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

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    [CrossRef]

2006

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]

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]

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]

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]

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]

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]

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]

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]

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]

2005

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]

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]

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]

L. Florescu and X. Zhang, "Semiclassical model of stimulated Raman scattering in photonic crystals," Phys. Rev. E 72, 016611 (2005).
[CrossRef]

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]

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]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

D. Englund, I. Fushman, and J. Vučković, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5975 (2005).
[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).
[CrossRef] [PubMed]

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]

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).
[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).
[CrossRef] [PubMed]

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]

2004

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]

V. R. Almeida and M. Lipson, "Optical bistability on a silicon chip," Opt. Lett. 29, 2387-2389 (2004).
[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).
[CrossRef] [PubMed]

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

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]

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]

O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004).
[CrossRef] [PubMed]

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]

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]

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]

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]

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. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nat. Mater. 3, 211-219 (2004).
[CrossRef] [PubMed]

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]

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]

2003

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]

M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

B. Min, T. J. Kippenberg, and K. J. Vahala, "Compact, fiber-compatible, cascaded Raman laser," Opt. Lett. 28, 1507-1509 (2003).
[CrossRef] [PubMed]

B. S. Song, S. Noda, and T. Asano, "Photonic devices based on in-plane hetero photonic crystals," Science 300, 1537 (2003).
[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]

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]

2002

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]

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. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10,670-684 (2002).
[PubMed]

2001

V. E. Perlin and H. G. Winful, "Stimulated Raman Scattering in nonlinear periodic structures," Phys. Rev. A 64, 043804 (2001).
[CrossRef]

1999

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]

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]

1997

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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).
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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).
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Song, B. S.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

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]

B. S. Song, S. Noda, and T. Asano, "Photonic devices based on in-plane hetero photonic crystals," Science 300, 1537 (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]

Song, B. -S.

Soref, R. A.

R. A. Soref and B. R. Bennett, "Electrooptical Effects in Silicon," IEEE J. Quantum Electron. 23, 123-129 (1987).
[CrossRef]

Sparacin, D. K.

Spector, S. J.

Spillane, M.

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]

Spillane, S. M.

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]

Spirito, P.

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]

Srinivasan, K.

Takano, H.

Tan, H. W.

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]

Tanabe, T.

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]

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).
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Tsang, H. K.

T. K. Liang and H. K. Tsang, "Efficient Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 85, 3343-3345 (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]

Uesugi, T.

Vahala, K. J.

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).
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K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
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B. Min, T. J. Kippenberg, and K. J. Vahala, "Compact, fiber-compatible, cascaded Raman laser," Opt. Lett. 28, 1507-1509 (2003).
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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]

van Driel, H. M.

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).
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Villeneuve, P. R.

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]

Vlasov, Y. A.

Vuckovic, J.

Walker, C.

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]

Wang, J.

Watanabe, T.

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]

Wehrspohn, R. B.

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]

Winful, H. G.

V. E. Perlin and H. G. Winful, "Stimulated Raman Scattering in nonlinear periodic structures," Phys. Rev. A 64, 043804 (2001).
[CrossRef]

Wong, C. S.

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).
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Wong, C. W.

Xu, Q.

Yablonovitch, E.

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
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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).
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Yang, X.

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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).
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Zeni, L.

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).
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Zhang, X.

L. Florescu and X. Zhang, "Semiclassical model of stimulated Raman scattering in photonic crystals," Phys. Rev. E 72, 016611 (2005).
[CrossRef]

Zhang, Z.

Appl. Phys. Lett.

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

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]

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).
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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]

IEEE J. Quantum Electron.

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).
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R. A. Soref and B. R. Bennett, "Electrooptical Effects in Silicon," IEEE J. Quantum Electron. 23, 123-129 (1987).
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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]

IEEE J. Sel. Top. Quantum Electron.

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).
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J. Lightwave Technol.

Nat. Mater.

M. Soljacic and J. D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nat. Mater. 3, 211-219 (2004).
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B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

Nature

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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]

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).
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Opt. Express

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10,670-684 (2002).
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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]

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).
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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).
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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).
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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).
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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).
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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).
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Z. Zhang and M. Qiu, "Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs," Opt. Express 12,3988-3995 (2004).
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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).
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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).
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O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004).
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M. Krause, H. Renner, and E. Brinkmeyer, "Analysis of Raman lasing characteristics in silicon-on-insulator waveguides," Opt. Express 12, 5703-5710 (2004).
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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).
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O. Boyraz and B. Jalali, "Demonstration of directly modulated silicon Raman laser," Opt. Express 13, 796-800 (2005).
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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).
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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).
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[CrossRef]

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Figures (11)

Fig. 1.
Fig. 1.

SEM picture of L5 cavity coupled with photonic crystal waveguide.

Fig. 2.
Fig. 2.

The electric field profile (Ey ) of pump mode (a) and Stokes mode (b).

Fig. 3.
Fig. 3.

Threshold pump mode energy versus QS of L5 cavity for different values of free-carrier lifetimes τfc , the solid curve and dotted curve show the lasing and shutdown thresholds, respectively.

Fig. 4.
Fig. 4.

Input-output characteristics of photonic band gap defect cavity laser for different values of free-carrier lifetimes τfc , the solid curve and dashed curve correspond to QS = 30,000 and QS = 60,000, respectively.

Fig. 5.
Fig. 5.

Dynamics of Raman amplification with 60 mW CW pump wave and 10 μW CW Stokes seed signal, τfc , is 0.5 ns.

Fig. 6.
Fig. 6.

Dynamics of Raman amplification with 60 mW CW pump wave and 10 μW CW Stokes seed signal, τfc is 0.1 ns.

Fig. 7.
Fig. 7.

Dynamics of Raman amplification with pulse pump of 60 mW peak power, TFWHM = 50 ps and 10 μW CW Stokes signal, τfc , is 0.5 ns.

Fig. 8.
Fig. 8.

Raman on-off gain and on-off loss with pump pulse of 60 mW peak power, TFWHM = 50 ps and 1 mW CW probe signal, τfc is 0.5 ns.

Fig. 9.
Fig. 9.

Dynamics of Raman on-off gain with pump pulse of 60 mW peak power, TFWHM = 50 ps and 1 mW CW probe signal, τfc is 0.5 ns.

Fig. 10.
Fig. 10.

Dynamics of Raman on-off loss with pulse pump of 60 mW peak power, TFWHM = 50 ps and 1 mW CW probe signal, τfc is 0.5 ns.

Fig. 11.
Fig. 11.

Dynamics of Raman interaction of pump pulse with 60 mW peak power and Stokes pulse with 20 mW peak power, TFWHM = 50 ps, τfc is 0.5 ns.

Tables (1)

Tables Icon

Table 1. Parameters used in coupled-mode theory

Equations (50)

Equations on this page are rendered with MathJax. Learn more.

× × E p = ε p ε 0 c 2 2 E p t 2 = 1 ε 0 c 2 2 P NL ( 3 ) ( ω P ) t 2
× × E S = ε S ε 0 c 2 2 E S t 2 = 1 ε 0 c 2 2 P NL ( 3 ) ( ω S ) t 2
P NL ( 3 ) ( ω p ) = 6 ε 0 χ ijkl ( 3 ) ( ω p ) E S E S * E p
P NL ( 3 ) ( ω S ) = 6 ε 0 χ ijkl ( 3 ) ( ω S ) E p E p * E S
E p r t = a p ( t ) A p ( r ) N p e p t
E S r t = a S ( t ) A S ( r ) N S e S t
U i = a i 2 = 1 2 ε i ( r ) E i r t 2 d 3 r , and N i = 1 2 ε i ( r ) E i ( r ) 2 d 3 r , i = p , S
P NL ( 3 ) ( ω p ) = 6 ε 0 χ R ( 3 ) ( ω p ) a S 2 a p A S 2 A p N S N p e p t
P NL ( 3 ) ( ω S ) = 6 ε 0 χ R ( 3 ) ( ω S ) a p 2 a S A p 2 A S N p N S e S t
χ R ( 3 ) = χ ijkl ( 3 ) α * βλδ
da p dt A p = 3 ω p Im ( χ R ( 3 ) ( ω p ) ) ε p ε 0 ( A S 2 N S A p ) a S 2 a p
da S dt A S = 3 ω S Im ( χ R ( 3 ) ( ω S ) ) ε S ε 0 ( A p 2 N p A S ) a p 2 a S
da p dt = ( ω p ω S ) g S c a S 2 a p
da S dt = g S c a p 2 a S
g S c = 6 ω S Im [ χ R ( 3 ) ( ω S ) ] ε 0 n p 2 n S 2 V R
V R = n p 2 ( r ) A p ( r ) 2 d 3 r n S 2 ( r ) A S ( r ) 2 d 3 r Si n p 2 ( r ) A p ( r ) 2 n S 2 ( r ) A S ( r ) 2 d 3 r
g R B = 12 ω S Im [ χ R ( 3 ) ( ω S ) ] ε 0 n p n S c 2
g S c = ( c 2 2 n p n S V R ) g R B
E i , in r t = S i ( t ) S i ( r ) N i , in e i ω i t
da p dt = 1 2 τ p a p ( ω p ω S ) g S c a S 2 a p + κ p s p
da S dt = 1 2 τ S a S + g S c a p 2 a S + κ S s S
P in , th = π 2 n p n S λ p λ S V R g R B ( Q p , in Q p 2 Q s )
da p dt = ( 1 2 τ p , total + i Δ ω p ) a p ( ω p ω S ) g S c a S 2 a p + κ p s p
da S dt = ( 1 2 τ S , total + i Δ ω S ) a S + g S c a p 2 a S + κ S s S
1 τ i , total = 1 τ i , in + 1 τ i , v + 1 τ i , lin + 1 τ i , TPA + 1 τ i , FCA
1 τ p , TPA = β Si c 2 n p 2 V p , TPA a p 2 + β Si c 2 n p 2 V o , TPA 2 a S 2
1 τ S , TPA = β Si c 2 n S 2 V S , TPA a S 2 + β Si c 2 n S 2 V o , TPA 2 a p 2
V i , TPA = ( n i 2 ( r ) A i ( r ) 2 dr 3 ) 2 Si n i 4 ( r ) A i ( r ) 2 dr 3
1 τ i , FCA = c n i α i , FCA = c n i ( σ i , e + σ i , h ) N ( t )
σ i , e h = e 2 cn i ω i 2 ε 0 m e h * τ relax,e h
dN dt = N τ fc + G
G = β Si c 2 2 ħ ω p n p 2 V p , FCA 2 a p 4 + β Si c 2 2 ħ ω S n S 2 V S , FCA 2 a S 4 + β Si c 2 ħ ( ω p + ω S ) n p 2 V Sp , FCA 2 2 a S 2 a p 2 + β Si c 2 ħ ( ω p + ω S ) n S 2 V pS , FCA 2 2 a p 2 a S 2
V i , FCA 2 = ( n i 2 ( r ) A i r ) 2 dr 3 ) 3 Si n i 6 ( r ) A i ( r ) 6 dr 3
V Sp , FCA 2 = ( n p 2 ( r ) A p ( r ) 2 dr 3 ) 2 ( n S 2 ( r ) A S ( r ) 2 dr 3 ) Si n p 2 ( r ) A p ( r ) 4 n S 2 ( r ) A S ( r ) 2 dr 3
V pS , FCA 2 = ( n S 2 ( r ) A S ( r ) 2 dr 3 ) 2 ( n p 2 ( r ) A p ( r ) 2 dr 3 ) Si n S 2 ( r ) A S ( r ) 4 n p 2 ( r ) A p ( r ) 2 dr 3
Δ ω i ω i = Δ n i n i = ( Δ n i , Kerr n i + Δ n i , FCD n i + Δ n i , th n i )
Δ n p , Kerr n p = cn 2 n p 2 V p , Kerr a p 2 + cn 2 n p 2 V o , Kerr 2 a S 2
Δ n S , Kerr n S = cn 2 n S 2 V S , Kerr a S 2 + cn 2 n S 2 V o , Kerr 2 a p 2
Δ n i , FCD n i = 1 n i ( ζ i , e + ζ i , h ) N ( t )
ζ i , e h = e 2 2 n i ω i 2 ε 0 m e h *
Δ n i , th n i = 1 n i dn i dT Δ T
d Δ T dt = Δ T τ th + P abs ρ Si c p , Si V cavity
τ th = ρ Si c p , Si V cavity R
P abs = P p , abs + P S , abs + P R , abs
P i , abs = ( 1 τ i , lin + 1 τ i , TPA + 1 τ i , FCA ) a i 2
P R , abs = 2 ( ω p ω S 1 ) g S c a p 2 a S 2
g S c a p th 2 = 1 2 τ S , total
1 τ S , TPA = β Si c 2 n S 2 V o , TPA 2 a p th 2
N = τ fc G
G = β Si c 2 2 ħ ω p n p 2 V p , FCA 2 a p th 4

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