P. N. Butcher and D. Cotter, The elements of nonlinear optics, 1991.
DOI : 10.1017/CBO9781139167994

G. Agrawal, Nonlinear Fiber Optics, 3 ed, 2001.

Q. Lin, O. J. Painter, and G. P. Agrawal, Nonlinear optical phenomena in silicon waveguides: modeling and applications, Optics Express, vol.15, issue.25, pp.25-16604, 2007.
DOI : 10.1364/OE.15.016604

D. Aspnes, Recombination at semiconductor surfaces and interfaces, Surface Science, vol.132, pp.1-3, 1983.
DOI : 10.1016/0039-6028(83)90550-2

A. A. Said, M. Sheik-bahae, D. J. Hagan, T. H. Wei, J. Wang et al., Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe, Journal of the Optical Society of America B, vol.9, issue.3, pp.405-414, 1992.
DOI : 10.1364/JOSAB.9.000405

T. G. Ulmer, R. K. Tan, Z. Zhou, S. E. Ralph, R. P. Kenan et al., Two-photon absorption-induced self-phase modulation in GaAs???AlGaAs waveguides for surface-emitted second-harmonic generation, Optics Letters, vol.24, issue.11, pp.11-756, 1999.
DOI : 10.1364/OL.24.000756

I. , C. H. Agrawal, and G. P. , Unified description of ultrafast stimulated Raman scattering in optical fibers, J. Opt. Soc. Am. B, vol.13, issue.10, pp.2170-2177, 1996.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-heidari, C. Grillet et al., Slow Light Enhanced Nonlinear Optics in Silicon Photonic Crystal Waveguides, IEEE Journal of Selected Topics in Quantum Electronics, vol.16, issue.1, pp.344-356, 2010.
DOI : 10.1109/JSTQE.2009.2033019

T. Krauss, Slow light in photonic crystal waveguides, Journal of Physics D: Applied Physics, vol.40, issue.9, pp.2666-2670, 2007.
DOI : 10.1088/0022-3727/40/9/S07
URL : https://hal.archives-ouvertes.fr/hal-00570635

L. H. Frandsen, A. V. Lavrinenko, J. Fage-pedersen, and P. Borel, Photonic crystal waveguides with semi-slow light and tailored dispersion properties, Optics Express, vol.14, issue.20, pp.20-9444, 2006.
DOI : 10.1364/OE.14.009444
URL : http://orbit.dtu.dk/ws/files/10663970/2.pdf

M. D. Settle, R. J. Engelen, M. Salib, A. Michaeli, L. Kuipers et al., Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth, Optics Express, vol.15, issue.1, pp.1-219, 2007.
DOI : 10.1364/OE.15.000219

S. Kubo, D. Mori, and T. Baba, Low-group-velocity and low-dispersion slow light in photonic crystal waveguides, Optics Letters, vol.32, issue.20, pp.2981-2983, 2007.
DOI : 10.1364/OL.32.002981

B. Song, S. Noda, T. Asano, and Y. Akahane, Ultra-high-Q photonic double-heterostructure nanocavity, Nature Materials, vol.10, issue.3, p.207, 2005.
DOI : 10.1103/PhysRevLett.92.083901

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe et al., Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect, Applied Physics Letters, vol.88, issue.4, p.41112, 2006.
DOI : 10.1063/1.2167801

P. Velha, E. Picard, T. Charvolin, E. Hadji, J. Rodier et al., Ultra-High Q/V Fabry-Perot microcavity on SOI substrate, Optics Express, vol.15, issue.24, pp.24-16090, 2007.
DOI : 10.1364/OE.15.016090
URL : https://hal.archives-ouvertes.fr/hal-00394779

E. Yablonovitch, Inhibited Spontaneous Emission in Solid-State Physics and Electronics, Physical Review Letters, vol.58, issue.20, pp.2059-2062, 1987.
DOI : 10.1103/PhysRevLett.58.2059

S. John, Strong localization of photons in certain disordered dielectric superlattices, Physical Review Letters, vol.58, issue.23, pp.2486-2489, 1987.
DOI : 10.1103/PhysRevLett.58.2486

Y. A. Vlasov, M. O-'boyle, H. F. Hamann, and S. J. Mcnab, Active control of slow light on a chip with photonic crystal waveguides, Nature, vol.12, issue.7064, pp.7064-65, 2005.
DOI : 10.1038/nature04210

S. Combrie, S. Bansropun, M. Lecomte, O. Parillaud, S. Cassette et al., Optimization of an inductively coupled plasma etching process of GaInP???GaAs based material for photonic band gap applications, Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol.23, issue.4, pp.1521-1526, 2005.
DOI : 10.1116/1.1993617
URL : https://hal.archives-ouvertes.fr/hal-00903584

R. Soref, L. , and J. , Single-crystal silicon: a new material for 1.3 and 1.6 ??m integrated-optical components, Electronics Letters, vol.21, issue.21, pp.953-954, 1985.
DOI : 10.1049/el:19850673

S. Combrie, A. D. Rossi, L. Morvan, S. Tonda, S. Cassette et al., Time-delay measurement in singlemode, low-loss photonic crystal waveguides, Electronics Letters, vol.42, issue.2, pp.86-88, 2006.
DOI : 10.1049/el:20064129

S. Combrié, E. Weidner, A. Derossi, S. Bansropun, S. Cassette et al., Detailed analysis by Fabry-Perot method of slab photonic crystal line-defect waveguides and cavities in aluminium-free material system, Optics Express, vol.14, issue.16, pp.16-7353, 2006.
DOI : 10.1364/OE.14.007353.m001

M. Dinu, F. Quochi, and H. Garcia, Third-order nonlinearities in silicon at telecom wavelengths, Applied Physics Letters, vol.82, issue.18, pp.2954-2956, 2003.
DOI : 10.1063/1.1571665

S. Combrié, A. D. Rossi, Q. V. Tran, and H. Benisty, GaAs photonic crystal cavity with ultrahigh Q : microwatt nonlinearity at 1.55 µm, Opt. Lett, vol.33, p.16, 1908.

J. S. Blakemore, Semiconducting and other major properties of gallium arsenide, Journal of Applied Physics, vol.53, issue.10, pp.123-181, 1982.
DOI : 10.1063/1.331665

A. Ryasnyanskiy, N. Dubreuil, P. Delaye, R. Frey, and G. And-roosen, Fourier transformed picosecond synchronously pumped optical parametric oscillator without spectral filtering element, Journal of the European Optical Society: Rapid Publications, vol.3, p.8037, 2008.
DOI : 10.2971/jeos.2008.08037
URL : https://hal.archives-ouvertes.fr/hal-00560947

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. V. Tran et al., Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide, Optics Express, vol.17, issue.2, pp.552-557, 2009.
DOI : 10.1364/OE.17.000552
URL : https://hal.archives-ouvertes.fr/hal-00560953

V. Mizrahi, K. W. Delong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, Two-photon absorption as a limitation to all-optical switching, Optics Letters, vol.14, issue.20, pp.20-1140, 1989.
DOI : 10.1364/OL.14.001140

K. Ikeda and F. , Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities, Special Issue : Papers Selected from the NGC2007 Conference, pp.1376-1380, 2007.
DOI : 10.1016/j.sse.2007.06.012

C. Husko, A. D. Rossi, S. Combrie, Q. V. Tran, F. Raineri et al., Ultrafast all-optical modulation in GaAs photonic crystal cavities, Applied Physics Letters, vol.94, issue.2, p.21111, 2009.
DOI : 10.1063/1.3068755

R. Dekker, N. Usechak, M. Forst, and A. Driessen, Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides, Journal of Physics D: Applied Physics, vol.40, issue.14, pp.249-271, 2007.
DOI : 10.1088/0022-3727/40/14/R01

D. Miller, Optical interconnects to silicon, IEEE Journal of Selected Topics in Quantum Electronics, vol.6, issue.6, pp.1312-1317, 2000.
DOI : 10.1109/2944.902184
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.452.5789

T. Barwicz, H. Byun, F. Gan, C. W. Holzwarth, M. A. Popovic et al., Silicon photonics for compact, energyefficient interconnects, J. Opt. Netw, vol.6, pp.1-63, 2007.
DOI : 10.1364/jon.6.000063

F. Kroeger, A. Ryasnyanskiy, A. Baron, N. Dubreuil, P. Delaye et al., Saturation of the Raman amplification by self-phase modulation in silicon nanowaveguides, Applied Physics Letters, vol.96, issue.24, pp.24-241102, 2010.
DOI : 10.1063/1.3451466
URL : https://hal.archives-ouvertes.fr/hal-00561130

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, Influence of nonlinear absorption on Raman amplification in Silicon waveguides, Optics Express, vol.12, issue.12, pp.2774-2780, 2004.
DOI : 10.1364/OPEX.12.002774

T. K. Liang and H. K. Tsang, Efficient Raman amplification in silicon-on-insulator waveguides, Applied Physics Letters, vol.85, issue.16, pp.3343-3345, 2004.
DOI : 10.1063/1.1807960

R. Espinola, J. Dadap, R. Osgood, J. Mcnab, S. Vlasov et al., Raman amplification in ultrasmall silicon-on-insulator wire waveguides, Optics Express, vol.12, issue.16, pp.16-3713, 2004.
DOI : 10.1364/OPEX.12.003713

T. Liang, L. Nunes, M. Tsuchiya, K. Abedin, T. Miyazaki et al., High speed logic gate using two-photon absorption in silicon waveguides, Optics Communications, vol.265, issue.1, pp.171-174, 2006.
DOI : 10.1016/j.optcom.2006.03.031

D. Moss, L. Fu, I. Littler, and B. Eggleton, Ultrafast all-optical modulation via two-photon absorption in silicon-on-insulator waveguides, Electronics Letters, vol.41, issue.6, pp.320-321, 2005.
DOI : 10.1049/el:20058051

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts et al., Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5?????m wavelength, Applied Physics Letters, vol.80, issue.3, pp.416-418, 2002.
DOI : 10.1063/1.1435801

O. Boyraz, T. Indukuri, and B. Jalali, Self-phase-modulation induced spectral broadening in silicon waveguides, Optics Express, vol.12, issue.5, pp.829-834, 2004.
DOI : 10.1364/OPEX.12.000829

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, R. M. Osgood et al., Self-phase-modulation in submicron silicon-on-insulator photonic wires, Optics Express, vol.14, issue.12, pp.12-5524, 2006.
DOI : 10.1364/OE.14.005524

T. Liang and H. Tsang, Nonlinear absorption and Raman scattering in siliconon-insulator optical waveguides. Selected Topics in Quantum Electronics, IEEE Journal, vol.10, pp.5-1149, 2004.

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, Observation of Raman emission in silicon waveguides at 1.54 µm, Opt. Express, vol.10, pp.22-1305, 2002.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson et al., Broad-band optical parametric gain on a silicon photonic chip, Nature, vol.84, issue.7096, pp.7096-960, 2006.
DOI : 10.1038/nature04932

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa et al., Four-wave mixing in silicon wire waveguides, Optics Express, vol.13, issue.12, pp.12-4629, 2005.
DOI : 10.1364/OPEX.13.004629

O. Boyraz and B. Jalali, Demonstration of a silicon Raman laser, Optics Express, vol.12, issue.21, pp.5269-5273, 2004.
DOI : 10.1364/OPEX.12.005269

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak et al., A continuous-wave Raman silicon laser, Nature, vol.8, issue.7027, pp.7027-725, 2005.
DOI : 10.1364/OL.29.001224

Q. Xu, V. R. Almeida, and M. Lipson, Demonstration of high Raman gain in a submicrometer-size silicon-on-insulator waveguide, Optics Letters, vol.30, issue.1, pp.35-37, 2005.
DOI : 10.1364/OL.30.000035

Q. Xu, V. Almeida, and M. Lipson, Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides, Optics Express, vol.12, issue.19, pp.4437-4442, 2004.
DOI : 10.1364/OPEX.12.004437

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering, Optics Express, vol.12, issue.18, pp.18-4261, 2004.
DOI : 10.1364/OPEX.12.004261

D. R. Solli, P. Koonath, and B. Jalali, Broadband Raman amplification in silicon, Applied Physics Letters, vol.93, issue.19, 2008.

P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade et al., Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance, Applied Physics Letters, vol.89, issue.17, pp.17-171121, 2006.
DOI : 10.1063/1.2372581
URL : https://hal.archives-ouvertes.fr/hal-00394756

L. Yin and G. P. Agrawal, Impact of two-photon absorption on self-phase modulation in silicon waveguides, Optics Letters, vol.32, issue.14, pp.14-2031, 2007.
DOI : 10.1364/OL.32.002031

S. Roy, S. K. Bhadra, and G. P. Agrawal, Raman amplification of optical pulses in silicon waveguides: effects of finite gain bandwidth, pulse width, and chirp, Journal of the Optical Society of America B, vol.26, issue.1, pp.17-25, 2009.
DOI : 10.1364/JOSAB.26.000017

D. Sullivan, Nonlinear FDTD formulations using Z transforms. Microwave Theory and Techniques, IEEE Transactions on, vol.43, issue.3, pp.676-682, 1995.
DOI : 10.1109/22.372115

I. Rukhlenko, M. Premaratne, and G. Agrawal, Nonlinear Silicon Photonics : Analytical Tools. Selected Topics in Quantum Electronics, IEEE Journal, vol.16, issue.1, pp.200-215, 2010.
DOI : 10.1109/jstqe.2009.2026435

S. C. Pinault and M. J. Potasek, Frequency broadening by self-phase modulation in optical fibers, Journal of the Optical Society of America B, vol.2, issue.8, pp.1318-1319, 1985.
DOI : 10.1364/JOSAB.2.001318

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, All-optical control of light on a silicon chip, Nature, vol.5116, issue.7012, pp.7012-1081, 2004.
DOI : 10.1109/2944.902184

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, All-optical switches on a silicon chip realized using photonic crystal nanocavities, Applied Physics Letters, vol.87, issue.15, pp.15-151112, 2005.
DOI : 10.1063/1.2089185

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover et al., Optical signal processing using nonlinear semiconductor microring resonators, IEEE Journal of Selected Topics in Quantum Electronics, vol.8, issue.3, pp.75-82, 2002.
DOI : 10.1109/JSTQE.2002.1016376

M. Astic, P. Delaye, R. Frey, G. Roosen, R. André et al., Time resolved nonlinear spectroscopy at the band edge of 1D photonic crystals, Journal of Physics D: Applied Physics, vol.41, issue.22, pp.22-224005, 2008.
DOI : 10.1088/0022-3727/41/22/224005
URL : https://hal.archives-ouvertes.fr/hal-00554084

B. S. Wherrett, Scaling rules for multiphoton interband absorption in semiconductors, Journal of the Optical Society of America B, vol.1, issue.1, pp.67-72, 1984.
DOI : 10.1364/JOSAB.1.000067

M. Sheik-bahae, D. Hutchings, D. Hagan, V. Stryland, and E. , Dispersion of bound electron nonlinear refraction in solids, IEEE Journal of Quantum Electronics, vol.27, issue.6, pp.1296-1309
DOI : 10.1109/3.89946

S. Adachi, . Gaas, and A. Alas, As: Material parameters for use in research and device applications, Journal of Applied Physics, vol.58, issue.3, pp.1-29, 1985.
DOI : 10.1063/1.336070

D. Coquillat, G. Vecchi, C. Comaschi, A. M. Malvezzi, J. Torres et al., Enhanced second- and third-harmonic generation and induced photoluminescence in a two-dimensional GaN photonic crystal, Applied Physics Letters, vol.87, issue.10, pp.10-101106, 2005.
DOI : 10.1063/1.2037849

J. Pankove, S. Bloom, and G. Harbecke, Optical properties of GaN, RCA Rev, vol.36, p.163, 1975.

B. K. Meyer, D. Volm, A. Graber, H. C. Alt, T. Detchprohm et al., Shallow donors in GaN???The binding energy and the electron effective mass, Solid State Communications, vol.95, issue.9, pp.9-597, 1995.
DOI : 10.1016/0038-1098(95)00337-1

H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov et al., Large???band???gap SiC, III???V nitride, and II???VI ZnSe???based semiconductor device technologies, Journal of Applied Physics, vol.76, issue.3, pp.3-1363, 1994.
DOI : 10.1063/1.358463

A. C. Turner-foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem et al., Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides, Optics Express, vol.18, issue.4, pp.3582-3591, 2010.
DOI : 10.1364/OE.18.003582

C. Monat, C. Grillet, B. Corcoran, D. J. Moss, B. J. Eggleton et al., Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics, Optics Express, vol.18, issue.7, pp.6831-6840, 2010.
DOI : 10.1364/OE.18.006831

M. Ebnali-heidari, C. Monat, C. Grillet, and M. K. Moravvej-farshi, A proposal for enhancing four-wave mixing in slow light engineered photonic crystal waveguides and its application to optical regeneration, Optics Express, vol.17, issue.20, pp.20-18340, 2009.
DOI : 10.1364/OE.17.018340

B. Corcoran, C. Monat, D. Pudo, B. J. Eggleton, T. F. Krauss et al., Nonlinear loss dynamics in a silicon slow-light photonic crystal waveguide, Opt. Lett, vol.35, pp.7-1073, 2010.

S. Combrie, Q. V. Tran, A. D. Rossi, C. Husko, and P. Colman, High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption, Applied Physics Letters, vol.95, issue.22, pp.22-221108, 2009.
DOI : 10.1063/1.3269998

S. Mazoyer, J. P. Hugonin, and P. Lalanne, Disorder-Induced Multiple Scattering in Photonic-Crystal Waveguides, Physical Review Letters, vol.103, issue.6, p.63903, 2009.
DOI : 10.1103/PhysRevLett.103.063903
URL : https://hal.archives-ouvertes.fr/hal-00566690

M. C. Huy, A. Baron, S. Lebrun, R. Frey, and P. Delaye, Characterization of self-phase modulation in liquid filled hollow core photonic bandgap fibers, J. Opt. Soc. Am. B, vol.27, pp.9-1886, 2010.