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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 8 — Apr. 16, 2007
  • pp: 4763–4780

Coupled-mode theory for stimulated Raman scattering in high-Q/Vm silicon photonic band gap defect cavity lasers

Xiaodong Yang and Chee Wei Wong  »View Author Affiliations


Optics Express, Vol. 15, Issue 8, pp. 4763-4780 (2007)
http://dx.doi.org/10.1364/OE.15.004763


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Abstract

We examine the dynamics of stimulated Raman scattering in designed high-Q/Vm silicon photonic band gap nanocavities through the coupled-mode theory framework towards optically-pumped silicon lasing. The interplay of other χ(3) effects such as two-photon absorption and optical Kerr, related free-carrier dynamics, thermal effects, as well as linear losses such as cavity radiation and linear material absorption are included and investigated numerically. Our results clarify the relative contributions and evolution of the mechanisms, and demonstrate the lasing and shutdown thresholds. Our studies illustrate the conditions for continuous-wave and pulsed highly-efficient Raman frequency conversion for practical realization in monolithic silicon high-Q/Vm photonic band gap defect cavities.

© 2007 Optical Society of America

OCIS Codes
(140.3550) Lasers and laser optics : Lasers, Raman
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(230.5750) Optical devices : Resonators

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: November 1, 2006
Revised Manuscript: December 18, 2006
Manuscript Accepted: December 18, 2006
Published: April 4, 2007

Citation
Xiaodong Yang and Chee Wei 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)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-8-4763


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References

  1. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006). [CrossRef]
  2. T. Asano, B. -S. Song, and S. Noda, "Analysis of the experimental Q factors (~ 1 million) of photonic crystal nanocavities," Opt. Express 14, 1996-2002 (2006). [CrossRef] [PubMed]
  3. T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, "High-Q ring resonators in thin silicon-on-insulator," Appl. Phys. Lett. 85, 3346 (2004). [CrossRef]
  4. D. K. Sparacin, S. J. Spector, and L. C. Kimerling, "Silicon waveguide sidewall smoothing by wet chemical oxidation," J. Lightwave Technol. 23, 2455 (2005). [CrossRef]
  5. 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]
  6. V. R. Almeida and M. Lipson, "Optical bistability on a silicon chip," Opt. Lett. 29, 2387-2389 (2004). [CrossRef] [PubMed]
  7. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 1731-1739 (2003). [CrossRef] [PubMed]
  8. 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]
  9. T. K. Liang and H. K. Tsang, "Efficient Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 85, 3343-3345 (2004). [CrossRef]
  10. 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]
  11. Q. Xu, V. R. Almeida, and M. Lipson, "Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides," Opt. Express 12, 4437 - 4442 (2004). [CrossRef] [PubMed]
  12. O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004). [CrossRef] [PubMed]
  13. R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, "Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering," Opt. Express 13, 519-525 (2005). [CrossRef] [PubMed]
  14. 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]
  15. 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]
  16. O. Boyraz and B. Jalali, "Demonstration of directly modulated silicon Raman laser," Opt. Express 13, 796-800 (2005). [CrossRef] [PubMed]
  17. 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]
  18. E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  19. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  20. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light. (Princeton, NJ: Princeton University Press, 1995).
  21. K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10,670-684 (2002). [PubMed]
  22. D. Englund, I. Fushman, and J. Vučković, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5975 (2005). [CrossRef] [PubMed]
  23. Y.  Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003). [CrossRef] [PubMed]
  24. H. Ryu, M. Notomi, G. Kim, and Y. Lee, "High quality-factor whispering-gallery mode in the photonic crystal hexagonal disk cavity," Opt. Express 12,1708-1719 (2004). [CrossRef] [PubMed]
  25. Z. Zhang and M. Qiu, "Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs," Opt. Express 12,3988-3995 (2004). [CrossRef] [PubMed]
  26. B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005). [CrossRef]
  27. B. S. Song, S. Noda, and T. Asano, "Photonic devices based on in-plane hetero photonic crystals," Science 300, 1537 (2003). [CrossRef] [PubMed]
  28. K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003). [CrossRef] [PubMed]
  29. H. Takano, B. -S. Song, T. Asano, and S. Noda, "Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal," Opt. Express 14, 3491-3496 (2006). [CrossRef] [PubMed]
  30. H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, "Electrically driven single-cell photonic crystal laser," Science 305, 1444-1447(2004). [CrossRef] [PubMed]
  31. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432, 200-203 (2004). [CrossRef] [PubMed]
  32. M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nat. Mater. 3, 211-219 (2004). [CrossRef] [PubMed]
  33. 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]
  34. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005). [CrossRef] [PubMed]
  35. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-623 (2002). [CrossRef] [PubMed]
  36. 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]
  37. 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]
  38. 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]
  39. L. Florescu and X. Zhang, "Semiclassical model of stimulated Raman scattering in photonic crystals," Phys. Rev. E 72, 016611 (2005). [CrossRef]
  40. J. F. McMillan, X. Yang, N. C. Paniou, 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]
  41. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N. J., 1984).
  42. A. Yariv, Optical Electronics (Sanders College Publishing, Philadelphia, 1991).
  43. C.  Manolatou, M. J.  Khan, S.  Fan, P. R.  Villeneuve, H. A.  Haus, and J. D.  Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron.  35, 1322 (1999). [CrossRef]
  44. H. Ren, C. Jiang, W. Hu, M. Gao, and J. Wang, "Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity," Opt. Express 14, 2446-2458 (2006). [CrossRef] [PubMed]
  45. 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]
  46. C. Manolatou and M. Lipson, "All-Optical Silicon Modulators based on Carrier Injection by Two-Photon Absorption," J. Lightwave Technol. 24, 1433-1439 (2006). [CrossRef]
  47. T. Uesugi, B. Song, T. Asano, and S. Noda, "Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab," Opt. Express 14, 377-386 (2006). [CrossRef] [PubMed]
  48. D. Dimitropoulos, B. Houshmand, R. Claps, B. Jalali, "Coupled-mode theory of the Raman effect in silicon-on-insulator waveguides," Opt. Lett. 28, 1954-1956 (2003). [CrossRef] [PubMed]
  49. 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]
  50. X. Chen, N. C. Panoiu, and R. M. Osgood, "Theory of Raman-mediated pulsed amplification in silicon-wire waveguides," IEEE J. Quantum Electron. 42, 160-170 (2006). [CrossRef]
  51. V. E. Perlin and H. G. Winful, "Stimulated Raman Scattering in nonlinear periodic structures," Phys. Rev. A 64, 043804 (2001). [CrossRef]
  52. B. Min, T. J. Kippenberg, and K. J. Vahala, "Compact, fiber-compatible, cascaded Raman laser," Opt. Lett. 28, 1507-1509 (2003). [CrossRef] [PubMed]
  53. D. Braunstein, A. M. Khazanov, G. A. Koganov, and R. Shuker, "Lowering of threshold conditions for nonlinear effects in a microsphere," Phys. Rev. A 53, 3565-3572 (1996). [CrossRef] [PubMed]
  54. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, Hoboken, New Jersey, 2003) Chap. 10.
  55. H. W. Tan, H. M. van Driel, S. L. Schweizer, and R. B. Wehrspohn, "Influence of eigenmode characteristics on optical tuning of a two-dimensional silicon photonic crystal," Phys. Rev. B,  72, 165115 (2005). [CrossRef]
  56. R. A. Soref and B. R. Bennett, "Electrooptical Effects in Silicon," IEEE J. Quantum Electron. 23, 123-129 (1987). [CrossRef]
  57. Handbook of optical constants of solids, E. Palick, ed., (Academic Press, Boston, MA, 1985).
  58. M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003). [CrossRef]
  59. A. Cutolo, M. Iodice, P. Spirito, and L. Zeni, "Silicon Electro-Optic Modulator Based on a Three Terminal Device Integrated in a Low-Loss Single-Mode SOI Waveguide," J. Lightwave Technol. 15, 505-518 (1997). [CrossRef]
  60. S. Sze, Physics of semiconductor devices, 2nd ed. (John Wiley and Sons, New York, New York, 1981).
  61. T. Asano, W. Kunishi, M. Nakamura, B. S. Song, and S. Noda, "Dynamic wavelength tuning of channel-drop device in two-dimensional photonic crystal slab," Electron. Lett. 41, 37-38 (2005). [CrossRef]
  62. G. Cocorullo, F. G. Della Corte, and I. Rendina, "Temperature dependence of the thermo-optic coefficient in crystalline silicon between room temperature and 550 K at the wavelength of 1523 nm," Appl. Phys. Lett. 74, 3338-3340 (1999). [CrossRef]

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