Abstract

This paper analyze for the first time the impact of the charge carrier transport on the continuously pumped stimulated Raman amplification in silicon waveguides. A novel analytical model is developed using which the coupled differential equations of the pump and the probe optical signals and those of carrier transport are solved concurrently. The simulation and analysis suggest that the neglect of the carrier transport phenomenon, reported in the previously published works, is approximately justified only if the effective carrier lifetime is comparable to the carrier transit time, otherwise it can result in substantial overestimation of the free carrier density at the optical mode center.

© 2010 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature 433(7023), 292–294 (2005).
    [CrossRef] [PubMed]
  8. R. Jones, H. Rong, A. Liu, A. Fang, M. 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(2), 519–525 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  36. D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
    [CrossRef]

2010

Y. Huang, P. Shum, and C. Lin, “Proposal for loss reduction and output enhancement of silicon Raman laser using bi-directional pumping scheme,” Opt. Commun. 283(7), 1389–1393 (2010).
[CrossRef]

A. Singh, “Impact of optical pulse width on the frequency response of p-i-n photodiodes,” IEEE Photon. Technol. Lett. 22(8), 589–591 (2010).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman Amplifiers With Ring-Resonator-Enhanced Pump Power,” IEEE J. Sel. Top. Quantum Electron. 16(1), 216–225 (2010).
[CrossRef]

2009

2008

2007

2006

2005

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature 433(7023), 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(7027), 725–728 (2005).
[CrossRef] [PubMed]

D. Dimitropoulos, S. Fathpour, and B. Jalali, “Limitations of active carrier removal in silicon Raman amplifiers and lasers,” Appl. Phys. Lett. 87(26), 261108 (2005).
[CrossRef]

Q. Xu, V. R. Almeida, and M. Lipson, “Demonstration of high Raman gain in a submicrometer-size silicon-on-insulator waveguide,” Opt. Lett. 30(1), 35–37 (2005).
[CrossRef] [PubMed]

R. Jones, H. Rong, A. Liu, A. Fang, M. 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(2), 519–525 (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(5), 1716–1723 (2005).
[CrossRef] [PubMed]

V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, “Parametric Raman wavelength conversion in scaled silicon waveguides,” J. Lightwave Technol. 23(6), 2094–2102 (2005).
[CrossRef]

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[CrossRef]

2004

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Influence of nonlinear absorption on Raman amplification in Silicon waveguides,” Opt. Express 12(12), 2774–2780 (2004).
[CrossRef] [PubMed]

R. Espinola, J. Dadap, R. Osgood, S. McNab, and Y. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12(16), 3713–3718 (2004).
[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(18), 4261–4268 (2004).
[CrossRef] [PubMed]

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12(21), 5269–5273 (2004).
[CrossRef] [PubMed]

O. Boyraz and B. Jalali, “Demonstration of 11dB fiber-to-fiber gain in a silicon Raman amplifier,” IEICE Electron. Express 1(14), 429–434 (2004).
[CrossRef]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (2004).
[CrossRef]

T. K. Liang and H. K. Tsang, “Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(15), 2745–2747 (2004).
[CrossRef]

2003

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express 11(15), 1731–1739 (2003).
[CrossRef] [PubMed]

2002

R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman scattering in silicon waveguides,” Electron. Lett. 38(22), 1352–1354 (2002).
[CrossRef]

1994

K. J. Williams, R. D. Esman, and M. Dagenais, “Effects of high space-charge fields on the response of microwave photodetectors,” IEEE Photon. Technol. Lett. 6(5), 639–641 (1994).
[CrossRef]

1967

D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE 55(12), 2192–2193 (1967).
[CrossRef]

Agrawal, G. P.

Almeida, V. R.

Borlaug, D.

Boyraz, O.

Brinkmeyer, E.

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman Amplifiers With Ring-Resonator-Enhanced Pump Power,” IEEE J. Sel. Top. Quantum Electron. 16(1), 216–225 (2010).
[CrossRef]

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, “Gain enhancement in cladding-pumped silicon raman amplifiers,” IEEE J. Quantum Electron. 44(7), 692–704 (2008).
[CrossRef]

Caughey, D. M.

D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE 55(12), 2192–2193 (1967).
[CrossRef]

Claps, R.

Cohen, O.

V. Sih, S. Xu, Y. H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[CrossRef] [PubMed]

H. Rong, S. Xu, Y. H. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[CrossRef]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (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(7023), 292–294 (2005).
[CrossRef] [PubMed]

R. Jones, H. Rong, A. Liu, A. Fang, M. 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(2), 519–525 (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(5), 1716–1723 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (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(18), 4261–4268 (2004).
[CrossRef] [PubMed]

Dadap, J.

Dagenais, M.

K. J. Williams, R. D. Esman, and M. Dagenais, “Effects of high space-charge fields on the response of microwave photodetectors,” IEEE Photon. Technol. Lett. 6(5), 639–641 (1994).
[CrossRef]

Deane, J. H. B.

Dimitropoulos, D.

Dinu, M.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

Dissanayake, C.

Esman, R. D.

K. J. Williams, R. D. Esman, and M. Dagenais, “Effects of high space-charge fields on the response of microwave photodetectors,” IEEE Photon. Technol. Lett. 6(5), 639–641 (1994).
[CrossRef]

Espinola, R.

Fang, 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(7023), 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(7027), 725–728 (2005).
[CrossRef] [PubMed]

R. Jones, H. Rong, A. Liu, A. Fang, M. 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(2), 519–525 (2005).
[CrossRef] [PubMed]

Fathpour, S.

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, “Gain enhancement in cladding-pumped silicon raman amplifiers,” IEEE J. Quantum Electron. 44(7), 692–704 (2008).
[CrossRef]

K. K. Tsia, S. Fathpour, and B. Jalali, “Energy harvesting in silicon wavelength converters,” Opt. Express 14(25), 12327–12333 (2006).
[CrossRef] [PubMed]

S. Fathpour, K. K. Tsia, and B. Jalali, “Energy harvesting in silicon Raman amplifiers,” Appl. Phys. Lett. 89(6), 061109 (2006).
[CrossRef]

D. Dimitropoulos, S. Fathpour, and B. Jalali, “Limitations of active carrier removal in silicon Raman amplifiers and lasers,” Appl. Phys. Lett. 87(26), 261108 (2005).
[CrossRef]

Garcia, H.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

Gardes, F. Y.

Gwilliam, R.

Hak, D.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (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(7023), 292–294 (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(5), 1716–1723 (2005).
[CrossRef] [PubMed]

R. Jones, H. Rong, A. Liu, A. Fang, M. 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(2), 519–525 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (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(18), 4261–4268 (2004).
[CrossRef] [PubMed]

Han, Y.

Headley, W. R.

Huang, Y.

Y. Huang, P. Shum, and C. Lin, “Proposal for loss reduction and output enhancement of silicon Raman laser using bi-directional pumping scheme,” Opt. Commun. 283(7), 1389–1393 (2010).
[CrossRef]

Jalali, B.

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, “Gain enhancement in cladding-pumped silicon raman amplifiers,” IEEE J. Quantum Electron. 44(7), 692–704 (2008).
[CrossRef]

D. Dimitropoulos, D. R. Solli, R. Claps, O. Boyraz, and B. Jalali, “Noise figure of silicon Raman amplifiers,” J. Lightwave Technol. 26(7), 847–852 (2008).
[CrossRef]

V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a Mid-infrared silicon Raman amplifier,” Opt. Express 15(22), 14355–14362 (2007).
[CrossRef] [PubMed]

S. Fathpour, K. K. Tsia, and B. Jalali, “Energy harvesting in silicon Raman amplifiers,” Appl. Phys. Lett. 89(6), 061109 (2006).
[CrossRef]

K. K. Tsia, S. Fathpour, and B. Jalali, “Energy harvesting in silicon wavelength converters,” Opt. Express 14(25), 12327–12333 (2006).
[CrossRef] [PubMed]

V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, “Parametric Raman wavelength conversion in scaled silicon waveguides,” J. Lightwave Technol. 23(6), 2094–2102 (2005).
[CrossRef]

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[CrossRef]

D. Dimitropoulos, S. Fathpour, and B. Jalali, “Limitations of active carrier removal in silicon Raman amplifiers and lasers,” Appl. Phys. Lett. 87(26), 261108 (2005).
[CrossRef]

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Influence of nonlinear absorption on Raman amplification in Silicon waveguides,” Opt. Express 12(12), 2774–2780 (2004).
[CrossRef] [PubMed]

O. Boyraz and B. Jalali, “Demonstration of 11dB fiber-to-fiber gain in a silicon Raman amplifier,” IEICE Electron. Express 1(14), 429–434 (2004).
[CrossRef]

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12(21), 5269–5273 (2004).
[CrossRef] [PubMed]

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express 11(15), 1731–1739 (2003).
[CrossRef] [PubMed]

R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman scattering in silicon waveguides,” Electron. Lett. 38(22), 1352–1354 (2002).
[CrossRef]

Jhaveri, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[CrossRef]

Jones, R.

Knights, A. P.

Krause, M.

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman Amplifiers With Ring-Resonator-Enhanced Pump Power,” IEEE J. Sel. Top. Quantum Electron. 16(1), 216–225 (2010).
[CrossRef]

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, “Gain enhancement in cladding-pumped silicon raman amplifiers,” IEEE J. Quantum Electron. 44(7), 692–704 (2008).
[CrossRef]

Kuo, Y. H.

H. Rong, S. Xu, Y. H. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[CrossRef]

V. Sih, S. Xu, Y. H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[CrossRef] [PubMed]

Liang, T. K.

T. K. Liang and H. K. Tsang, “Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(15), 2745–2747 (2004).
[CrossRef]

Lin, C.

Y. Huang, P. Shum, and C. Lin, “Proposal for loss reduction and output enhancement of silicon Raman laser using bi-directional pumping scheme,” Opt. Commun. 283(7), 1389–1393 (2010).
[CrossRef]

Lin, Q.

Lipson, M.

Litvinenko, K. L.

Liu, A.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (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(7023), 292–294 (2005).
[CrossRef] [PubMed]

R. Jones, H. Rong, A. Liu, A. Fang, M. 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(2), 519–525 (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(5), 1716–1723 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (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(18), 4261–4268 (2004).
[CrossRef] [PubMed]

Liu, Y.

Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90(21), 211105 (2007).
[CrossRef]

Y. Liu and H. K. Tsang, “Nonlinear absorption and Raman gain in helium-ion-implanted silicon waveguides,” Opt. Lett. 31(11), 1714–1716 (2006).
[CrossRef] [PubMed]

Mashanovich, G. Z.

McNab, S.

Nicolaescu, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature 433(7023), 292–294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (2004).
[CrossRef]

Osgood, R.

Painter, O. J.

Paniccia, M.

H. Rong, S. Xu, Y. H. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[CrossRef]

V. Sih, S. Xu, Y. H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[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(7027), 725–728 (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(7023), 292–294 (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(5), 1716–1723 (2005).
[CrossRef] [PubMed]

R. Jones, H. Rong, A. Liu, A. Fang, M. 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(2), 519–525 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (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(18), 4261–4268 (2004).
[CrossRef] [PubMed]

Premaratne, M.

Quochi, F.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

Raday, O.

H. Rong, S. Xu, Y. H. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[CrossRef]

V. Sih, S. Xu, Y. H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[CrossRef] [PubMed]

Raghunathan, V.

Reed, G. T.

Renner, H.

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman Amplifiers With Ring-Resonator-Enhanced Pump Power,” IEEE J. Sel. Top. Quantum Electron. 16(1), 216–225 (2010).
[CrossRef]

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, “Gain enhancement in cladding-pumped silicon raman amplifiers,” IEEE J. Quantum Electron. 44(7), 692–704 (2008).
[CrossRef]

Rice, R. R.

Rong, H.

H. Rong, S. Xu, Y. H. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[CrossRef]

V. Sih, S. Xu, Y. H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[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(7027), 725–728 (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(7023), 292–294 (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(5), 1716–1723 (2005).
[CrossRef] [PubMed]

R. Jones, H. Rong, A. Liu, A. Fang, M. 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(2), 519–525 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (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(18), 4261–4268 (2004).
[CrossRef] [PubMed]

Rukhlenko, I. D.

Shum, P.

Y. Huang, P. Shum, and C. Lin, “Proposal for loss reduction and output enhancement of silicon Raman laser using bi-directional pumping scheme,” Opt. Commun. 283(7), 1389–1393 (2010).
[CrossRef]

Sih, V.

V. Sih, S. Xu, Y. H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[CrossRef] [PubMed]

H. Rong, S. Xu, Y. H. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[CrossRef]

Singh, A.

A. Singh, “Impact of optical pulse width on the frequency response of p-i-n photodiodes,” IEEE Photon. Technol. Lett. 22(8), 589–591 (2010).
[CrossRef]

Smith, A. J.

Solli, D. R.

Thomas, R. E.

D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE 55(12), 2192–2193 (1967).
[CrossRef]

Thomson, D. J.

Tsang, H. K.

Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90(21), 211105 (2007).
[CrossRef]

Y. Liu and H. K. Tsang, “Nonlinear absorption and Raman gain in helium-ion-implanted silicon waveguides,” Opt. Lett. 31(11), 1714–1716 (2006).
[CrossRef] [PubMed]

T. K. Liang and H. K. Tsang, “Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(15), 2745–2747 (2004).
[CrossRef]

Tsia, K. K.

K. K. Tsia, S. Fathpour, and B. Jalali, “Energy harvesting in silicon wavelength converters,” Opt. Express 14(25), 12327–12333 (2006).
[CrossRef] [PubMed]

S. Fathpour, K. K. Tsia, and B. Jalali, “Energy harvesting in silicon Raman amplifiers,” Appl. Phys. Lett. 89(6), 061109 (2006).
[CrossRef]

Vlasov, Y.

Williams, K. J.

K. J. Williams, R. D. Esman, and M. Dagenais, “Effects of high space-charge fields on the response of microwave photodetectors,” IEEE Photon. Technol. Lett. 6(5), 639–641 (1994).
[CrossRef]

Woo, J. C. S.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[CrossRef]

Wright, N. M.

Xu, Q.

Xu, S.

V. Sih, S. Xu, Y. H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[CrossRef] [PubMed]

H. Rong, S. Xu, Y. H. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[CrossRef]

Appl. Phys. Lett.

S. Fathpour, K. K. Tsia, and B. Jalali, “Energy harvesting in silicon Raman amplifiers,” Appl. Phys. Lett. 89(6), 061109 (2006).
[CrossRef]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (2004).
[CrossRef]

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

T. K. Liang and H. K. Tsang, “Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(15), 2745–2747 (2004).
[CrossRef]

D. Dimitropoulos, S. Fathpour, and B. Jalali, “Limitations of active carrier removal in silicon Raman amplifiers and lasers,” Appl. Phys. Lett. 87(26), 261108 (2005).
[CrossRef]

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[CrossRef]

Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90(21), 211105 (2007).
[CrossRef]

Electron. Lett.

R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman scattering in silicon waveguides,” Electron. Lett. 38(22), 1352–1354 (2002).
[CrossRef]

IEEE J. Quantum Electron.

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, “Gain enhancement in cladding-pumped silicon raman amplifiers,” IEEE J. Quantum Electron. 44(7), 692–704 (2008).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman Amplifiers With Ring-Resonator-Enhanced Pump Power,” IEEE J. Sel. Top. Quantum Electron. 16(1), 216–225 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

A. Singh, “Impact of optical pulse width on the frequency response of p-i-n photodiodes,” IEEE Photon. Technol. Lett. 22(8), 589–591 (2010).
[CrossRef]

K. J. Williams, R. D. Esman, and M. Dagenais, “Effects of high space-charge fields on the response of microwave photodetectors,” IEEE Photon. Technol. Lett. 6(5), 639–641 (1994).
[CrossRef]

IEICE Electron. Express

O. Boyraz and B. Jalali, “Demonstration of 11dB fiber-to-fiber gain in a silicon Raman amplifier,” IEICE Electron. Express 1(14), 429–434 (2004).
[CrossRef]

J. Lightwave Technol.

Nat. Photonics

H. Rong, S. Xu, Y. H. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007).
[CrossRef]

Nature

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature 433(7023), 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(7027), 725–728 (2005).
[CrossRef] [PubMed]

Opt. Commun.

Y. Huang, P. Shum, and C. Lin, “Proposal for loss reduction and output enhancement of silicon Raman laser using bi-directional pumping scheme,” Opt. Commun. 283(7), 1389–1393 (2010).
[CrossRef]

Opt. Express

R. Jones, H. Rong, A. Liu, A. Fang, M. 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(2), 519–525 (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(5), 1716–1723 (2005).
[CrossRef] [PubMed]

N. M. Wright, D. J. Thomson, K. L. Litvinenko, W. R. Headley, A. J. Smith, A. P. Knights, J. H. B. Deane, F. Y. Gardes, G. Z. Mashanovich, R. Gwilliam, and G. T. Reed, “Free carrier lifetime modification for silicon waveguide based devices,” Opt. Express 16(24), 19779–19784 (2008).
[CrossRef] [PubMed]

I. D. Rukhlenko, C. Dissanayake, M. Premaratne, and G. P. Agrawal, “Maximization of net optical gain in silicon-waveguide Raman amplifiers,” Opt. Express 17(7), 5807–5814 (2009).
[CrossRef] [PubMed]

K. K. Tsia, S. Fathpour, and B. Jalali, “Energy harvesting in silicon wavelength converters,” Opt. Express 14(25), 12327–12333 (2006).
[CrossRef] [PubMed]

V. Sih, S. Xu, Y. H. Kuo, H. Rong, M. Paniccia, O. Cohen, and O. Raday, “Raman amplification of 40 Gb/s data in low-loss silicon waveguides,” Opt. Express 15(2), 357–362 (2007).
[CrossRef] [PubMed]

V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a Mid-infrared silicon Raman amplifier,” Opt. Express 15(22), 14355–14362 (2007).
[CrossRef] [PubMed]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
[CrossRef] [PubMed]

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express 11(15), 1731–1739 (2003).
[CrossRef] [PubMed]

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Influence of nonlinear absorption on Raman amplification in Silicon waveguides,” Opt. Express 12(12), 2774–2780 (2004).
[CrossRef] [PubMed]

R. Espinola, J. Dadap, R. Osgood, S. McNab, and Y. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12(16), 3713–3718 (2004).
[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(18), 4261–4268 (2004).
[CrossRef] [PubMed]

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12(21), 5269–5273 (2004).
[CrossRef] [PubMed]

Opt. Lett.

Proc. IEEE

D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE 55(12), 2192–2193 (1967).
[CrossRef]

Other

S. M. Sze, and K. K. Ng, Physics of Semiconductor Devices, 3rd ed. (Wiley, New York, 2007).

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Figures (5)

Fig. 1
Fig. 1

A p-i-n diode silicon on insulator rib waveguide (a) Slice waveguide model (SWM). The waveguide is divided into 'M' slices each of width Δs, with a negligible inter-slice separation. The input beam is centered at the origin of the co-ordinate axis, which is assumed to be located at the center of the intersection of the slab and the rib region of the waveguide. (b) 2-D cross-section of the waveguide with reverse bias. (c) Flowchart depicting the procedure for evaluating the output pump power, signal power and Raman gain using the SWM.

Fig. 2
Fig. 2

Influence of the carrier transport and ECL on the estimation of the carrier density along the length of the waveguide, evaluated at the origin of the co-ordinate axis (optical mode center) (a) DOT case: solid line for τ = 1 ns, broken line for τ = 10 ns and dotted line for τ = 100 ns. (b) HRB case: solid line for τ = 0.1 ns, broken line for τ = 1 ns and dotted lines for τ = 10 ns. Curve with τ = 1 ns superimpose the curve with τ = 10 ns (c) DOT case: Effect of the inclusion and neglect of the diffusion phenomenon, solid line for τ = 1 ns, broken line for τ = 10 ns and dotted line for τ = 100 ns. (d) HRB case: Effect of the inclusion and neglect of the transport phenomenon, solid line for τ = 0.1 ns, broken line for τ = 1 ns and dotted lines for τ = 10 ns. Curve with τ = 1 ns superimpose the curve with τ = 10 ns. In all the four plots, pump power used is 1 Watt.

Fig. 3
Fig. 3

Influence of the inclusion/neglect of the free carrier transport on the estimation of the (a) Probe net gain (b) Output pump power; as a function of the input pump power. In both the plots, black color lines are used for “with transport” case and blue color lines are used for “without transport” case. Both black and blue color lines corresponding to ECL of 0.1 ns are shown by solid curves; for ECL of 1 ns, with broken curves and for ECL of 16 ns, with dotted curves. Note that the two curves (black lines) corresponding to the “with transport” (HRB) case are superimposing each other in both the plots. Experimental data from Ref [8].

Fig. 4
Fig. 4

Contour of the free carrier density generated by a Gaussian beam at the input face of the waveguide. The contours are normalized by 1016, τ = 10 ns, mode spot size 1 μm. Pump power = 1 W.

Fig. 5
Fig. 5

Electric field vs depletion region width as a function of (a) reverse bias voltage (in volts), with P+ doping of 1020 cm−3 and intrinsic region doping of 1015 cm−3 (b) doping density of the intrinsic region at a fixed reverse bias of 25 volts.

Equations (21)

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

d P p ( z ) d z = α p l i n P p ( z ) α p F C A ( z ) P p ( z ) β P p 2 ( z ) A eff
d P s ( z ) d z = α s l i n P s ( z ) α s F C A ( z ) P s ( z ) + ( g R 2 β ) P s ( z ) P p ( z ) A eff
α p ( s ) F C A ( z ) = σ e ( λ p ( s ) / 1.55 ) 2 × n ( z ) + σ p ( λ p ( s ) / 1.55 ) 2 × p ( z )
n ( x , z , t ) t = D n 2 n ( x , z , t ) x 2 + υ n n ( x , z , t ) x + G n ( x , z , t ) n ( x , z , t ) τ n
p ( x , z , t ) t = D p 2 p ( x , z , t ) x 2 υ p p ( x , z , t ) x + G p ( x , z , t ) p ( x , z , t ) τ p
P p = P p o ( α p + α p F C A ) e ( α p + α p F C A ) Δ s ( α p + α p F C A ) + β A eff P p o [ 1 e ( α p + α p F C A ) Δ s ]
P s = P s o ( α p + α p F C A ) ( 2 β g R ) / β { e ( α p + α p F C A ) Δ s } α s + α s F C A α p + α p F C A [ ( α p + α p F C A ) + β A eff P p o { 1 e ( α p + α p F C A ) Δ s } ] ( 2 β g R ) / β
n = p = β τ 2 h υ P p o 2 A eff 2
G i = 10 log ( P s P s o )
G = i = 1 i = M G i
G n , p = β 2 h ν P p o 2 A eff 2 × ( 1 W H ) W / 2 W / 2 h ( H h ) e ( x 2 + y 2 σ 0 2 ) d x d y = β 2 h ν P p o 2 A eff 2 × π σ 0 2 2 × ( 1 W H ) × e r f ( W 2 σ 0 ) × [ e r f ( h σ 0 ) e r f ( H + h σ 0 ) ]
n ( x ) = G n τ n × [ 1 e x p ( T 2 L n ) e x p ( T L n ) + 1 × { e x p ( x L n ) + e x p ( x L n ) } ]
n ( x ) = C 1 e x p ( k 1 x ) + C 2 e x p ( k 2 x ) + G n τ n
k 1 , k 2 = ( υ n 2 D n ) × [ 1 ± 1 + 4 D n τ n υ n 2 ]
C 1 = 1 Δ n | G n τ n e x p (- k 2 T / 2 ) 0 e x p ( k 2 T / 2 ) × k 2 |
C 2 = 1 Δ n | e x p ( k 1 T / 2 ) G n τ n e x p ( k 1 T / 2 ) × k 1 0 |
Δ n = | e x p ( k 1 T / 2 ) e x p ( k 2 T / 2 ) e x p ( k 1 T / 2 ) × k 1 e x p ( k 2 T / 2 ) × k 2 |
E p ( x ) = q N a ε ( x p + x ) ; x p < x < 0
E i ( x ) = q N d ε ( x i x ) ; 0 < x < x i
x p = 2 ε ( V b i V ) q × N d N a ( N a + N d )
x i = 2 ε ( V b i V ) q × N a N d ( N a + N d )

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