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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 25 — Dec. 10, 2007
  • pp: 16604–16644

Nonlinear optical phenomena in silicon waveguides: Modeling and applications

Q. Lin, Oskar J. Painter, and Govind P. Agrawal  »View Author Affiliations

Optics Express, Vol. 15, Issue 25, pp. 16604-16644 (2007)

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Several kinds of nonlinear optical effects have been observed in recent years using silicon waveguides, and their device applications are attracting considerable attention. In this review, we provide a unified theoretical platform that not only can be used for understanding the underlying physics but should also provide guidance toward new and useful applications. We begin with a description of the third-order nonlinearity of silicon and consider the tensorial nature of both the electronic and Raman contributions. The generation of free carriers through two-photon absorption and their impact on various nonlinear phenomena is included fully within the theory presented here. We derive a general propagation equation in the frequency domain and show how it leads to a generalized nonlinear Schrödinger equation when it is converted to the time domain. We use this equation to study propagation of ultrashort optical pulses in the presence of self-phase modulation and show the possibility of soliton formation and supercontinuum generation. The nonlinear phenomena of cross-phase modulation and stimulated Raman scattering are discussed next with emphasis on the impact of free carriers on Raman amplification and lasing. We also consider the four-wave mixing process for both continuous-wave and pulsed pumping and discuss the conditions under which parametric amplification and wavelength conversion can be realized with net gain in the telecommunication band.

© 2007 Optical Society of America

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW
(320.7110) Ultrafast optics : Ultrafast nonlinear optics
(250.4390) Optoelectronics : Nonlinear optics, integrated optics

ToC Category:
Nonlinear Optics for Functional Devices and Applications

Original Manuscript: October 9, 2007
Revised Manuscript: November 22, 2007
Manuscript Accepted: November 25, 2007
Published: November 29, 2007

Virtual Issues
Focus Serial: Frontiers of Nonlinear Optics (2007) Optics Express

Q. Lin, Oskar J. Painter, and Govind P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: modeling and applications," Opt. Express 15, 16604-16644 (2007)

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  1. L. Pavesi and D. J. Lockwood, Eds., Silicon Photonics (Springer, New York, 2004).
  2. G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (Wiley, Hoboken, NJ, 2004). [CrossRef]
  3. R. A. Soref, "The Past, Present, and Future of Silicon Photonics," IEEE J. Sel. Top. Quantum Electron. 12, 1678-1687 (2006). [CrossRef]
  4. R. A. Soref, S. J. Emelett, and W. R. Buchwald, "Silicon waveguided components for the long-wave infrared region," J. Opt. A: Pure Appl. Opt. 8, 840-848 (2006). [CrossRef]
  5. M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003). [CrossRef]
  6. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplifi-cation in silicon waveguides," Opt. Express 11, 1731-1739 (2003). [CrossRef] [PubMed]
  7. H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, "Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 μm wavelength," Appl. Phys. Lett. 80, 416-418 (2002). [CrossRef]
  8. O. Boyraz, T. Indukuri, and B. Jalali, "Self-phase-modulation induced spectral broadening in silicon waveguides," Opt. Express 12, 829-834 (2004). [CrossRef] [PubMed]
  9. G.W. Rieger, K. S. Virk, and J. F. Yong, "Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides," Appl. Phys. Lett. 84, 900-902 (2004). [CrossRef]
  10. A. R. Cowan, G. W. Rieger, and J. F. Young, "Nonlinear transmission of 1.5 μm pulses through single-mode silicon-on-insulator waveguide structures," Opt. Express 12, 1611-1621 (2004). [CrossRef] [PubMed]
  11. H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, "Nonlinear-optic silicon-nanowire waveguides," Jpn. J. Appl. Phys. 44, 6541-6545 (2005). [CrossRef]
  12. E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006). [CrossRef] [PubMed]
  13. L. Yin, Q. Lin, and G. P. Agrawal, "Dispersion tailoring and soliton propagation in silicon waveguides," Opt. Lett. 31, 1295-1297 (2006). [CrossRef] [PubMed]
  14. R. Dekker, A. Driessen, T. Wahlbrink, C. Moormann, J. Niehusmann, and M. Först, "Ultrafast Kerr-induced all-optical wavelength conversion in silicon waveguides using 1.55 μm femtosecond pulses," Opt. Express 14, 8336-8346 (2006). [CrossRef] [PubMed]
  15. I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R.M. Osgood, Jr., S. J. McNab, and Y. A. Vlasov, "Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides," Opt. Express 14, 12380-12387 (2006). [CrossRef] [PubMed]
  16. L. Yin, Q. Lin, and G. P. Agrawal, "Soliton fission and supercontinuum generation in silicon waveguides," Opt. Lett. 32, 391-393 (2007). [CrossRef] [PubMed]
  17. J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, "Optical solitons in a silicon waveguide," Opt. Express 15, 7682-7688 (2007). [CrossRef] [PubMed]
  18. P. Koonath, D. R. Solli, and B. Jalali, "Continuum generation and carving on a silicon chip," Appl. Phys. Lett. 91, 061111 (2007). [CrossRef]
  19. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, "All-optical regeneration on a silicon chip," Opt. Express 15, 7802-7809 (2007). [CrossRef] [PubMed]
  20. R. Dekker, N. Usechak, M. Först, and A. Driessen, "Ultrafast nonlinear all-optical processes in silicon-oninsulator waveguides," J. Phys. D: Appl. Phys. 40, R249-R271 (2007). [CrossRef]
  21. L. Yin and G. P. Agrawal, "Impact of two-photon absorption on self-phase modulation in silicon waveguides," Opt. Lett. 32, 2031-2033 (2007). [CrossRef] [PubMed]
  22. N. Suzuki, "FDTD analysis of two-photon absorption and free-carrier absorption in Si high-index-contrast waveguides," J. Lightwave Technol. 25, 2495-2501 (2007). [CrossRef]
  23. I-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C-Y. Chou, F. Xia,W. M. Green, Y. A. Vlasov, and R. M. Osgood, Jr., "Supercontinuum generation in silicon photonic wires," Opt. Express 15, 15242-15248 (2007). [CrossRef] [PubMed]
  24. A. Hache and M. Bourgeois, "Ultrafast all-optical switching in a silicon-based photonic crystal," Appl. Phys. Lett. 77, 4089-4091 (2000). [CrossRef]
  25. Ö. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, "All optical switching and continuum generation in silicon waveguides," Opt. Express 12, 4094-4102 (2004). [CrossRef] [PubMed]
  26. I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, Jr., S. J. McNab, and Y. A. Vlasov, "Crossphase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires," Opt. Express 15, 1135-1146 (2007). [CrossRef] [PubMed]
  27. R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, "Observation of Raman emission in silicon waveguide at 1.54 μm," Opt. Express 10, 1305-1313 (2002). [PubMed]
  28. D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, "Coupled-mode theory of the Raman effect in siliconon-insulator waveguides," Opt. Lett. 28, 1954-1956 (2003). [CrossRef] [PubMed]
  29. J. I. Dadap, R. L. Espinola, R. M. Osgood, Jr., S. J. McNab, and Y. A. Vlasov, "Spontaneous Raman scattering in ultrasmall silicon waveguides," Opt. Lett. 29, 2755-2757 (2004). [CrossRef] [PubMed]
  30. R. L. Espinola, J. I. Dadap, R.M. Osgood, Jr., S. J. McNab, and Y. A. Vlasov, "Raman amplification in ultrasmall silicon-on-insulator wire waveguides," Opt. Express 12, 3713-3718 (2004). [CrossRef] [PubMed]
  31. Q. Xu, V. R. Almeida, and M. Lipson, "Time-resolved study of Raman gain in highly confined silicon-oninsulator waveguides," Opt. Express 12, 4437-4442 (2004). [CrossRef] [PubMed]
  32. 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," Opt. Express 12, 4261-4268 (2004). [CrossRef] [PubMed]
  33. H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, "Raman gain and nonlinear optical absorption measurement in a low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004). [CrossRef]
  34. T. K. Liang and H. K. Tsang, "Efficient Raman amplificationin silicon-on-insulator waveguides," Appl. Phys. Lett. 85, 3343-3345 (2004). [CrossRef]
  35. T. K. Liang and H. K. Tsang, "Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 84, 2745-2747 (2004). [CrossRef]
  36. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, "Influence of nonlinear absorption on Raman amplification in silicon waveguides," Opt. Express 12, 2774-2780 (2004). [CrossRef] [PubMed]
  37. T. K. Liang and H. K. Tsang, "Nonlinear absorption and Raman scattering in silicon-on-insulator optical waveguides," IEEE J. Quantum Electron. 10, 1149-1153 (2004). [CrossRef]
  38. O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004). [CrossRef] [PubMed]
  39. M. Krause, H. Renner, and E. Brinkmeyer, "Analysis of Raman lasing characteristics in silicon-on-insulator waveguides," Opt. Express 12, 5703-5710 (2004). [CrossRef] [PubMed]
  40. Q. Xu, V. R. Almeida, and M. Lipson, "Demonstration of high Raman gain in a submicrometer-size silicon-oninsulator waveguide," Opt. Lett. 30, 35-37 (2005). [CrossRef] [PubMed]
  41. H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005). [CrossRef] [PubMed]
  42. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, "A continuous-wave Raman silicon laser," Nature 433, 725-728 (2005). [CrossRef] [PubMed]
  43. O. Boyraz and B. Jalali, "Demonstration of directly modulated silicon Raman laser," Opt. Express 13, 796-800 (2005). [CrossRef] [PubMed]
  44. V. Raghunathan, O. Boyraz, ann B. Jalali, "20 dB on-off Raman amplification in silicon waveguides," Proc. Conf. Lasers Electro-Optics (OSA, Washington, DC, 2005), pp. 349-351.
  45. R. Jones, A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, "Lossless optical modulation in a silicon waveguide using stimulated Raman scattering," Opt. Express 13, 1716-1723 (2005). [CrossRef] [PubMed]
  46. X. Yang and C. W. Wong, "Design of photonic band gap nanocavities for stimulated Raman amplification and lasing in monolithic silicon," Opt. Express 13, 4723-4730 (2005). [CrossRef] [PubMed]
  47. X. Chen, N. C. Panoiu, R. M. Osgood, Jr., "Theory of Raman-mediated pulsed amplification in silicon-wire waveguides," IEEE J. Quantum Electron. 42, 160-170 (2006). [CrossRef]
  48. V. M. N. Passaro and F. D. Leonardis, "Space-time modeling of Raman pulses in silicon-on-insulator optical waveguides," IEEE J. Lightwave Technol. 24, 2920-2931 (2006). [CrossRef]
  49. J. F. McMillan, X. Yang, N. C. Panoiu, R. M. Osgood, and C.W. Wong, "Enhanced stimulated Raman scattering in slow-light photonic crystal waveguides," Opt. Lett. 31, 1235-1237 (2006). [CrossRef] [PubMed]
  50. S. Blair and K. Zheng, "Intensity-tunable group delay using stimulated Raman scattering in silicon slow-light waveguides," Opt. Express 14, 1064-1069 (2006). [CrossRef] [PubMed]
  51. Y. Okawachi, M. A. Foster, J. E. Sharping, A. L. Gaeta, Q. Xu, and M. Lipson, "All-optical slow-light on a photonic chip," Opt. Express 14, 2317-2322 (2006). [CrossRef] [PubMed]
  52. A. Liu, H. Rong, R. Jones, O. Cohen, D. Hak, and M. Paniccia, "Optical amplification and lasing by stimulated Raman scattering in silicon waveguides," IEEE J. Lightwave Technol. 24, 1440-1455 (2006). [CrossRef]
  53. B. Jalali, V. Raghunathan, D. Dimitropoulos, and O. Boyraz, "Raman-based silicon photonics," IEEE J. Sel. Top. Quantum Electron. 12, 412-421 (2006). [CrossRef]
  54. H. Rong, S. Xu, Y. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, "Low-threshold continuous-wave Raman silicon laser," Nature Photon. 1, 232-237 (2007). [CrossRef]
  55. X. Yang and C.W. Wong, "Coupled-mode theory for stimulated Raman scattering in high-Q/Vm silicon photonic band gap defect cavity lasers," Opt. Express 15, 4763-4780 (2007). [CrossRef] [PubMed]
  56. V. Sih, S. Xu, Y. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, "Raman amplification of 40 Gb/s data in low-loss silicon waveguides," Opt. Express 15, 357-362 (2007). [CrossRef] [PubMed]
  57. V. Raghunathan, H. Renner, R. R. Rice, and B. Jalali, "Self-imaging silicon Raman amplifier," Opt. Express 15, 3396-3408 (2007). [CrossRef] [PubMed]
  58. F. De Leonardis and V. M. N. Passaro, "Modelling of Raman amplification in silicon-on-insulator optical microcavities," New J. Phys. 9, 25 (2007). [CrossRef]
  59. F. De Leonardis and V. M. N. Passaro, "Modeling and performance of a guided-wave optical angular-velocity sensor based on Raman effect in SOI," IEEE J. Lightwave Technol. 25, 2352-2366 (2007). [CrossRef]
  60. V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, "Demonstration of a mid-infrared silicon Raman ampli-fier," Opt. Express 15, 14355-14362 (2007). [CrossRef] [PubMed]
  61. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, "Anti-Sotkes Raman conversion in silicon waveguides," Opt. Express 11, 2862-2872 (2003). [CrossRef] [PubMed]
  62. D. Dimitropoulos, V. Raghunathan, R. Claps, and B. Jalali, "Phase-matching and nonlinear optical processes in silicon waveguides," Opt. Express 12, 149-160 (2003). [CrossRef]
  63. V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, "Wavelength conversion in silicon using Raman induced four-wave mixing," Appl. Phys. Lett. 85, 34-36 (2004). [CrossRef]
  64. R. L. Espinola, J. I, Dadap, R. M. Osgood, Jr., S. J. McNab, and Y. A. Vlasov, "C-band wavelength conversion in silicon photonic wire waveguides," Opt. Express 13, 4341-4349 (2005). [CrossRef] [PubMed]
  65. H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, "Four-wave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005). [CrossRef] [PubMed]
  66. V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, "Parametric Raman wavelength conversion in scaled silicon waveguides," IEEE J. Lightwave Technol. 23, 2094-2102 (2005). [CrossRef]
  67. H. Rong, Y. Kuo, A. Liu, M. Paniccia, and O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006). [CrossRef] [PubMed]
  68. Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, "Ultrabroadband parametric generation and wavelength conversion in silicon waveguides," Opt. Express 14, 4786-4799 (2006). [CrossRef] [PubMed]
  69. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, "Broad-band optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006). [CrossRef] [PubMed]
  70. D. Dimitropoulos, D. R. Solli, R. Claps, and B. Jalali, "Noise figure and photon statistics in coherent anti-Stokes Raman scattering," Opt. Express 14, 11418-11432 (2006). [CrossRef] [PubMed]
  71. K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji, and S. Itabashi, "All-optical efficient wavelength conversion using silicon photonic wire waveguide," IEEE Photon. Technol. Lett. 18, 1046-1048 (2006). [CrossRef]
  72. Y. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, and O. Cohen, "Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides," Opt. Express 14, 11721-11726 (2006). [CrossRef] [PubMed]
  73. Q. Lin and G. P. Agrawal, "Silicon waveguides for creating quantum-correlated photon pairs," Opt. Lett. 31, 3140-3142 (2006). [CrossRef] [PubMed]
  74. N. C. Panoiu, X. Chen, and R. M. Osgood, Jr., "Modulation instability in silicon photonic nanowires," Opt. Lett. 31, 3609-3611 (2006). [CrossRef] [PubMed]
  75. J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, "Generation of correlated photons in nanoscale silicon waveguides," Opt. Express 14, 12388-12393 (2006). [CrossRef] [PubMed]
  76. N. Vermeulen, C. Debaes, and H. Thienpont, "Mitigating heat dissipation in near- and mid-infrared silicon-based Raman lasers using CARS," IEEE J. Sel. Top. Quantum Electron. 13, 770-787 (2007). [CrossRef]
  77. A. C. Turner, M. A. Foster, A. L Gaeda, and M. Lipson, "Ultra-low power frequency conversion in silicon microring resonators," Proc. Conf. Lasers Electro-Optics (OSA, Washington, DC, 2007), paper CPDA3.
  78. S. Ayotte, H. Rong, S. Xu, O. Cohen, and M. Paniccia, "Multichannel dispersion compensation using a silicon waveguide-based optical phase conjugator," Opt. Lett. 32, 2393-2395 (2007). [CrossRef] [PubMed]
  79. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, "Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides," Opt. Express 15, 12949-12958 (2007). [CrossRef] [PubMed]
  80. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Boston, 2007).
  81. R. A. Soref and B. R. Bennett, "Electrooptical effects in silicon," IEEE J. Quantum Electron. 23, 123-129 (1987). [CrossRef]
  82. V. Raghunathan, R. Shori, O. M. Stafsudd, B. Jalali, "Nonlinear absorption in silicon and the prospects of midinfrared silicon Raman lasers," Physica Status Solidi A 203, R38-R40 (2006). [CrossRef]
  83. A. D. Bristow, N. Rotenberg, and H. M. van Driel, "Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm," Appl. Phys. Lett. 90, 191104 (2007). [CrossRef]
  84. Q. Lin, J. Zhang, G. Piredda, R.W. Boyd, P. M. Fauchet, and G. P. Agrawal, "Dispersion of silicon nonlinearities in the near-infrared region," Appl. Phys. Lett. 90, 021111 (2007). [CrossRef]
  85. M. Foster and A. L. Gaeta, "Wavelength dependence of the ultrafast third-order nonlinearity of Silicon," Proc. Conf. Lasers Electro-Optics (OSA, Washington, DC, 2007), Paper CTuY5.
  86. D. J. Moss, H. M. van Driel, and J. E. Sipe, "Dispersion in the anisotropy of optical third-harmonic generation in silicon," Opt. Lett. 14, 57-59 (1989). [CrossRef] [PubMed]
  87. J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, "Anisotropic nonlinear response of silicon in the near-infrared region," Appl. Phys. Lett. 90, 071113 (2007). [CrossRef]
  88. P. E. Barclay, K. Srinivasan, and O. Painter, "Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper", Opt. Express 13, 801-820 (2005). [CrossRef] [PubMed]
  89. T. J. Johnson,M. Borselli, and O. Painter, "Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator," Opt. Express 14, 817-831 (2006). [CrossRef] [PubMed]
  90. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 431, 1081-1084 (2004). [CrossRef] [PubMed]
  91. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "All-optical switches on a silicon chip realized using photonic crystal nanocavities," Appl. Phys. Lett. 87, 151112 (2005). [CrossRef]
  92. S. F. Preble, Q. Xu, B. S. Schmidt, and M. Lipson, "Ultrafast all-optical modulation on a silicon chip," Opt. Lett. 30, 2891-2893 (2005). [CrossRef] [PubMed]
  93. T. G. Eusera and W. L. Vos, "Spatial homogeneity of optically switched semiconductor photonic crystals and of bulk semiconductors," J. Appl. Phys. 97, 043102 (2005). [CrossRef]
  94. C. Manolatou and M. Lipson, "All-optical silicon modulators based on carrier injection by two-photon absorption," IEEE J. Lightwave Technol. 24, 1433-1439 (2006). [CrossRef]
  95. F. Gan, F. J. Grawert, J. M. Schley, S. Akiyama, J. Michel, K. Wada, L. C. Kimerling, and F. X. K¨artner, "Design of all-optical switches based on carrier injection in Si/SiO2 split-ridge waveguides (SRWs)," IEEE J. Lightwave Technol. 24, 3454-3463 (2006). [CrossRef]
  96. K. Ikeda and Y. Fainman, "Nonlinear Fabry-Perot resonator with a silicon photonic crystal waveguide," Opt. Lett. 31, 3486-3488 (2006). [CrossRef] [PubMed]
  97. E. Tien, N. S. Yuksek, F. Qian, and O. Boyraz, "Pulse compression and modelocking by using TPA in silicon waveguides," Opt. Express 15, 6500-6506 (2007). [CrossRef] [PubMed]
  98. T. K. Liang, L. R. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. R. A. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. K. Tsang, "Ultrafast all-optical switching by cross-absorption modulation in silicon wire waveguides," Opt. Express 13, 7298-7303 (2005). [CrossRef] [PubMed]
  99. D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, "Ultrafast all-optical modulation via two-photon absorption in silicon-on-insulator waveguides," Electron. Lett. 41, 320-321 (2005). [CrossRef]
  100. T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, "High speed logic gate using two-photon absorption in silicon waveguides," Opt. Commun. 265, 171-174 (2006). [CrossRef]
  101. J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006). [CrossRef]
  102. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, New York, 1991).
  103. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, Boston, 2003).
  104. Y. R. Shen and N. Bloembergen, "Theory of stimulated Brillouin and Raman scattering," Phys. Rev. 137, A1787- A1805 (1965). [CrossRef]
  105. M. D. Lvenson and N. Bloembergen, "Dispersion of the nonlinear optical susceptibility tensor in centrosymmetric media," Phys. Rev. B 10, 4447-4463 (1974). [CrossRef]
  106. M. Cardona, "Resonance phenomena," in Light Scattering in Solid II, M. Cardona and G. Güntherodt eds. (Springer-Verlag, New York, 1982).
  107. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, "Raman response function of silica-core fibers," J. Opt. Soc. Am. B 6, 1159-1166 (1989). [CrossRef]
  108. P. A. Temple and C. E. Hathaway, "Multiphonon Raman spectrum of silicon," Phys. Rev. B 7, 3685-3697 (1973). [CrossRef]
  109. T. R. Hart, R. L. Aggarwal, and B. Lax, "Temperature dependence of Raman scattering in silicon," Phys. Rev. B 1, 638-642 (1970). [CrossRef]
  110. A. Zwick and R. Carles, "Multiple-order Raman scattering in crystalline and amorphous silicon," Phys. Rev. B 48, 6024-6032 (1993). [CrossRef]
  111. R. Loudon, "The Raman effect in crystals," Adv. Phys. 50, 813-864 (2001). [CrossRef]
  112. J. R. Sandercock, "Brillouin-scattering measurements on silicon and germanium," Phys. Rev. Lett. 28, 237-240 (1972). [CrossRef]
  113. M. Dinu, "Dispersion of phonon-assisted nonresonant third-order nonlinearities," IEEE J. Quantum Electron. 39, 1498-1503 (2003). [CrossRef]
  114. H. Garcia and R. Kalyanaraman, "Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz-Keldysh effect in indirect gap semiconductor," J. Phys. B 39, 2737-2746 (2006). [CrossRef]
  115. M. Sheik-Bahae and E. W. Van Stryland, "Optical nonlinearities in the transparency region of bulk semiconductors," in Nonlinear Optics in Semiconductors I, E. Garmire and A. Kost, eds., Semiconductors and Semimetals, (Academic, Boston, 1999) vol. 58.
  116. G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic Press, Boston, 2007).
  117. R. W. Hellwarth, "Third-order optical susceptibilities of liquids and solids," Prog. Quantum Electron. 5, 1-68 (1977). [CrossRef]
  118. P. D. Maker and R.W. Terhune, "Study of optical effects due to an induced polarization third order in the electric field strength," Phys. Rev. 137, A801-A818 (1965). [CrossRef]
  119. S. S. Jha and N. Bloembergen, "Nonlinear optical susceptibilities in group-IV and III-V semiconductors," Phys. Rev. 171, 891-898 (1968). [CrossRef]
  120. J. J. Wynne, "Optical third-order mixing in GaAs, Ge, Si, and InAs," Phys. Rev. 178, 1295-1303 (1969). [CrossRef]
  121. R. Buhleier, G. Lüpke, G. Marowsky, Z. Gogolak, and J. Kuhl, "Anisotropic interference of degenerate four-wave mixing in crystalline silicon," Phys. Rev. B 50, 2425-2431 (1994). [CrossRef]
  122. W. K. Burns and N. Bloembergen, "Third-harmonic generation in absorbing media of cubic or isotropic symmetry," Phys. Rev. B 4, 3437-3450 (1971). [CrossRef]
  123. D. J. Moss, H. M. van Driel, and J. E. Sipe, "Third harmonic generation as a structure diagonostic of ionimplanted amorphous and crystalline silicon," Appl. Phys. Lett. 48, 1150-1152 (1986). [CrossRef]
  124. C. C. Wang, J. Bomback, W. T. Donlon, C. R. Huo, and J. V. James, "Optical third-harmonic generation in reflection from crystalline and amorphous samples of silicon," Phys. Rev. Lett. 57, 1647-1650 (1986). [CrossRef] [PubMed]
  125. D. J. Moss, E. Ghahramani, J. E. Sipe, and H. M. van Driel, "Band-structure calculation of dispersion and anisotropy in χ(3) for third-harmonic generation in Si, Ge, and GaAs," Phys. Rev. B 41, 1542-1560 (1990). [CrossRef]
  126. J. F. Reintjes and J. C. McGroddy, "Indirect two-photon transition in Si at 1.06 μm", Phys. Rev. Lett. 30, 901-903 (1973). [CrossRef]
  127. 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," Opt. Lett. 14, 1140-1142 (1989). [CrossRef] [PubMed]
  128. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, "Dispersion of bound electronic nonlinear refraction in solids," IEEE J. Quantum Electron. 27, 1296-1309 (1991). [CrossRef]
  129. R. Salem and T. E. Murphy, "Polarization-insensitive cross correlation using two-photon absorption in a silicon photodiode," Opt. Lett. 29, 1524-1526 (2004). [CrossRef] [PubMed]
  130. T. Kagawa and S. Ooami, "Polarization dependence of two-photon absorption in Si avalanche photodiodes," Jpn. J. Appl. Phys. 46, 664-668 (2007). [CrossRef]
  131. S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed. (Wiley, Hoboken, NJ, 2007).
  132. A. Othonos, "Probing ultrafast carrier and phonon dynamics in semiconductors," J. Appl. Phys. 83, 1789-1830 (1998), and references therein. [CrossRef]
  133. A. J. Sabbah and D. M. Riffe, "Femtosecond pump-probe reflectivity study of silicon carrier dynamics," Phys. Rev. B 66, 165217 (2002). [CrossRef]
  134. A. Kost, "Resonant optical nonlinearities in semiconductors," in Nonlinear Optics in Semiconductors I, E. Garmire and A. Kost, Eds., Semiconductors and Semimetals, vol. 58 (Academic, Boston, 1999).
  135. R. A. Soref and B. R. Bennett, "Kramers-Kronig analysis of electro-optical switching in silicon," Proc. SPIE 704, 32-37 (1987).
  136. D. S. Chemla, "Ultrafast transient nonlinear optical processes in semiconductors," in Nonlinear Optics in Semiconductors I, E. Garmire and A. Kost, Eds., Semiconductors and Semimetals, (Academic, Boston, 1999) vol. 58 .
  137. Q. Lin, T. Johnson, R. Perahia, C. Michael, and O. J. Painter, "Highly tunable optical parametric oscillation in silicon micro-resonators," submitted for publication.
  138. M. J. Adams, S. Ritchie, and M. J. Robertson, "Optimum overlap of electric and optical fields in semiconductor waveguide devices," Appl. Phys. Lett. 18, 820-822 (1986). [CrossRef]
  139. D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, "Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides," Appl. Phys. Lett. 86, 071115 (2005). [CrossRef]
  140. Y. Liu and H. K. Tsang, "Nonlinear absorption and Raman gain in helium-ion-implanted silicon waveguides," Opt. Lett. 31, 1714-1716 (2006). [CrossRef] [PubMed]
  141. Y. Liu and H. K. Tsang, "Time dependent density of free carriers generated by two photon absorption in silicon waveguides," Appl. Phys. Lett. 90, 211105 (2007). [CrossRef]
  142. M. Först, J. Niehusmann, T. Plötzing, J. Bolten, T. Wahlbrink, C. Moormann, and H. Kurz, "High-speed alloptical switching in ion-implanted silicon-on-insulator microring resonators," Opt. Lett. 32, 2046-2048 (2007). [CrossRef] [PubMed]
  143. T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, and M. Notomi, "Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities," Appl. Phys. Lett. 90, 031115 (2007). [CrossRef]
  144. D. Dimitropoulos, S. Fathpour, and B. Jalali, "Limitations of active carrier removal in silicon Raman amplifiers and lasers," Appl. Phys. Lett. 87, 261108 (2005). [CrossRef]
  145. J. M. Ralston and R. K. Chang, "Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon", Phys. Rev. B 2, 1858 (1970). [CrossRef]
  146. J. B. Renucci, R. N. Tyte, and M. Cardona, "Resonant Raman scattering in silicon", Phys. Rev. B 11, 3885 (1975). [CrossRef]
  147. T. A. Birks,W. J. Wadsworth, and P. St. J. Russell, "Supercontinuum generation in tapered fibers," Opt. Lett. 25, 1415-1416 (2000). [CrossRef]
  148. P. St. J. Russell, "Photonic crystal fibers," IEEE J. Lightwave Technol. 24, 4729-4749 (2006). [CrossRef]
  149. A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous group-velocity dispersion in silicon channel waveguides," Opt. Express 14, 4357-4362 (2006). [CrossRef] [PubMed]
  150. N. Bloembergen and P. Lallemand, "Complex intensity-dependent index of refraction, frequency broadening of stimulated Raman scattering, and stimulated Rayleigh scattering," Phys. Rev. Lett. 16, 81-84 (1966). [CrossRef]
  151. K. Kikuchi, "Highly sensitive interferometric autocorrelator using Si avalanche photodiode as two-photon absorber," Electron. Lett. 34, 123-125 (1998). [CrossRef]
  152. C. Xu, J. M. Roth, W. H. Knox, K. Bergman, "Ultra-sensitive autocorrelation of 1.5 μm light with single photon counting silicon avalanche photodiode," Electron. Lett. 38, 86-88 (2002). [CrossRef]
  153. T. K. Liang, H. K. Tsang, T. E. Day, J. Drake, A. P. Knights, M. Asghari, "Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for autocorrelation measurements," Appl. Phys. Lett. 81, 1323-1325 (2002). [CrossRef]
  154. D. Panasenko, Y. Fainman, "Single-shot sonogram generation for femtosecond laser pulse diagnostics by use of two-photon absorption in a silicon CCD camera," Opt. Lett. 27, 1475-1477 (2002). [CrossRef]
  155. R. Salem, G. E. Tudury, T. U. Horton, G.M. Carter, T. E. Murphy, "Polarization-insensitive optical clock recovery at 80 Gb/s using a silicon photodiode," IEEE Photon. Technol. Lett. 17, 1968-1970 (2005). [CrossRef]
  156. M. Dinu, D. C. Kilper, H. R. Stuart, "Optical performance monitoring using data stream intensity autocorrelation," IEEE J. Lightwave Technol. 24, 1194-1202 (2006). [CrossRef]
  157. K. Taira, Y. Fukuchi, R. Ohta, K. Katoh, and K. Kikuchi, "Background-free intensity autocorrelator employing Si avalanche photodiode as two-photon absorber," Electron. Lett. 38, 1465-1466 (2002). [CrossRef]
  158. T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, "Theoretical and Experimental Study of Stimulated and Cascaded Raman Scattering in Ultrahigh-Q Optical Microcavities," IEEE J. Sel. Top. Quantum Electron. 10, 1219-1228 (2004). [CrossRef]
  159. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, "Fiber-based optical parametric amplifiers and their applications," IEEE J. Sel. Top. Quantum Electron. 8, 506-520 (2002). [CrossRef]
  160. S. Fathpour, K. K. Tsia, and B. Jalali, "Energy harvesting in silicon Raman amplifiers," Appl. Phys. Lett. 89, 061109 (2006). [CrossRef]
  161. K. K. Tsia, S. Fathpour, and B. Jalali, "Energy harvesting in silicon wavelength converters," Opt. Express 14, 12327-12333 (2006). [CrossRef] [PubMed]
  162. T. Torounidis and P. Andrekson, "Broadband single-pumped fiber-optic parametric amplifiers," IEEE Photon. Technol. Lett. 19, 650-652 (2007). [CrossRef]
  163. J. M. Chavez Boggio, J. D. Marconi, S. R. Bickham, and H. L. Fragnito, "Spectrally flat and broadband double-pumped fiber optical parametric amplifiers," Opt. Express 15, 5288-5309 (2007). [CrossRef] [PubMed]
  164. M. D. Levenson, C. Flytzanis, and N. Bloembergen, "Interference of resonant and nonresonant three-wave mixing in diamond," Phys. Rev. B 6, 3962-3965 (1972). [CrossRef]
  165. M. D. Levenson and S. Kano, Intronduction to Nonlinear Laser Spectroscopy (Academic Press, Boston, 1988).
  166. B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, "Prospects for silicon Mid-IR Raman Lasers," IEEE J. Sel. Top. Quantum Electron. 12, 1618-1627 (2006). [CrossRef]
  167. H. Takesue and K. Inoue, "Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop," Phys. Rev. A 70, 031802(R) (2004). [CrossRef]
  168. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, "Optical-Fiber Source of Polarization-Entangled Photons in the 1550 nm Telecom Band," Phys. Rev. Lett. 94, 053601 (2005). [CrossRef] [PubMed]
  169. J. Fulconis, O. Alibart, W. J. Wadsworth, P. St. J. Russell, and J. G. Rarity, "High brightness single mode source of correlated photon pairs using a photonic crystal fiber," Opt. Express 13, 7572-7582 (2005). [CrossRef] [PubMed]
  170. J. Fan, A. Migdall, and L. J. Wang, "Efficient generation of correlated photon pairs in a microstructure fiber," Opt. Lett. 30, 3368-3370 (2005). [CrossRef]
  171. X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications: Improved generation of correlated photons," Opt. Express 12, 3737-3744 (2004). [CrossRef] [PubMed]
  172. Q. Lin, F. Yaman, and G. P. Agrawal, "Photon-pair generation by four-wave mixing in optical fibers," Opt. Lett. 31, 1286-1288 (2006). [CrossRef] [PubMed]
  173. Q. Lin, F. Yaman, and G. P. Agrawal, "Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization," Phys. Rev. A 75, 023803 (2007). [CrossRef]
  174. H. Takesue and K. Inoue, "1.5- μm band quantum-correlated photon pair generation in dispersion-shifted fibers: suppression of noise photons by cooling fiber," Opt. Express 13, 7832-7839 (2005). [CrossRef] [PubMed]
  175. K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, "Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber," Opt. Lett. 31, 1905-1907 (2006). [CrossRef] [PubMed]

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