Nonlinear Optics of Nanoparticles and Nanocomposites

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Nonlinear Optics of Nanoparticles and Nanocomposites Quandou Wang Changchun Institute of Optics, Fine Mechanics and Physics, Changchun, China

Jianfeng Xu University of Arizona, Tucson, Arizona, USA

Rui-Hua Xie Queen’s University, Kingston, Canada

CONTENTS 1. Introduction 2. Nonlinear Optics of Nanoparticles 3. Nonlinear Optics of Nanocomposites 4. Conclusions Glossary References

1. INTRODUCTION In the past 10 years, the scientiﬁc activity of the synthesis and study of so-called “nanoparticles” [1–17], indicating particles with diameter in the range of 1 to 20 nm, has became a major interdisciplinary area [18–21] of research in the world. As the sizes of the particle become smaller, the ratio of the surface atoms to those in the interior increases, thereafter leading those kinds of particles to play an important role in the properties of novel functional material. Those signiﬁcant properties, such as chemical, electronic, mechanical, and optical properties, of nanoparticles obviously distinguish them from those of the corresponding “bulk” material. In particular, one of those signiﬁcant properties is the nonlinear optical (NLO) response of nanoparticles, which is enhanced remarkably with respect to the relative “bulk” materials, due not only to their atomic scale structures but also their interface and surface structures [22]. Materials with large third-order optical nonlinearity and fast response time are essential for future optical device applications [16, 17]. Thanks to such a high nonlinear optical ISBN: 1-58883-064-0/$35.00 Copyright © 2004 by American Scientiﬁc Publishers All rights of reproduction in any form reserved.

response of these NLO materials, they are thought to be good candidates for use in ﬁber-optic communication systems, such as all-optical switching [23], routing units, digital signal restoration, and multiplexing and demultiplexing, as well as optical storage media and optical limitter applications [17]. Therefore, intensive investigations on NLO of nanoparticles have recently been carried out. In the meantime, nanocomposites [24–28] formed by metal or semiconductor nanocrystals embedded in dielectric hosts have been intensively studied as these materials might also become an attractive alternative for the development of all-optical switching devices in waveguides [29]. Strong optical nonlinearities observed due to dielectric or quantum conﬁnement effects, such as nonlinear optical absorption and second and third optical nonlinearities, can be studied for making optical limiters, optical modulators, and laser second and third harmonic generators [16, 17]. In this chapter, we brieﬂy highlight and review the current advances and achievements in studying the NLO properties of nanoparticles and nanocomposites in Sections 2 and 3, respectively. Remarks and outlooks are given in Section 4.

2. NONLINEAR OPTICS OF NANOPARTICLES 2.1. Theoretical Explanation The ﬁrst experimental study of nonlinear optical properties of metal nanoparticle colloids was reported by Ricard et al. [30]. Later, Hache et al. [31] gave a theoretical model calculating the electric-dipole third-order susceptibility of conduction electrons in a metal sphere. They ascribed that Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 8: Pages (101–111)

102 the large effective third-order nonlinear susceptibility, 3 , of metal nanoparticle colloids is substantially enhanced by a resonance that is due to the effective medium, the surface plasma resonance: collective oscillation of the conduction electrons of the metal under the inﬂuence of an applied electromagnetic wave, as expected by direct extension of the Maxwell–Garnett theory. The enhancement of the local electric ﬁeld, which occurs in the particles at frequencies close to the surface plasmon resonance, is responsible for the ampliﬁcation of their NLO properties as compared with those of bulk metal. For the large third-order nonlinear susceptibility of semiconductor nanoparticles, Chemla and Miller [32] identiﬁed that the enhancement of nonlinearity is due to the combination of local ﬁeld effects from dielectric conﬁnement and saturable excitonic resonance. In addition, they predicted that these effects would be greatly enhanced since the particles are so small that they also exhibit quantum conﬁnement. Many other authors also have predicted enhanced optical nonlinearities, resulting from quantum conﬁnement effects, with respect to the corresponding bulk materials [33–35]. Hanamura [36] analyzed theoretically the oscillator strength and the third-order optical polarizability 3 due to excitons in semiconductor microcrystallites. The NLO polarizability is shown to be greatly enhanced for an assembly of such microcrystallites as the exciton is quantized due to the conﬁnement effect and the excitons in a single microcrystallite interact strongly enough to make the excitons deviate from idea harmonic oscillators. Cotter et al. [35] have found that three-dimensional quantum conﬁnement can alter radically the nonlinear optical properties of semiconductors in transparency region. This discovery that introducing quantum conﬁnement can enhance this ratio has opened new opportunities for practical exploitation of the quantum-size effect in NLO devices. Schwarze et al. [37] have developed a new model that combines the interaction between two physical mechanisms responsible for bulk third-order optical nonlinearity. The two physical mechanisms are: (i) saturable absorption, due to quantum conﬁnement in nanoparticles, (ii) electrostriction, causing particles to migrate in the ﬂuid host. Schwarze et al. [37] have shown that enhanced optical nonlinearities are predicted to result from local ﬁeld coupling and those oscillations can occur under certain conditions. In such a computationally feasible theoretical model, which describes the interaction between two nonlinear optical mechanisms, particles are free to move and cluster in the presence of optical ﬁeld gradients, modifying the local electric ﬁeld, which in turn modiﬁes the effective permittivity of each nanoparticle. The coupling together of these phenomena can lead to signiﬁcantly enhanced 3 coefﬁcients, and we have shown that oscillatory behavior can occur under certain conditions. The numerical simulations based on this model have shown the change in the bulk refractive index as a function of the particle size, concentration, and incident intensity. The model also has implications for designing some novel switching devices, which are optimal in the sense that particle sizes and concentrations can be

Nonlinear Optics of Nanoparticles and Nanocomposites

chosen to maximize the magnitude of the third-order optical susceptibility, 3 . Very recently, Prot et al. [38] have initially applied a recursive transfer matrix method to calculate the electromagnetic ﬁeld response for three-dimensional systems of scattering spheres to the study of nanocomposite material. Their calculations have shown that mutual interactions between nanoparticles are responsible for large local ﬁeld enhancements as compared with ﬁelds inside isolated particles. According to the experimental study to measure the third-order nonlinear susceptibility of Au:SiO2 , they discovered that the imaginary part of 3 values diverges from the theoretical predictions and does not vary linearly with the metal concentration. This discrepancy, attributed to the large enhancement of the local ﬁeld, proves the qualitative agreement between the local ﬁeld calculations and experimental nonlinear measurement.

2.2. Experimental Techniques In the study of optical nonlinearity of nanoparticles, there are huge research works concerning the measurements of third-order nonlinear susceptibility, 3 . In these works, experimental technique plays a very important role in carrying out the NLO measurement of 3 . In our review of the NLO of nanoparticles, it is necessary to introduce several primary measurement approaches to obtain 3 . The most powerful or popular methods to measure the third-order nonlinear susceptibility 3 may be degenerate four-wave mixing experiments (DFWM) and the Z-scan technique [17]. DFWM is a nonlinear optical technique that produces a coherent signal by nonlinear interaction of light with the samples in the beam-crossing region. The coherent signal obtained with such a nonlinear technique is in the form of a laser beam that is coherent and directional. It can be spatially separated and spectrally ﬁltered to reject the intense luminosity in many application ﬁelds. DFWM showed a great promise for sensitive measurements of transient species. DFWM involves the interactions of three beams incident on a sample. The three beams are arranged in such a way that two of the beams (pump beams) are counterpropagating each other and the third beam acts as a probe. The fourth beam, which constitutes the conjugate beam, retraces exactly the path of the probe beam. Three input beams of nearly equal power are divided by the beamsplitters. Two of the input beams have the translation stages so that the arrival time at the sample can be varied. The beam spot size in the sample is approximately 0.5 mm in diameter. The beam geometry is shown in Figure 1. The three input beams are labeled 1, 2, and 3, and 4 is the output beam, which is generated by the input beams through 3 . Beam 2 is time advanced or delayed relative to beams 1 and 3 (which are coincident in time), providing the temporal response of 3 . The angle between beams 1 and 3 in the sample is about 1 degree. This geometry permits the generated beam, 4, to be spatially separated from the more intense incident pulses and gives a high signal-to-noise ratio. This is important for DFWM experiments because all the beams have the same frequency. The signal beam, 4, is directed to the entrance slit of a spectrometer, recorded, and then analyzed by using

103

Nonlinear Optics of Nanoparticles and Nanocomposites Y

K2

X

K1 K3 Z

K3

K4

K1

K2

LENS

SAMPLE APERTURE

Figure 1. The beam geometry of DFWM techniques. The three input beams are labeled 1, 2, and 3. The output beam is labeled 4.

a photomultiplier and a boxcar interfaced to a microcomputer. Three beams were polarized parallel to the Y -axis. 3 The tensor component 1111 is measured, and the value of 3 1111 can be expressed as a function of beam energies by using the four-wave mixing model described in [39], 3 1111

1/2 cn2 0 20 45E4 l expl/2 ≈ 32 2 2 l 8E1 E2 E3 1 − exp−l

(1)

where c is the speed of light in vacuum, n is the index of refraction of the sample, Ei is the pulse energy of the ith beam, 0 is the laser beam waist at the focus, is the pulse width, l is the sample length, and is the sample absorption coefﬁcient at the incident wavelength 0 . Z-scan [40–42] is also a simple, sensitive technique which relies on the transformation of nonlinear phase shifts into far-ﬁeld amplitude deﬂections to obtain the complex nonlinear refractive index n2 = n2 + in2 . However, the Z-scan technique has great advantages compared to the DFWM method, which consists of its ability to separate the imaginary and real parts of 3 and, additionally, to determine the signs of the two components. It is essentially a derivative of the ubiquitous single-beam-power-in versus power-out transmission measurement [43] but attains greater efﬁciency by focusing the beam and translating the sample. The technique involves the measurement of the transmittance through an aperture placed in the far ﬁeld as the sample is translated through the focus of a Gaussian beam. For a sufﬁciently small aperture, this procedure provides a measurement of the real part of the nonlinear refractive index n2 . If the aperture is fully opened so that the detector collects all the light, then the Z-scan provides a measurement of the imaginary part of the nonlinear refractive index n2 or, alternatively, the nonlinear absorption coefﬁcient . If > 0, then the Z-scan will result in a trough, indicative of an induced absorption. If < 0, then the Z-scan will produce a peak, indicating an induced transparency. Since all the ﬂux from the sample is collected at the detector, the transmitted power may be calculated without having to perform the free-space Fresnel propagation to the aperture. The normalized transmittance may be expressed as [44] T z =

m=0

m + 1−3/2

−I0 Leff 1 + z2 /z20

2 (2)

where z is the longitudinal displacement of the sample from the focus, is the nonlinear absorption coefﬁcient, I0 is the

on-axis peak intensity at the focus, Leff is the effective interaction length, z0 is the Rayleigh diffraction length, and the temporal proﬁle of the pulse has been assumed to be Gaussian. Typically, if the series converge, only the ﬁrst few terms are needed for numerical evaluation. Hence, the coefﬁcient may be determined from a ﬁt of this expression to the empirical data. Femtosecond optical kerr effect (OKE) [45–48] and transient grating scattering [49–51] techniques are also available approaches to measure nonresonant third-order optical nonlinearity of nanoparticles. Both techniques rely on an impulsive stimulated scattering [52–54]. Both the fundamental and the (anti)stokes frequency involved in this process are supplied by the ultrashort laser pulses. For 50 fs pulses the nuclear motions between 0 and 300 cm are probed.

2.3. Third-Order Nonlinear Optical Response Pincon et al. [55] have studied the third-order NLO response of Au:SiO2 thin ﬁlms, under the inﬂuence of gold nanoparticle concentration and morphologic parameters. Based on their result, we ﬁnd that, as the metal concentration reaches a few percent, the mutual electromagnetic interactions between particles greatly enlarge the nonlinear optical response of the material and cannot be neglected in the theoretical analysis. Moreover, the thermal treatment leads, for a given concentration, to a signiﬁcant increase of the nonlinear response, which is ascribed to a modiﬁcation of the material morphology. They ﬁnally point out that the material nonlinear properties are very sensitive to the incident wavelength through the local ﬁeld enhancement phenomenon. In their study, the nonlinear optical measurements are performed by using the Z-scan technique. Vales of Im 3 range from −0049 ± 0009 × 10−6 to −64 ± 12 × 10−6 esu as a function of the variation of metal concentrations before the thermal treatment. After anneal, it gives values from −069 ± 006 × 10−6 to −60 ± 06 × 10−6 esu. Smith et al. [56] also used the Z-scan technique at a wavelength (532 nm) near the transmission window of bulk gold to measure the nonlinear absorption coefﬁcient of continuous approximately 50-Å-thick gold ﬁlms, deposited onto surface-modiﬁed quartz substrates. They have fulﬁlled both open- and closed-aperture Z-scans to determine either the real or imaginary part of the third-order susceptibility that requires a measurement of both nonlinear absorption and nonlinear refraction. Closed-aperture Z-scans did not yield a sufﬁcient signal for the determination of the nonlinear refraction. However, open-aperture Z-scans yielded values ranging from 51.931023 to 5.331023 cm/W in good agreement with predictions, which ascribe the nonlinear response to a Fermi smearing mechanism [31]. It should be mentioned that the sign of the optical nonlinearity is reversed from that of gold nanoparticle composites, in accordance with the predictions of mean ﬁeld theories. For the other metal nanoparticles, Takeda et al. [57] have applied a negative Cu ion-implantation technology to obtain the nanoparticle on the silica glass substrate. The DFWM method was performed to measure the 3 at 532 nm with a second harmonic generation (SHG) light of Nd:YAG lasers and 561 nm with a SHG-pumped dye laser. As a standard

104

Nonlinear Optics of Nanoparticles and Nanocomposites

sample, CS2 was used to evaluate absolute values of 3 . Nonlinear optical susceptibility 3 of Cu implanted silica exhibits values of 20 × 10−9 ± 20 × 10−8 esu near the peak of the plasma resonance. The estimated value of 3 for the Cu nanoparticles is 90 × 10−9 –80 × 10−8 esu. For semiconductor nanoparticles, the most studied is cadmium sulﬁde [58, 59]. The others, like InP, CdSe, CdTe, ZnS, ZnSe, Pbs, and PbSe, were reported in lots of studies. Those nanomaterials with large third-order optical nonlinearity and fast response time are essential for optical device applications in optical computing, real time holography, optical correlators, and phase conjugators [60]. Therefore, CdS and Pbs semiconductor nanoparticles as “quantum dot” materials are of interest for their large third-order NLO response and have been extensively investigated [61–64]. In works of Liu et al. [65], they use the Z-scan technique with 150-fs laser pulses at 780-nm wavelength to carry out the third-order susceptibility measurement of Pbs-coated CdS nanoparticles. The ion displacement technique was used in their work to obtain the Pbs-coated CdS nanocomposites. In such a technique, semiconductor material (Pbs) grows on a seed of CdS in microemulsion media. Their experimental result of high third-order refractive nonlinearity of conﬁned semiconductor nanoparticles in the transparent region is in agreement with the prediction of Cotter et al. [66], who conﬁrmed that the optical Stark effect makes a dominant contribution to the third-order refractive nonlinearity in this case when the absorptive nonlinearity can be negligible. Other types of nanoparticles, such as magnetic nanoparticles, can be found, for example, in the review paper of Aktsipetrov [67]. In summary, three aspects of nonlinear magneto-optics of magnetic nanoparticles are considered: (a) Correlation between GMR and NOMOKE has been experimentally approved [68]. (b) Magnetization-induced hyper-Rayleigh scattering has been observed [69]. (c) An internal homodyne mechanism for weakly nonlinear processes is suggested [69, 70].

Most recently, Pan et al. [71] have investigated the thirdorder optical nonlinearity of nanopolyacetylene using a femtosecond OKE technique at wavelengths from 790 to 860 nm. The ultrafast nonresonant effective second-order hyperpolarizibility for single polyacetylene nanoparticles was estimated to be as large as 10 × 10−27 esu, which corresponds to a single carbon atom contribution equal to 50 × 10−33 esu. We ascribe such observations to the highly ordered structure of nanopolyacetylene and suppose that the delocalization of the electrons along the conjugated chains is responsible for such properties. For convenience, Table 1 summarizes some results of the third-order optical nonlinearities of nanoparticles.

3. NONLINEAR OPTICS OF NANOCOMPOSITES 3.1. Metal Nanocomposites We consider nanometric metal spheres dispersed in a thin dielectric ﬁlm. The optical constants of the nonlinear medium are intensity dependent and can be written as n = n + I

(3)

= + I

(4)

where n , and I are linear refractive index, linear absorption coefﬁcient, and the instantaneous light intensity, respectively. The nonlinear absorption coefﬁcient and nonlinear refraction coefﬁcient are proportional to the imaginary or real parts of the third-order optical susceptibility 3 as = 3 3 /40 cn2

(5)

= 3k 3 /20 cn2

(6)

where k is the modulus of the wave vector in vacuum and c is the speed of light in vacuum. The experimentally measured optical susceptibility 3 of the composite material is

Table 1. Third-order optical nonlinearities of nanoparticles measured by different experimental techniques. Nanoparticles Au:SiO2 as deposited Au:SiO2 as annealed Au@CdS Cu Polyacetylene Au:BaTiO3 CdS:BaTiO3 Au:TiO2 Rh:BaTiO3 Si-nc Au doped in aluminum Ad doped in aluminum ZnTe PbS by PVB CdS Au:BaTiO3

(nm) 532 532 800 532 790–860 800 800 780 308 813 532 532 532 595 470 800

7 ns 7 ns 100 fs 120 fs 100 fs 100 fs 130 fs 17 ns 60 fs 5 ns 25 ns 400 fs 120 fs

3 (10−10 esu)

Method

State of material

Ref.

−490 to −64000 −6900 to 60,000 0.724±0.140 90 to 800 0.001 0.066 0.158 2300 5710 4 to 28 3.2 to 9.0 1.9 to 2.5 27,000 106,000 11000 100 to 10

Z-scan Z-scan OKE DFWM OKE OKE OKE OKE Z-scan Z-scan DFWM DFWM DFWM DFWM DFWM OKE

ﬁlm ﬁlm ﬁlm ﬁlm solution ﬁlm ﬁlm ﬁlm ﬁlm ﬁlm ﬁlm ﬁlm ﬁlm ﬁlm solution ﬁlm

[55] [55] [108] [57] [71] [108] [108] [109] [110] [111] [112] [112] [113] [114] [115] [116]

Note: and are the wavelength and pulse duration of the laser source, respectively.

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Nonlinear Optics of Nanoparticles and Nanocomposites 3

related to the intrinsic NLO third-order susceptibility m of metal crystal [72] 3 = pf 2 f 2 m3

(7)

f = 30 / + 20

(8)

where p is the volume fraction of metal nanocrystal, f is the local ﬁeld effect, and 0 and are the dielectric constants of the matrix and metal, respectively. Near the surface plasmon resonance ( + 20 = 0), f becomes resonant and 3 is thus enhanced by local ﬁeld effects. Metal nanocomposites can be synthesized by several techniques, such as sol–gel [73], sputtering [74], ion implantation [75], and pulsed laser deposition [76]. These nanocomposites normally present linear optical absorption due to both surface-plasmon resonance and strong third-order nonlinear optical susceptibility. The spatial conﬁnement of the metallic electrons by the insulating host produces an enhanced electromagnetic ﬁeld due to the large dipole moment induced by an optical ﬁeld. Furthermore, for very small nanocrystals, the conﬁnement of the electronic wave functions in either the initial or ﬁnal states to a volume, which is much smaller than their bulk mean free path, produces an additional contribution to the electric susceptibility. Sella et al. [77, 78] have synthesized Au:SiO2 nanocomposites by radio frequency sputtering techniques. The metal concentration varies from 8% to 35%. Several characterization techniques such as transmission electron microscopy and small angle x-ray scattering have shown that the metal particles are spherical and randomly dispersed, the mean particle size varying from 2.6 to 4.8 nm as a function of the metal concentration. The Z-scan technique [79], as described in Section 2, is a simple and useful method to measure the third-order nonlinear properties of materials. This method enables us to measure both the real and the imaginary parts of 3 , proportional to the nonlinear refractive index and nonlinear absorption coefﬁcient, respectively. Sella et al. [77, 78] have measured the optical nonlinearities of these Au:SiO2 ﬁlms with a metal volume fraction of 20% using a Q-switched Nd:YAG laser frequency doubled at 532 nm and characterized by a pulse duration of 7 ns at a repetition rate of 10 Hz. Open aperture measurement exhibits a maximum close to the waist of light, which reveals a large negative coefﬁcient. They derived Im 3 = −30 ± 05 × 10−6 esu. The absolute value for the real part is smaller than 3 × 10−9 cm2 /W. Liao et al. [80] also investigated the optical nonlinearity within Au:SiO2 ﬁlms in the picosecond range at 532 nm by the DFWM method. They found that the third-order susceptibility increases quickly and reaches a maximum value of 25 × 10−6 esu at 40% Au. For 20% Au, their work led to 3 = 20 × 10−7 esu, much smaller than the result of Z-scans in the nanosecond range. This is due to the fact that the third-order optical susceptibility 3 contains two components: a fast component and a slow one [81]. When a picosecond laser is used, the slower component would not have enough time to respond. Thus, the 3 signal measured by picosecond pulses could be much smaller than that measured by nanosecond pulses. Ballesteros et al. [82] have successfully deposited Cu nanocomposite ﬁlms comprising Cu nanocrystals embedded

in an amorphous Al2 O3 matrix by a pulsed laser deposition (PLD) technique. The mean diameter of Cu nanocrystals ranges from 3 to 6 nm. The third-order susceptibility 3 of the ﬁlms was determined by means of a Z-scan technique using a cavity-dumped synchronously pumped, mode-locked rhodamine 6G laser tuned at 590 nm (slightly off the SPR at 578 nm) and providing 30 ps laser pulses at a repetition rate of 400 kHz. They have investigated metal size dependence of the third-order nonlinearity within Cu:Al2 O3 thin ﬁlms. Both thermal effect and electronic components were found to contribute to the nonlinear refractive index. The thermal contribution goes up with the increase of the metal size. This is understandable because the increase of metal diameter is accompanied by an increase of absorption of the ﬁlm near the SPR; thus the thermal load of the medium also increases. It was observed that the electronic contribution to nonlinear refractive index increases from 8 × 10−10 to 14 × 10−9 cm2 /W when the nanocrystal is decreased. From the nanocrystal size dependence, the authors clearly demonstrated that the nonlinearity is caused by quantum conﬁnement effects whose large contribution is associated to intraband electronic transitions. The large nonlinear refractive index and 3 have led many authors to suggest potential applications for the metal nanocomposites in optoelectronics. However, some difﬁculties remain to be addressed before these types of device application will be realized. Flytzanis et al. [83] deﬁne a ﬁgure of merit for strongly absorbing nonlinear optical materials to be 3 / , where is a relaxation time. We can get metal nanocomposites with high values of 3 , but both 3 and have a peak near the same wavelength (surface plasmon resonance wavelength). The high value of and the long thermal relaxation time of the insulating matrix decrease the ﬁgure of merit, particularly for laser excitation lasting longer than a few picoseconds. Recently work has been aimed at ﬁnding methods of maintaining a high 3 while decreasing the surface plasmon absorption. One way to accomplish this is to get a narrow size distribution of extremely small crystals. Because there exists the difﬁculty of producing a suitably narrow size distribution, some researchers have aimed at forming bimetallic core–shell nanoparticles [84]. Changes in the electronic properties across the core–shell boundary add an additional degree of freedom for the reduction of and for increasing 3 . Recently, some researchers [85] have synthesized transparent Ag nanocomposite ﬁlms by incorporating surface-modiﬁed silver nanoparticles into polystyrene through solution mixing and static casting. The Ag nanoparticles could be redispered well in the polymer matrix. By time-resolved femtosecond OKE experiments at 830 nm, they found that the 3 increases with increasing the particle size.

3.2. Semiconductor Nanocomposites The effects of particle size on optical properties are more pronounced in semiconductor nanoparticles. In metals, the Fermi level is in the center of the conduction band where the energy levels are closely spaced, whereas in semiconductors, the band edges control the optoelectronic behavior. As the average particle size decreased, the optical

106 absorption onset shifted to higher energies [86]. This is one example of quantum conﬁnement induced shift in semiconductor nanocrystals. Semiconductor nanocrystals have been proposed as light-emitting diodes [87] and single-electron transistors [88]. They have potential applications in optical limiting, optical computing, real time holography, optical correlators, and phase conjugators because of their high optical nonlinearity. Semiconductor nanocrystals embedded in glass may be synthesized by co-sputtering and thermal annealing. Other techniques for producing nanocomposites include direct chemical reaction in aqueous or organic solution [89] or inverse microemulsion techniques [90]. Among them, more attention has been paid on the sol–gel process in recent years due to the very low temperature involved in preparing this kind of NLO material. The third-order NLO susceptibility 3 can be measured by four-wave mixing or the Z-scan technique. The experiments normally were performed with a low power continuous wave, Ar ion, and high power Nd:YAG lasers operating at different laser wavelengths and pulse duration. The origin of the third-order optical nonlinearity may come from nonlinear refraction and nonlinear absorption. Normally, the optical nonlinearity is composed of an electric component (short time response) and thermal part (long time response); these can be separated by different measurements. The second-order nonlinear optical susceptibility 2 can be measured by second harmonic generation or Maker fringes. The optical limiting effect is easily observed in nonlinear optical materials. The need to protect optical sensors and human eyes from the damage induced by the high ﬂuences of pulsed lasers has led to increased attention for optical limiting materials [17]. Oak et al. [91] reported earlier the intensity-dependent transmission of CdSx Se1−x and CdSex Te1−x particle doped glasses at wavelengths of 1054 nm employing a mode-locked Nd:glass laser with a pulse width of 6 ps. They found that the transmission for the samples dropped down when the input energy increased. The linear absorption is negligible; the main mechanism of energy loss is from two-photon absorption. However, at higher intensities additional absorption induced by the laser-generated electron–hole pairs was observed. By a modiﬁed inverse microemulsion technique, Han et al. [90] synthesized Ag2 S coated CdS nanoparticles (about 10 nm in diameter). They measured by the Z-scan technique the nonlinear absorption in the Ag2 S/CdS nanocomposites at 532 nm with both 25 ps and 7 ns pulses from two frequency-doubled Nd:YAG lasers. Enhanced nonlinear absorption in the nanocomposites was observed in comparison with the CdS nanoparticles, due to photo-excited free carriers. The relaxation times of the free carriers in the Ag2 S/CdS nanocomposites were determined to be a few nanoseconds. Furthermore, optical nonlinearities in the nanocomposites depend on the ratio of Cd2+ and Ag+ , which enables us to optimize and synthesize desired optical materials. Wu et al. [92] investigated the optical nonlinearity of nanosized CdO–organosol. Two samples, CdO–CTAB (cetyltrimethyl ammonium bromide) and CdO–DBS (dodecylbenzene sulfonate) organosols, were measured by using the Z-scan technique with an 85 fs pulse of a Ti:sapphire

Nonlinear Optics of Nanoparticles and Nanocomposites

laser operating at a wavelength of 800 nm with a repetition rate of 82 MHz. Nonlinear absorption and refraction from the samples were observed. The real and imaginary parts of 3 at 800 nm have been determined to be −155 × 10−16 m2 /W and 0.91 cm/GW for CdO–CTAB organosol, and −697 × 10−16 m2 /W and 8.64 cm/GW for CdO–DBS organosol. The optical Stark effect and surface trapped states are the possible origins of the observed optical nonlinearity. Liu et al. [93] prepared PbS–polymer (C1-PEO-C11MA-40, NMA, AN, EGDMA, etc.) nanocomposites by polymerized bicontinuous microemulsions. The size of PbS nanocrystal is about 5 nm formed in aqueous domains embedded in the NMA/AN/C1-PEO-R-MA-40 copolymer network. They measured the nonlinearity of the nanocomposites at 780 nm using 150 fs pulses delivered by a mode-locked Ti/sapphire laser, operating at a repetition rate of 76 MHz. Its third-order nonlinear refractive index () at 780 nm is −68 × 10−12 cm2 /W, three orders higher than that of commercial bulk materials. Such a large optical nonlinearity might be due to the surface-induced large separation of charges between the delocalized electrons and localized holes. Two-photon absorption generally involves a transition from the ground state of a system to a higher lying system by simultaneous absorption of two photons and leads to a fast optical limiting phenomena in semiconductors, such as ZnO, ZnSe, InSb, etc. [94], as well as in some organic materials. Recently, Sanz and Lbanez [95] synthesized sol–gel glasses doped with nanocrystals of stilbene 3. The organic– inorganic nanocomposite materials can be highly doped with active molecules through the control of nanometerscale crystallization. In the nanosecond regime, nonlinear absorption was observed in the spectral range from 450 to 650 nm. The nonlinear absorption occurs in a two-step process, which is characterized by two-photon absorption and excited-state absorption spectroscopies. The two-photon absorption spectrum of stilbene 3 nanocrystals shows a resonance at 620 nm with a cross-section !TPA = 33 × 10−48 cm4 s/photon molecule. The excited state absorption spectrum of stilbene 3 nanocrystals, which was obtained by using a pump–probe ( = 355 nm) geometry supercontinuum laser light with a 30 ps time resolution, exhibits a broad resonance with a maximum at 670 nm and a decrease of quasilinear absorption at blue wavelengths. It is interesting to mention that Maciel et al. [96] reported nonlinear absorption experiments which were performed with a class of ferroelectric glass–ceramic samples. The samples were prepared by heat treatment of (in molar %) 35 SiO2 –31 Nb2 O5 –19 Na2 O–11 K2 O–2 CdO–2 B2 O3 glass. A set of glass–ceramic samples with different volume fractions of sodium niobate (NaNbO3 ) crystallites was obtained. The samples exhibit a large transparency window from the near infrared to the visible average, and the sizes of NaNbO3 crystallites are around 10 nm. The optical transmission was measured by using a Q-switched Nd:YAG laser (532 nm, 1064 nm, 15 ns, 5 Hz). The energies of the incident and the transmitted pulses were simultaneously measured by using two large area photodetectors connected to a fast oscilloscope. The photodetector used to monitor the transmitted beam was placed in the far-ﬁeld region and the light

107

Nonlinear Optics of Nanoparticles and Nanocomposites

intensity was totally collected to avoid misinterpretation of the data due to contributions of nonlinear refraction. They found that samples show a nonlinear absorption at 532 nm, and some of samples exhibit optical limiting depending on the bandgap of these samples. The nonlinear coefﬁcients of two-photon and three-photon absorption were determined. The approaches for increasing optical nonlinearity of nanocomposites materials are as follows: (i) increasing particle concentration, (ii) working at near-resonant wavelength, (iii) adding the dielectric conﬁnement effect beside the quantum conﬁnement effect. For example, the 3 of 2% CdS doped glass was estimated to be 15 × 10−10 esu at 390 nm, while 3 values increase to 63 × 10−7 esu after increasing the doping concentration of CdS up to 8% by the sol–gel process [97]. Optical nonlinearity can be enhanced by the dielectric conﬁnement effect, which is a surface polarization effect induced by trapped state and atomic vacancy defects, as discussed. This includes two cases: (a) nanoparticles with high refractive index, such as SnO2 , CdS, and Pbs doped in a matrix with low refractive index, such as SiO2 and PMMA; (b) nanoparticles with a high refractive index, coated with a low refractive index layer, such as stearic acid. Very recently, Murugan and Varma [98] have fabricated glass nanocomposites in the system (100−x)Li2 B4 O7−x · SrBi2 Ta2 O9 (0 ≤ x ≤ 225) by a melt quenching technique followed by heat treatment. They found that the optical transmission properties of these glass nanocomposites were composition dependent. The 3 values of the system are higher for compositions containing higher SrBi2 Ta2 O9 (SBT) content. The heat-treated samples could have larger 3 values than as-quenched ones. The third-order nonlinear optical susceptibility 3 for glass nanocomposites x = 15 is determined to be 3046 × 10−21 cm3 . SHG was observed in the transparent glass nanocomposites. The dependence of second harmonic intensity on the angle of incidence is weak for the compositions with x = 5 and 15. However, an appreciable change in the SH intensity with the angle of incidence is observed for the composition corresponding to x = 20 possibly due to larger crystallites of SBT.

3.3. Other Nanocomposites Zhang et al. [99] prepared well-crystallized SBT thin ﬁlms by the PLD technique. The nonlinear optical measurements were performed by using a single-beam Z-scan method. A mode-locked Nd:YAG laser (1064 nm, 38 ps, 10 Hz) was used as the light source. They performed an open aperture Z-scan measurement and no nonlinear absorption was found. However, closed-aperture Z-scan experiments revealed a signal proﬁle with a peak followed by a valley, indicating a negative (self-defocusing) optical nonlinearity. The calculated value of the nonlinear refractive index of the sample is 19 × 10−6 esu, which compares favorably with the nonlinearities of other representative third-order NLO materials, such as V2 O5 , high-density Au-dispersed SiO2 and TiO2 composites. This shows that SBT thin ﬁlms are promising materials for applications in NLO devices. In

another recent work [100], Yang et al. have reported reﬂection results from SBT and PbZrx Ti1−x O3 (PZT, x = 030, 0.53, 0.8) samples employing laser pulses of 8 ns at 1064 nm. For the SBT sample, when the input energy is low, the output energy increases linearly with incident energy. However, in excess of 270 "J/pulse, the output energy is nearly a constant value of 185.6 "J/pulse. Saturation occurs for higher inputs and functionally appears as typical limiting behavior. They found that the output energy of the PZT sample also shows an optical nonlinearity, and the behavior depends on the atomic ratio of Zr and Ti. As to the mechanism, the bandgap of the sample is too wide to make any nonlinear absorption. The authors suggest that the nonlinearity may result from a scattering of the incident light by the ferroelectric domains in the ﬁlms. Recently, carbon nanotubes and their nanocomposites have been investigated [15–17]. Their third-order optical nonlinearity and optical limiting properties have been reported [15–17, 101–103]. Recently, Xu et al. [104] obtained another tube-shaped material, vanadium oxide (VOx ), by a sol–gel technique. These VOx nanotubes are dispersed in water or embedded in PMMA ﬁlms. Their nonlinear optical transmission was measured using 8 ns pulses from a Nd:YAG laser with an f /40 optical system. At 532 nm the transmittance of VOx in water drops when input ﬂuence increases. The behavior is similar with that of carbon nanotube suspensions. However, the phenomena of VOx embedded in PMMA is much better than that of carbon nanotube–PMMA nanocomposites because the mechanism in VOx nanocomposites is two-photon absorption, different from the nonlinear scattering that occurred in carbon nanotubes. For convenience, Table 2 summarizes some results of the third-order optical nonlinearities of nanocomposites.

3.4. Optical Limiting Effect A currently important problem in science and technology is related to the task of protecting the human eye and the sensors of instruments detecting high-power light beams from radiation damage [15, 17]. A solution to this problem is the use of passive optical limiters as protection devices. An ideal optical limiter is material or device that exhibits linear transmission at low incident ﬂuence, but output light ﬂuence will reach a saturated value when the incident light ﬂuence is over one threshold due to the optical nonlinearity of materials. The possibility to fabricate an applicable optical limiter based on nanocomposites materials was widely investigated. optical limiting effects can be observed in several materials and with different mechanisms [15, 17, 105], such as reverse saturable absorption (RSA), two or three absorption, nonlinear scattering, or nonlinear refraction. Among the nonlinear optical absorptions, RSA is a primary mechanism for some organic molecules and is demonstrated to be one of the best processes to use for optical limiting because it reduces the total pulse energy rather than simply reducing the ﬂuence or irradiance [15, 17]. RSA occurs when a larger absorption from an excited state compared to that from the ground state is observed. For example, C60 and its derivatives represent such an interesting class

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Nonlinear Optics of Nanoparticles and Nanocomposites

Table 2. Third-order optical nonlinearities of some nanocomposites measured by Z-scan (ZS), degenerate four-wave mixing (DFWM), nonlinear transmission (NLT), or Kerr experiment (Kerr), where and are laser wavelength and pulse width, respectively. Material and state Au/SiO2 ﬁlm Au/SiO2 ﬁlm Au/silica ﬁlm Au/BaTiO3 ﬁlm Ag/polystyrene ﬁlm Ag/BaTiO3 ﬁlm Cu/Al2 O3 ﬁlm Cu/Al2 O3 ﬁlm Fe/BaTiO3 ﬁlm Si/SiO2 ﬁlm CdS/PDA ﬁlm CdO/CTAB organosol CdO/DBS organosol PbS/polymer PbS/CdS solution NaNbO3 /glass–ceramic CuCl/glass Rh /BaTiO3 ﬁlm GaSb/SiO2 ﬁlm InP/SiO2 ﬁlm PbO/glass Cu/silica glass Ge/silica Ge/silica PbS/microemulsion

(nm) 532 532 532 532 830 532 596 590 532 813 530 800 800 780 780 532 1330 532 6328 6328 532 532 780 532 780

3 (10−10 esu)

7 70 7 10

ns ps ns ns

10 ns 6 ps 30 ps 10 ns 60 fs 5 ns 85 fs 85 fs 150 fs 150 fs 70 ps 10 ns 5 ns 6 ps 150 fs 35 ps 150 fs

of molecules for optical limiting in visible range [17]. C60 exhibits optical limiting behavior with a saturation threshold lower than other materials. RSA is its dominant mechanism [17]: there exist allowed broadband transitions from the ﬁrst excited singlet and triplet to the higher excited states and this results in absorption in the visible and near infrared range that is much stronger than the absorption from the ground state, leading to RSA. In comparison with the C60 – toluene system, a reduction of the saturated threshold by a factor of 3 to 5 was obtained by Belousov et al. in a C60 – CCl4 system [106]. Further experiments show that the optical limiting performance of C60 in room temperature solution toward nanosecond laser pulses at 532 nm strongly depends on the fullerene solution concentrations. Optical limiting from fullerenes in solid materials, such as SiO2 matrix, was reported [17]. Measurements at 532 nm on samples with two C60 concentrations exhibited RSA. The sample with a larger concentration shows a lower limiting ﬂuence. The presence of thermal effects, scattering, and other effects besides RSA makes it difﬁcult to get their relative contributions [17]. The fullerene–metal nanocomposites remain a relatively unexplored area [17]. Recently, Sun et al. [107] prepared a novel fullerene–Ag nanocomposite (DTC60 –Ag) by the in-situ reduction of silver ions encapsulated in a new monofunctionalized methano-[60] fullerene derivative (DTC60 ) with reverse micellelike structure. Their experimental measurements demonstrated that the optical limiting behavior of DTC60 –Ag is better than that of both C60 and DTC60 .

10,000 10,000 30,000 6600 1011 10,000 2.06 1000 7200 13 1.67 8.22

3590

(10−20 m2 /W)

2,930,000 8,000,000 1010 −15500 −69700 −68000 1013 10 3.3 1011 −109 1580 108 108 1013 −48000

Method

Ref.

ZS DFWM ZS ZS Kerr ZS ZS ZS ZS ZS ZS ZS ZS ZS ZS ZS ZS ZS ZS ZS ZS ZS ZS ZS ZS

[117] [70] [68] [118] [75] [119] [72] [66] [120] [121] [122] [82] [82] [55] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133]

We have observed optical limiting effects in Ag–polymer nanocomposites. Here Ag can be nanoparticles with diameter from 2 to 10 nm or nanorods with length–diameter ratios of 2:1 to 8:1. Optical limiting at different wavelength was observed by adjusting the particle size or the length– diameter ratio of the Ag rod. The limiting comes from nonlinear scattering from the Ag due to the absorption of surface-plasmon resonance. Oak et al. [91] found optical limiting within CdSx Se1−x doped glasses at 1054 nm in the range of 6 ps. They attributed the main mechanism of limiting to two-photon absorption. At higher input intensities, additional absorption due to laser-generated carriers was observed. Recently, Sanz and Lbanez [95] synthesized sol–gel glasses doped with nanocrystals of stilbene 3. The organic–inorgnic nanocomposite materials can be highly doped with active molecules through the control of nanometer scale crystallization. For sample thickness and concentration to be 1 mm and 300 g/L, in a f /5 optical system, laser pulse 2.6 ns, at low energy (<5 "J), the sample is transparent and the transmitted energy increases linearly with the incident energy. At higher incident energies, the output energy is damped below 20 "J within the visible range due to two-photon absorption and excited state absorption.

4. CONCLUSIONS We have not discussed the second-order optical nonlinearities of nanoparticles in this chapter. More details can be found in the work of Wang et al. [59].

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As discussed, the novel properties of nanoparticles and nanocomposites are dominated by two major effects: surface effects and unique characteristics of electrons in conﬁned systems. The increasing surface energy associated with the larger surface-to-volume ratio of small particles determines the physical and thermodynamic properties of the nanoparticles and nanocomposite, such as melting points. Surface effects and electron conﬁnement combine to produce novel electronic properties that can be manifested in a wide range of effects, such as a large nonlinear optical susceptibility, etc. For metal nanocomposites, people wish to have higher 3 and lower linear absorption as higher linear absorption and the corresponding long thermal relaxation time of the insulating matrix decrease the ﬁgure of merit for these materials. 3 varies as 1/r 3 . Thus, it would be the goal to produce extremely small particles with narrow size distribution and higher volume ratio of metal particles in the matrix. For the ideal case of materials composed of linearly arranged particles, very large enhancements can be obtained provided that the particles are aligned in the polarization direction of the incident ﬁeld. In this case, very high intensities are induced inside the particles at the center of the linear chain and the local ﬁeld ampliﬁcation is accompanied by a shift of the spectral location of the resonance. Semiconductor nanoparticles and nanocomposites have also attracted much attention because they were shown to have large third-order optical nonlinear susceptibility. Basically, quantum size and interfacial effects are those we must consider when we want to increase the optical nonlinearity. For example, various chemical methods are developed to passivate the surface of nanoparticles. For the second case, various functional molecules are used to modify the surface of nanoparticles to form core–shell structure. Another factor to increase optical nonlinearity of nanocomposite materials is the dielectric conﬁnement effect. This effect depends on the dielectric constant ratio, such as high refractive index nanoparticles doped in low refractive index matrix or coated with a low refractive index layer. Finally, we would like to point out that the optical nonlinearity of nanoparticles and nanocomposites could be enhanced by the change of coupling between light and materials. We observed strong nonlinear absorption in VOx nanotubes at 532 nm, but the nonlinear absorption vanishes when these nanotubes were unrolled into platelets. Another example is that a larger optical nonlinearity was observed in B, N doped carbon nanotubes compared to pure carbon nanotubes (see the chapter entitled “Doped Carbon Nanotubes” in this encyclopedia [15]). This means that the dimensional and electronic structures play important roles in the NLO properties of nanoparticles and nanocomposites.

GLOSSARY DFWM The nonlinear interaction of three optical waves of the same frequency to generate a fourth, re-emitted wave is known as DFWM, and the method has provided a wealth of knowledge about the behavior of excitons in III–V semiconductors. Gaussian beam Lowest divergence, smallest radius laser beam possible for a given oscillator. It is created when the laser is operating in the TEM00 mode.

Hyperpolarizabilities The coefﬁcient of the higher than linear terms in the relation between the electric dipole moment of a molecule and the electric ﬁeld which acts on the molecule. Kerr effect A quadratic nonlinear electro-optic effect found in particular liquids and crystals that are capable of advancing or retarding the phase of the induced ordinary ray relative to the extraordinary ray when an electric current is applied. It varies as the square of the voltage. Rayleigh scattering Scattering of radiation in the course of its passage through a medium containing particles, the sizes of which are small compared with the wavelength of the radiation. Method an OTDR uses. Spectrometer A device used to measure radiant intensity or to determine the wavelengths of various radiations. Surface plasmon resonance (SPR) phenomenon The collective oscillation of the conduction electrons of the metal under the inﬂuence of an applied electromagnetic (EM) wave. Third-order nonlinear susceptibility Used to characterize the degree of third-order optical nonlinearity. Transmittance The ratio of the radiant power transmitted by an object to the incident radiant power. Z-scan technique Used to measure the sign and the magnitude of the refractive and the absorptive nonlinearities with single beam.

ACKNOWLEDGMENTS We thank Dr. H. S. Nalwa, Professor V. H. Smith, Jr., and Professor J. Gao for valuable comments. We thank Qin Rao for the plot of Figure 1. J. X. thanks the University of Arizona for ﬁnancial support. Q. D. W. gratefully acknowledges the Changchun Institute of Optics, Fine Mechanics, and Physics for ﬁnancial support.

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