Abstract

The concept and design of L5 photonic band gap nanocavities in two-dimensional photonic crystal slabs for enhancement of stimulated Raman amplification and lasing in monolithic silicon is suggested for the first time. Specific high quality factor and small modal volume nanocavities are designed which supports the required pump-Stokes modal spacing in silicon, with ultralow lasing thresholds.

© 2005 Optical Society of America

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  1. L. Pavesi and D. J. Lockwood, Silicon Photonics, (Springer-verlag, New York, 2004); G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (John Wiley, West Sussex, 2004).
  2. K. Wada, K., H. C. Luan, D. R. C. Lim and L. C. Kimerling., �??On-chip interconnection beyond semiconductor roadmap: silicon microphotonics,�?? Proc. SPIE 4870, 437-443 (2002).
    [CrossRef]
  3. 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); V. R. Almeida and M. Lipson, �??Optical bistability on a silicon chip,�?? Opt. Letters 29, 2387-2389 (2004).
    [CrossRef] [PubMed]
  4. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731</a>
    [CrossRef] [PubMed]
  5. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3713">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3713</a>
    [CrossRef] [PubMed]
  6. T. K. Liang and H. K. Tsang, �??Efficient Raman amplification in silicon-on-insulator waveguides,�?? Appl. Phys. Lett. 85, 3343-3345 (2004).
    [CrossRef]
  7. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-18-4261">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-18-4261</a>
    [CrossRef] [PubMed]
  8. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4437">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4437</a>
    [CrossRef] [PubMed]
  9. O. Boyraz and B. Jalali, �??Demonstration of a silicon Raman laser,�?? Opt. Express 12, 5269-5273 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5269">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5269</a>
    [CrossRef] [PubMed]
  10. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-519">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-519</a>; 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); 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]
  11. O. Boyraz and B. Jalali, �??Demonstration of directly modulated silicon Raman laser,�?? Opt. Express 13, 796-800 (2005), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-796">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-796</a>
    [CrossRef] [PubMed]
  12. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1716">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1716</a>
    [CrossRef] [PubMed]
  13. K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670</a>
    [PubMed]
  14. 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]
  15. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1708">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1708</a>
    [CrossRef] [PubMed]
  16. Z. Zhang and M. Qiu, "Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs," Opt. Express 12, 3988-3995 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-3988">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-3988</a>
    [CrossRef] [PubMed]
  17. B. S. Song, S. Noda, T. Asano, and Y. Akahane, �??Ultra-high-Q photonic double-heterostructure nanocavity,�?? Nature Materials 4, 207-210 (2005); B. S. Song, S. Noda, and T. Asano, �??Photonic devices based on in-plane hetero photonic crystals,�?? Science 300, 1537 (2003).
    [CrossRef]
  18. P. Koonath, T. Indukuri, and B. Jalali, �??Vertically-coupled microdisk resonators realized using three-dimensional sculpting in silicon,�?? Appl. Phys. Lett. 85, 1018-1020 (2003).
    [CrossRef]
  19. M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, �??Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,�?? Appl. Phys. Lett. 85, 3693-3695 (2004).
    [CrossRef]
  20. K. J. Vahala, �??Optical microcavities,�?? Nature 424, 839-846 (2003).
    [CrossRef] [PubMed]
  21. 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]
  22. 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]
  23. M. Soljacic, and J. D. Joannopoulos, �??Enhancement of nonlinear effects using photonic crystals,�?? Nature materials 3, 211-219 (2004).
    [CrossRef] [PubMed]
  24. J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, �??Coupled resonator optical waveguides: toward the slowing and storage of light,�?? Optics & Photonics News 16 (2), 36-40, (2005).
    [CrossRef]
  25. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801</a>
    [CrossRef] [PubMed]
  26. 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2678">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2678</a>
    [CrossRef] [PubMed]
  27. 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]
  28. T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, �??Ultralow-threshold microcavity Raman laser on a microelectronic chip,�?? Optics Letters 29, 1224-1226 (2004).
    [CrossRef] [PubMed]
  29. 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]
  30. X. Yang, J. Yan, and C. W. Wong, �??Design and fabrication of L5 photonic band gap nanocavities for stimulated Raman amplification in monolithic silicon,�?? CLEO/QELS, CMU2, Baltimore, Maryland (2005).
  31. Y. R. Shen, The Principles of Nonlinear Optics, (Wiley, Hoboken, New Jersey, 2003); Y. R. Shen and N. Bloembergen, �??Theory of stimulated Brillouin and Raman scattering,�?? Phys. Rev. 137 (6A), A1787 (1965).
  32. F. X. Kärtner, D. J. Dougherty, H. A. Haus, E. P. Ippen, �??Raman noise and soliton squeezing,�?? J. Opt. Soc. Am. B. 11, 1267 (1994); 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 (1989).
    [CrossRef]
  33. K. J. Blow and D. Wood, �??Theoretical description of transient stimulated Raman scattering in optical fibers,�?? IEEE J. Quan. Elect. 25, 2665 (1989).
    [CrossRef]
  34. A. Höök, �??Influence of stimulated Raman scattering on cross-phase modulation between waves in optical fibers,�?? Opt. Lett. 17, 115 (1992).
    [CrossRef] [PubMed]
  35. E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, �??Mutual influence of the parametric effects and stimulated Raman scattering in optical fiberes,�?? IEEE J. of Quan. Elect. 26 (10), 1815 (1990).
    [CrossRef]
  36. R. G. Zaporozhchenko, S. Ya. Kilin, A. G. Smirnov, �??Stimulated Raman scattering of light in a photonic crystal,�?? Quan. Elect. 30, 997 (2000).
    [CrossRef]
  37. X. Chen, Nicolae C. Panoiu, and R. M. Osgood, Jr., Microelectronics Sciences Laboratories, Columbia University, New York, NY 10027, (personal communication, 2005).
  38. V. E. Perlin and H. G. Winful, �??Stimulated Raman Scattering in nonlinear periodic structures,�?? Phys. Rev. A 64, 043804 (2001); H. G. Winful, V. E. Perlin, and M. Franke, �??Stimulated Raman and Brillouin Scattering in nonlinear periodic structures,�?? in Proc. of Nonlinear Optics: Materials, Fundamentals, and Applications, Kaua�??i-Lihue, Hawaii (2000).
    [CrossRef]
  39. M. Krause, H. Renner, and E. Brinkmeyer, �??Analysis of Raman lasing characteristics in silicon-on-insulator waveguides,�?? Opt. Express 12, 5703-5710 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-23-5703">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-23-5703</a>
    [CrossRef] [PubMed]
  40. C. Sauvan, P. Lalanne, and J.P. Hugonin, �??Slow-wave effect and mode-profile matching in Photonic Crystal microcavities,�?? Phys. Rev. B. (to be published), <a href= "http://arxiv.org/abs/cond-mat/0502664">http://arxiv.org/abs/cond-mat/0502664</a>.
  41. A. B. Matsko, A. A. Savchenkov, R. J. Letargat, V. S. Ilchenko, and L. Maleki, �??On cavity modification of stimulated Raman scattering,�?? J. Opt. B: Quantum Semiclass. Opt. 5, 272-278 (2003).
    [CrossRef]
  42. H.-B. Lin and A. J. Campillo, �??cw nonlinear optics in droplet microcavities displaying enhanced gain,�?? Phys. Rev. Lett. 73, 2440 (1994); H.-B. Lin and A. J. Campillo, �??Microcavity enhanced Raman gain,�?? Opt. Comm. 133, 287 (1997).
    [CrossRef] [PubMed]
  43. H. Yokoyama and S. D. Brorson, �??Rate equation analysis of microcavity lasers,�?? J. Appl. Phys. 66 (10), 4801 (1989).
    [CrossRef]
  44. H. M. Lai, P. T. Leung, K. Young, �??Electromagnetic decay into a narrow resonance in an optical cavity,�?? Phys. Rev. A. 37, 1597 (1988).
    [CrossRef] [PubMed]
  45. B. Min, T. J. Kippenberg, and K. J. Vahala, �??Compact, fiber-compatible, cascaded Raman laser,�?? Optics Lett. 28 (17), 1507 (2003).
    [CrossRef]
  46. Y. Wu, X. Yang, and P. T. Leung, �??Theory of microcavity-enhanced Raman gain,�?? Opt. Lett. 24, 345 (1999); Y. Wu and P. T. Leung, �??Lasing threshold for whispering-gallery-mode microsphere lasers,�?? Phys. Rev. A 60, 630 (1999).
    [CrossRef]
  47. For a one-dimensional cavity, the enhancement reduces to the Yokoyama-Brorson factor (Ref. [43]) as suggested in Ref. [46].
  48. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>
    [CrossRef] [PubMed]
  49. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2000); RSoft FullWave commercial software used.
  50. S. G. Johnson, MIT, Cambridge, MA, personal communication, 2005; V. A. Mandelshtam and H. S. Taylor, �??Harmonic inversion of time signals,�?? J. Chem. Phys. 107, 6756 (1997); Erratum, ibid. 109, 4128 (1998).

Appl. Phys. Lett. (4)

T. K. Liang and H. K. Tsang, �??Efficient Raman amplification in silicon-on-insulator waveguides,�?? Appl. Phys. Lett. 85, 3343-3345 (2004).
[CrossRef]

P. Koonath, T. Indukuri, and B. Jalali, �??Vertically-coupled microdisk resonators realized using three-dimensional sculpting in silicon,�?? Appl. Phys. Lett. 85, 1018-1020 (2003).
[CrossRef]

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, �??Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,�?? Appl. Phys. Lett. 85, 3693-3695 (2004).
[CrossRef]

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]

CLEO/QELS 2005 (1)

X. Yang, J. Yan, and C. W. Wong, �??Design and fabrication of L5 photonic band gap nanocavities for stimulated Raman amplification in monolithic silicon,�?? CLEO/QELS, CMU2, Baltimore, Maryland (2005).

IEEE J. of Quan. Elect. (1)

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, �??Mutual influence of the parametric effects and stimulated Raman scattering in optical fiberes,�?? IEEE J. of Quan. Elect. 26 (10), 1815 (1990).
[CrossRef]

IEEE J. Quan. Elect. (1)

K. J. Blow and D. Wood, �??Theoretical description of transient stimulated Raman scattering in optical fibers,�?? IEEE J. Quan. Elect. 25, 2665 (1989).
[CrossRef]

J. Appl. Phys. (1)

H. Yokoyama and S. D. Brorson, �??Rate equation analysis of microcavity lasers,�?? J. Appl. Phys. 66 (10), 4801 (1989).
[CrossRef]

J. Chem. Phys. (1)

S. G. Johnson, MIT, Cambridge, MA, personal communication, 2005; V. A. Mandelshtam and H. S. Taylor, �??Harmonic inversion of time signals,�?? J. Chem. Phys. 107, 6756 (1997); Erratum, ibid. 109, 4128 (1998).

J. Opt. B: Quantum Semiclass. Opt. (1)

A. B. Matsko, A. A. Savchenkov, R. J. Letargat, V. S. Ilchenko, and L. Maleki, �??On cavity modification of stimulated Raman scattering,�?? J. Opt. B: Quantum Semiclass. Opt. 5, 272-278 (2003).
[CrossRef]

J. Opt. Soc. Am. B. (1)

F. X. Kärtner, D. J. Dougherty, H. A. Haus, E. P. Ippen, �??Raman noise and soliton squeezing,�?? J. Opt. Soc. Am. B. 11, 1267 (1994); 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 (1989).
[CrossRef]

Nature (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); V. R. Almeida and M. Lipson, �??Optical bistability on a silicon chip,�?? Opt. Letters 29, 2387-2389 (2004).
[CrossRef] [PubMed]

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]

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]

K. J. Vahala, �??Optical microcavities,�?? Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

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]

Nature Materials (1)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, �??Ultra-high-Q photonic double-heterostructure nanocavity,�?? Nature Materials 4, 207-210 (2005); B. S. Song, S. Noda, and T. Asano, �??Photonic devices based on in-plane hetero photonic crystals,�?? Science 300, 1537 (2003).
[CrossRef]

M. Soljacic, and J. D. Joannopoulos, �??Enhancement of nonlinear effects using photonic crystals,�?? Nature materials 3, 211-219 (2004).
[CrossRef] [PubMed]

Opt. Express (15)

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>
[CrossRef] [PubMed]

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670</a>
[PubMed]

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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731</a>
[CrossRef] [PubMed]

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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1708">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1708</a>
[CrossRef] [PubMed]

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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3713">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3713</a>
[CrossRef] [PubMed]

Z. Zhang and M. Qiu, "Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs," Opt. Express 12, 3988-3995 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-3988">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-3988</a>
[CrossRef] [PubMed]

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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-18-4261">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-18-4261</a>
[CrossRef] [PubMed]

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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4437">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4437</a>
[CrossRef] [PubMed]

O. Boyraz and B. Jalali, �??Demonstration of a silicon Raman laser,�?? Opt. Express 12, 5269-5273 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5269">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5269</a>
[CrossRef] [PubMed]

M. Krause, H. Renner, and E. Brinkmeyer, �??Analysis of Raman lasing characteristics in silicon-on-insulator waveguides,�?? Opt. Express 12, 5703-5710 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-23-5703">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-23-5703</a>
[CrossRef] [PubMed]

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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-519">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-519</a>; 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); 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]

O. Boyraz and B. Jalali, �??Demonstration of directly modulated silicon Raman laser,�?? Opt. Express 13, 796-800 (2005), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-796">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-796</a>
[CrossRef] [PubMed]

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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801</a>
[CrossRef] [PubMed]

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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1716">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1716</a>
[CrossRef] [PubMed]

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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2678">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2678</a>
[CrossRef] [PubMed]

Opt. Lett. (2)

Optics & Photonics News (1)

J. Scheuer, G. T. Paloczi, J. K. S. Poon, and A. Yariv, �??Coupled resonator optical waveguides: toward the slowing and storage of light,�?? Optics & Photonics News 16 (2), 36-40, (2005).
[CrossRef]

Optics Lett. (1)

B. Min, T. J. Kippenberg, and K. J. Vahala, �??Compact, fiber-compatible, cascaded Raman laser,�?? Optics Lett. 28 (17), 1507 (2003).
[CrossRef]

Optics Letters (1)

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, �??Ultralow-threshold microcavity Raman laser on a microelectronic chip,�?? Optics Letters 29, 1224-1226 (2004).
[CrossRef] [PubMed]

Phys. Rev. A (1)

V. E. Perlin and H. G. Winful, �??Stimulated Raman Scattering in nonlinear periodic structures,�?? Phys. Rev. A 64, 043804 (2001); H. G. Winful, V. E. Perlin, and M. Franke, �??Stimulated Raman and Brillouin Scattering in nonlinear periodic structures,�?? in Proc. of Nonlinear Optics: Materials, Fundamentals, and Applications, Kaua�??i-Lihue, Hawaii (2000).
[CrossRef]

Phys. Rev. A. (1)

H. M. Lai, P. T. Leung, K. Young, �??Electromagnetic decay into a narrow resonance in an optical cavity,�?? Phys. Rev. A. 37, 1597 (1988).
[CrossRef] [PubMed]

Phys. Rev. B (1)

C. Sauvan, P. Lalanne, and J.P. Hugonin, �??Slow-wave effect and mode-profile matching in Photonic Crystal microcavities,�?? Phys. Rev. B. (to be published), <a href= "http://arxiv.org/abs/cond-mat/0502664">http://arxiv.org/abs/cond-mat/0502664</a>.

Phys. Rev. Lett. (1)

H.-B. Lin and A. J. Campillo, �??cw nonlinear optics in droplet microcavities displaying enhanced gain,�?? Phys. Rev. Lett. 73, 2440 (1994); H.-B. Lin and A. J. Campillo, �??Microcavity enhanced Raman gain,�?? Opt. Comm. 133, 287 (1997).
[CrossRef] [PubMed]

Proc. SPIE (1)

K. Wada, K., H. C. Luan, D. R. C. Lim and L. C. Kimerling., �??On-chip interconnection beyond semiconductor roadmap: silicon microphotonics,�?? Proc. SPIE 4870, 437-443 (2002).
[CrossRef]

Quan. Elect. (1)

R. G. Zaporozhchenko, S. Ya. Kilin, A. G. Smirnov, �??Stimulated Raman scattering of light in a photonic crystal,�?? Quan. Elect. 30, 997 (2000).
[CrossRef]

Science (1)

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]

Other (5)

L. Pavesi and D. J. Lockwood, Silicon Photonics, (Springer-verlag, New York, 2004); G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (John Wiley, West Sussex, 2004).

Y. R. Shen, The Principles of Nonlinear Optics, (Wiley, Hoboken, New Jersey, 2003); Y. R. Shen and N. Bloembergen, �??Theory of stimulated Brillouin and Raman scattering,�?? Phys. Rev. 137 (6A), A1787 (1965).

X. Chen, Nicolae C. Panoiu, and R. M. Osgood, Jr., Microelectronics Sciences Laboratories, Columbia University, New York, NY 10027, (personal communication, 2005).

For a one-dimensional cavity, the enhancement reduces to the Yokoyama-Brorson factor (Ref. [43]) as suggested in Ref. [46].

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publishers, 2000); RSoft FullWave commercial software used.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Resonant frequencies of the pump and Stokes modes within the photonic band gap. (b) Qpump and QStokes as a function of shift S1 .

Fig. 2.
Fig. 2.

The electric field profile (Ey ) (a) and 2D FT spectrum (b) of pump mode.

Fig. 3.
Fig. 3.

The electric field profile (Ey ) (a) and 2D FT spectrum (b) of Stokes mode.

Fig. 4.
Fig. 4.

SEM picture of the PhC L5 nanocavity for Raman lasing in silicon.

Tables (1)

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Table 1. Design summary of photonic crystal L5 nanocavity for Raman lasing in silicon.

Equations (6)

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± A p ± z + 1 v p A p ± t = { g p 2 ( A S + 2 + A S 2 ) + i γ p [ A p ± 2 + 2 ( A p 2 + A S + 2 + A S 2 ) ] α p 2
β [ A p ± 2 + 2 ( A p 2 + A S + 2 + A S 2 ) ] φ ̅ λ p 2 N ̅ eff } A p ±
± A S ± z + 1 v s A S ± t = { g s 2 ( A p + 2 + A p 2 ) + i γ s [ A S ± 2 + 2 ( A S 2 + A p + 2 + A p 2 ) ] α s 2
β [ A S ± 2 + 2 ( A S 2 + A p + 2 + A p 2 ) ] φ ̅ λ S 2 N ̅ eff } A S ±
+ i κ A S + i δ β A S ±
P threshold = π 2 n s n p g s ξ λ s λ p V m Q s Q p

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