing the entangled states over sufficiently short segments of a channel, which can be purified and connected via the entanglement. However, due to their rather low success probabilities in the initial entanglement distribution, these protocols feature the very low communication rates. In this paper, we have made a similar system of the reference9 but in this work, we use a nonlinear fiber optic ring resonator to form the delay and interfere signals, which when polarized generates the pulsed polarization-entangled photons. This is a new scheme that uses all fiber optic system without any optical pumping part to from a polarized light pulses. We have demonstrated that the use of an all fiber optic incorporating a nonlinear fiber optic ring resonator can use to generate the pulsed polarization-entangled photon pairs, which based on the conventional time-bin entanglement arrangement. In case of the regeneration using weak light input (i.e. without pumping part and component), the fiber acts as a nonlinear medium because of the optical Kerr effect and four-wave mixing in fiber ring resonator. When a polarized pulse or polarization entangled photon enters into a fiber ring resonator incorporating an erbium-doped fiber (EDF). Results obtained have shown that the use of such a simple optical set up can be used to generate the entangled photon pairs. 2. Operating Principles A system of an optical fiber interferometer incorporating the entangled states generation setup is as shown schematically in Fig. 1. The entangled photons are generated by the first part of the setup, which was well confirmed by Yupapin and Suchat. There are only the signal and idler entered into a 2 × 2 coupler with the 50/50 coupling ratio. This generates two pairs of the entangled photons which one is entered into the sensing and the other into the reference arm where both arms are coated to obtain the maximum reflected powers. The difference between the round-trip times of two arms is set at. As a result, we can obtain the following polarization entangled state:13 |Φip = |1, His |1, Hii + |2, His |2, Hii

(1)

In the expression |k, Hi , k is the number of time slots (1 or 2), where denotes the state of polarization (horizontal (H) or vertical (V )), and the subscript identifies whether the state is the signal (s) or the idler (i) state. In Eq. (1), for simplicity we have omitted an amplitude term that is common to all product states. We employ the same simplification in subsequent equations in this paper. This two-photon state with H polarization shown by Eq. (1) is input into the orthogonal polarization-delay circuit shown schematically in Fig. 2. The delay circuit consists of a coupler and the difference between the round-trip times of the fiber ring resonator,10 which is equal to ∆t. The polarization controller (PC) is tilted by changing the round trip of the fiber ring is converted into V at the delay circuit output. That is the delay circuits convert; |k, Hi to r |k, Hi + t2 exp(i1 φ) |k + 1, Vi + rt2 exp(i2 φ) |k + 2, Hi + r2 t2 exp(i3 φ) |k + 3, Vi. Where t and r is

Fig. 1.

A schematic diagram of the polarization delay circuit that uses in the experiment.

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Fig. 2. A schematic diagram of the fiber optic ring resonator incorporating an erbium-doped fiber. PC: Polarization control, EDF: erbium-doped fiber, PBC: polarization beam combiner and Ds: avalanche photo detector.

the amplitude transmittances to cross and bar ports in a coupler. Then Eq. (1) is converted into the polarized state by the delay circuit as12 |Φi = |1, His |1, Hii + eiφi |1, His |2, V ii + eiφs |2, V is |1, Hii + ei(φs +φi ) |2, V is |2, V ii + |2, His |2, Hii + eiφi |2, V is |2, V ii + eiφs |3, V is |2, Hii + ei(φs +φi ) |3, V is |3, V ii

(2)

By the coincidence counts in the second time slot, we can extract the fourth and fifth terms. As a result, we can obtain the following polarization entangled state as |Φi = |2, His |2, Hii + ei(φs +φi ) |2, V is |2, V ii

(3)

In this case the fiber acts as a nonlinear medium as a result of the optical Kerr effect. The use of long fiber with a small core is attractive for achieving a high optical intensity and long interaction length. The nonlinearity of the fiber is assumed to be of the Kerr type, i.e., the refractive index is given by11 In case of the system using weak light input (i.e. without pumping part and component), the fiber acts as a nonlinear medium because of the four-wave mixing in fiber ring resonator. When a polarized pulse or polarization entangled photon enters into a fiber ring resonator incorporating an erbium-doped fiber (EDF) as shown in Fig. 2, the nonlinear effect i.e. Kerr type occurs which is induced the entangled states in Eq. (3). An optical amplifier with an intensity gain G.14,15 It is the input amplitude to the coupler 1 and output is the recirculating amplitude in the ring. The resonator recirculating power is extracted from the coupler 2. Where γ and κ are the fractional intensity loss and intensity coupling coefficient of the coupler 1. Fiber attenuation and the fiber ring length are represented as α and L, respectively. The fractional over-all loss of optical components in the ring is η. This includes the power extracted by coupler 2. Full resonance, in particular, is attained when the round-trip intensity loss through the ring is just compensated for by the fractional intensity coupling at coupler 1. Thus, full resonance an optical amplifier with an intensity gain an be writing as G=

e−2αL (1

1 . − γ)(1 − κ)

(4)

When H and V are the states of polarization [horizontal (H) or vertical (V)], and the subscript identifies whether the states is the signal (s) or the idler (i) state. In Eq. (1), for simplicity we have omitted an amplitude term that is common to all product states. As a result, we can obtain the following polarization entangled states. In general, the weak entangled photon states can also be recovered after circulating in

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the amplified fiber optic medium and the photon states can be re-generated by adjusting the polarization controller (PC) of the amplified photons, where the regenerated entangled states can be achieved. Finally, the change in birefringence of the fiber, a transversal walk-off the extraordinary beam and longitudinal walk-off between the ordinary and extraordinary beam is occurred. The transversal walk-off produces a shift between the ordinary and extraordinary while the longitudinal walk-off introduces a time delay between horizontally and vertically polarized photons. The amount of the walk-off depends on the location where the photon-pairs are created within the fiber. This position is completely random due to the coherent nature of light in fiber optic. To compensate the longitudinal timing-walk-off effect, a polarization controller is recommended to ensure that the polarization rotation is the same on both photons from the entangled pair. Additionally the compensator fiber is used to change the relative phase φ of the states of the polarized light. Because of the change in birefringence, the tilting of the compensator allows to apply a phase shift to the entangled states of the two photons, which are given by Eq. (5), 1 |ψi12 = √ (|Hi1 ⊗ |V i2 + |V i1 ⊗ |Hi2 ) 2

(5)

In applications, the walk-off entangled state parameters involving in the measurement are related to the changes in the applied physical parameters such as force, stress, strain, heat, and pressure etc and the fiber optic properties. However, the interested parameters in this proposed systems are concerned the fiber optic birefringence parameters, which can be given by ∆φ =

2π(nx − ny )Lw λ

(6)

where ∆n = (nx − ny ) is the fiber optic birefringence, Lw is the entangled states walk-off length, and λ is the light source wavelength. In principle, the measurement of the change in applied physical parameter relating to the entangled states walk-off length or fiber birefringence is proposed. To obtain the optimal visibility of the entangled photons after walk-off compensation, then the measurement relationship between the polarization orientation phase shift and the applied parameter is temperature in the erbium-doped fiber. When the change a temperature that can be change of phase shift (∆φ). The photon states can also be recovered after circulating in the amplified fiber optic medium by adjusting the polarization controller (PC) or change a temperature of the amplified photons, where the regenerated entangled states can be achieved. The measurement data is obtained by the detector D1 and D2. 3. Experiment and Results The Kerr type nonlinearly of the effect of light pulses in the optical fiber is occurred while circulating in fiber ring resonator. Because of the strong pulses acquire an intensity dependent phase shift during propagation in fiber optic ring resonator. The interference of light pulses at a coupler 1 introduces the out put beam, which is entangled. Due to the polarization states of light pulses are changed and converted while circulating in the delay circuit, where the polarization entangled photon pairs can be generated. To confirm the entangled states the rotation of polarization orientation form 0 to 180◦ can be performed before launched pulse into the polarization beam combined is in a setup. The polarization angle adjustment device is applied to investigate the orientation and optical output intensity. The entangled photons of the nonlinear fiber optic ring resonator are separated to be the signal and idler photon probability. The polarization angle adjustment device is applied to investigate the orientation and optical output intensity. A phase shifter consisting of which could be varied by polarization control fiber (PC1). The output pulses consists of two well-separated pulses which denote them shot and long respectively, which is presented the basis of quantum bit (qubit) space, similarly to the usual vertical |V i and horizontal |Hi linear polarization states. The output photons were detected by the avalanche photodiodes D1 and D2. The delay circuit consists of a coupler and the difference between the round-trip times of the fiber ring resonator, which is equal to 9.9 µs and shown by Fig. 3.

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Fig. 3.

The output pulses from experiment of the time delay between the pair of pulses after pass fiber ring resonator.

Fig. 4. The schematic of the experimental setup diagram; PCs: Polarization Controllers, Ls: Fiber optic length, Ds: Avalanche Photo-detector, PBS: Polarization beam combiner.

The entangled photons probability is shown in term of the optical output intensity which generated by an all fiber optic system of phase difference φ = 0◦ as shown in Fig. 5(a), which is in good agreement with the previous work.7 Figure 5(b) presents the optical intensity at the output of the polarization output, where the phase difference of the signal at first peak and the delay peak of the nonlinear fiber ring resonator is φ = 45◦ . It is shown that the time delay of the signal circulated in the ring resonator is ∆t = 9.9 µs. Results obtained have confirmed that the polarization entanglement of the signal and idler photons are realized and occurred. However, to maintain the output of polarization states for long-haul communication may be require the polarization transmission components to link between the sender and receiver before entering into detector, where the sending information is preserved i.e. unchanged. In practice, the use of all fiber optic components is needed to fulfill the use of quantum communication via fiber optic cable, where the perfect security is realized. The other advantage of such a system is that the ease of fiber optic cable connectors can be applied and realized, then the long haul communication link is secured from Eve. The setup of the entangled photon states and amplitude recovery using a fiber ring resonator incorporating an EDF is shown in Fig. 4. The gain media is a length of high concentration EDF with peak

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Fig. 5.

Graphs of the measured optical signals: (a) φ = 0◦ , (b) φ = 45◦ .

absorption near 1530 nm of 5.0–8.0 dB/m, mode field diameter at 1550 nm of 4.9–6.3 µm. Fiber cladding has a diameter of 125 ± 1 µm, core-cladding concentricity < 0.3 µm, and numerical apertures are in the range of 0.21–0.25. A laser diode pump at 980 nm with maximum power 150 mW is connected to the EDF ring resonator via WDM coupler 2 and 3 with insertion loss is less than 0.3 dB. The optical tunable filter with large tuning range is employed to obtain the entangled photon states at the required wavelengths. The Erbium-doped fiber can be designed to obtain precisely the required amplified signals, while the change in phase is controlled by using the polarization controller (PC2). The adjusting of the polarization angle from 0 to 90◦ , this can be performed by tilting the PC, which caused the change of both entangled states and optical output intensity. To confirm the existence of entangled states, then each photon was input into a polarizer and orientation from 0 to 180◦ before launching into the PBC. The output photons were detected by the avalanche photodiodes. The experimental results are shown in Fig. 6, where (a) is a plot of the optical output intensity of the system (D3 and D4) as a function of polarization angle. Notice that the generated two-photon state is entangled with phase difference φ = 90◦ , which is detected by the avalanche photo detectors D3 and D4. The measurement errors of 4 % are shown by the error bar. The entangled photons due to the nonlinear effect in fiber optic ring resonator are specified by the signal and idler photons. Figure 6(b) shows the output spectrum of the light pulse after circulating in the fiber ring resonator incorporation the EDF. Results obtained have shown that the signal gain up to 16 dB could be achieved, and the polarization entangled states recovered. We found that the noisy signals occurred on the detected spectrum, due to the Kerr effect nonlinear type which is low power and amplified, become the noise floor of the experimental results. However, the detected output still can be performed the entangled photon visibility and valid.

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Fig. 6. Experimental results: (a) The output intensity versus polarization angle, (b) The output spectrum after circulating in the fiber ring resonator incorporating an EDF.

4. Conclusion We have presented a technique that could be used to generate and regenerate pulsed polarization-entangled photon pairs by using an orthogonal pulse polarization delay circuit. The system used is based on the system called time bin quantum entanglement, incorporating a nonlinear fiber optic ring resonator for which the response time of the Kerr effect is much less than the cavity round-trip time. The entangled photon pairs were formed by the interference of randomly delayed orthogonal polarized light pulses while circulating in the fiber ring resonator. In conclusion, we have demonstrated the use of our scheme which is consisted of a fiber ring resonator incorporating the EDF as shown in Fig. 2, where the low optical power entangled states recovery. The results obtained have shown that the entangled states with the lower input can be recovered with higher amplitude by pumping EDF and tilting PC, respectively. This system can be used to recover both low polarized input

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light pulse or polarization entangled states, while the entangled states can be recovered and suitable for long distance quantum communication link. Acknowledgments The authors would like to acknowledge the Department of Applied Physics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang (KMITL), Thailand, for supporting the laboratory facilities. We would like to acknowledge to Department of Physics, Faculty of Science and Technology, Thammasat University, Thailand for some financial support of his study. References 1. C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W.K. Wootters, Teleporting an Unknown Quantum State via Dual Classical an Eistein-Podolsky-Rosen, Phys. Rev. Lett. 70 (1993) 1895–1899. 2. T.C. Ralph, Mach-Zehnder Interferometer and the Teleporter, Physical Review A. 61 (2000) 44301–44304. 3. E. Kreyzig, Introductory Functional Analysis with Applications, John Wiley & Sons, New York, (1978). 4. K. Mattle, H. Weinfurter, P.G. Kwiat, and A. Zeilinger (1996), Dense Coding in Experimental Quantum Communication, Physical Review Letters. 76 (1996) 4656–4659. 5. H. Weinfurter and Ch. Kurtsiefer, Entanglement Based Quantum Communication, KMITL Science Journal. 1 (2001) 35–39. 6. S. Suchat and P.P. Yupapin, An Optical Pulse Generated using Mach-Zehnder Interferometer with a LiNbO3 Crystal Modulator, Proc. ILLMC’ 2001 Conference, Shanghai, China. (2001) 129–132. 7. J. Brendel, N. Gisin, W. Tittel and H. Zbinden, Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication, Physical Review Letters. 82(12), (1999) 4656–4659. 8. H. Takesue, K. Inoue, O. Tadanaga, Y. Nishida and M. Asobe, Generation of Pulsed Polarization-Entangled Photon Pairs in a 1.55- m Band with a Periodically Poled Lithium Niobate Waveguide and an Orthogonal Polarization Delay Circuit, Optics Letters. 30(3) (2005) 293–295. 9. Ch. Silberhorn, P.K. Lam, O. Weib, F. Konig, N. Korolkova, and G. Leuchs, Generation of Continuous Variable Einstein-Podolsky-Rosen Entanglement via the Kerr Nonlinearity in an Optical Fiber, Physical Review Letters. 86(19) (2001) 4267–4270. 10. J.E. Heebner, V. wong, A. Schweinsberg, R.W. Boyd and D.J. Jackson, Optical Transmission Characteristics of Fiber Ring Resonators, IEEE J. of Quantum Electronics. 40(6) (2004) 726–730. 11. K. Ogusu, H. Shigekuni, and Yokota , Dynamic Transmission properties of a nonlinear fiber ring resonator, Optics Letters. 20(22) (1995) 2288–2290. 12. P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, Kae Nemoto, W. J. Munro and Y. Yamamoto, Hybrid Quantum Repeater Using Bright Coherent Light, eprint: quant-ph/0510202 (2006). 13. P.P. Yupapin and S. Suchat, Entangle Photon Generation Using Fiber Optic Mach-Zehnder Interferometer Incorporating Nonlinear Effect in a Fiber Ring Resonator, Journal of Nanophotonics (JNP). 1 (2007) 13504. 14. H. Okamura and K. Iwatsuki, A Finesse-Enhanced Er-Doped-Fiber Ring Resonator, J. Lightwave Technol. 9 (1991) 1554–1560. 15. A. Bananej and Chunfei Li, Controllable All-Optical Switch Using an EDF-Ring Coupled M-Z Interferometer, IEEE Photon. Technol. Lett. 16 (2004) 2102–2104.

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NONLINEAR EFFECTS IN FIBER GRATING TO NANO-SCALE MEASUREMENT RESOLUTION P. PHIPHITHIRANKARN, P. YABOSDEE AND P. P. YUPAPIN Advanced Research Center for Photonics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520

We propose the results of optical Kerr effects in fiber grating for the measurement resolution. When the high power laser is launched into fiber grating, optical Kerr effects are induced in grating region then the effective refractive index is changed depending on the input power. The results that are given by the mathematical simulation, have shown the relation between the reflectivity and Bragg wavelength. All results can be used to analyze and improve the resolution of measurement system for fiber grating sensors and its applications.

1. Introduction Fiber grating has been widely used in both optical fiber sensors and optical fiber communications. In the optical fiber sensors, it becomes very important element for sensing systems to measure strain, temperature, pressure and other parameters [1–6]. Strain sensors have used in a wide range of industry applications such as aircraft, high buildings, nuclear boilers, turbine blades, tunnels, elevators, bridges, oil and gas pipelines and earthquake monitoring [7–9]. Fiber grating has been continually developed and improved to accurately measure. Recently, P.P. Yupapin et al. proposed the nano-scale strain monitoring system using the perturbation method on the fiber grating stretching length to improve the measurement resolution. In the optical fiber communications, it has widely used in optical network such as optical switching, optical add-drop multiplexer, wavelength and time division multiplex [10–12]. The principle used many identical difference of fiber gratings and reflective-transmission properties for coincidently optical processing. Although most applications of fiber grating have focused on the linear properties but some nonlinear properties becomes very importance for the development of optical devices in present such as Hojoon Lee studied the optical pulses transmitted though fiber grating using by phase-shifted grating and nonlinear effect to compare their performance in optical switching [13]. When high pump laser light is incident on fiber grating, optical Kerr effects are induced and modified depending on signal power. The results are optical switching of signal light by intense pump light [14]. Pedro M. Ramos et al. studied the influence of the Kerr-like nonlinearity on the pulse propagation in two types of fiber gratings which are uniform and raised-cosine apodized gratings. H. Alatas et al. studied the result of solitons which propagated in nonlinear Bragg grating, the result shown that the bifurcation is induced and soliton energy is varied [15]. Yosia et al. shown the Cross Phase Modulation (XPM) effect between CW probe and strong Gaussian pump in a fiber grating. The result appeared three potential nonlinear switching applications as optical switching, optical inverter and optical limiter [16]. For the fabrication of nonlinear fiber grating such as H. Liu et al. proposed a novel and flexible method for controlling the chirp rate of a linearly chirped fiber Bragg grating and nonlinearly chirped FBG by adhering a uniform FBG onto a plastic plate with a pre-calculated curvature and applying an axial force on the plate [17]. R.T. Zheng et al. reported a novel fabrication method to generate continuous chirp in a fiber Bragg grating using a uniform phase mask. The result of method has a nonlinear group delay response and an asymmetric bandpass spectrum [18]. From previous paragraph shown widely used of fiber grating and its nonlinear applications. Thus this paper studies the nonlinear effect in fiber grating for the improvement of the measurement resolution. The results will be shown the relation between the characteristics of the fiber grating and the optical Kerr effects.

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2. Mathematical Modeling Consider a uniform fiber grating consists of an average refractive index n0 and a periodic modulation of refractive index in the fiber core. Thus the refractive index profile can be given by

 2π  n( z ) = n0 +∆n⋅cos z Λ  

(1)

where z is the distance along the longitudinal fiber axis, Λ is the grating period, ∆n is the refractive index variation sometime it is called the refractive index perturbation (typically 10−5 to 10−3). It is slowly varying compare to the grating period which is shown in Fig.1. When broadband light is launched into fiber grating. The major wavelength is transmitted but have a specific wavelength is reflected. A specific wavelength is called the Bragg wavelength which depends on grating period and effective refractive index (neff ), is given by

λ B = 2 neff Λ

(2)

Fig. 1. Refractive index modulation profile of fiber grating. Normally the effective refractive index and the grating period are constant for the uniform fiber grating. Using the coupled-mode theory, the reflectivity power at Bragg wavelength can be given by R ( L, λ) =

κ2 sinh 2 ( sL) ∆β2 sinh 2 ( sL) + s 2 cosh 2 ( sL)

(3)

where R( L, λ) is the reflectivity power, which is a function of the grating length and wavelength, L is the grating length, κ is the coupling coefficient, ∆β is the detuning wavevector and s = ( κ2 −∆β2 )1/ 2 . At the center wavelength of the fiber grating the wavevector detuning is zero, therefore the Eq. (3) becomes

R( L, λ) = tanh 2 ( κL )

(4)

When the high power laser is launched into fiber grating, the optical Kerr effect are induced in grating region and the refractive index profile changed which is proportion to the intensity of light, thus Eq. (1) can be rewritten as

 2π  2 n( z ) = n0 +∆n⋅cos z + n2 E ( z ) Λ  

(5)

where E ( z ) is the electric field, n2 is the nonlinear Kerr coefficient. Eq. (3) consists of the first term is average refractive index in fiber core, the second term is the refractive index perturbation and the last term is nonlinear Kerr effect. The third term in Eq. (5) is the main parameter to effect the change of Bragg wavelength, which is discussed. 3. Numerical Results and Discussion Consider the uniform fiber grating with Bragg wavelength at 1550 nm can be plotted the spectrum reflectivity is as shown in Fig. 2.

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Fig. 2. Spectrum reflectivity of the uniform fiber grating with Bragg wavelength at 1550 nm. From Eq. (2) shown the refractive index which consists of an average refractive index (n0 ) and a refractive index perturbation (∆n). Because of n0 is constant thus the refractive index is depending on ∆n which is slowly varying. Figure 3(A) shown the spectrum reflectivity of the uniform fiber grating with the three refractive index perturbation. The Bragg wavelength is linear shifted with ∆n in Fig. 3(B). Normally, a fiber grating have a refractive index perturbation thus the effective refractive index of fiber grating is constant, therefore a fiber grating have a Bragg wavelength which is a specific characteristic of the fiber grating. When the high power laser is launched into fiber grating, optical Kerr effects are induced in grating region. This effect is cause to change the effective refractive index which is shown in Eq. (5) which is consisted of the normally refractive index and nonlinear Kerr effect term. Thus the relation between the variation of Bragg wavelength and optical Kerr effects can be plotted in Fig. 4. From Fig. 4, Bragg wavelength shift when input power is increased because nonlinear term in Eq. (5) to be change, thus the effective refractive index is changed too. Besides Bragg wavelength is changed, the reflectivity of fiber grating is decreased, can be shown in Fig. 5.

Fig. 3. Spectrum reflectivity of the uniform fiber grating with Bragg wavelength at 1550 nm with the variation of the refractive index perturbations.

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Fig. 4. Spectrum reflectivity of the uniform fiber grating with Bragg wavelength at 1550 nm changes due to optical pump power 0 kW, 50 kW, 100 kW respectively.

Fig. 5. Reflectivity and Bragg Wavelength of the uniform fiber grating changes due to optical pump power. From Fig. 5, when input power is continually increased. Bragg wavelength is nonlinear increased and reflectivity is nonlinear decreased. Therefore reflectivity and Bragg wavelength is nonlinear changed when the optical Kerr effect is appeared. However, in practice, the fiber grating sensors are required the linear measurement and high accuracy so the nonlinear effects in fiber grating may be limited the measurement resolution. In opposite, some optical communication systems are required the nonlinear phenomenon such as optical switching required many state of switching which can be created by nonlinear effect, nonlinear effect can be expanded optical bandwidth etc. 4. Conclusion According to the simulation results, the measurement resolution for fiber grating sensors are reduced by nonlinear effects. The simulation results obtained have shown the relation of the characteristics fiber grating as reflectivity and Bragg wavelength are nonlinear changed when Kerr effect is induced. All results can be used to analyze and introduce the problems and factors are impacted to the resolution of measurement system. However, the error from simulated data may be occurred by the determination of fiber grating parameters but the trend isn’t difference. Further, the nonlinear effects on the optical switching by fi ber grating will be investigated in the future work.

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Acknowledgments The authors would like to acknowledge the Advanced Research Center for Photonics (ARCP) for supporting the laboratory research and P. Yabosdee would like to acknowledge the Department of Physics, Faculty of Science, Rajabhat Udornthani University, Thailand, for the scholarships. References 1. Kersey A.D., Davis M.A., Patrick H.J., LeBlac M., Koo K.P., Askins C.G., Putnam M.A., Friebele E.J., “Fiber Grating Sensors”, Journal Lightwave Technology, Vol. 15, No. 8, 1997, pp. 1442–1463. 2. Jaehoon Jung, Hui Nam, Ju Han Lee, Namkyoo Park, and Byoungho Lee, “Simultaneous measurement of strain and temperature by use of a single-fiber Bragg grating and an erbium-doped fiber amplifier”, Applied Optics, Vol. 38, No. 13, 1999. 3. Falciai R., Mignani A.G., Vannini A., “Long period gratings as solution concentration sensors”, Sensors Actuators B, 74 (2001), pp. 74–77. 4. Chen-Chun Ye, Staines S.E., James S.W. and Tatam R.P., “A polarization-maintaining fibre Bragg grating interrogation system for multi-axis strain sensing”, Sci. Technol., Vol. 13, 2002, pp. 1446–1449. 5. Pereira D.A., Frazao O., Santos J.L., “Fiber Bragg grating sensing system for simultaneous measurement of salinity and temperature”, Optical Engineering, Vol. 43, 2004, pp. 299. 6. Iadicicco A., Campopiano S., Cutolo A., Giordano M., Cusano A., “Non-Uniform Thinned Fiber Bragg Gratings for Simultaneous Refractive Index and Temperature Measurements”, IEEE Photonics Technology Letters, Vol. 17, No. 7, July 2005. 7. Hedi Bellil, Mustafa and Abushagur A.G., “Heterodyne detection for Fiber Bragg Grating sensors”, Optics & Laser Technology, 32 (2000), pp. 297–300. 8. Xinyong Dong, Yunqi Liu, Zhiguo Liu and Xiaoyi Dong, “Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor, Optics Communication”, 192 (2001), pp. 213– 217. 9. Moyo P., Brownjohn J.M.W., Suresh R., Tjin S.C., “Development of fiber Bragg grating sensor for monitoring civil infrastructure, Engineering Structures, 27 (2005), pp. 1828–1834. 10. Goh C.S., Set S.Y. and Kikuchi K., “Widely Tunable Optical Filters Based on Fiber Bragg Gratings”, IEEE Photon. Technol. Lett., Vol. 14, 2002, pp. 1306–1308. 11. C. H. Kim, H. Yoon, S. B. Lee, C.-H. Lee, and Y. C. Chung, “All-optical gain-controlled bidirectional add-drop amplifier using fiber Bragg gratings”, IEEE Photonics Technology Letters, Vol. 12, No. 7, 2000. 12. Wilson A., James S.W. and Tatam R.P., “Time-division-multiplexed interrogation of fibre Bragg grating sensors using laser diodes”, Meas. Sci. Technol. 12 (2001), pp. 181–187. 13. Hojoon Lee, “Nonlinear Switching of Optical Pulses in Fiber Bragg Graings”, IEEE Journal of Quantum Electronics, Vol. 39, No. 3, 2003. 14. Masaaki IMAI and Shinya SATO, “Optical Switching Devices Using Nonlinear Fiber-Optic Grating Coupler”, IPAP Books, 2 (2005), pp. 293–302. 15. Alatas H., Iskandar A.A., Tjia M.O. and Valkering T.P., “Rational solitons in deep nonlinear optical Bragg gratings”, Physical Review E, 73, 066606 (2006). 16. Yosia, Shum Ping and Lu Chao, “Bistability threshold inside hysteresis loop of nonlinear fiber Bragg gratings”, Optics Express, Vol. 13, No. 13, 2005. 17. Liu H., Tjin S.C., Ngo N.Q., Tan K.B., Chan K.M., Ng J.H. and Lu C., “A novel method for creating linearly and nonlinearly chirped fiber Bragg gratings”, Optics Communications, 217 (2003), pp. 179–183. 18. Zheng R.T., Ngo N.Q., Binh L.N., Tjin S.C. and Yang J.L., “Nonlinear group delay using asymmetric chirped gratings written in fiber under pre-stretched conditions”, Optics Communications, 242 (2004), pp. 259–265.

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QUANTUM CHAOTIC SIGNALS GENERATED BY A NONLINEAR MICRO RING RESONATOR

C. SRIPAKDEE∗ Department of Applied Physics, Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon, Bangkok 10800, Thailand ∗E-mail: [email protected] W. SUWANCHAROEN and P. P. YUPAPIN† Advanced Research Center for Photonics, Department of Applied Physics Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang Bangkok 10520, Thailand †E-mail: [email protected]

This paper presents a new concept of quantum-chaotic encoding of light travelling in a fiber optic ring resonator. The Kerr nonlinear effects type of light in a fiber optic ring resonator is induced, and the four-wave mixing of the propagating waves at resonance occurred. The output signals can generate the double security which one is the quantum bits i.e. code, and the other is the chaotic signal/code. The proposed system has shown the potential of using for communication security, where the double security via the quantum-chaotic encoding can be performed. Keywords: Nonlinear optics; quantum encoding; chaotic encoding.

1. Introduction Nonlinear of light in the optical devices have shown the potential of broad areas in communications, where the nonlinear penalty of light is now become benefit. The investigation of the nonlinear polarization of light in micro ring resonator1 has shown the promising application for communication security, where the others such as polarization chaos,2 quantum coding,3 quantum chaotic,4 and quantum security5 in optical communication systems have also been investigated. Further, the compared parameters in the parallel-cascaded semiconductor micro ring resonators have also been studied.6 Recent interest in quantum cryptography has been stimulated by the fact that quantum algorithms, such as Shor’s algorithms for integer factorization and discrete logarithm,3 threaten the security of classical cryptosystems. Up to date, the ranges of quantum cryptographic protocols for key distribution, bit commitment, oblivious transfer and other problems4 have been extensively studied. Furthermore, the implementation of quantum cryptographic protocols has turned out to be significantly easier than the implementation of quantum algorithms: although practical quantum computers are still some way in the future, quantum cryptography has already been demonstrated in nonlaboratory settings5 and is on the way to becoming an important technology. Currently, in most high-speed quantum key distribution system (QKD) systems the avalanche photo-detectors (APDs) for detection of different bases and key bit values operate independently in free-running mode. By this means, the highest sifted-key rate achievable equals twice of the inverse of the dead time of the APDs. Moreover, even one could sufficiently increase the quantum channel transmission rate (QCTR) to approach this ultimate limit, the dead time could also induce significant correlation between neighboring sifted-key bits.7 This paper presents the use of two properties of light, i.e. quantum and chaos to encode the chaotic signals generated by the nonlinear polarized light in the micro ring resonator, the signals can be secured under two different codes: quantum key and chaotic codes, which can be performed the information security. In this paper is organized as follows, in sections 2 and 3 we describe the chaotic and quantum behaviors of light in the micro ring resonator respectively. Finally, the result and conclusion sections are presented. 2. Chaotic Behaviors The architecture of a nonlinear micro ring resonator as illustrated in Fig. 1, which is constructed by a single fiber coupler and one micro ring resonator. We assume that the nonlinearity of the fiber ring is of the

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Fig. 1.

Schematic diagram of a micro ring resonator.

Kerr-type, i.e., the refractive index is given by n = n0 + In2 = n0 +



P Aef f



n2 ,

(1)

where n0 and n2 are the linear and nonlinear refractive indexes, respectively. I and P are the optical intensity and optical field power, respectively. The effective mode core area of the fiber is Aef f . The input light (Ein ) is launched in port 3 and the output (Eout ) emerges from port 4. It is worth noting that such a device has no reflected wave or no cross-phase modulation occurred at coupler. The ports 1 and 2 are connected with a micro ring (fiber) having a nonlinear refractive index n2 and a linear absorption coefficient α. The coupling region has an intensity coupling coefficient κ and γ is a coupling loss for the field amplitude. We assume hereafter (without loss of generality) that the optical ring is on resonance for the operating wavelength in the limit of vanishing incident power, i.e. in the linear case. In addition, we assume that the coupler acts as a point device. The coupler is assumed to be reciprocal and the transmission coefficients for the fields are: √ t34 = t21 = (1 − γ) 1 − κ, √ (2) t31 = t24 = i(1 − γ) κ, t32 = t41 = 0. The following relations of the electric fields arise from Eq. (1): E1 = t31 Ein + t21 E2 ,

(3a)

Eout = t34 Ein + t24 E2 .

(3b)

The relation between the electric fields E1 and E2 , in the stationary state, can be obtained from the nonlinear propagation equation: ∂ 2πn2 1 E=i |E|2 E − αE. ∂z λ 2

(4)

Integrating Eq. (4) direct, we can thus obtain the following relation: E2 = E1 τ e−iφ = E1 τ e−i(φ0 +φN L )

(5)

where φ0 = kLn0 and φN L = kLn2 |E1 |2 are the linear and nonlinear phase shift, k = 2π/λ is the wave propagation number in a vacuum, and L is the micro ring resonator length. τ = exp(−αL/2) is a one round trip loss in micro ring resonator (MRR).

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From Eqs. (3) and (5) the relation can be written as p √ E1 (t) = i(1 − γ) κ Ein + (1 − γ) (1 − κ) τ × E1 (t − tR )e−iφ , p √ Ej+1 = i(1 − γ) κ Ein + (1 − γ) (1 − κ) τ × Ej e−iφ ,

(6) (7)

where the subscript “j” denotes the number of round trips inside the MRR. Using Eq. (7), the nonlinear map can be iterated for a given value of the input power Pin (∝ |Ein |2 ). The results show that the output of the MRR can become time dependent even for a CW input. Moreover, the output becomes chaotic signals following a period-doubling route in a certain range of input parameters. From the Eq. (6), we have p √ (8) E1 = i(1 − γ) κ Ein + (1 − γ) (1 − κ) τ E1 eiφ .

While the output field at steady state as Eout

" p = (1 − γ)Ein (1 − κ) −

# (1 − γ)κτ eiφ p . 1 − (1 − γ) (1 − κ) τ eiφ

Thus the normalized of the light field from Eq. (9) can be expressed as " # 2 2 Eout 2 κ[1 − (1 − γ) τ ] 2 Ein = (1 − γ) 1 − 1 + (1 − γ)2 (1 − κ)τ − 2(1 − γ)p(1 − κ) τ cos φ .

(9)

(10)

Equations (7) and (10) are mathematical relations, which they are used for characterizing the nonlinear behaviors such as bifurcation, chaos, and optical bistability, respectively.

Fig. 2.

Optical system for rotating the principal axis of elliptically polarized light by an arbitrary angle.

The polarization rotation system is as shown in Fig. 2, it rotates the principal axis of elliptically polarized light by an arbitrary angle and acts as an optical rotator. The optical system consists of a variable phase plate (the LCSLM) inserted between two crossed quarter-wave plates (QWP’s). The extraordinary axis of the first QWP is parallel to the x axis. The extraordinary axis of the variable phase plate is oriented at 45◦ , and the extraordinary axis of the second QWP is oriented parallel to the y axis. Note that the first QWP in Fig. 2 can be omitted if the incident beam is linearly polarized along the x direction (the direction of the first absent QWP). The Jones matrix M for this system is given by " #" #" # i 0 cos(φ/2) i sin(φ/2) −i 0 M= 0 1 i sin(φ/2) cos(φ/2) 0 1 =

"

cos(φ/2)

sin(φ/2)

− sin(φ/2)

cos(φ/2)

#

(11)

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This matrix is equivalent to an optical rotation matrix R(θ) that will rotate an input Jones vector by an angle θ = φ/2. Therefore this optical system simply rotates the incident Jones vector by an angle that can be controlled by one changing the phase retardation φ of the wave plate.9 3. Quantum-Chaos Polarization Behaviors Yupapin and Suwancharoen8 have shown that the chaotic behaviors of light within a fiber ring can be generated and controlled. The major parameters are the fiber ring radius and the input laser source power which can be ranged from few microns to few meters and few mW to hundred watts, respectively. However the other suitable parameters such as a coupler coupling ratio and fiber loss are also required. From Fig. 1, when a laser source is launched via an input of a design coupler, then the superposition of light is occurred before the resonance at the coupling region. The nonlinear effects are Kerr effects and four-wave mixing presented, where the number of roundtrip i.e. time depends on the input light and ring parameters. In practice, the coupling ratio of light circulation within the ring resonator can be selected to maintain the chaotic behaviors. The possible ring radius is also required to keep in the active device. For instance, the ring radius of 10 micron can be performed such behaviors. The polarization property of light in the micro ring device is required to obtain the optimum entangled photon states at the output detectors D2 and D3 .

Fig. 3. A Schematic of a fiber ring resonator with a pumping part (EDFA). PC: Polarization Controller, BS: Beamsplitter, PBS: Polarizing Beamsplitter, DS: Detectors.

In practice, when the polarization beam splitter is applied into output port of the system. The orthogonal modes are separately detected, where the different time slot between the signal and idler of the generated entangled pair can be used to confirm the transmission states between Alice and Bob. The quantum-chaotic codes can then be generated as following details. Firstly, the quantum bits can be generated by Alice, and the received states can be confirmed by Bob as shown in Fig. 3. Secondly, the chaotic signals or codes can be retrieved by chaotic signal cancellation. Thus, the first random codes represent the first two bits (qubits), and followed by the chaotic signals (codes). This means the concept of using the double security by the proposed technique is plausible. The chaotic behavior of light in fiber ring resonator is detected by a detector D1 . The quantum signals i.e. signal and idler are randomly detected by the two detectors D2 and D3 , respectively, where the entangled pair, i.e. qubits (codes) can be formulated, and the random encoding

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using a quantum-chaotic can be generated. Two photons |Hi , |V i and |V i , |Hi are the entangled photon pair which randomly detected and easy to distinguish due to the different time slots. 4. Simulation Results The polarized light is launched into a ring device as shown in Fig. 3, the simulation results with some given parameters are shown in Figs. (A1)–(A3) in appendix A. The chaotic signals are occurred, the orthogonal modes, i.e. horizontal and vertical components are seen, where the entangled property is also seen. Figure A1 shows the chaotic signal generated by the micro ring resonator, where (a) is the Gaussian input signal, (b) is the chaotic polarizing signals, (c) and (d) is the chaotic polarizing horizontal and vertical signals, (e) and (f) is the magnitude of chaotic horizontal and vertical signals, and (g) is the total magnitude of the horizontal and vertical signals. The parameters are κ = 0.0225 and R = 12 µm. Figure A2 shows the Gaussian input signal in (a), (b) is the chaotic and quantum signals, (c) and (d) is the chaotic horizontal and vertical signals, when κ = 0.025 and R = 10 µm. Figure A3 shows the Gaussian input signal in (a), (b) is the quantum chaotic signals, (c) and (d) is the chaotic horizontal and vertical signals, when κ = 0.025 and R = 7 µm. 5. Conclusion In conclusion, such a proposed technique can be used incorporating the communication link, where the quantum-chaotic codes can be generated and retrieved in transmitted in the link. The quantum chaotic signals can also be randomly formed a set of digital codes, then the switching i.e. a block of codes can also be employed into the system. Which means the secure information can be implemented and plausible. Acknowledgments One of the authors (W. Suwancharoen) would like to acknowledge the Rajamangala University of Technology Isan Sakon-nakon Campus, Thailand for giving him a scholarship in higher education at King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand. References 1. C. Fietz and G. Shvets, Nonlinear polarization conversion using micro ring resonator, Optics Letters 32, (2007), pp. 1683–1685. 2. X. Tang, L.Ma, A. Mink, A.Nakassis, H. Xu, B. Hershman, J. C. Bienfang, D. Su, R. F. Boisvert, Charles W. C. and C. J. Williams, Experimental study of high speed polarization coding quantum key distribution with sifted-key rates over Mbit/s, Optics Express 14 (2006), pp. 2062–2070. 3. P. Shor, Algorithms for quantum computation: discrete logarithms and factoring, IEEE Proceedings on 35th Annual Symposium on Foundations of Computer Science, (1994), pp. 124–134. 4. G. Brassard and C. C´repeau, Quantum bit commitment and coin tossing protocols, in Advances in Cryptology - CRYPTO ’90, A. Menezes and S. Vanstone, Eds. Springer-Verlag, (1991), pp. 49–61, Volume 537 of Lecture Notes in Computer Science. 5. A. Poppe, A. Fedrizzi, T. Loruenser, O. Maurhardt, R. Ursin, H. Boehm, M. Peev, M. Suda, C. Kurtsiefer, H. Weinfurter, T. Jennewein, and A. Zeilinger, Practical quantum key distribution with polarization entangled photons, Quantum Physics Archive: arXiv:quant-ph/0404115, (2004). 6. R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, Parallel-Cascaded Semiconductor Micro ring Resonators for High-Order and Wide-FSR Filters, IEEE J. Lightwave Technol. 20(5), (2002), pp. 900–905. 7. Xiao Tang, Lijun Ma, Alan Mink, Anastase Nakassis, Hai Xu, Barry Hershman, Joshua C. Bienfang, David Su, Ronald F. Boisvert, Charles W. Clark and Carl J. Williams, Experimental study of high speed polarizationcoding quantum key distribution with sifted-key rates over Mbit/s, Optics Express 14, (2006), pp. 2062–2070. 8. P.P. Yupapin, P. Saeung and W. Suwancharoen, Coupler-loss and coupling-coefficient dependence of bistability and instability in a fiber ring resonator: nonlinear behaviors, JNOPM. 16, (2007), pp. 111–118. 9. J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator, Applied Optics 39(10), (2000), pp. 1549–1554.

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Appendix A. The simulation results

Fig. A1. Shows the signals in the micro ring resonator, (a) the Gaussian input signal, (b) the quantum chaotic signal, (c) the chaotic horizontal and (d) vertical signals, (e) the magnitude of the horizontal and (f) vertical signals, (g) the total magnitude, when κ = 0.0225 and R = 12 µm.

Fig. A2. Shows the Gaussian input signal in (a), and (b) the chaotic and quantum signals, the horizontal (c) and vertical (d) components, when κ = 0.025 and R = 10 µm.

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Fig. A3. Shows the Gaussian input signal in (a), and (b) the chaotic and quantum signals, (c) the horizontal (c) and vertical (d) components, when κ = 0.025 and R = 7 µm.

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INVESTIGATION OF PHOTONIC DEVICES PIGTAILING USING LASER WELDING TECHNIQUE M. FADHALI, SAKTIOTO, J. ZAINAL, Y. MUNAJAT, J. ALI AND R. ABDUL-RAHMAN Advanced Photonics Science Institute, Science Faculty, Universiti Teknologi Malaysia (UTM) 81310 Skudai, Johor Bahru, Malaysia *Corresponding author e-mail:[email protected]

Coupling of highly elliptical laser diode emission into single mode fiber using two spherical ball lenses is investigated and the effectiveness of the mode matching with the circular mode field of the fiber is realized. Coupling efficiency is theoretically analyzed by employing ray and Gaussian beam optics. A 100% coupling efficiency is obtained at an optimum working distance of 3.5 mm. the coupling efficiency is found to be largely affected by the angular, lateral and transversal offsets. It can also be controlled significantly by optimizing the lenses separation distance. The experimental measurements agree with the theoretical calculations. However, the maximum coupling efficiency obtained is around 75% due to some practical limitations regarding the positioning of ball lenses and their separation. From the variations of coupling efficiency with lateral, transversal and angular offsets, the effective mode matching is inferred. Laser welding technique with active alignment facilities have been used in the alignment and attachment of all the coupling components. Laser welding pulse parameters have been optimized for reliable weld yields. Keywords: Coupling efficiency; laser welding; misalignment tolerances; mode field; ball lenses.

1. Introduction Coupling of photonic devices into single mode fibers using certain optical coupling schemes can be achieved either directly through butt (direct) coupling or using coupling optical systems such as lenses or fiber tapers4,5,6,8. Butt coupling is found to be inefficient ~ (5–20%) due to the mismatching between the laser diode and single mode fiber mode fields. Different types of microlenses fabricated on the fiber tip from the fiber itself, reported to give significant coupling efficiencies5,9. But the problem of asymmetries in forming the lens on the fiber tip makes them very sensitive to axial, lateral and angular offsets. Besides that they are not cost effective for production. Optical elements and discrete lenses are the best practical methods which can be employed using different types of lenses and a combination of two or more lenses4,5. However, there are some difficulties in using discrete lenses of small sizes for miniaturized photonic devices modules regarding alignment, positioning, and fixing the lenses. For coupling of laser diode into single mode fiber with optimum coupling efficiency and relaxed misalignment tolerances, it is very necessary to adjust all the coupling components at their optimum position which require very high precision and then fixing them at their optimum positions using a reliable and strong attachment method. Apart form the problem of lens aberrations that affect the coupling efficiency, single lens or a combination of two lenses are promising methods for improving the coupling efficiency with wide lateral and angular misalignments. Ball lenses of small diameters have been reported7,8 to be suitable for coupling laser diodes to single mode fibers, but they have been found to be very stringent in alignment and positioning fixation. These difficulties become feasible with the current advancement in laser applications. In this research the process of alignment and fixing of ball lenses inside their holders to the substrate in the path between the laser diode and the fiber can be performed via laser welding technique with dual Nd:YAG laser beams (LW 4000S, Newport) which is employed in this research for coupling and packaging 1550 nm high power laser diode module. Laser welding because of its low distortion of the workpiece, strong and reliable fixing of all the coupling components, cleanliness and automation feasibility is applied for the pigtailing of laser diode modules. The possibility of driving the pigtailed laser diode module during the alignment and welding process along with the measurements of the coupled power at the other end of the fiber provide an active alignment procedure for precise adjustments of all the coupling components at their optimum

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positions. The fiber tip which is to be attached to the module is metallically feruled to enable the welding to the substrate via certain type of welding clips. Relaxed working distance and misalignment tolerances are advantageous for any packaged laser diode module which may enable inserting any optical component and allow flexibility in aging and environmental variations. Moreover, photonic devices that comprise high power laser diodes coupled into single mode fibers require a suitable coupling system for effectively transforming the elliptical mode field of the laser diode into circular mode field that matches very well with the circular mode field of the single mode fiber. 2. Theoretical Analysis The coupling arrangement between the laser diode and the single mode fiber is shown in Fig. 1.

Fig. 1. Laser to fiber coupling arrangement. The elliptical mode field of the laser diode ψ1L at a distance d1 from the laser diode facet is given by1

  x2 y2 2 / π w1 x w1 y exp − + 2   w1 y 2   w1 x

ψ 1L =

  x2 y2 exp − jK 1  +  2R 2 R1 y    1x

   

   

(1)

K1 = 2 πn0 / λ is the wave number or the propagation constant in free space and λ is the wavelength in free space, w1x , w1 y are the beam waist radii perpendicular and parallel to the junction plane of the laser diode facet respectively, the beam waist sizes w1 x , w1 y are the waist radii defined at 1/e2 points of the emitted optical power in the transverse direction. R1x , R1 y are the radii of wavefront curvature perpendicular and parallel to the junction plane respectively. The mode field of the single mode fiber can be expressed as2 ψ

f

=

 x2 + y2 2 / π w f 2 ex p − w 2  f

   

(2)

w f is waist radius of field at the single-mode fiber. After the coupling optics arrangement the laser field is get transformed to become  1

ψ 2 L = 2 /(πw 2 x w 2 y ) exp − x 2  w 

2 2x

+

jK 2 2R2 x

 1 jK 2 exp − y 2  +  w2 y 2 2 R2 y 

   

(3)

   

ω2x, ω2y are the transformed beam waists. R2x and R2y are the transformed radii of curvature in the X and Y directions; k2 is the wave number in the coupling medium. The coupling efficiency is expressed by the overlap integral4

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η =

∫∫ ψ ∫∫

ψ

2 2L

2L

ψ

dxdy

∗ f

2

dxdy

∫∫

(4) 2

ψ

f

dxdy

After substitution, we obtained − 12

η = 4w f

2

2 4   2 K w / w2 x w2 y  (1 + w f 2 / w2 x 2 ) + 2 f 2  4 R2 x    − 12

(5)

2 4   2 K w  (1 + w f 2 / w2 y 2 ) + 2 f 2  4 R2 y   

ABCD ray tracing matrix can be used to express w2 x , w2 y and R2x, R2y in terms of their counterparts before transformations. If the lateral offset is considered, analytical analysis suggests that the coupling efficiency is given as;

 −1  K 2 w 4  2  2 2 2 2 2  η′ =η exp−2dx / w2x (1+wf / w2 x ) + 2 f 4R2 x2      −1   K 2 w 4  2  2 2 2 2 2 2 f  −2d y / w2 y (1+wf / w2 y ) + 4R2 y2      

(6)

where, dx is the lateral offset on X-axis and dy is the lateral offset on Y-axis. When the angular offset is considered, the coupling efficiency is given by

 −1 K 2w 4  2 K22wf 2 2  2 2 2 2 f  + η′′=ηexp− φx (1+wf / w2x ) + 4R2x2  2      −1   K 2 w 4  2  2 2 2 2 2 f  φy (1+wf / w2 y ) + 4R2 y2      

(7)

where φ x , φ y are the tilt angles in the X and Y directions respectively.

3. Experimental Procedure In this research we employed the system of laser weld (LW4000S, Newport) schematically shown in Fig. 2, which consists of an Nd:YAG laser with dual laser beams, welding workstation and motorized stage for laser diode module housing which is connected to a laser diode controller for driving the laser diode module with active alignment facilities. During the alignment of coupling components, the system continuously measures the output power of the laser diode at the free end of the fiber in order to determine the coupling efficiency as illustrated in Fig. 3. A machine vision system pre-positions the housing, and after the system locates the light in the fiber, alignment routines determine the optimum coupling position. The coupling parts are then fixed using two simultaneous laser weld spots.

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Fig. 2. Dual beam laser weld with active alignment.

Fig. 3. Lens alignment and positioning using pneumatic gripper. The laser weld pulse energy and duration as well as the sequence of the spot welds have to be adjusted to compensate the expected deformation and guarantee a well-performing welding joint without introducing unnecessary heat. The spot welds are placed symmetrically to reduce thermal influence. This process compensates for the stress introduced by the welds. The alignment process for all components and the spot-weld quality are monitored by CCD cameras on the welding optics. The welding laser heads include pilot laser beam, which simplifies positioning of the spots and the development of the welding process. In addition, the spot welds can be viewed to determine optimum welding parameters. Two pneumatic grippers are equipped with the system, one for gripping the ferruled fiber tip at the position of maximum coupling power and the other is for gripping the holder of the first lens that is facing laser diode, i.e., collimating lens. The process of realignment and adjustment is performed before using laser welding to fix the lens in its holder on the substrate. The process is repeated for the second lens (focusing lens). Before welding the second lens the alignment process and adjustment of the separations between the two lenses as well as between lenses and laser diode or the fiber tip have to be performed to ensure maximum coupling efficiency with relaxed misalignment tolerances.

4. Results and Discussion In this work a coupling scheme comprising two ball lenses of I mm diameter and different refractive indices have been proposed and investigated theoretically by employing the Gaussian and ray optics to the mode field propagation and transformations. This coupling scheme is then realized experimentally. The experimental measurements agree with the theoretical analysis. The first ball lens which is facing the laser diode has a refractive index of nm = 1.5 which is made of BK7, Grade A Fine Annealed glass and the other lens which is facing the fiber tip has a refractive index of nl = 1.8333, which is made of LaSF N9, grade A, fine annealed optical glass. This coupling scheme shows a very effective mode matching between the mode field of the highly elliptical 1550 nm high power laser diode and the circular mode field of the single mode fiber. Theoretical calculations of coupling

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efficiency with working distance (the separation between the coupling system and the single mode fiber tip) are shown in Fig. 4 for a divergence ratio of θx /θy = 8/33. This result shows that the coupling efficiency is maximum with a wide range of relaxed working distance at the range of (d2 = 2.5–4.5 mm) for an optimum coupling distance d1 of 3.5 mm. the coupling efficiency can reach 100% at an optimum working distance of 3.5 mm. Figure 5 depicts the experimentally obtained coupling efficiency versus working distance. This result shows that the maximum coupling efficiency is around 75% at d2 = 2.25 mm, the working distance can be between (2–3 mm) with some reduction in the coupling efficiency. It is very difficult to fix the lenses at a very tight separation distance as those used in the theoretical calculations. But the possibility of getting similar results is there if the experimental technique can be developed for attaching lenses at very small separation distances.

Fig. 4. Variation of coupling efficiency with the working distance, theoretically.

Fig. 5. Variation of coupling efficiency with the working distance, experiment.

The relationship between the beam waist radii of the elliptical emission of the laser diode on both X and Y directions with the working distance before and after the lens are shown in Figs. 6, 7 respectively. It is clear that the waist radii of the transformed mode field are becoming closer to each other at a range of working distance and are exactly equal at around 3.5 mm whereas before the coupling system as shown in Fig. 7, they are very different except at a very critical working distance at which the coupling efficiency can not exceed 20%. Therefore, Fig. 6 provides the evidence of the effective mode matching and transformation of the highly elliptical mode field

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into circular one that match effectively with the circular mode field of the single mode fiber. The optimum range for the separation between the two lenses is calculated for the case of the experimental divergence ratio (θ x / θ y = 8 / 33) and at the optimum coupling and working distances as shown in Fig. 8. This result illustrates that the optimum range is between 0.35 mm to 0.45 mm which is enclosed by the red dotted vertical lines. The variation of coupling efficiency with both the lateral (d x ) and transversal (d y ) offsets for coupling of a high power 1550 nm laser diode with divergence ratio (θ x / θ y = 8 / 33) and at the optimum coupling parameters is depicted in Fig. 9.

Fig. 6. The variation of the mode waist radii with the working distance for dual ball lenses coupling scheme.

Fig. 7. The variation of the mode waist radii with the working distance before the coupling system.

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Fig. 8. Coupling efficiency variation with the ball lenses separation.

Fig. 9. Effect of lateral and transversal offset on coupling efficiency. This result clearly demonstrates the effective mode matching by efficiently transforming the highly elliptical mode field of the laser diode into circular one. It is evident from the exactly similar effect of both lateral and transversal offsets on the coupling efficiency which is unity when no offset exist and at the optimum coupling parameters mentioned earlier. The experimental variation of coupling efficiency with the lateral and transversal offsets is shown in Fig. 10, which also demonstrate the effectiveness of mode matching and high coupling efficiency that agrees with the theoretical result but with lower coupling efficiency due to the theoretical assumptions and some practical limitations. The same illustration can also be recognized by the theoretical variation of coupling efficiency with the angular offsets as shown in Fig. 11. The ready pigtailed module using laser welding technique is shown in Fig. 12, where the coupling system consists of two ball lenses with the above specifications fixed inside their holders into the main substrates through welding clips using three weld spots from each side. The laser weld spots used for attachment and fixing the components are clear at all interfaces of the welded parts. The pigtailed fiber has been metalized and ferruled inside a metallic tube made of Invar and attached to the main substrate through a saddle-shaped welding clip. Moreover welding materials and welding tools design play a major role in the attachment reliability of all components in the pigtailed module.

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Fig. 10. The experimental variation of coupling efficiency with both lateral and transversal offsets.

Fig. 11. The variation of coupling efficiency with the angular offsets.

Fig. 12. The ready coupled and pigtailed module.

5. Conclusion This paper presented some theoretical and experimental analysis on pigtailing high power laser diode with single mode fiber through two ball lenses coupling scheme. The attachments of all coupling components have been done using laser welding with dual Nd:YAG laser beams during active alignment processes. The mentioned coupling scheme is proven to be very efficient with wide misalignment tolerances due to the effective transformation of the

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elliptical mode field of the laser diode into circular one that matches very well with the circular mode field of the single mode fiber. Theoretically, a 100% coupling efficiency can be obtained at a very relaxed working distance centered at 3.5 mm. The experimental value of coupling efficiency is quite high (75%) compared to the published values for other coupling schemes. It can also be further enhanced by optimizing the parameters of the coupling scheme as shown by theoretical calculations. The optimum working distance is found to be 2.25 mm, which is a wide working distance comparing to the dimension of the module. In employing laser welding technique for packaging of photonic devices that include sensitive optical components in miniaturized modules, laser welding beam parameters have to be optimized to get good and strong weld yields with less heat affected zone to prevent the damage that may happen to those components and at the same time achieving a very localized and strong weld yields.

References 1. A. Yariv and P. Yeh, Photonics; Optical Electronics in Modern Communications, 6th Ed., chap. 2, Oxford University Press, New York, 2007. 2. B. Saleh and M. Teich, Fundamentals of Photonics, John Wiley & Sons, USA & Canada, 1991. 3. M. Saruwatari and T. Sugie T., “Efficient Laser Diode to Single-mode Fiber Coupling Using a Combination of Two Lenses in Confocal Condition,” J. of Quantum Elec., Vol. QE-17, No. 6, 1981. 4. S. Sarker, K. Thyagaralan and A. Kumar, “Gaussian approximation of the fundamental mode in single mode elliptic core fibers,” Opt. Comm. Vol. 49, No. 3, pp. 178–183, 1984. 5. K. Holger and D. Karsten, “Loss Analysis of Laser Diode to Single-Mode Fiber Couplers with Glass spheres or Silicon Plano-Convex Lenses,” J. of LightWave Tech., Vol. 8, No. 5, 1990. 6. V. Shah L. Curtis, R. Vodhanel, D. Bour and W. Young, “Efficient Power Coupling from 980nm, broad area laser to single-Mode Fiber Using a wedge-Shaped Fiber Endace,” J. of Lightwave Tech., Vol. 8, No. 9, pp. 1313–1318, 1990. 7. W. Joyce and B. Deloach, “Alignment of Gaussian Beams,” J. Appl. Opt., Vol. 23, No. 23, pp. 4187–4196, 1984. 8. L. Reith, W. Mann, G. Lalk, R Krchnavek, N. Andreadakis and C. Zah, “Relaxed-Tolerance Optoelectronic Device Packaging”, J. of LightWave Tech., Vol. 9, No. 4, pp. 477–484, 1991. 9. C. Edwards, H. Presby and C. Dragone, “Ideal microlenses for laser-to-fiber coupling,” J. Lightwave Tech., Vol. 11, No. 2, pp. 252–257, 1993. 10. H. Yang, S. Huang, C. Lee, T. Lay and W. Cheng, “High Coupling Tapered Hyperbolic Fiber Microlens and Taper Assymetry Effect,” J. Lightwave Tech., Vol. 22, No. 5, pp. 1395–1401, 2004. 11. Y. Murakami, J. Yamada, J. Sakai, and T Kimura, “Microlens tipped on a single-mode fiber end in GaAsP laser coupling improvement,” Electron. Lett., Vol. 16, No. 6, pp. 321–322, 1980. 12. Y. Odagiri, M. Seki, H. Nomura, M. Sugimoto, and K. Kobayashj, “Practical 1.5 µm LD-isolator-single-modefiber module using a V-grooved diamond heatsink,” in Proc. 6th Eur. Conf. Optical Communication, (York, U.K.), pp. 282–285, 1980. 13. E. Weidel, “New coupling method for GaAs laser- fiber coupling,” Electron Lett., Vol. 11, pp. 436–437, 1975.

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A SOLITON PULSE IN A NONLINEAR MICRO RING RESONATOR SYSTEM: UNEXPECTED RESULTS AND APPLICATIONS P. P. YUPAPIN AND S. PIPATSART Advanced Research Center for Photonics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand N. PORNSUWANCHAROEN Department of Electronic Engineering, Faculty of Industry and Technology, Rajamangala University of Technology Isan, Sakonnakon 47160, Thailand

We present the interesting results of nonlinear behaviors of light within a nonlinear ring resonator system, where optical and electrical signals conversion in frequency, wavelength and time domains can be made by using the chaotic signals generated within the micro ring system. There are three forms of applications using the chaotic behaviors are presented. Firstly, a new system of the simultaneous fast and slow light generation using a soliton pulse propagating within the nonlinear micro ring resonators. Secondly, we propose the simple system of an extreme narrow light pulse generation by using a soliton pulse circulating in the integrated micro ring devices. Finally, a simple system of fast light generation by using a soliton pulse circulating in the integrated micro ring devices is proposed. Using such a system, an attosecond pulse and beyond can be easily generated.

1. Introduction Mobile telephone has been brought to the world for two decades, where there are some technologies involved in many areas of research. Up to date, the searching for new devices and technologies are still needed. For instance, Yupapin and Suwancharoen have reported the use of chaotic signals generated by micro ring resonator for communication security [1, 2], where the transmission signals could be secured by using the analog or digital methods. The increasing in the channel capacity could be achieved by the technique called the chaotic encoding and packet switching [3], where the information could be secured with highly capacity [4, 5]. Recently, Chaiyasoonthorn et al. [6] have reported the interesting results when the ultrafast pulse with pulse width of as could be easily generated by using a soliton pulse travelling in the nonlinear micro ring resonators. The interesting idea is that the system is very small which is capable to implement within the mobile telephone hand set, whereas the required applications can be employed. In this work, we present the other application, where the technique of uplink and down-link can be integrated within a small device called the micro ring devices. Several systems of optical wireless up-down-link converters have been reported [7, 8], however, there is no such a system that can be performed the link within a single system. Our proposed system can be implemented within the mobile telephone handset, where the links can be performed by using the frequency bands generated by the technique called chaotic filtering, where the required frequency bands can be selected and used. Results obtained have shown the good potential application for mobile telephone up-link and down-link device. Lithography has been the well known subject of the electronic device fabrication for years. Several techniques have been developed to meet the new fabrication resolution [11–14], whereas the optical lithography has shown the promising technique of device fabrication due to the dramatically decreased in device dimension. One of them has announced the latest technique where the fabricated resolution within the range of 30–50 nm is achieved [15], whereas the ultra violet (UV) light source is the key operator that can be functioned with the device materials. The optical technique known as harmonic generation is introduced into the technology which can be served the demand of searching such a specific wavelength light source. By using this technique, the specific light source, especially, UV- wavelength can be easily generated. Some works [16, 17] have proposed the harmonic generation technique

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that can be used to generate the specific light source. However, the systems are limited and complicated. Yupapin et al. [18] have reported the interesting results of the ultra-short pulse generation using the nonlinear micro ring resonators, where the attosecond(as) pulse and beyond generation is achieved. After this work, the tremendous works of the chaotic signal generations within nonlinear micro ring resonator have been reported. For instance, the use of chaotic signals in various applications such as signal security [19, 4], high capacity data encoding [5], fast and slow light and ultra-fast switching [6] has been repotred. There are some current works in our research group using the chaotic behaviors in nonlinear micro ring resonators, whereas the searching for novel devices and technologies is the research target [1]. Therefore, the idea of using the spatial mode of the ultra short pulse to increase the resolution of the optical lithography is introduced. In experience, the optical micro ring resonators have been widely investigated [20, 21], which they found that the use of such devices are rapidly increased. We also found that the device scale of few microns was fabricated and available [9] for various applications. Recently, the possibility of using nano ring resonator for realistic applications has been reported [22, 23], where the fabrication of a nano ring resonator or fiber ring device within the range of 200–400 nm in length and the ring radius of 5 µm is plausible. In this paper, the third harmonic generation of the soliton pulse within the micro ring device system is presented, where the generation of the spectral width of 50 pm at the UV-wavelength (512 nm) using the simple system is achieved. Furthermore, the generation of pulse width beyond pm using the proposed technique is also plausible. We have also analyzed the general form of the chaotic signal generation within the micro and nano ring devices. Finally, the potential applications of the super narrow pulse for high density CD writing and reading, high resolution interferometer, surface roughness, atomic imaging and bio tissue non-destructive testing are also discussed. Ultra short light pulses have been the broad areas of research and investigation in many subjects, which is recognized as the important tool for fast improvement of frontier research in the areas. For examples, the areas of applications such as high small scale lithography, high density compact disk writing and reading, high resolution interferometer and surface roughness, high speed switching and communication, high speed optical and quantum computer are included. The sub femtosecond light pulse generations have been reported [24, 25], especially, when the ultra short pulse of few hundreds attosecond pulse was generated and realized. Recently, Yiping Hou et al. [26] have shown that a single attosecond pulse with pulse width of 40 as could be generated in the multicycle-driver regime by adding a weak second-harmonic field. However, in practice, the more flexible and reliable device and system are still required to use in realistic application. Recently, Yupapin et al. have shown the promising idea that the nonlinear effects of light in fiber optic and micro ring resonators [19, 27] could be used in several applications. In principle, the nonlinear effects of light in the device known as Kerr effects and four-wave mixing have shown the potential of applications. The extended details of nonlinear benefits of light were described by Mario [28]. In practice, the micro ring device with the radius of few microns has been constructed [21, 29], where the micro ring devices with radii ranging from 3-15 microns could be fabricated. Storing light is needed when the use of quantum computer being realized. The ability to slow down the speed of light, and to coherently stop and store optical pulses, holds the key to ultimate control of light and has shown potential for optical communications and quantum information processing [30, 31]. There are two major approaches, employing either electronics or optical resonant, however, most of the system impose severe constraints. One of the recent works was proposed, where the general analysis for the criteria to stop and store light coherently using array micro cavities was proposed by Yanik and Fan [32, 33]. However, the system is still complicated, which is difficult to make the realistic implementation. Therefore, the searching for the suitable devices and technologies are still required. Recently, Yupapin et al. [34] have shown that the large bandwidth light pulses can be generated and compressed coherently, whereas the use of such a proposed device in various applications has been reported [35, 36, 37]. 2. Chaotic Soliton Generation An optical soliton is recognized as a powerful laser pulse, which can be used to enlarge the optical bandwidth when propagates within the nonlinear micro ring resonator [5]. Moreover, the soliton self-phase modulation (SPM) keeps

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the large output gain. When the soliton pulse is introduced into the multi-stage micro ring resonators as shown in Fig. 1, the input optical field (Ein) is given by  T   z   Ein = A sec h exp  T0   2 LD 

(1)

Where A and z are the optical field amplitude and propagation distance, respectively. T is a soliton pulse propagation time, and LD = T02 β2 i is the dispersion length of the soliton pulse. β2 is propagation constant. This solution describes a pulse that keeps its temporal width invariance as it propagates, and thus is called a temporal soliton. When a soliton peak intensity ( β2 / γT02 ) is given, then is known. For instance, when the soliton pulse is input into a micro ring resonator at wavelength of 1.55 µm, with a 12 W peak power, then To = 50 ns, which is a pulse of about 2 mm (in z). For the soliton pulse in the micro ring device, a balance should be achieved between the dispersion length (LD) and the nonlinear length (LNL= (1/ γφNL), where γ and φNL are a coupling loss of the field amplitude and nonlinear phase shift. They are the length scales over which dispersive or nonlinear effects make the beam becomes wider or narrower. For a soliton pulse, there is the balance between dispersion and nonlinear lengths, hence LD = LNL .  n  2  n = n0 + n2 I = n0 + (2)  A P,  eff  where n0 and n2 are the linear and nonlinear refractive indexes, respectively. I and P are the optical intensity and optical power, respectively. The effective mode core area of the device is given by Aeff . For the micro ring and nano ring resonators, the effective mode core areas range from 0.50 to 0.1 µm2 [37]. When a soliton pulse is input and propagated within a micro ring resonator as shown in Fig. 1, which can be a series micro ring resonators. The resonant output is formed, thus, the normalized output of the light field can be expressed as

    2 Eout (t) (1−(1−γ) x )κ  =(1−γ)1−  Ein (t) 2 2 φ (1−x 1−γ 1−κ) +4 x 1−γ 1−κ sin     2   2

(3)

The close form of equation (3) indicates that a ring resonator in the particular case to very similar to a Fabry-Perot cavity, which has an input and output mirror with a field reflectivity, (1− κ ), and a fully reflecting mirror. Where κ is the coupling coefficient, and x = exp (−αL / 2 ) represents a roundtrip loss coefficient, φ0 = kLn0 and 2 are the linear and nonlinear phase shifts, k = 2 π / λ is the wave propagation number in a vacuum. φNL = kLn2 Ein Where L and α are a waveguide length and linear absorption coefficient, respectively.

3. Results 3.1. Frequency Converters In this section the key point is that the two different frequencies can be simultaneously generated, where the updown-link converters can be simultaneously operated within a single system. The proposed system of the simultaneous fast and slow light generation is as shown in Fig. 1. The single mode soliton pulse is become many modes (noisy signals) after circulating within the first micro ring device due to the nonlinear Kerr effects of light within the micro ring resonator. The chaotic filtering characteristics of the signals are formed by the other ring resonators within the system. However, in practice, the evidence of such a device in realistic application is required and found in reference [9]. By using the material parameters of InGaAsP/InP, the specified frequency bands can be

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Fig. 1. The schematic diagram of a simultaneous fast and slow light generation. Rs: ring radii, and κs: coupling coefficients. obtained by using the appropriate ring parameters, finally, we ended up with the following details. The soliton waveform with the center frequency at 2 GHz is input into the first micro ring resonator (R1). The optical power is fixed to 550 mW, f0 = 2 GHz, n0 = 3.34, n2 = 2.2 x 10−17 m2W−1, Aeff = 0.50 µm2, α = 0.5 dBmm−1, γ = 0.1, with 20,000 roundtrips. The chaotic signals are generated within the first ring (R1), where the broad frequency band is observed in ring R2. The clearer filtering signals are seen in ring R3 and R4. Figure 2 shows graph of the simultaneous fast and slow light generation for up-down-link converters. Where the parameters are R1 = 10 µm, κ1 = 0.9713, R2 = 10 µm, κ2 = 0.9718, R3 = 10 µm, κ3 = 0.9718, R4 = 15 µm, κ4 = 0.9728. The down-link and up-link converters are shown in Figs. 3 and 4, respectively. Figure 3 shows graph of fast and slow light generation for down-link converter. Where the parameters used are R1 = 10 µm, κ1 = 0.9713, R2 = 10 µm, κ2 = 0.9718, R3 = 10 µm, κ3 = 0.9718, R4 = 15 µm, κ4 = 0.9728. Figure 4 shows graph of fast and slow light generation for up-link converter. When the parameters used are R1 = 10 µm, κ1 = 0.9713, R2 = 10 µm, κ2 = 0.973, R3 = 10 µm, κ3 = 0.9732, R4 = 15 µm, κ4 = 0.9777. In application, the upstream and downstream communication information can be linked via a single system of devices as shown in Fig. 1, for the up-down-link converters. In principle, the communication signals are formed by the signal interchanging devices known as Electrical to Optical (E/O) and Optical to Electrical (O/E) converters. In the system the up-link and down-link frequency bands can be simultaneously generated, therefore, the next step is that the specified frequency band will be selected (filtered) to form the required link converters. By using the proposed system, the wide range of the spread wavelength domain can also be generated and available, which means that the wavelength multiplexing, especially, dense wavelength division multiplexing (DWDM) via optical wireless link is plausible. Moreover, the use of the quantum key distribution via optical wireless link is confirmed by Suchat et al. [10]. However, they have proposed the system of fiber optic ring resonator. By using our proposed system, the quantum key distribution can be generated within the micro ring device which will be able to use with the mobile telephone, therefore, the message can be kept in secret via quantum cryptography. This is shown the indication that the perfect security via mobile telephone network is plausible.

Fig. 2. Graph of simultaneous fast and slow light generation for up-down-link converters, (a) noisy chaotic signals, (b) frequency bands, (c) filtering signals, (d) Up-down-link signals.

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Fig. 3. Graph of fast and slow light generation for down-link converter, (a) noisy chaotic signals, (b) frequency bands, (c) filtering signals, (d) down-link signal (500MHz).

Fig. 4. Graph of fast and slow light generation for up-link converter, (a) noisy chaotic signals, (b) frequency bands, (c) filtering signals, (d) up-link signal (2GHz).

3.2. Wavelength Converters The remarkably simple system of the ultra-short pulse generation using a serial micro ring resonator is as shown in Fig. 5. When a soliton pulse is input into the nonlinear Kerr effects medium (i.e. a nonlinear micro ring resonator), the nonlinear behavior known as chaos is introduced as shown in Fig. 6. For instance, to make the system associate with the practical device, the selected parameters of the system are fixed to λ0 = 1.55 µm, n0 = 3.34 (InGaAsP/InP), Aeff = 0.50 µm2, α = 0.02 dBkm−1, γ = 0.1, and R1 = 20 µm. The coupling coefficient of the micro ring resonator is fixed at κ = 0.5–0.9. The nonlinear refractive index is n2 = 2.2 × 10−17 m2/W. In this work, the system of the third harmonic generation consist the multi-stage micro ring resonators, where the ring radii are selected between 5 and 30 µm. The soliton pulse is coupled into the system with optical power of 1 W, coupling constants (kappa), κ = 0.5–0.9. The selected input pulse widths are 50 ns, 50 ps, 50 fs and 50 as, with the centre wavelength at 1550 nm.

Fig. 5. A schematic of the attosecond pulse generation using the multi-stage micro ring resonators.

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(a)

(b) Fig. 6. Results of the third harmonic generation of the system in Fig. 1, where the input soliton pulses are (a) 50 ns, R1 = 20 µm, R2 = 5 µm, R3 = 28 µm, and (b) 50 as, R1 = 15 µm, R2 = 5 µm, R3 = 32 µm.

After the first micro ring resonator, there optical power is coupled into the second and third ring resonator, respectively. In this case, the wave guided loss used is 0.5dBmm−1. In Fig. 6, when the input soliton with pulse width of 50 ns is input into the system, the chaotic behaviors are occurred within the micro ring resonators R1 and R2, when the ring radii are 20 and 5 µm, respectively. The required filtering signal at the UV wavelength is obtained within the last micro ring, i.e. R3, with the ring radius of 28 µm. The coupling constants used are 0.9 and 0.5 for κ1 and κ2 = κ3, respectively. Similarly, when the other soliton pulses with different pulse widths is input into the same system. The comparison of the third harmonic pulses of the different input soliton pulses are shown in Fig. 7(a). When the selected input soliton pulse width is 50 as, the attosecond pulse with the spectral width of 0.4 nm at wavelength of 516 nm is as shown in Fig. 7(b). Whereas the spectral width obtained is 0.4 nm (400 pm), with the peak power of 200 mW. This is extremely narrow, which can be used for new generation lithography. In principle, the generation pulse width beyond the attosecond input pulse, i.e. zeptosecond, is also plausible.

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(a)

(b) Fig. 7. Results of the third harmonic generation obtained, where (a) all cases from the previous input pulses, and (b) the third harmonic pulse with FWHM of 0.4 nm(400 pm). The simple system of the ultra-short pulse generation using a serial ring resonator system is as shown in Fig. 8. When a soliton pulse is input into the nonlinear Kerr effects medium (i.e. a nonlinear micro/nano ring resonator), the nonlinear behavior known as chaos is introduced as shown in Fig. 9. The soliton pulse is sliced into a broad spectrum covering the large spectrum range due to the optical soliton property and chaotic behavior. To make the system associate with the practical device, for instance, the selected parameters of the system are fixed to λ0 = 1.55 µm, n0 = 3.34 (InGaAsP/InP), Aeff = 0.50 µm2 (for a micro ring), α = 0.02 dBkm−1, γ = 0.1, and R1 = 20 µm. The coupling coefficient (kappa, κ) of the micro ring resonator is ranged from 0.5 to 0.9. The nonlinear refractive index is n2 = 2.2 × 10−17 m2/W. In this work, the system of the third harmonic generation consist the multi-stage micro ring resonators, where the ring radii used are selected between 5 and 32 µm. The soliton pulse is coupled into the system with the optical power of 1 W. The soliton input pulses with pulse widths of 50 ns, 50 ps, 50 fs and 50 as are simulated. After the first micro ring resonator, the optical power is coupled into the second and third ring resonator, respectively. In this case, the wave guided loss used is 0.5 dBmm−1. As shown in Fig. 9, when the input soliton pulse with pulse width of 50 ns is input into the system, the chaotic behaviors are occurred within the micro ring resonators R1 and R2, with the ring radii are 20 and 5 µm, respectively. The UV wavelength pulse is filtered and obtained within the third micro ring, i.e. R3, with the ring radius of 28 µm. The coupling constants used are 0.9 and 0.5 for κ1 and κ2 = κ3, respectively.

Fig. 8. A schematic of an UV pulse generation using a NMRR system.

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(a)

(b) Fig. 9. Results of the third harmonic generation, where the input soliton pulses is 50 ns. The other parameters are R1 = 20 µm, R2 = 5 µm, R3 = 28 µm, and (b) 50 as, R1 = 15 µm, R2 = 5 µm, R3 = 32 µm. Similarly, for the soliton pulses with different pulse widths are input into the same system. The comparison of the third harmonic pulses when the different input pulses used are from ns to as, as shown in Fig. 10(a). When the selected input soliton pulse width is 50 ns, the generation of the spectral width of 0.4 nm at wavelength of 516 nm is achieved as shown in Fig. 10(b). Whereas the spectral width obtained is 400 pm, with the peak power of 550 mW is obtained. In general, the input shorter pulse, i.e. ps/fs into the system can be performed the shorter spectral with, which is allowed the generation of the fs spectral width for fm-lithography. The extended result of the narrow UV pulse generation is as shown in Fig. 4. In this case is differed from the three ring resonators case, whereas the generation of the 50 pm spectral width at FWHM is achieved by connecting the last ring into the previous system. For instance, the ring parameters used are R1 = 16.5 µm, R2 = 12 µm, R3 = 10 µm. The couple coefficients are к1 = 0.95, к2 = 0.2, к3 = 0.95 and к5 = 0.9. The effective areas of the three micro rings are the same, which is equal to 0.25 µm2. The nano ring regime is introduced when the effective area of the last ring of 0.1 µm2 is introduced [37], where the radius of the nano ring used is 5 µm, the coupling coefficient is 0.9. In this case the coupling loss between the effective areas of the third ring (micro ring) and last ring (nano ring) is introduced, which is equal to 0.1 dB (i.e. κ4 = 0.9). The other parameters are the same with the micro ring ones. Results obtained have shown that the extremely narrow pulse generation which can be used for new generation lithography is achieved. The generation of the UV pulse width at FWHM of 50 pm at the center wavelength at 511.125 nm is achieved, where the peak power obtained is 35 mW is. Results obtained from both schemes (i.e. micro ring and nano ring systems) have shown that the generation of a pm spectral width of UV pulse is achieved when the input pulse with pulse width of 50 ns is input into the system. In principle, the generation of the pulse width beyond the ns, for instance, ps, fs and as is also available, which means the generation

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(a)

(b) Fig. 10. Results of the third harmonic generation obtained, where (a) all cases from the previous input pulses, and (b) the third harmonic pulse with FWHM of 0.4 nm (400 pm).

Fig. 11. Result of the UV pulse output obtained from the nano ring (R4), with the pulse width at FWHM is 0.05 nm (50 pm). of the fm pulse width using the proposed scheme is also available. Which is shown that the potential applications of such a extremely narrow pulse for pm and beyond scale lithography, high density compact disk recording, high resolution interferometer and surface roughness using the extremely narrow pulse width are plausible.

3.3. Fast Light Generation The simple system of the attosecond pulse generation using a serial micro ring resonator is a similar system as shown in Fig. 8. When a soliton pulse is input into the nonlinear Kerr effects medium, the nonlinear behavior of light traveling in a micro ring resonator is introduced. To make the system associate with the practical device, the parameters of the system are fixed to λ0 = 1.55 µm, n0 = 3.34 (InGaAsP/InP), Aeff = 0.50 µm2, α = 0.02 dBkm−1, γ = 0.1, and R1 = 10 µm. The coupling coefficient of the micro ring resonator is fixed at κ = 0.25–0.5. The nonlinear

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refractive index is n2 = 2.2 x 10−13 m2/W, and the plot of 20,000 iterations are operated. The system of the attosecond pulse generation consist the multi-stage micro ring resonators, where the ring radii are 10, 5 and 10 microns, respectively. The soliton pulse is coupled into the system with κ = 0.25–0.5.The selected input pulse widths are 50 ns, 50 ps and 50 fs, with wavelength of 1550 nm. After the first micro ring resonator, there is some of the optical power coupled into the second and third ring resonator, respectively. The wave guided loss of 0.5 dBmm−1 is noted. The simulation results with different input peak powers of 7.5, 12.0 and 20.0 W, with pulse widths of 50 ns, ps, fs, as, and zs are investigated. The simulation results of the output signals at the resonant peak power with 20,000 roundtrips are shown in Figs. 12–17. One set of the simulation results has shown that the clear single attosecond pulse could be generated as shown in Fig. 17(b), by using the simulation parameters as followings: ring radii 5–10 microns, input power 12 W, pulse width 50 fs, coupling coefficient к = 0.5. However, all parameters may be changed to investigate more behaviors and characteristics of the devices. The plot of two different input powers and coupling coefficients are shown in Figs. 17 and 18, which is found that the generation of the clear single attosecond peak is achieved when the input peak power is 12 W with к = 0.5 as shown in Figs. 14(d) and 18(c), where the used parameters can be used to generate the single attosecond pulse, which the others could not properly be generated the attosecond pulse. In Fig. 15, the generated attosecond pulse width of 50 as at FWHM is expanded within 20,000 roundtrips, which the one roundtrip is 2.9 × 10−12 sec. The input pulse width of 50 fs is applied into the system as shown in Fig. 18(c). Where the other pulses are interfered and lost within the device. The time lack of those pulses is presented by the link between the devices, which is neglected. The detection of the specific output is specified by time difference. However, the output peak is amplified by the Kerr nonlinear effect within the ring devices. The resonant peak is obtained by the superposition which is called four-wave mixing type. In practice, the input power is used the commercial laser diode [38], which is available in the commercial market.

Fig. 12. The attosecond switching pulse generated by using the multi-stage micro ring devices with 50 ns (a) input pulse, coupling constant к = 0.5, where the ring radii are 10 µm (b), 5 µm (c) and 10 µm (d).

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Fig. 13. The attosecond switching pulse generated by using the multi-stage micro ring devices with 50 ps (a) input pulse (a), coupling constant к = 0.5, where the ring radii are 10 µm (b), 5 µm (c) and 10 µm (d).

Fig. 14. The attosecond switching pulse generated by using the multi-stage micro ring devices with 50 fs input pulse (a), coupling constant к = 0.5, where the ring radii are 10 µm (b), 5 µm (c) and 10 µm (d).

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Fig. 15. The attosecond switching pulse generated by using the multi-stage micro ring devices with 50 as input pulse (a), coupling constant к = 0.5, where the ring radii are 10 µm (b), 5 µm (c) and 10 µm (d).

Fig. 16. The attosecond switching pulse generated by using the multi-stage micro ring devices with 50 zs input pulse (a), coupling constant к = 0.5, where the ring radii are 10 µm (b), 5 µm (c) and 10 µm (d).

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Fig. 17. The relationship between the output pulse and roundtrips (time) with a 50 fs input pulse, the coupling constant к = 0.5, where the input powers are (a) 7.5, (b) 12.0 and (c) 20.0 W.

Fig. 18. Plot of the relationship between the output pulse and roundtrips (time) with a 50 fs input pulse, the different coupling constants are (a) 0.25, (b) 0.35 and (c) 0.5, the ring radii are 10 µm, 5 µm and 10 µm.

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Fig. 19. Shows the pulse width expansion of the output pulse in Fig. 14(d) with the fraction of time of 10−3 of the input power.

3.3. High Capacity Packet Switching This nonlinear behavior investigation of light traveling in a single ring resonator, where the parameters of the system were fixed to λ0 = 1.55 µm, n0 = 3.34, Aeff = 0.30 µm2, α = 0.5 dBmm−1 are the bending loss of the waveguide InGaAsP/InP, γ = 0.1, r1 = 7–15 µm. The coupling coefficient of the optical coupler was fixed in this investigation to к1 = 0.1–0.4. The nonlinear refractive indices were ranged from n2 = 1.7 × 10−13 m2/W, and plot 20,000 iterations of roundtrips inside the optical ring. Figure 20 shows the diagram µ-ring resonator the multi-users via an add/drop device, which is formed by a µ-ring resonator in optical communication network. When the input signal is launched into the communication systems, the multi-users can retrieve the required signals by the drop ports. The soliton pulse with peak power of 2 W is input into the µ-ring resonator in shown in Fig. 1. Figure 21(a) is the wave form of the soliton pulse with pulse width of 50 ps, which is input into the system. Figure 21(b) shows the output signal within the µ-ring resonator, where the chaotic wave form is seen. When the radius used is 10 µm. Simulation results with different input powers are shown in Fig. 22. The input power (A) of 2 W is as shown in Fig. 22(a), where the chaotic soliton behavior is seen when the roundtrips between 9,000 and 11,000. Similarly, In Figs. 22(b) to 22(d), with the input peak powers between 3 and 5 W, with the roundtrips between 8,000–12,500 roundtrips. In this work, the chosen input power is 2 W for our investigation. Figure 23 shows the behaviors of the output of the micro ring device with different ring radii, where the soliton chaotic behavior is occurred with mostly constant output intensity, when the roundtrips are 6,000–14,000, and the ring radius is 7 µm. When the ring radii are 7 and 10 µm, the soliton chaotic behaviors are occurred with the roundtrips between 7,800–12,800 as shown in the Figs. 23(a) and (b). In Figs. 23(c) and (d), the results of the different ring radii of 12 µm and 15 µm have shown that the soliton behaviors are neglected, which means only chaotic oscillation is seen.

Fig. 20. Shows the diagram µ-ring resonator with multi-user via an add/drop devices in the optical network.

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Fig. 21. Shows plot of the input power and the output power with time (roundtrips).

(a)

(b) Fig. 22. Shows graph between the output amplitude intensity and time (roundtrips) with different input peak powers(A).

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(c) Fig. 22. (Continued )

(a)

(b) Fig. 23. Graph of the chaotic behaviors of the output micro ring resonator with different ring radii (R).

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(c) Fig. 23. (Continued )

(a)

(b) Fig. 24. Plot of the chaotic behaviors of the output of micro ring resonator with different couple coefficient (к).

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(c) Fig. 24. (Continued ) Results of the different coupling constants from 0.1–0.4 are shown in Fig. 24. Figures 24(a) and (b) show that the soliton chaotic behaviors are seen with the roundtrips between 4,500–15,500 and 6,100–14,000, with the coupling coefficients are 0.1 and 0.2 respectively. While, the chaotic soliton is not properly occurred in Figs. 24(c) and (d), with the coupling coefficient and к = 0.3 and к = 0.4, respectively. The concept of packet switching and bandpass filtering signal are seen in Figs. 23(b) and 24(b), where a packet of data can be transmitted via a bandpass filter, the there is no data transmitted when the band-stop filter is applied. Which means the packet of data can be secured under band-stop filter operation.

3.4. Long Distance Quantum Communication The remarkably simple system of the intense short pulse generation using a serial micro ring resonator is shown in Fig. 25. When a soliton pulse is input into the nonlinear Kerr effects medium, the nonlinear behavior of light traveling in a micro ring resonator is introduced. In principle, the clear second harmonic light mode is required in this technique, therefore, the chaotic signal is recommended to generate within the series micro ring resonators. After the soliton pulse is input into the first micro ring device as shown in Fig. 25, there are some light modes generated with smaller spectral with than the input pulse, which is obtained by the generated chaotic signals. The selected wavelengths or modes at the specific wavelength are required to obtain the specific use. The optical filter characteristics is employed by using the appropriate ring parameters such as input power and wavelength, ring material refractive index, radius and coupling constant etc.

Fig. 25. Show a schematic diagram of the micro ring resonators for long distance link, where PBS is a Polarizing beamsplitter and Ds are the avalanched detectors.

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Fig. 26. Shows of the chaotic soliton generated by within micro ring resonators.

Fig. 27. Graph of the entangled photon visibility versus the polarization angle. In this investigation, the soliton input power is 450 mW, with centre wavelength at λ0 = 1.55 µm, n0 = 3.34, n2 = 2.2 × 10−15 m2W−1, Aeff = 0.25 µm2, α = 0.5 dBmm−1, γ = 0.1, roundtrips of 20,000. The wave guided loss used is 0.5 dBmm−1. Figure 26 shows the signal behaviors when light pulse is input into the series ring resonators. This can be made to design and select the specific output signal by using the appropriate ring radius and the coupling coefficient (к). When the soliton input power of 450 mW, with pulse width of 50 fs is input into the first ring, the chaotic signal is generated. The clear second harmonic pulses are obtained by the last ring (R3). Where the filtering chaotic signal is obtained with the lower and higher wavelengths at λL = 775 and λH = 2,325 nm, respectively. The centre wavelength is λ0 = 1.55 µm. After the clear second harmonic pulses are combined via the PBS as shown in Fig. 25, the optimum entangled photon visibility is obtained as shown in Fig. 3. The remaining optical power is more than 80% of the input power, which means that there is an amplified part in the system. The soliton behavior is seen, which is suitable for long distance link, while the multi light sources used are also available. Generally, there are two pairs of the possible polarization entangled photons generated within the ring device radius R3, which they are represented by the four polarization orientation angles as [0o, 90 o], [135 o and 180 o]. They can be formed by using the optical component called the polarization rotatable device and PBS. In this concept, we assume that the polarized entangle photon can be performed by using the proposed arrangement. Where each pair of the transmitted qubits can be randomly formed the entangled pairs. To begin this concept, we introduce the

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technique that can be used to create the entangled photon pair (qubits) as shown in Fig. 1, a polarization coupler (i.e. last ring) that separates the basic vertical and horizontal polarization states corresponds to an optical switch between the short and the long pulses. We assume those horizontally polarized pulses with a temporal separation of ∆ t . The coherence time of the consecutive pulses is larger than ∆ t . Then the following state is created by Eq. (4).

Φ

p

= 1, H

s

1, H i + 2, H

s

2, H

(4)

i

In the expression k , H , k is the number of time slots (1 or 2), where denotes the state of polarization [horizontal H or vertical V ], and the subscript identifies whether the state is the signal (s) or the idler (i) state. In Eq. (4), for simplicity we have omitted an amplitude term that is common to all product states. We employ the same simplification in subsequent equations in this paper. This two-photon state with H polarization shown by Eq. (4) is input into the orthogonal polarization-delay circuit shown schematically in Fig. 1. The delay circuit consists of a coupler and the difference between the round-trip times of the micro ring resonator, which is equal to ∆t. The micro ring is tilted by changing the round trip of the ring is converted into V at the delay circuit output. That is the delay circuits convert k , H to be

r k , H + t2 exp(iφ) k +1,V + rt2 exp(i2 φ ) k + 2, H + r2 t2 exp(i3 φ) k + 3, V . Where t and r is the amplitude transmittances to cross and bar ports in a coupler. Then Eq. (4) is converted into the polarized state by the delay circuit as

Φ = [ 1, H s + exp(iφs ) 2, V

] ×[ 1, H i + exp(iφi ) 2,V i ] +[ 2, H s + exp(iφs ) 3,V s ] ×[ 2, H i + exp(iφi ) 2 , V i ] = [ 1, H s 1, H i + exp(iφi ) 1, H s 2, V i ] + exp(iφs ) 2, V s 1, H +exp[i (φs + φi )] 2,V s 2,V i + 2, H s 2, H i + exp (iφi ) 2, H s 3,V i +exp (iφs ) 3,V s 2, H i +exp[i (φs +φi )] 3,V s 3,V i s

i

(5)

By the coincidence counts in the second time slot, we can extract the fourth and fifth terms. As a result, we can obtain the following polarization entangled state as

Φ = 2, H

s

2, H

i

+ exp [ i ( φs + φi )] 2 , V

s

2,V

i

(6)

We assume that the response time of the Kerr effect is much less than the cavity round-trip time. Because of the Kerr nonlinearity of the optical device, the strong pulses acquire an intensity dependent phase shift during propagation. The interference of light pulses at a coupler introduces the output beam, which is entangled. Due to the polarization states of light pulses are changed and converted while circulating in the delay circuit, where the polarization entangled photon pairs can be generated. The entangled photons of the nonlinear ring resonator are separated to be the signal and idler photon probability. The polarization angle adjustment device is applied to investigate the orientation and optical output intensity. To generate the polarized photons, the rotatable polarizer is employed into the system after the ring device as shown in Fig. 1. The polarization control of the output polarized states at polarizing beam splitter is realized. The randomly polarized light in the ring device is formed the specific rotation angle by those two devices. The two orthogonal polarized modes [ H and V ] are performed and detected by the two detectors, where the entangled photon visibility is plotted and seen. The polarization rotation of light travelling along the optical devices is represented by the rotation matrix as equation (6).

M (θ ) = R(θ )MR(− θ )

(7)

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Where,

cos θ R=  sin θ

− sin θ  1 0 =   , , a horizontal linear polarizer cos θ  0 0

 cos 2 θ 0 0  a vertical linear polarizer = 0 1 , and a linear polarizer at θ = cos θ sin θ   

cos θ sin θ   sin 2 θ 

Generally, there are two pairs of the possible entangled photons, which they are represented by the four polarization orientation angles as 0o, 90 o, 135 o and 180 o. The latter pair is formed by using the optical component called quarter wave plate. The entangled photon visibility is obtained by projecting the polarized photon on the measurement detector via a polarized beam splitter as shown in Fig. 24. Two pairs of the entangled photons are occurred by rotating the rotatable polarizer in front the PBS. The optimum entangled photon is obtained when the specific second harmonic modes is generated. In application, for long distance link the optimum entangled photon condition is described by using Bells’ states as the following details. For confirmation of the generality of our Bell-state analyzer, the input state was created by the micro ring to a position where the visibility in the ± basis was almost 0. The output settings of the polarizer result in the highest count rates for a φ+ and a φ− respectively, while the settings for the ψ± input state just measured noise counts. This confirms that the analyzer functions as expected, detecting both the φ+ and φ− components from the input state. To obtain the optimal entangled photon, ψ± =

1 2

( H sVi

± H iVs

) and

Φ± =

1 2

( H s Hi

± ViVs

)

From the above relations, the optimal entangled photon states can be performed by the entangled photon Bells’ states, where the random measurements can be made along the transmission line. In case of an error occurs, the change of initial codes (qubits) can be easily made between Alice and Bob. This is made the difficulty for eavesdropper to attract the codes. When polarized light propagates in optical ring device, the change in birefringence is introduced. This means the changed in phase of the entangled photon pair is occurred. Where the transversal walk-off produces a shift between the ordinary and extraordinary, while the longitudinal walk-off introduces a time delay between horizontally and vertically polarized photons. The amount of the walk-off depends on the location where the photon-pairs are created within the device. This position is completely random due to the coherent nature of light in the optical device. To compensate the longitudinal timing-walk off effect, a polarization controller is recommended to ensure that the polarization rotation is the same on both photons from the entangled pair. Additionally the compensator device is used to change the relative phase φ of the states of the polarized light. Because of the change in birefringence, the tilting of the compensator allows to apply a phase shift to the entangled states of the two entangled photons, which is given by Eq. (8) as ψ

12

=

1 2

(H

1

⊗ V

2

+ e iφ V 1 ⊗ H

2

)

(8)

In applications, the walk-off entangled state parameters involving in the measurement are related to the changes in the applied physical parameters such as force, stress, strain, heat, and pressure etc and the fiber optic properties. However, the interested parameters in this proposed systems are concerned the fiber optic birefringence parameters, which can be given by

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∆φ =

2π ( n x − n y ) L w

λ

(9)

Where ∆n = (nx – ny) is the fiber optic birefringence, Lw is the entangled states walk-off length, and l is the light source wavelength. However, the compensation can be made by using the related parameters as shown in Eq. (9). For instance, the polarization angle rotation can be made by using the rotatable polarizer as shown in Eq. (4). The advantage of this system is that the quantum repeater can be redundant in long distance communication. In case of long distance link, the initial state is required to confirm the correct quantum codes between Alice and Bob, whereas the multi-users are also applicable respecting to the available link power in the transmission line.

3.5. Fast and Slow Lights When the optical power in the form of soliton pulse is input into the first ring of the system as shown in Fig. 27, the nonlinear behaviour occurs, which is induced the noisy signal called chaotic signals. In this case, the optical power of 5W is input into the first micro ring device, where the other parameters are λ0 = 1.55 µm, n0 = 3.34, Aeff = 0.25 µm2. The waveguide ring resonator loss is α = 0.5 dBmm−1. The propagation is loss as low as 1.3 ± 0.02 dBmm−1 at 1.55 µm. The fractional coupler intensity loss is γ = 0.1, and R1 = R2 = R3 = 10 µm. The nonlinear refractive index used is n2 = 2.2 × 10−17 m2W−1, and the data of 20,000 iterations of roundtrips inside the optical micro ring is generated. We assume that φL = 0 for simplicity, however, the change in phase is slightly altered the optical output, which means the dispersion can be neglected when the resonant output is occurred. After the soliton pulse of 5W at the time To = 5 ns is input into the first ring as shown in Fig. 28(a), the chaotic signal is generated as shown in Fig. 28(b). The coupling coefficient κ1 is 0.5. The chaotic cancellation is obtained by using the add/drop filter at drop port 1 as shown in Fig. 28(c), when κ2 = κ 7 = 0.3, and the radius ring resonator R4 = 12 µm. The drop signal obtained is slower in time than the original input signal, which can be named as fast (input) and slow (output) light behaviors. From the result, this is confirmed that the remaining optical power is available for long distance link.

Fig. 28. Schematic diagram of micro ring devices and add/drop multiplexers in the communication link.

Fig. 29. Shows the chaotic and the filter signals obtained at R1 and R4 respectively, (a) input signal (fast light), (b) chaotic signal, (c) drop port signal (slow light).

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In Fig. 30, the output signals at the drop ports of R4, R5 and R6 are seen. There are two forms of the signals, which one is obtained by the bandstop filter, the other is bandpass filter. Where the ring radius R4 = 15 µm, and the coupling coefficient κ2 = κ7 = 0.1 is as shown in Fig. 30(a). There are the identical signals with the separation time of 18 ns. We have named these two signals as “Ghost” and “Signal” for faster and slower in times respectively. Figure 30(b) is the output signal obtained when κ4 = κ8 = 0.3, the ring radius (R5) is 10 µm. Figure 30(c) shows the signal after the cancellation (i.e. bandpass filter) with the parameters used are R6 = 10 µm and the coupling coefficients κ4 = κ8 = 0.3.

Fig. 30. Shows the output signals obtained at drop port R4, R5 and R6, (a) Ghost and Signal, (b) signal and (c) signal.

Fig. 31. Shows the chaotic signals generated by R1, R2 and R3 and the output signals at drop ports R4, R5 and R6, (a) input signal, (b) input and output power, (c) chaotic signal, (d) Ghost and Signal, (e) chaotic signal, (f ) drop port signal, (g) chaotic signal, (h) Ghost and Signal. In Fig. 31, the input power waveform with the center peak at 2 ns is shown in Fig. 31(a), where the relationship between the input and output power is shown in Fig. 31(b). The slower chaotic signals are seen in Figs. 31(c), 31(e) and 31(g), where the corresponding drop port signals are shown in Figs. 31(d), 31(f ) and 31(h). The parameters used are R1 = R3 = R4 = 15 µm, R2 = R5 = 10 µm, R6 = 21 µm, κ2 = κ7 = 0.1, κ4 = κ8 = 0.3 and κ6 = κ9 = 0.1. The bandstop filter signals are obtained in Figs. 31(d) and 31(h), where the bandpass filter signal with slower time (µs) is obtained in Fig. 31(f ). In applications, the communication security can be performed in the networks. By using the proposed system, the chaotic signals can be generated and transmitted into the optical communication link, whereas the specified users along the networks who know the corrected details of the add/drop device can retrieve the required information. However, there are two schemes in the proposed system. Firstly, the chaotic cancellation can be made by using the fast and slow light method. Secondly, a pair of signal and ghost can be used to confirm each other by using the

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specified separation time. In practice, two key points of this application are the secret parameters, and the proposed device is now fabricated and available, which will be implemented in the near future.

3.6. Trapping Light within a Nano-waveguide In this work, the iterative method is introduced to obtain the result as shown in equation (3), similarly, when the output field is connected and input into the other ring resonators. In order to coherently stop a pulse with a given bandwidth, the following criteria must be satisfied; (i) the system must process an initial state with a sufficiently large bandwidth, and (ii) the modulation accomplishes coherent frequency conversion for all spectral components and reversibly compresses the pulse bandwidth. In operation, the large bandwidth within the micro ring device can be generated by using a soliton pulse input into the nonlinear micro ring resonator. The schematic diagram of the proposed system is as shown in Fig. 32, a soliton pulse with 20 ns pulse width, peak power at 500 mW is input into the system. By using the suitable ring parameters, for instance, ring radii R1 = 10 µm, R2 = 5 µm, and R3 = 2.5 µm. To make the system associate with the practical device, the selected parameters of the system are fixed to λ0 = 1.55 µm, n0 = 3.34 (InGaAsP/InP), Aeff = 0.50, 0.25 µm2 and 0.12 µm2 for a micro ring and nano ring respectively, α = 0.5 dBmm−1, γ = 0.1. The coupling coefficient (kappa, κ) of the micro ring resonator is ranged from 0.50 to 0.975. The nonlinear refractive index is n2 = 2.2 × 10−17 m2/W. In this case, the wave guided loss used is 0.5 dBmm−1. As shown in Fig. 2, the signal is chopped (sliced) into a smaller signal spreading over the spectrum as shown in Fig. 2(a), which is shown that the large bandwidth is formed within the first ring device. The compress bandwidth with smaller group velocity is obtained within the ring R2. The amplified gain is obtained within a nano ring device (i.e. ring R3). The stopping light pulse situation can be formed by using the constant gain condition, where a small group velocity is seen. The attenuation of the optical power within a nano ring device is required in order to keep the constant output gain, where the next round input power is attenuated and kept the same level with the R2 output, which they are 30 and 40 mW respectively as shown in Fig. 33. This means that the remaining power of the stopped (stored) light pulse can be absorbed the coupling loss and distributed into the employed system. The other interesting property of the stop light pulse is that the adiabatic behavior of the stopped light pulse is occurred when the roundtrip time is vanished (i.e. stopped) or the stored light pulse switching time is vanished (small group velocity). The stop light concept is formed when the constant gain of the tuned light pulse is achieved as shown in Fig. 34. Since, we have found that the tuned light pulse gain recovery can be obtained by connecting the nano ring device into the system (i.e. R2), therefore, the coupling loss is included due to the different core effective areas between micro and nano ring devices, which is given by 0.1dB. However, we have already described that the other ring parameters are also very important to keep stopping light pulse behavior. We can conclude that the tuned light pulse can be stored or stopped in the nano ring device when the output gain is reached a constant value which is time independence, as shown in Figs. 33 and 34. By using equation (3), the output gain of light pulse within a ring R3 is obtained. The output gain of a ring R3 can be attenuated and reached the value that can be used for the next storing input power, which is shown in Fig. 34(d). The main parameters that can provide the constant are κ31, κ32 and the output power.

Fig. 32. A schematic of an all optical stopped and stored light pulse system, Rs: ring radii, κs: coupling coefficients, κ31 and κ32 are coupling losses.

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(a)

(b) Fig. 33. Results obtained when a soliton pulse is input into a ring resonator system, where the parameters used are (a) R1 = 10 µm, R2 = 5 µm, R3 = 2.5 µm, center wavelength at 1,550 nm, and (b) R1 = 10 µm, R2 = 5 µm, R3 = 4 mm, center wavelength at 1,550 nm, with 50,000 roundtrips.

Fig. 34. Results obtained when light is stored within a nano ring device with 25,000 roundtrips, the ring radii are R1 = 10 µm, R2 = 5 µm, R3 = 4 µm, optical memory time (tom) is 1.505–1.506 ns. In principle, the soliton behavior known as SPM is performed when the balance between the dispersion and nonlinear length phase shift is presented, which is induced the soliton pulse gain recovery is occurred. When light pulse is slow down and completely stopped within a ring R3, the stopped and stored light pulse time of 1ps (10−12 s) is achieved. In application, the memory (ROM) time can be increased by expanding the gain constant time. Furthermore, the adiabatic fashion of light pulse is seen when the number of roundtrip (circulation time) is small comparing to the switching time, for instance, when the pulse is stopped while the switching pulse reaches the switching time at ps, fs, as, zs, etc. The switching time is not a negative value, i.e. positive, therefore, the number of roundtrip of stopping light pulse that can be stored light within the nano ring resonator (waveguide) is vanished, which is induced the ratio of number of roundtrip and switching time is vanished (i.e. time is vanished). This is the concept of cold light when the adiabatic and reversible pulse bandwidth compression process is introduced.

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4. Conclusion We have proposed the very interesting results that the simultaneous fast and slow light could be generated by using the nonlinear micro ring devices. The system is consisted by a series of four nonlinear micro ring devices. We have shown that the two different frequency bands could be generated and selected, which they are normally used in the up-down-link converters in optical wireless link system. The key advantages of the system are the simultaneous generation of up and down link frequency bands, and the frequency band generation can be formed in the single system. The optical power in the system is generated by using a soliton pulse within the nonlinear Kerr type micro ring devices. Therefore, the remaining optical power is able to perform the link. Further, there are more frequency bands available, which is suitable to implement more applications. The remarkably simple scheme of third harmonic generation using soliton pulse propagating in micro ring devices is presented. This is shown the potential applications of such a narrow pulse for pm scale lithography, high density compact disk recording, high resolution interferometer and surface roughness. In applications, the exact roundtrips time at the resonant peak power can be controlled and selected, where the required pulse width can be selected and used. Further, the pulse width beyond the pico pulse width can also be generated with the same principle. This is available for the applications such as new generation of ultra fast switching and lithography, including high capacity compact disk processing, high resolution image construction, and high resolution interferometer. The simple scheme for fast light pulse generation has been proposed, where light pulse with switching time of attosecond and beyond is generated, using the multi-stage nonlinear micro ring devices. We found that the generation of the extremely short pulse in the range of 50 zeptosecond and beyond is plausible. In practice, the temporal mode detection of such a narrow pulse (i.e. short response time) is the problem in the realistic application due to the optical material bandwidth limitation, therefore, the detection technique is become the subject of investigation rather than the device material. However, the use the spatial mode is useful, where the new generation optical lithography with a very fine pen will be the next generation lithography. We have shown that a large bandwidth of the arbitrary wavelength of light pulse can be compressed and tuned to store within a nano-waveguide. The tuned pulse can be slow down and stopped coherently when the matching between dispersion and nonlinear length is exhibited, whereas the soliton SPM pulse exhibits the gain constant within the soliton period. The selected light pulse can be trapped and used to perform the memory. The adiabatic storing pulse process to preserve the coherent information encoded can also be performed. The key advantages of the system are the reversely compress bandwidth and the maintaining power, which can be tuned to obtain the arbitrary pulse for optical/quantum memory (ROM). By using the proposed system, the applications such as quantum repeater, quantum entangled photon source and quantum logic gate can also be available, which can be fulfilled the concept of computer by light i.e. quantum computer being realized.

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AUTHORS INDEX

Asgari, A. 1 Bavili, M.A. 1 Chaiyasoonthorn, S. 42 Chunpang, P. 48 Fadhali, M.M.A. 72 He, X. 18 Huang, D. 18 Jukgoljun, B. 31 Khunnam, W. 52 Konaka, K. 7 Nukeaw, J. 24 Pecharapa, W. 24, 31

Phipithirankarn, P. 60 Pipatsart, S. 81 Pornsuwancharoen, N. 81 Saeung, P. 35, 48 Sripakdee, C. 65 Suchat, S. 52 Suwancharoen, W. 42, 65 Tangtrongbenjasil, C. 7 Techitdheera, W. 24, 31 Thanomngam, P. 24 Thongmee, S. 42 Wang, D.N. 18 Yabosdee, P. 60 Yu, Y. 18 Yupapin, P.P. 35, 42, 48, 50, 60, 65, 81