Observation of stimulated Raman amplification in silicon waveguides

R. Claps; D. Dimitropoulos; V. Raghunathan; Y. Han; B. Jalali

doi:10.1364/OE.11.001731

Observation of stimulated Raman amplification in silicon waveguides

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali

Optics Express
Vol. 11,
Issue 15,
pp. 1731-1739
(2003)
•https://doi.org/10.1364/OE.11.001731

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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)

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Table of Contents Category
- Research Papers
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Waveguides (230.7370)
- Integrated optoelectronic circuits (250.3140)
- Optical amplifiers (250.4480)

About this Article
History
- Original Manuscript: June 24, 2003
- Revised Manuscript: July 14, 2003
- Published: July 28, 2003

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Open Access

Abstract

We report the first observation of Stimulated Raman Scattering (SRS) in silicon waveguides. Amplification of the Stokes signal, at 1542.3 nm, of up to 0.25 dB has been observed in Silicon-on-Insulator (SOI) waveguides, using a 1427 nm pump laser with a CW power of 1.6 W, measured before the waveguide. Two-Photon-Absorption (TPA) measurements on these waveguides are also reported, and found to be negligible at the pump power where SRS was observed.

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References

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Publication

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[Crossref] [PubMed]
S. Coffa, “ST sets world record for silicon light emission”, ST Press Release, Issue No. 3, November (2002).
H.S. Han, S.Y. Seo, J.H. Shin, and N. Park, “Coefficient determination related to optical gain in erbium-doped silicon-rich silicon oxide waveguide amplifier,” Appl. Phys. Lett. 81, 3720–3722 (2002).
[Crossref]
K. Dovidenko, J.C. Lofgren, F. de Freitas, Y.J. Seo, and R. Tsu, “Structure and optoelectronic properties of Si/O superlattice,” Physica E 16, 509–516 (2003).
[Crossref]
T. Stoica, L. Vescan, A. Muck, B. Hollander, and G. Schope, “Electroluminescence on electron hole plasma in strained SiGe epitaxial layers,” Physica E 16, 359–365 (2003).
[Crossref]
T. Trupke, J. Zhao, A. Wang, R. Corkish, and M. A. Green, “Very efficient light emission from bulk crystalline silicon,” Appl. Phys. Lett. 82, 2996–2998 (2003).
[Crossref]
L. Dal Negro, M. Cazanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, “Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals,” Physica E 16, 297–308 (2003).
[Crossref]
R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman Scattering in Silicon Waveguides,” IEE Electron. Lett. 38, 1352–1354 (2002).
[Crossref]
R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, “Observation of Raman emission in silicon waveguides at 1.54 µm,” Opt. Express 10, 1305–1313 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1305
[Crossref] [PubMed]
P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. B 7, 3685–3697 (1973).
[Crossref]
D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,” Optics Letters, accepted for publication (2003).
D. Dimitropoulos, R. Claps, Y. Han, and B. Jalali, “Nonlinear Optics in Silicon Waveguides: Stimulated Raman Scattering and Two-Photon Absorption,” Integrated Optics: Devices, Materials, and Technologies VII, Y. S. Sidorin and Ari Tervonen, Editors, Proceedings of SPIE Vol. 4987140–148 (2003).
[Crossref]
A. Yariv, Quantum Electronics, (John Wiley and Sons, Inc.1989) ISBN 0-471-60997-8.
J.M. Ralston and R.K. Chang, “Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,” Phys. Rev. B 2, 1858–1862 (1970).
[Crossref]
G.P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001) ISBN 0-12-045143-3.
Spectra-Physics Telecom: “Model RL5 Raman Fiber Laser Specifications”.
E.A. Golovchenko, P.V. Mamyshev, A.N. Pilipetskii, and E.M. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. of Quant. Elect. 26, 1815–1820 (1990).
[Crossref]
H.K. Tsang, C.S. Wong, T.K. Lang, 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. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954–2956 (2003).
[Crossref]
F. Reintjes and J.C. McGroddy, “Indirect Two-Photon Transitions in Si at 1.06 µm,” Phys. Rev. Lett. 30, 901–903 (1973).
[Crossref]
Chris Xu and Winfried Denk, “Two-photon optical beam induced current imaging through the backside of integrated circuits,” Appl. Phys. Lett. 712578–2580 (1997).
[Crossref]
K. Kikuchi, “Optical sampling system at 1.5 µm using two photon absorption in Si avalanche photodiode,” IEE Elecron. Lett. 34, 1354–1355 (1998).
[Crossref]
M. Grimsditch and M. Cardona, “Absolute Cross-Section for Raman Scattering by Phonons in Silicon,” Phys. Stat. Sol. B 102, 155 (1980).
[Crossref]

2003 (5)

K. Dovidenko, J.C. Lofgren, F. de Freitas, Y.J. Seo, and R. Tsu, “Structure and optoelectronic properties of Si/O superlattice,” Physica E 16, 509–516 (2003).
[Crossref]

T. Stoica, L. Vescan, A. Muck, B. Hollander, and G. Schope, “Electroluminescence on electron hole plasma in strained SiGe epitaxial layers,” Physica E 16, 359–365 (2003).
[Crossref]

T. Trupke, J. Zhao, A. Wang, R. Corkish, and M. A. Green, “Very efficient light emission from bulk crystalline silicon,” Appl. Phys. Lett. 82, 2996–2998 (2003).
[Crossref]

L. Dal Negro, M. Cazanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, “Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals,” Physica E 16, 297–308 (2003).
[Crossref]

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

2002 (4)

H.S. Han, S.Y. Seo, J.H. Shin, and N. Park, “Coefficient determination related to optical gain in erbium-doped silicon-rich silicon oxide waveguide amplifier,” Appl. Phys. Lett. 81, 3720–3722 (2002).
[Crossref]

H.K. Tsang, C.S. Wong, T.K. Lang, 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]

R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman Scattering in Silicon Waveguides,” IEE Electron. Lett. 38, 1352–1354 (2002).
[Crossref]

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, “Observation of Raman emission in silicon waveguides at 1.54 µm,” Opt. Express 10, 1305–1313 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1305
[Crossref] [PubMed]

2000 (1)

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[Crossref] [PubMed]

1998 (1)

K. Kikuchi, “Optical sampling system at 1.5 µm using two photon absorption in Si avalanche photodiode,” IEE Elecron. Lett. 34, 1354–1355 (1998).
[Crossref]

1997 (1)

Chris Xu and Winfried Denk, “Two-photon optical beam induced current imaging through the backside of integrated circuits,” Appl. Phys. Lett. 712578–2580 (1997).
[Crossref]

1990 (1)

E.A. Golovchenko, P.V. Mamyshev, A.N. Pilipetskii, and E.M. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. of Quant. Elect. 26, 1815–1820 (1990).
[Crossref]

1980 (1)

M. Grimsditch and M. Cardona, “Absolute Cross-Section for Raman Scattering by Phonons in Silicon,” Phys. Stat. Sol. B 102, 155 (1980).
[Crossref]

1973 (2)

F. Reintjes and J.C. McGroddy, “Indirect Two-Photon Transitions in Si at 1.06 µm,” Phys. Rev. Lett. 30, 901–903 (1973).
[Crossref]

P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. B 7, 3685–3697 (1973).
[Crossref]

1970 (1)

J.M. Ralston and R.K. Chang, “Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,” Phys. Rev. B 2, 1858–1862 (1970).
[Crossref]

Agrawal, G.P.

G.P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001) ISBN 0-12-045143-3.

Asghari, M.

Cardona, M.

M. Grimsditch and M. Cardona, “Absolute Cross-Section for Raman Scattering by Phonons in Silicon,” Phys. Stat. Sol. B 102, 155 (1980).
[Crossref]

Cazanelli, M.

Chang, R.K.

J.M. Ralston and R.K. Chang, “Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,” Phys. Rev. B 2, 1858–1862 (1970).
[Crossref]

Claps, R.

R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman Scattering in Silicon Waveguides,” IEE Electron. Lett. 38, 1352–1354 (2002).
[Crossref]

D. Dimitropoulos, R. Claps, Y. Han, and B. Jalali, “Nonlinear Optics in Silicon Waveguides: Stimulated Raman Scattering and Two-Photon Absorption,” Integrated Optics: Devices, Materials, and Technologies VII, Y. S. Sidorin and Ari Tervonen, Editors, Proceedings of SPIE Vol. 4987140–148 (2003).
[Crossref]

D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,” Optics Letters, accepted for publication (2003).

Coffa, S.

S. Coffa, “ST sets world record for silicon light emission”, ST Press Release, Issue No. 3, November (2002).

Corkish, R.

T. Trupke, J. Zhao, A. Wang, R. Corkish, and M. A. Green, “Very efficient light emission from bulk crystalline silicon,” Appl. Phys. Lett. 82, 2996–2998 (2003).
[Crossref]

Daldosso, N.

Day, I.E.

de Freitas, F.

K. Dovidenko, J.C. Lofgren, F. de Freitas, Y.J. Seo, and R. Tsu, “Structure and optoelectronic properties of Si/O superlattice,” Physica E 16, 509–516 (2003).
[Crossref]

Denk, Winfried

Chris Xu and Winfried Denk, “Two-photon optical beam induced current imaging through the backside of integrated circuits,” Appl. Phys. Lett. 712578–2580 (1997).
[Crossref]

Dianov, E.M.

Dimitropoulos, D.

R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman Scattering in Silicon Waveguides,” IEE Electron. Lett. 38, 1352–1354 (2002).
[Crossref]

D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,” Optics Letters, accepted for publication (2003).

Dinu, M.

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

Dovidenko, K.

K. Dovidenko, J.C. Lofgren, F. de Freitas, Y.J. Seo, and R. Tsu, “Structure and optoelectronic properties of Si/O superlattice,” Physica E 16, 509–516 (2003).
[Crossref]

Drake, J.

Franzo, G.

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[Crossref] [PubMed]

Gaburro, Z.

Garcia, H.

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

Golovchenko, E.A.

Green, M. A.

T. Trupke, J. Zhao, A. Wang, R. Corkish, and M. A. Green, “Very efficient light emission from bulk crystalline silicon,” Appl. Phys. Lett. 82, 2996–2998 (2003).
[Crossref]

Grimsditch, M.

M. Grimsditch and M. Cardona, “Absolute Cross-Section for Raman Scattering by Phonons in Silicon,” Phys. Stat. Sol. B 102, 155 (1980).
[Crossref]

Han, H.S.

Han, Y.

Harpin, A.

Hathaway, C.E.

P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. B 7, 3685–3697 (1973).
[Crossref]

Hollander, B.

T. Stoica, L. Vescan, A. Muck, B. Hollander, and G. Schope, “Electroluminescence on electron hole plasma in strained SiGe epitaxial layers,” Physica E 16, 359–365 (2003).
[Crossref]

Houshmand, B.

D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,” Optics Letters, accepted for publication (2003).

Iacona, F.

Jalali, B.

R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman Scattering in Silicon Waveguides,” IEE Electron. Lett. 38, 1352–1354 (2002).
[Crossref]

D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,” Optics Letters, accepted for publication (2003).

Kikuchi, K.

K. Kikuchi, “Optical sampling system at 1.5 µm using two photon absorption in Si avalanche photodiode,” IEE Elecron. Lett. 34, 1354–1355 (1998).
[Crossref]

Lang, T.K.

Lofgren, J.C.

K. Dovidenko, J.C. Lofgren, F. de Freitas, Y.J. Seo, and R. Tsu, “Structure and optoelectronic properties of Si/O superlattice,” Physica E 16, 509–516 (2003).
[Crossref]

Mamyshev, P.V.

Mazzoleni, C.

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[Crossref] [PubMed]

McGroddy, J.C.

F. Reintjes and J.C. McGroddy, “Indirect Two-Photon Transitions in Si at 1.06 µm,” Phys. Rev. Lett. 30, 901–903 (1973).
[Crossref]

Muck, A.

T. Stoica, L. Vescan, A. Muck, B. Hollander, and G. Schope, “Electroluminescence on electron hole plasma in strained SiGe epitaxial layers,” Physica E 16, 359–365 (2003).
[Crossref]

Negro, L. Dal

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[Crossref] [PubMed]

Pacifici, D.

Park, N.

Pavesi, L.

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[Crossref] [PubMed]

Pilipetskii, A.N.

Priolo, F.

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[Crossref] [PubMed]

Quochi, F.

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

Ralston, J.M.

J.M. Ralston and R.K. Chang, “Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,” Phys. Rev. B 2, 1858–1862 (1970).
[Crossref]

Reintjes, F.

F. Reintjes and J.C. McGroddy, “Indirect Two-Photon Transitions in Si at 1.06 µm,” Phys. Rev. Lett. 30, 901–903 (1973).
[Crossref]

Roberts, S.W.

Schope, G.

T. Stoica, L. Vescan, A. Muck, B. Hollander, and G. Schope, “Electroluminescence on electron hole plasma in strained SiGe epitaxial layers,” Physica E 16, 359–365 (2003).
[Crossref]

Seo, S.Y.

Seo, Y.J.

K. Dovidenko, J.C. Lofgren, F. de Freitas, Y.J. Seo, and R. Tsu, “Structure and optoelectronic properties of Si/O superlattice,” Physica E 16, 509–516 (2003).
[Crossref]

Shin, J.H.

Stoica, T.

T. Stoica, L. Vescan, A. Muck, B. Hollander, and G. Schope, “Electroluminescence on electron hole plasma in strained SiGe epitaxial layers,” Physica E 16, 359–365 (2003).
[Crossref]

Temple, P.A.

P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. B 7, 3685–3697 (1973).
[Crossref]

Trupke, T.

T. Trupke, J. Zhao, A. Wang, R. Corkish, and M. A. Green, “Very efficient light emission from bulk crystalline silicon,” Appl. Phys. Lett. 82, 2996–2998 (2003).
[Crossref]

Tsang, H.K.

Tsu, R.

K. Dovidenko, J.C. Lofgren, F. de Freitas, Y.J. Seo, and R. Tsu, “Structure and optoelectronic properties of Si/O superlattice,” Physica E 16, 509–516 (2003).
[Crossref]

Vescan, L.

T. Stoica, L. Vescan, A. Muck, B. Hollander, and G. Schope, “Electroluminescence on electron hole plasma in strained SiGe epitaxial layers,” Physica E 16, 359–365 (2003).
[Crossref]

Wang, A.

T. Trupke, J. Zhao, A. Wang, R. Corkish, and M. A. Green, “Very efficient light emission from bulk crystalline silicon,” Appl. Phys. Lett. 82, 2996–2998 (2003).
[Crossref]

Wong, C.S.

Xu, Chris

Chris Xu and Winfried Denk, “Two-photon optical beam induced current imaging through the backside of integrated circuits,” Appl. Phys. Lett. 712578–2580 (1997).
[Crossref]

Yariv, A.

A. Yariv, Quantum Electronics, (John Wiley and Sons, Inc.1989) ISBN 0-471-60997-8.

Zhao, J.

T. Trupke, J. Zhao, A. Wang, R. Corkish, and M. A. Green, “Very efficient light emission from bulk crystalline silicon,” Appl. Phys. Lett. 82, 2996–2998 (2003).
[Crossref]

Appl. Phys. Lett. (5)

T. Trupke, J. Zhao, A. Wang, R. Corkish, and M. A. Green, “Very efficient light emission from bulk crystalline silicon,” Appl. Phys. Lett. 82, 2996–2998 (2003).
[Crossref]

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

Chris Xu and Winfried Denk, “Two-photon optical beam induced current imaging through the backside of integrated circuits,” Appl. Phys. Lett. 712578–2580 (1997).
[Crossref]

IEE Elecron. Lett. (1)

K. Kikuchi, “Optical sampling system at 1.5 µm using two photon absorption in Si avalanche photodiode,” IEE Elecron. Lett. 34, 1354–1355 (1998).
[Crossref]

IEE Electron. Lett. (1)

R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman Scattering in Silicon Waveguides,” IEE Electron. Lett. 38, 1352–1354 (2002).
[Crossref]

IEEE J. of Quant. Elect. (1)

Nature (1)

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000).
[Crossref] [PubMed]

Opt. Express (1)

Phys. Rev. B (2)

P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. B 7, 3685–3697 (1973).
[Crossref]

J.M. Ralston and R.K. Chang, “Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,” Phys. Rev. B 2, 1858–1862 (1970).
[Crossref]

Phys. Rev. Lett. (1)

F. Reintjes and J.C. McGroddy, “Indirect Two-Photon Transitions in Si at 1.06 µm,” Phys. Rev. Lett. 30, 901–903 (1973).
[Crossref]

Phys. Stat. Sol. B (1)

M. Grimsditch and M. Cardona, “Absolute Cross-Section for Raman Scattering by Phonons in Silicon,” Phys. Stat. Sol. B 102, 155 (1980).
[Crossref]

Physica E (3)

K. Dovidenko, J.C. Lofgren, F. de Freitas, Y.J. Seo, and R. Tsu, “Structure and optoelectronic properties of Si/O superlattice,” Physica E 16, 509–516 (2003).
[Crossref]

T. Stoica, L. Vescan, A. Muck, B. Hollander, and G. Schope, “Electroluminescence on electron hole plasma in strained SiGe epitaxial layers,” Physica E 16, 359–365 (2003).
[Crossref]

Other (6)

S. Coffa, “ST sets world record for silicon light emission”, ST Press Release, Issue No. 3, November (2002).

D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,” Optics Letters, accepted for publication (2003).

A. Yariv, Quantum Electronics, (John Wiley and Sons, Inc.1989) ISBN 0-471-60997-8.

G.P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001) ISBN 0-12-045143-3.

Spectra-Physics Telecom: “Model RL5 Raman Fiber Laser Specifications”.

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Fig. 1. Experimental setup: Pump-CRC fiber laser; Ch-Chopper; PBS-Polarization Beam Splitter; LIA- Lock-in amplifier; ECDL-External cavity diode laser (tunable); FG-Function generator (60 GHz freq. range); VOA-Variable optical attenuator; PD-optically-broadband photodetector. Thick lines represent electrical connections and wiring, thin lines represent free-space optical beams, and colored lines represent optical fiber.

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Fig. 2. (a) Measured spectral characteristic of the Stimulated Raman Scattering (SRS) in the silicon waveguide. The error bars are the standard deviation from this average. The pump power was 0.64 W at the front facet of the waveguide. SRS Net Gain is the ratio of the amplitude of the LIA output to the average signal power throughput. (b) Spontaneous Raman Spectra of the same waveguide with the same pump power as in (a).

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Fig. 3. The maxima from each spectral scan are plotted against effective pump power coupled into the front facet of the waveguide. A maximum of 0.25 dB (6%) amplification is obtained.

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Fig. 4. Experimental setup for measuring TPA. The waveguide in this case is different from the one used for SRS. PC-Polarization controller; VOA-Variable optical attenuator; PBS - Polarization beam splitter; PD₁ and PD₂ photo-detectors (identical, Newport 1830-C).

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Fig. 5. Output power vs. input power results, using a mode-locked laser, and depicting a nonlinear relationship.

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Fig. 6. TPA measurement result. The input power, P_in, is not corrected for coupling losses. The linear behavior is maintained up to ~ 400 W.

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Equations (5)

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

{\overset{\leftrightarrow}{R}}_{1} = \frac{1}{\sqrt{2}} (\begin{matrix} 0 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 0 \end{matrix}); {\overset{\leftrightarrow}{R}}_{2} = \frac{1}{\sqrt{2}} (\begin{matrix} 0 & 0 & 1 \\ 0 & 0 & - 1 \\ 1 & - 1 & 0 \end{matrix}); {\overset{\leftrightarrow}{R}}_{3} = (\begin{matrix} 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & 0 \end{matrix}) .

S = S_{o} \sum_{j = 1, 2, 3} {∣ {\hat{e}}_{s} \cdot {\overset{\leftrightarrow}{R}}_{j} \cdot {\hat{e}}_{i} ∣}^{2}, S_{o} = \frac{k_{o}^{4}}{32 π^{2} n} V χ_{R}^{2}

g_{s} = \frac{8 π c^{2} ω_{p}}{ħ ω_{s}^{4} n^{2} (ω_{s}) (N + 1) Δ ω} S

P_{S} (L) = P_{S} (0) \exp (- γ L + \frac{g_{s} P_{p} (0)}{A \cdot (1 + \frac{Δ ν_{p} (P_{p})}{Δ ν_{R}})} L_{eff}) .

\frac{P_{in}}{P_{out}} = e^{γ L} (1 + \frac{β L_{eff}}{A} P_{in}) .