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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References

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    [Crossref]
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2005 (5)

2004 (13)

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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1708
[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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-3988
[Crossref] [PubMed]

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]

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713–3718 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3713
[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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-18-4261
[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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4437
[Crossref] [PubMed]

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12, 5269–5273 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5269
[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,” Nature materials 3, 211–219 (2004).
[Crossref] [PubMed]

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]

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

2003 (6)

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]

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

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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731
[Crossref] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

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]

2002 (4)

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. 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]

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

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]

2001 (1)

2000 (1)

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

1992 (1)

1990 (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]

1989 (2)

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

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

1988 (1)

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

Akahane, Y.

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]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Materials4, 207–210 (2005); B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science300, 1537 (2003).
[Crossref]

Almeida, V. R.

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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4437
[Crossref] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431, 1081–1084 (2004); V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Letters29, 2387–2389 (2004).
[Crossref] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431, 1081–1084 (2004); V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Letters29, 2387–2389 (2004).
[Crossref] [PubMed]

Armani, D. K.

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]

Asano, T.

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]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Materials4, 207–210 (2005); B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science300, 1537 (2003).
[Crossref]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Materials4, 207–210 (2005); B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science300, 1537 (2003).
[Crossref]

Asghari, M.

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]

Baek, J. H.

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]

Barclay, P. E.

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431, 1081–1084 (2004); V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Letters29, 2387–2389 (2004).
[Crossref] [PubMed]

Bloembergen, N.

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).

Blow, K. J.

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

Borselli, M.

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]

Boyraz, O.

Brinkmeyer, E.

Brorson, S. D.

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

Campillo, A. J.

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]

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]

Chen, X.

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

Claps, R.

Cohen, O.

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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1716
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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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-18-4261
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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. Express13, 519–525 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-519 ; H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature433, 292–294 (2005); H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433, 725–728 (2005).
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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. Express13, 519–525 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-519 ; H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature433, 292–294 (2005); H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433, 725–728 (2005).
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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. Express13, 519–525 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-519 ; H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature433, 292–294 (2005); H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433, 725–728 (2005).
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Day, I. E.

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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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Dougherty, D. J.

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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. 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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Espinola, R. L.

Fang, A.

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Fang, A. W.

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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).
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F. X. Kärtner, D. J. Dougherty, H. A. Haus, and 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).
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Hak, D.

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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1716
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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. Express13, 519–525 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-519 ; H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature433, 292–294 (2005); H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433, 725–728 (2005).
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Harpin, A.

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Hugonin, J.P.

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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).
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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).
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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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1716
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Lee, Y. H.

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Opt. Express (14)

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

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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)

Tables Icon

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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