Enhanced gain coefficient in Raman amplifier based on silicon nanocomposites

Available online at www.sciencedirect.com

Photonics and Nanostructures – Fundamentals and Applications 9 (2011) 1–7 www.elsevier.com/locate/photonics

Review

Enhanced gain coefficient in Raman amplifier based on silicon nanocomposites M.A. Ferrara a,*, L. Sirleto a, G. Nicotra b, C. Spinella b, I. Rendina a a

b

National Research Council-Institute for Microelectronics and Microsystems, via P. Castellino 111, I-80131 Napoli, Italy National Research Council-Institute for Microelectronics and Microsystems, Stradale Primosole 50, I-95121 Catania, Italy Received 1 April 2010; received in revised form 19 July 2010; accepted 19 July 2010 Available online 29 July 2010

Abstract In this paper, silicon nanoparticles dispersed into a silica phase by sol–gel processing has been investigated by structural and nonlinear-optical characterization. The structural characterization has been performed by energy filtered and scanning transmission electron microscopy. A silicon nanoparticles mean radius of about 49 nm and a nanoparticle density of about 1.62  108 dots/cm2 have been obtained. Regarding nonlinear optics characterization, the observation of stimulated Raman scattering and the realization of a Raman amplifier based on silicon nanocomposites are described. Using a 1427 nm cw pump laser, amplification of Stokes signal, at 1542.2 nm, up to 1.4 dB/cm is demonstrated. A preliminary valuation of approximately a fivefold enhancement of the gain coefficient a significant reduction of threshold power are reported. Our findings have a potential interest for silicon-based Raman lasers. # 2010 Elsevier B.V. All rights reserved. Keywords: Stimulated Raman scattering; Nanostructured silicon; Raman amplifier

Contents 1. 2. 3. 4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sample realization and its structural characterisation . . . . . . . . . . . . . . . . . Nonlinear optic characterisation: stimulated Raman scattering measurements Discussion of results and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Raman amplification, demonstrated in the early 1970s, is an interesting approach for optical amplifica-

* Corresponding author. Tel.: +39 081 6132 343; fax: +39 081 6132 598. E-mail address: [email protected] (M.A. Ferrara). 1569-4410/$ – see front matter # 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.photonics.2010.07.007

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

1 2 3 5 6

tion, because it is only restricted by the pump wavelength and Raman active modes of the gain medium [1,2]. The base phenomenon governing Raman amplification is stimulated Raman scattering (SRS), which generates vibrations in the lattice of the medium (optical phonons) and transforms the photons of the pump radiation, turning them into lower energy ones. This process allows a gain on an optical signal to be created, provided that the signal is propagated at the frequency of the diffused light [3].

2

M.A. Ferrara et al. / Photonics and Nanostructures – Fundamentals and Applications 9 (2011) 1–7

Fused silica has been, for the past century, the key material used for long and short haul transmission of optical signals, because of its good optical properties and attractive figure of merit (i.e. trade-off between Raman gain and losses). A breakthrough in fiber optics communications was achieved with the reduction of the water absorption peak at 1400 nm, which opened up the available communication range to span from 1270 to 1650 nm, corresponding to about 50 THz bandwidth [4,5]. This dramatic increase in bandwidth rules out the use of existing Er-doped fiber amplifiers, leaving Raman gain as the main mechanism for future amplification needs. However, the main disadvantage of the current silica fiber amplifiers is the limited usable bandwidth for Raman amplification (5 THz, approximately 150 cm1) [6,7]. On the other hand, in the last few years several strategies have been developed to engineer efficient light sources and amplifiers in Si-based materials, with the aim to demonstrate a convenient path to monolithic integration of optical and electronic devices within the mainstream Si technology [8]. In particular, light amplification by stimulated Raman scattering (SRS) in silicon waveguides has recently achieved significant results [8–12], despite intrinsic limitations related to the nature of the bulk Si materials [13,14]. The narrow-band (105 GHz) of stimulated Raman gain in Si limits its applicability in the context of Si photonics, and makes it unsuitable for its use in broadband division multiplexing (WDM) applications, unless expensive multi-pump schemes are implemented. Additionally, even if the Raman effect in silicon is more than 10,000 times stronger than in glass fiber, therefore instead of kilometres of fiber, only centimetres of silicon are required, Raman amplification in Si is still a small effect. As a consequences, in order to build a laser based on stimulated Raman effects in Si, very high power intensity and very low absorption losses are required. Finally, in order to get Raman laser in silicon, the main difficult was due to the competing nonlinear effect of two-photon absorption (TPA), which reduces the efficiency of SRS. This effect generates electron-hole pairs, which remain excited in the sample for a long time (micro to milliseconds) and lead to strong absorption at both the pump and signal frequencies [13,14]. Taking all these issues into account, the investigation of new materials possessing both large Raman gain coefficients and broader spectral bandwidth than fused silica and/or silicon is becoming mandatory in order to satisfy the increasing telecommunications demands. On this line of argument, in our previous papers [15,16], some advantages of silicon nanostructure with

respect to silicon were pointed out. Experimental results proving spontaneous Raman scattering in silicon nanostructures at the wavelength of interest for telecommunications (1.54 mm) were reported in Ref. [15]. According to phonon confinement model in Ref. [16], two significant improvement of Raman approach in silicon quantum dots with respect to silicon were reported: the broadening of spontaneous Raman emission and the tuning of the Stokes shift. Considering silicon quantum dots having crystal size of 2 nm, a significant broadening of about 65 cm1 and a peak shift of about 19 cm1 were obtained. Because the width of C-band telecommunication is 146 cm1, taking into account the broadening and the shift of spontaneous Raman emission, more than the half of Cband could be cover using silicon quantum dots, without implementing the multi-pump scheme. Finally prospects of Raman amplifier in silicon nanostructure were discussed [16]. The crucial point, i.e. the possibility to enhance the Raman gain coefficient and to reduce twophoton absorption, at the same time, in silicon quantum dot was addressed, too [16]. In this paper, Si nanocomposites embedded in a continuous silica matrix by sol–gel processing has been realized and investigated. The observation of stimulated Raman scattering and the realization of a Raman amplifier based is described. Finally, the experimental demonstration of the enhancement of a Raman gain coefficient and a significant reduction of threshold power in silicon nanocomposites with respect to silicon is reported. 2. Sample realization and its structural characterisation Sol–gel technology appears ideal for preparing nanocomposite materials, essentially made of two phases: a discontinuous semiconducting phase (Si nanoparticles) dispersed in a continuous dielectric phase (silica) [17,18]. Si nanoparticles were obtained by crushing a silicon wafer and reducing their dimensions by a thermal dry oxidation. Afterward, an etching of the oxidized silicon nanoparticles was performed by a solution prepared by hydrofluoric acid and ethanol with a volumetric rate of HF:C2H5OH = 1:1. The SiO2 sol was prepared by mixing the precursor tetraethyl orthosilicate Si(OC2H5)4 (TEOS–Sigma–Aldrich) with the solvent (94% denaturated ethanol); an homogeneous and continuous film was obtained with a 0.5 M solution. Acidulated water (0.01N HCl:CH3COOH = 1:1) was added in a hydrolysis ratio HR = 4. Fluoresce´ine was used as surfactant. Suspension was prepared mixing 5 ml

M.A. Ferrara et al. / Photonics and Nanostructures – [(Fig._1)TD$IG] Fundamentals and Applications 9 (2011) 1–7

of HF:C2H5OH = 1:1 solution with silicon nanoparticles into 20 ml of sol–gel solution. The biggest silicon particles were eliminated filtering the solution by a membrane with pore radius of 0.2 mm. The deposition onto a glass substrate was realised by spin coating. Finally, two thermal treatment, for water and alcohol condensation, were performed. The thin-film so obtained has a thickness of 0.5 mm and its total length is 1.95 cm. As far as the structural characterization, energy filtered transmission electron microscopy (EFTEM) and scanning transmission electron microscopy (STEM) were used. We note that EFTEM provides a direct and reliable quantitative estimation of Si nanostructures [19,20], while STEM, in particular in plan view configuration [21], allows to detect the density of silicon nanoparticles dispersed into silica. The sample was prepared for TEM observation by mechanical thinning followed by ion milling polishing process. A JEOL JEM 2010F STEM/TEM with a Schottky fieldemission gun operated at 200 kV and equipped with ultra high-resolution (UHR) objective lens polepiece, a Jeol annular dark field detector, and a post-column imaging filter (GIF) was used. The GIF has an energy resolution of about 0.8 eV. Due to the energy difference between the Si plasmon signal (16 eV) and the SiO2 bulk plasmon signal (25 eV), the EFTEM image, in cross view, was obtained with a high signal to noise ratio, as you can see from Fig. 1(a), where the shape of a crystalline silicon nanoparticle, in white contrast, is shown. Regarding plan view analysis, the STEM approach provided the best results, in fact the Si nanoparticles, white spots in Fig. 1(b), are clearly visible with respect to the SiO2 substrate. The STEM analysis in plan view configuration allowed us to evaluate the mean radius (49 nm) of the silicon dots and also the dot density (1.62  108 dots/cm2) [19–21].

3

Fig. 1. (a) EFTEM micrograph taken at 16 eV. The white spot is a silicon nanoparticles embedded into the silica matrix. (b) STEM micrograph clearly detects Si nanoparticles, white spots, embedded into the silica matrix.

Eq. (1) can be linearized as 3. Nonlinear optic characterisation: stimulated Raman scattering measurements

I S ¼ I S0 ð1 þ I P gLÞ

(2)

In order to investigate Raman gain in silicon nanocomposites, the steady-state linear (no pump depletion) regime of SRS was considered. In this regime the intensity of the output Stokes radiation is expressed by [3]

Therefore, in the presence of a low pump power IP, the fractional change in the probe beam (G), is given by:

I S ðLÞ ¼ I S ð0Þ  expðI P ð0ÞgLÞ

Assuming no losses at the Stokes frequency, the value of the gain coefficient g can be obtained by fitting Eq. (1), which is readily transformed into

(1)

where IS0 is the intensity of the input Stokes radiation (Stokes seed), IS is the intensity of the output Stokes radiation, IP is the intensity of the pump radiation, g is the Raman gain coefficient, and L is the effective length. When the power intensity is small, the exponent in

G¼

dI S ¼ I P gL I S0

SRS ¼ 10  log10

  I S ðLÞ ¼ 4:34  gLI P ð0Þ I S ð0Þ

(3)

4[(Fig._2)TD$IG]

M.A. Ferrara et al. / Photonics and Nanostructures – Fundamentals and Applications 9 (2011) 1–7

Fig. 2. Experimental setup for SRS measurements: pump-Raman laser; IRC-infra-red collimator; F1-bandpass filter at 1427 nm; probe: ECDLexternal cavity diode laser (tunable); OI-optical insulator; DF-dichroic filter; OB1 (OB2)-microscope objective lens 50 (20); F2-longpass filter at 1500 nm; Ch-Chopper; PD-optically-broadband photodetector; LIA-Lock-in amplifier. Black lines represent electrical connections and wiring, green lines represent freespace optical beams, and magenta lines represent optical fiber. The inset shows how the pump and the probe interact with the sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

where Ip = P/A with P as the power incident onto the sample and A as the effective area of pump beam. Being the sample transparent to the incident light, L is taken to be equal to the thickness of the sample along the path of the incident light (L = 1.95 cm). For calculations of the effective area, the waist of pump laser was measured by the knife-edge technique. A value of 5 mm was obtained. In Fig. 2 is shown the experimental setup used in order to measure SRS in silicon nanocomposities. The pump laser is a CW pump-Raman laser operating at 1427 nm. The probe laser is a tunable external cavity diode laser (1520–1620 nm). The probe beam is split by a Y fiber optic junctions. One of the branches is used in order to monitor probe fluctuations. The other one and the pump laser are combined on a dichroic mirror and subsequently coupled to a long working distance 50 infrared objective in order to be focused onto the sample. The sample is mounted parallel to the path of the incident beam (as shown in the inset of Fig. 2).

Estimated coupling losses were about 4 dB. The transmitted signals from the sample are collected by a 20 microscope objective. In order to separate the probe from the pump, a dichroic filter and a longpass filter were used. An optically broadband photodetector (PD) was used to collect the probe signal. The signal from the PD is demodulated by a lock-in amplifier, which is externally referenced to the 180 Hz chopper. Each data point is averaged 1000 times before being acquired. Additionally, four measured values are averaged for each data point. The accuracy of measurement is 0.1 dB. In Fig. 3, the measured fractional change in the probe beam (G) as a function of the probe laser wavelength is shown. The probe laser wavelength with a line width of 200 kHz was scanned, continuously over the Stokes wavelength range (1538–1542.5 nm) while the focused pump power was fixed at 0.2 W. Being the Raman gain coefficient related to the differential cross section of Raman scattering, Fig. 3 reflects the spontaneous

[(Fig._3)TD$IG]

M.A. Ferrara et al. / Photonics and Nanostructures – Fundamentals and Applications 9 (2011) 1–7

5

effective focal volume inside the sample, by our data, a preliminary evaluation of approximately a fivefold enhancement of the gain coefficient in Raman amplifier based on silicon nanocomposities with respect to silicon is obtained [25]. Furthermore our data prove a significant threshold power reduction (about 60%) in silicon nanocomposities (Pth  100 mW) with respect to silicon (Pth  250 mW).

4. Discussion of results and conclusions

Fig. 3. Measured spectral characteristic of G in silicon nanocomposites.

Raman scattering directly [22]. In Fig. 3 the fitting of the experimental results to a theoretical curve (solid line) obtained by a phonon confinement model [23,24] is also reported. We note that in our samples the gain peak of the stimulated emission occurs at 1542.2 nm. In Fig. 4, the maxima of the signal wavelength scans are plotted versus the effective pump power (including the pass through the filter and objective). The maximum SRS gain obtained was 1.4 dB/cm. In Fig. 4 the SRS gain in a float zone high purity and high resistivity bulk silicon plotted versus the effective pump power is also reported. For both plots in Fig. 4, the behaviors are approximately linear, as expected for the SRS gain of a Raman amplifier as a function of pump power. As shown in Fig. 4, Raman amplifier based on silicon nanocomposites exhibits a SRS gain significantly greater than bulk silicon. Although the estimation of [(Fig._4)TD$IG]g is not straightforward, due to the uncertainty in the

Fig. 4. The SRS gain (amplification of the stokes signal in dB/cm) is plotted against the effective pump power at the sample surface both for silicon nanocomposites (& red) and for bulk silicon (* black). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

At this point, we suggest that the enhancement of gain coefficient could be related to the enhancement of the third order nonlinear susceptibility x(3) in Si nanocomposities. It is well known that third-order nonlinear effects are generally characterized by the nonlinear absorption (b) and the nonlinear refractive index (g). The nonlinear coefficients, namely b and g, are described by a(I) = a0 + bI and n(I) = n0 + gI where a0 and n0 stand for the linear absorption and refractive index respectively. The b and g values are used to evaluate the imaginary (Im x(3)) and real (Re x(3)) parts of the thirdorder nonlinear susceptibility. We note that the real part describes the phenomena related to the intensity dependent index of refraction, while the imaginary part describes two-photon absorption and stimulated Raman scattering (SRS). In the last decade, there has been a great deal of progress in the analysis of nonlinear materials that could be actually useful in optical active device fabrication. Promising results come from semiconductors, with their rich variety of nonlinear mechanisms, and from organic materials. However, the materials investigated up to now exhibit nonlinearities which are still too low for realistic high speed devices performing at low optical powers. A way to enhance the real part of cubic nonlinearities in materials is that of artificially ‘shrinking’ the electrons in regions much shorter than their natural delocalization length in the bulk. In such morphologies, optical resonances will usual appear, resulting from dielectric or quantum confinement, the former prevailing in metal nanocrystals, the latter prevailing in semiconductor nanocrystals. Quantum confinement occurs at a nanometer scale when the electron and hole envelope functions are restricted within a region whose spatial extension is lower than the exciton Bohr radius. This leads to quasi-discrete energy level structures, eventually showing sharp absorption lines. The concentration of the oscillator strength into these discrete levels leads to enhancement of the optical

6

M.A. Ferrara et al. / Photonics and Nanostructures – Fundamentals and Applications 9 (2011) 1–7

transitions rates and to a size-dependent nonlinear optical susceptibility [26]. In materials, different physical mechanisms can induce optical nonlinearities related to third order susceptibilities x(3). The most important are: thermal, resonant and non-resonant optical nonlinearities. Nonresonant nonlinearities take place when the light linear absorption is negligible (at frequencies well below the absorption edge). They are related to the anharmonic motion (or virtual excitations) of bound electrons, and are very fast: typical recovery times are of the order of picoseconds. Despite the fact that into transparence range, nanostructured materials may be more convenient for x(3) based nonlinear devices, resonant optical nonlinearities in quantum confined materials have been investigated in some details, whereas very few works have been published on non-resonant nonlinearities. However, an enhancement of the real part of the third order nonlinear susceptibility in silicon nanostructure, due to quantum confinement, in the transparency range has already been proved by several authors [27]. Regarding SRS, even if this phenomena in low dimensional silicon has never been studied before, an enhancement of the imaginary part of the third order nonlinear susceptibility is also expected. It is well known that SRS is dependent on the pump intensity and on a gain coefficient g, which depends on the material. The gain coefficient depends on scattering efficiency, the larger the spontaneous scattering efficiency of materials is, the higher the Raman gain for a given intensity is obtained. In silicon nanocrystals, Raman scattering efficiency should be stronger than crystalline silicon [28], as a consequences a stronger gain is expected. In order to try to explain why the presence of silicon nanoparticles can increase the Raman gain coefficient, we suggest two possible options. In the former, it is well known that the nonlinear optical properties of composites material are characterized an ‘‘enhancement of local field’’ [29]. Off resonance, the electric field amplitude of an incident laser beam becomes no uniformly distributed between the two constituents of composite and the electric field strength within the more nonlinear constituent will exceed the spatially averaged field strength. Therefore, the effective real part of third order susceptibility of the composite can exceed that of each of its constituents [29]. At the same way, in our opinion, the enhancement of Raman gain could be related to the local field enhancement. The latter option is related to the optical transport properties of complex photonics structures on the intermediate regime between complete order or disorder. Light waves in disordered materials perform a random walk, which

could lead to a multiple scattering process and to a strong localization of dielectric field. Of particular interest for photonic applications are disordered materials that provide optical amplification via stimulated emission [30]. In our opinion the localization could play an important role on SRS and the combination of localization and SRS gain could be of particular interest for photonic application, where disordered materials could provide optical amplification via SRS. However, the structure of the Si/SiO2 interfaces, the stoichiometric material disorder and the clusters dimensionality are also important parameters that are expected to significantly influence Raman amplification, although a theoretical understanding of their respective roles remains to be established. Further studies will be carried on in the near future addressing the physical origin of enhanced Raman gain in nanocomposities Si systems. In addition, a systematic experimental study considering different Si clusters dimensions and thicknesses is in progress. In conclusions, in this paper, we experimentally demonstrate that Si nanocomposities are suitable for Raman amplification. We report observation of SRS in silicon nanocomposities, and we provide larger gain values and reduced threshold value than bulk Si systems. We believe that our results have the merit to open the way to interesting investigations which could be an important step towards to silicon-based Raman laser.

References [1] M.N. Islam, Raman amplifiers for telecommunications, IEEE J. Selected Top. Quantum Electron. 8 (2002) 548–559. [2] A. Mori, H. Masuda, K. Shikano, M. Shimizu, Ultra-wide-band tellurite-based fiber Raman amplifier, J. Lightwave Technol. 21 (2003) 1300. [3] Y.R. Shen, N. Bloembergen, Theory of stimulated Brillouin and Raman scattering, Phys. Rev. 137 (1965) A1787. [4] C. Rivero, K. Richardson, R. Stegeman, G. Stegeman, T. Cardinal, E. Fargin, M. Couzi, V. Rodriguez, Quantifying Raman gain coefficients in Tellurite glasses, J. Non-Cryst. Solids 345/346 (2004) 396–401. [5] J.J. Refi, Optical fibers for optical networking, Bell Labs Tech. J. 4 (1999) 246–261. [6] F.L. Galeener, J.C. Mikkelsen, R.H. Geils, W.J. Mosby, The relative Raman cross sections of vitreous SiO2, GeO2, B2O3, and P2O5, Appl. Phys. Lett. 32 (1978) 34. [7] G.E. Walrafen, P.N. Krishnan, Model analysis of the Raman spectrum from fused silica optical fibers, Appl. Opt. 21 (1982) 359–360. [8] R. Soref, The past, present, and future of silicon photonics, IEEE J. Selected Top. Quantum Electron. 12 (2006) 1678–1687. [9] O. Boyraz, B. Jalali, Demonstration of a silicon Raman laser, Opt. Express 12 (2004) 5269–5273.

M.A. Ferrara et al. / Photonics and Nanostructures – Fundamentals and Applications 9 (2011) 1–7 [10] H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, An all-silicon Raman laser, Nature 433 (2005) 292–294. [11] H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, Low-threshold continuous-wave Raman silicon Laser, Nature 433 (2005) 725–727. [12] H. Rong, S. Xu, Y.H. Kuo, V. Sih, O. Cohen, O. Raday, M. Paniccia, A cascaded silicon Raman laser, Nat. Photonics 1 (2007) 232–237. [13] B. Jalali, V. Raghunathan, D. Dimitropoulos, O. Boyraz, Ramanbased silicon photonics, IEEE J. Selected Top. Quantum Electron. 12 (2006) 412–421. [14] R. Dekker, N. Usechak, M. Fo¨rst, A. Driessen, Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides, J. Phys. D: Appl. Phys. 40 (2007) R249–R271. [15] L. Sirleto, V. Raghunathan, A. Rossi, B. Jalali, Raman emission in porous silicon at 1.54 mm, Electron. Lett. 40 (19) (2004) 121–122. [16] L. Sirleto, M.A. Ferrara, I. Rendina, B. Jalali, Broadening and tuning of spontaneous Raman emission in porous silicon at 1.5 micron, Appl. Phys. Lett. 88 (2006) 211105. [17] L.C. Klein, Processing of nanostructured sol–gel materials, in: A.S. Edelstein, R.C. Cammarata (Eds.), Nanomaterials: Synthesis, Properties and Application, Institute of Physics Publishing, Bristol, UK, 1996. [18] E. Borsella, M. Falconieri, S. Botti, S. Martelli, F. Bignoli, L. Costa, S. Grandi, L. Sangaletti, B. Allieri, L. Depero, Optical and morphological characterization of Si nanoclusters/Silica composites prepared by sol–gel processing, Mater. Sci. Eng. B 79 (2001) 55. [19] G. Nicotra, R.A. Puglisi, S. Lombardo, C. Spinella, M. Vulpio, G. Ammendola, M. Bileci, C. Gerardi, Nucleation kinetics of Si quantum dots on SiO2, J. Appl. Phys. 88 (2004) 2049. [20] C. Spinella, C. Bongiorno, G. Nicotra, E. Rimini, A. Muscara`, S. Coffa, Quantitative determination of the clustered silicon con-

[21]

[22] [23] [24]

[25]

[26]

[27]

[28]

[29]

[30]

7

centration in substoichiometric silicon oxide layer, Appl. Phys. Lett. 87 (2005) 044102. G. Nicotra, Hui-Ting Chou, N.D. Henning Stahlberg, Browning, Avoiding charge induced drift in vitrified biological specimens through scanning transmission electron microscopy, Microsc. Microanal. 12 (2006) 246–247. A. Owyoung, Coherent Raman gain spectroscopy using cw laser sources, IEEE J. Quantum Electron. 14 (1978) 192. H. Ritcher, Z.P. Wang, L. Ley, The one phonon Raman spectrum in microcrystalline silicon, Solid State Commun. 39 (1981) 625. H. Campbell, P.M. Fauchet, The effects of microcrystal size and shape on the one phonon Raman spectra of crystalline semiconductors, Solid State Commun. 58 (1986) 739. J.M. Ralston, R.K. Chang, Spontaneous-Raman-scattering efficiency and stimulated scattering in. Silicon, Phys. Rev. B 2 (1970) 1858. L.C. Klein, in: A.S. Edelstein, R.C. Cammarata (Eds.), Nanomaterials: Synthesis, Properties and Application, Institute of Physics, Bristol, UK, 1996. S. Herna´ndez, P. Pellegrino, A. Martı´nez, Y. Lebour, B. Garrido, R. Spano, M. Cazzanelli, N. Daldosso, L. Pavesi, E. Jordana, J.M. Fedeli, Linear and nonlinear optical properties of Si nanocrystals in SiO2 deposited by plasma-enhanced chemical-vapor deposition, J. Appl. Phys. 103 (2008) 064309. L. Khriachtchev, M. Rasanen, S. Novikov, Free-standing silica film containing Si nanocrystals: photoluminescence, Raman scattering, optical waveguiding, and laser-induced thermal effects, Appl. Phys. Lett. 86 (2005) 141911. G.L. Fischer, R.W. Boyd, R.J. Gehr, S.A. Jenekhe, J.A. Osaheni, J.E. Sipe, L.A. Weller-Brophy, Enhanced nonlinear optical response of composite materials, Phys. Rev. Lett. 74 (1995) 1871. D.S. Wiersma, R. Sapienza, S. Mujumdar, M. Colocci, M. Ghulinyan, L. Pavesi, Optics of nanostructured dielectrics, J. Opt. A: Pure Appl. Opt. 7 (2005) S190.