Abstract

An analytical model for mid-infrared (mid-IR) silicon Raman lasers (SRLs) is developed. The relative intensity noise (RIN) transfer from the pump to the Stokes in the lasers is also investigated. The analytical model can be used as a versatile and efficient tool for analysis, design and optimization of mid-IR SRLs. It is shown that conversion efficiency of 70% is attainable and the low-frequency RIN transfer may be suppressed to below 1 dB by pumping low-loss waveguides at high intensities.

© 2012 OSA

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  1. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol.24(12), 4600–4615 (2006).
    [CrossRef]
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    [CrossRef]
  3. V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a Mid-infrared silicon Raman amplifier,” Opt. Express15(22), 14355–14362 (2007).
    [CrossRef] [PubMed]
  4. D. Borlaug, S. Fathpour, and B. Jalali, “Extreme value statistics in silicon photonics,” IEEE Photon. J.1(1), 33–39 (2009).
    [CrossRef]
  5. T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on sapphire integrated waveguides for the mid-infrared,” Opt. Express18(12), 12127–12135 (2010).
    [CrossRef] [PubMed]
  6. R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics4(8), 495–497 (2010).
    [CrossRef]
  7. X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4(8), 557–560 (2010).
    [CrossRef]
  8. S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
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    [CrossRef]
  11. O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express12(21), 5269–5273 (2004).
    [CrossRef] [PubMed]
  12. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
    [CrossRef] [PubMed]
  13. A. Liu, L. Liao, and H. Rong, “Recent development in silicon photonics: 2.5 Gb/s silicon optical modulator and silicon Raman laser,” Proc. SPIE5730, 80–93 (2005).
    [CrossRef]
  14. X. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron.42(2), 160–170 (2006).
    [CrossRef]
  15. M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, “Cascaded silicon Raman lasers as mid-infrared sources,” Electron. Lett.42(21), 1224–1225 (2006).
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    [CrossRef]
  18. H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008).
    [CrossRef]
  19. M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-to-Stokes RIN transfer in Raman fiber lasers and its impact on the performance of co-pumped Raman amplifiers,” Opt. Commun.260(2), 656–661 (2006).
    [CrossRef]
  20. X. Sang, D. Dimitropoulos, and B. Jalali, “Influence of pump-to-signal RIN transfer on noise figure in silicon Raman amplifiers,” IEEE Photon. Technol. Lett.20(24), 2021–2023 (2008).
    [CrossRef]
  21. I. D. Rukhlenko, I. Udagedara, M. Premaratne, and G. P. Agrawal, “Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers,” Opt. Lett.35(14), 2343–2345 (2010).
    [CrossRef] [PubMed]
  22. X. Liu, X. Sang, B. Yan, K. Wang, C. Yu, and W. Dou, “Influences of pump-to-Stokes RIN transfer on the single order silicon Raman lasers,” J. Optoelectron. Adv. Mater.4, 1284–1288 (2010).
  23. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express11(15), 1731–1739 (2003).
    [CrossRef] [PubMed]
  24. S. Pearl, N. Rotenberg, and H. M. van Driel, “Three-photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 131102 (2008).
    [CrossRef]
  25. F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004).
    [CrossRef]
  26. J. Zhou, J. Chen, X. Li, G. Wu, and Y. Wang, “Exact analytical solution for Raman fiber lasers,” IEEE Photon. Technol. Lett.18(9), 1097–1099 (2006).
    [CrossRef]
  27. Z. Qin, X. Zhou, Q. Li, H. Wu, and Z. Zhou, “An improved theoretical model of nth-order cascaded Raman fiber lasers,” J. Lightwave Technol.25(6), 1555–1560 (2007).
    [CrossRef]
  28. S. A. Babin, D. V. Churkin, and E. V. Podivilov, “Intensity interactions in cascades of a two-stage Raman fiber laser,” Opt. Commun.226(1-6), 329–335 (2003).
    [CrossRef]
  29. C. Huang, Z. Cai, C. Ye, H. Xu, and Z. Luo, “Optimization of dual-wavelength cascaded Raman fiber lasers using an analytic approach,” Opt. Commun.272(2), 414–419 (2007).
    [CrossRef]
  30. K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun.271(1), 257–262 (2007).
    [CrossRef]
  31. H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express14(15), 6705–6712 (2006).
    [CrossRef] [PubMed]

2012 (1)

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J.4(1), 104–113 (2012).
[CrossRef]

2011 (1)

2010 (7)

T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on sapphire integrated waveguides for the mid-infrared,” Opt. Express18(12), 12127–12135 (2010).
[CrossRef] [PubMed]

I. D. Rukhlenko, I. Udagedara, M. Premaratne, and G. P. Agrawal, “Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers,” Opt. Lett.35(14), 2343–2345 (2010).
[CrossRef] [PubMed]

X. Liu, X. Sang, B. Yan, K. Wang, C. Yu, and W. Dou, “Influences of pump-to-Stokes RIN transfer on the single order silicon Raman lasers,” J. Optoelectron. Adv. Mater.4, 1284–1288 (2010).

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron.16(1), 200–215 (2010).
[CrossRef]

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics4(8), 495–497 (2010).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4(8), 557–560 (2010).
[CrossRef]

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

2009 (1)

D. Borlaug, S. Fathpour, and B. Jalali, “Extreme value statistics in silicon photonics,” IEEE Photon. J.1(1), 33–39 (2009).
[CrossRef]

2008 (3)

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008).
[CrossRef]

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three-photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 131102 (2008).
[CrossRef]

X. Sang, D. Dimitropoulos, and B. Jalali, “Influence of pump-to-signal RIN transfer on noise figure in silicon Raman amplifiers,” IEEE Photon. Technol. Lett.20(24), 2021–2023 (2008).
[CrossRef]

2007 (4)

C. Huang, Z. Cai, C. Ye, H. Xu, and Z. Luo, “Optimization of dual-wavelength cascaded Raman fiber lasers using an analytic approach,” Opt. Commun.272(2), 414–419 (2007).
[CrossRef]

K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun.271(1), 257–262 (2007).
[CrossRef]

Z. Qin, X. Zhou, Q. Li, H. Wu, and Z. Zhou, “An improved theoretical model of nth-order cascaded Raman fiber lasers,” J. Lightwave Technol.25(6), 1555–1560 (2007).
[CrossRef]

V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a Mid-infrared silicon Raman amplifier,” Opt. Express15(22), 14355–14362 (2007).
[CrossRef] [PubMed]

2006 (7)

H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express14(15), 6705–6712 (2006).
[CrossRef] [PubMed]

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol.24(12), 4600–4615 (2006).
[CrossRef]

M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-to-Stokes RIN transfer in Raman fiber lasers and its impact on the performance of co-pumped Raman amplifiers,” Opt. Commun.260(2), 656–661 (2006).
[CrossRef]

J. Zhou, J. Chen, X. Li, G. Wu, and Y. Wang, “Exact analytical solution for Raman fiber lasers,” IEEE Photon. Technol. Lett.18(9), 1097–1099 (2006).
[CrossRef]

B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron.12(6), 1618–1627 (2006).
[CrossRef]

X. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron.42(2), 160–170 (2006).
[CrossRef]

M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, “Cascaded silicon Raman lasers as mid-infrared sources,” Electron. Lett.42(21), 1224–1225 (2006).
[CrossRef]

2005 (2)

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

A. Liu, L. Liao, and H. Rong, “Recent development in silicon photonics: 2.5 Gb/s silicon optical modulator and silicon Raman laser,” Proc. SPIE5730, 80–93 (2005).
[CrossRef]

2004 (2)

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004).
[CrossRef]

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express12(21), 5269–5273 (2004).
[CrossRef] [PubMed]

2003 (2)

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express11(15), 1731–1739 (2003).
[CrossRef] [PubMed]

S. A. Babin, D. V. Churkin, and E. V. Podivilov, “Intensity interactions in cascades of a two-stage Raman fiber laser,” Opt. Commun.226(1-6), 329–335 (2003).
[CrossRef]

Agrawal, G. P.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron.16(1), 200–215 (2010).
[CrossRef]

I. D. Rukhlenko, I. Udagedara, M. Premaratne, and G. P. Agrawal, “Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers,” Opt. Lett.35(14), 2343–2345 (2010).
[CrossRef] [PubMed]

Alic, N.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Asher, W.

Babin, S. A.

S. A. Babin, D. V. Churkin, and E. V. Podivilov, “Intensity interactions in cascades of a two-stage Raman fiber laser,” Opt. Commun.226(1-6), 329–335 (2003).
[CrossRef]

Baehr-Jones, T.

Bayart, D.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004).
[CrossRef]

Boggio, J. M. C.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Borlaug, D.

D. Borlaug, S. Fathpour, and B. Jalali, “Extreme value statistics in silicon photonics,” IEEE Photon. J.1(1), 33–39 (2009).
[CrossRef]

V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a Mid-infrared silicon Raman amplifier,” Opt. Express15(22), 14355–14362 (2007).
[CrossRef] [PubMed]

Borne, S.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004).
[CrossRef]

Boyraz, O.

Brinkmeyer, E.

M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, “Cascaded silicon Raman lasers as mid-infrared sources,” Electron. Lett.42(21), 1224–1225 (2006).
[CrossRef]

M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-to-Stokes RIN transfer in Raman fiber lasers and its impact on the performance of co-pumped Raman amplifiers,” Opt. Commun.260(2), 656–661 (2006).
[CrossRef]

Cai, Z.

C. Huang, Z. Cai, C. Ye, H. Xu, and Z. Luo, “Optimization of dual-wavelength cascaded Raman fiber lasers using an analytic approach,” Opt. Commun.272(2), 414–419 (2007).
[CrossRef]

Castella, F.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004).
[CrossRef]

Chartier, P.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004).
[CrossRef]

Chen, J.

J. Zhou, J. Chen, X. Li, G. Wu, and Y. Wang, “Exact analytical solution for Raman fiber lasers,” IEEE Photon. Technol. Lett.18(9), 1097–1099 (2006).
[CrossRef]

Chen, X.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J.4(1), 104–113 (2012).
[CrossRef]

X. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron.42(2), 160–170 (2006).
[CrossRef]

Chen, Y. M.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J.4(1), 104–113 (2012).
[CrossRef]

Cheng, Z.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J.4(1), 104–113 (2012).
[CrossRef]

Churkin, D. V.

S. A. Babin, D. V. Churkin, and E. V. Podivilov, “Intensity interactions in cascades of a two-stage Raman fiber laser,” Opt. Commun.226(1-6), 329–335 (2003).
[CrossRef]

Cierullies, S.

M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-to-Stokes RIN transfer in Raman fiber lasers and its impact on the performance of co-pumped Raman amplifiers,” Opt. Commun.260(2), 656–661 (2006).
[CrossRef]

Claps, R.

Cohen, O.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008).
[CrossRef]

H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express14(15), 6705–6712 (2006).
[CrossRef] [PubMed]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Dimitropoulos, D.

X. Sang, D. Dimitropoulos, and B. Jalali, “Influence of pump-to-signal RIN transfer on noise figure in silicon Raman amplifiers,” IEEE Photon. Technol. Lett.20(24), 2021–2023 (2008).
[CrossRef]

B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron.12(6), 1618–1627 (2006).
[CrossRef]

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express11(15), 1731–1739 (2003).
[CrossRef] [PubMed]

Divliansky, I. B.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Dou, W.

X. Liu, X. Sang, B. Yan, K. Wang, C. Yu, and W. Dou, “Influences of pump-to-Stokes RIN transfer on the single order silicon Raman lasers,” J. Optoelectron. Adv. Mater.4, 1284–1288 (2010).

Draheim, R.

M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, “Cascaded silicon Raman lasers as mid-infrared sources,” Electron. Lett.42(21), 1224–1225 (2006).
[CrossRef]

Fang, A.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Faou, E.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004).
[CrossRef]

Fathpour, S.

D. Borlaug, S. Fathpour, and B. Jalali, “Extreme value statistics in silicon photonics,” IEEE Photon. J.1(1), 33–39 (2009).
[CrossRef]

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol.24(12), 4600–4615 (2006).
[CrossRef]

B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron.12(6), 1618–1627 (2006).
[CrossRef]

Fung, C. K. Y.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J.4(1), 104–113 (2012).
[CrossRef]

Green, W. M. J.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4(8), 557–560 (2010).
[CrossRef]

Hak, D.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Han, Y.

Hochberg, M.

Hu, Y.

Huang, C.

C. Huang, Z. Cai, C. Ye, H. Xu, and Z. Luo, “Optimization of dual-wavelength cascaded Raman fiber lasers using an analytic approach,” Opt. Commun.272(2), 414–419 (2007).
[CrossRef]

Huang, K.

K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun.271(1), 257–262 (2007).
[CrossRef]

Ilic, R.

Jalali, B.

D. Borlaug, S. Fathpour, and B. Jalali, “Extreme value statistics in silicon photonics,” IEEE Photon. J.1(1), 33–39 (2009).
[CrossRef]

X. Sang, D. Dimitropoulos, and B. Jalali, “Influence of pump-to-signal RIN transfer on noise figure in silicon Raman amplifiers,” IEEE Photon. Technol. Lett.20(24), 2021–2023 (2008).
[CrossRef]

V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a Mid-infrared silicon Raman amplifier,” Opt. Express15(22), 14355–14362 (2007).
[CrossRef] [PubMed]

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol.24(12), 4600–4615 (2006).
[CrossRef]

B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron.12(6), 1618–1627 (2006).
[CrossRef]

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express12(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. Express11(15), 1731–1739 (2003).
[CrossRef] [PubMed]

Jones, R.

H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express14(15), 6705–6712 (2006).
[CrossRef] [PubMed]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Krause, M.

M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-to-Stokes RIN transfer in Raman fiber lasers and its impact on the performance of co-pumped Raman amplifiers,” Opt. Commun.260(2), 656–661 (2006).
[CrossRef]

M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, “Cascaded silicon Raman lasers as mid-infrared sources,” Electron. Lett.42(21), 1224–1225 (2006).
[CrossRef]

Kuo, Y.-H.

Lee, M.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008).
[CrossRef]

Leplingard, F.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004).
[CrossRef]

Li, Q.

Li, X.

J. Zhou, J. Chen, X. Li, G. Wu, and Y. Wang, “Exact analytical solution for Raman fiber lasers,” IEEE Photon. Technol. Lett.18(9), 1097–1099 (2006).
[CrossRef]

Liao, L.

A. Liu, L. Liao, and H. Rong, “Recent development in silicon photonics: 2.5 Gb/s silicon optical modulator and silicon Raman laser,” Proc. SPIE5730, 80–93 (2005).
[CrossRef]

Liu, A.

H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express14(15), 6705–6712 (2006).
[CrossRef] [PubMed]

A. Liu, L. Liao, and H. Rong, “Recent development in silicon photonics: 2.5 Gb/s silicon optical modulator and silicon Raman laser,” Proc. SPIE5730, 80–93 (2005).
[CrossRef]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Liu, X.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4(8), 557–560 (2010).
[CrossRef]

X. Liu, X. Sang, B. Yan, K. Wang, C. Yu, and W. Dou, “Influences of pump-to-Stokes RIN transfer on the single order silicon Raman lasers,” J. Optoelectron. Adv. Mater.4, 1284–1288 (2010).

Lorcy, L.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004).
[CrossRef]

Luo, Z.

C. Huang, Z. Cai, C. Ye, H. Xu, and Z. Luo, “Optimization of dual-wavelength cascaded Raman fiber lasers using an analytic approach,” Opt. Commun.272(2), 414–419 (2007).
[CrossRef]

Martinelli, C.

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004).
[CrossRef]

Mashanovich, G. Z.

Miloševic, M. M.

Mookherjea, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Moro, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Nedeljkovic, M.

Osgood, R. M.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4(8), 557–560 (2010).
[CrossRef]

X. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron.42(2), 160–170 (2006).
[CrossRef]

Owens, N.

Paniccia, M.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008).
[CrossRef]

H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express14(15), 6705–6712 (2006).
[CrossRef] [PubMed]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Panoiu, N. C.

X. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron.42(2), 160–170 (2006).
[CrossRef]

Park, J. S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Pearl, S.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three-photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 131102 (2008).
[CrossRef]

Penkov, B.

Podivilov, E. V.

S. A. Babin, D. V. Churkin, and E. V. Podivilov, “Intensity interactions in cascades of a two-stage Raman fiber laser,” Opt. Commun.226(1-6), 329–335 (2003).
[CrossRef]

Premaratne, M.

I. D. Rukhlenko, I. Udagedara, M. Premaratne, and G. P. Agrawal, “Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers,” Opt. Lett.35(14), 2343–2345 (2010).
[CrossRef] [PubMed]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron.16(1), 200–215 (2010).
[CrossRef]

Qin, Z.

Z. Qin, X. Zhou, Q. Li, H. Wu, and Z. Zhou, “An improved theoretical model of nth-order cascaded Raman fiber lasers,” J. Lightwave Technol.25(6), 1555–1560 (2007).
[CrossRef]

K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun.271(1), 257–262 (2007).
[CrossRef]

Raday, O.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008).
[CrossRef]

H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express14(15), 6705–6712 (2006).
[CrossRef] [PubMed]

Radic, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Raghunathan, V.

Renner, H.

M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-to-Stokes RIN transfer in Raman fiber lasers and its impact on the performance of co-pumped Raman amplifiers,” Opt. Commun.260(2), 656–661 (2006).
[CrossRef]

M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, “Cascaded silicon Raman lasers as mid-infrared sources,” Electron. Lett.42(21), 1224–1225 (2006).
[CrossRef]

Rice, R. R.

Rong, H.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008).
[CrossRef]

H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express14(15), 6705–6712 (2006).
[CrossRef] [PubMed]

A. Liu, L. Liao, and H. Rong, “Recent development in silicon photonics: 2.5 Gb/s silicon optical modulator and silicon Raman laser,” Proc. SPIE5730, 80–93 (2005).
[CrossRef]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Rotenberg, N.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three-photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 131102 (2008).
[CrossRef]

Rukhlenko, I. D.

I. D. Rukhlenko, I. Udagedara, M. Premaratne, and G. P. Agrawal, “Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers,” Opt. Lett.35(14), 2343–2345 (2010).
[CrossRef] [PubMed]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron.16(1), 200–215 (2010).
[CrossRef]

Sang, X.

X. Liu, X. Sang, B. Yan, K. Wang, C. Yu, and W. Dou, “Influences of pump-to-Stokes RIN transfer on the single order silicon Raman lasers,” J. Optoelectron. Adv. Mater.4, 1284–1288 (2010).

X. Sang, D. Dimitropoulos, and B. Jalali, “Influence of pump-to-signal RIN transfer on noise figure in silicon Raman amplifiers,” IEEE Photon. Technol. Lett.20(24), 2021–2023 (2008).
[CrossRef]

Shori, R.

B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron.12(6), 1618–1627 (2006).
[CrossRef]

Sih, V.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008).
[CrossRef]

Soref, R.

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics4(8), 495–497 (2010).
[CrossRef]

Spott, A.

Stafsudd, O.

B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron.12(6), 1618–1627 (2006).
[CrossRef]

Teo, E. J.

Tsang, H. K.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J.4(1), 104–113 (2012).
[CrossRef]

Udagedara, I.

van Driel, H. M.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three-photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 131102 (2008).
[CrossRef]

Vlasov, Y. A.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4(8), 557–560 (2010).
[CrossRef]

Wang, K.

X. Liu, X. Sang, B. Yan, K. Wang, C. Yu, and W. Dou, “Influences of pump-to-Stokes RIN transfer on the single order silicon Raman lasers,” J. Optoelectron. Adv. Mater.4, 1284–1288 (2010).

Wang, Y.

J. Zhou, J. Chen, X. Li, G. Wu, and Y. Wang, “Exact analytical solution for Raman fiber lasers,” IEEE Photon. Technol. Lett.18(9), 1097–1099 (2006).
[CrossRef]

Wong, C. Y.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J.4(1), 104–113 (2012).
[CrossRef]

Wu, G.

J. Zhou, J. Chen, X. Li, G. Wu, and Y. Wang, “Exact analytical solution for Raman fiber lasers,” IEEE Photon. Technol. Lett.18(9), 1097–1099 (2006).
[CrossRef]

Wu, H.

K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun.271(1), 257–262 (2007).
[CrossRef]

Z. Qin, X. Zhou, Q. Li, H. Wu, and Z. Zhou, “An improved theoretical model of nth-order cascaded Raman fiber lasers,” J. Lightwave Technol.25(6), 1555–1560 (2007).
[CrossRef]

Xiong, B.

Xu, H.

C. Huang, Z. Cai, C. Ye, H. Xu, and Z. Luo, “Optimization of dual-wavelength cascaded Raman fiber lasers using an analytic approach,” Opt. Commun.272(2), 414–419 (2007).
[CrossRef]

Xu, K.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J.4(1), 104–113 (2012).
[CrossRef]

Xu, S.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008).
[CrossRef]

H. Rong, Y.-H. Kuo, S. Xu, A. Liu, R. Jones, M. Paniccia, O. Cohen, and O. Raday, “Monolithic integrated Raman silicon laser,” Opt. Express14(15), 6705–6712 (2006).
[CrossRef] [PubMed]

Yan, B.

X. Liu, X. Sang, B. Yan, K. Wang, C. Yu, and W. Dou, “Influences of pump-to-Stokes RIN transfer on the single order silicon Raman lasers,” J. Optoelectron. Adv. Mater.4, 1284–1288 (2010).

Ye, C.

C. Huang, Z. Cai, C. Ye, H. Xu, and Z. Luo, “Optimization of dual-wavelength cascaded Raman fiber lasers using an analytic approach,” Opt. Commun.272(2), 414–419 (2007).
[CrossRef]

Yu, C.

X. Liu, X. Sang, B. Yan, K. Wang, C. Yu, and W. Dou, “Influences of pump-to-Stokes RIN transfer on the single order silicon Raman lasers,” J. Optoelectron. Adv. Mater.4, 1284–1288 (2010).

Zhou, J.

J. Zhou, J. Chen, X. Li, G. Wu, and Y. Wang, “Exact analytical solution for Raman fiber lasers,” IEEE Photon. Technol. Lett.18(9), 1097–1099 (2006).
[CrossRef]

Zhou, X.

K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun.271(1), 257–262 (2007).
[CrossRef]

Z. Qin, X. Zhou, Q. Li, H. Wu, and Z. Zhou, “An improved theoretical model of nth-order cascaded Raman fiber lasers,” J. Lightwave Technol.25(6), 1555–1560 (2007).
[CrossRef]

Zhou, Z.

Z. Qin, X. Zhou, Q. Li, H. Wu, and Z. Zhou, “An improved theoretical model of nth-order cascaded Raman fiber lasers,” J. Lightwave Technol.25(6), 1555–1560 (2007).
[CrossRef]

K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun.271(1), 257–262 (2007).
[CrossRef]

Zlatanovic, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three-photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett.93(13), 131102 (2008).
[CrossRef]

Electron. Lett. (1)

M. Krause, R. Draheim, H. Renner, and E. Brinkmeyer, “Cascaded silicon Raman lasers as mid-infrared sources,” Electron. Lett.42(21), 1224–1225 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

X. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron.42(2), 160–170 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron.16(1), 200–215 (2010).
[CrossRef]

B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron.12(6), 1618–1627 (2006).
[CrossRef]

IEEE Photon. J. (2)

D. Borlaug, S. Fathpour, and B. Jalali, “Extreme value statistics in silicon photonics,” IEEE Photon. J.1(1), 33–39 (2009).
[CrossRef]

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Y. Fung, Y. M. Chen, and H. K. Tsang, “Mid-infrared grating couplers for silicon-on-sapphire waveguides,” IEEE Photon. J.4(1), 104–113 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

X. Sang, D. Dimitropoulos, and B. Jalali, “Influence of pump-to-signal RIN transfer on noise figure in silicon Raman amplifiers,” IEEE Photon. Technol. Lett.20(24), 2021–2023 (2008).
[CrossRef]

F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, D. Bayart, F. Castella, P. Chartier, and E. Faou, “Modeling of multiwavelength Raman fiber lasers using a new and fast algorithm,” IEEE Photon. Technol. Lett.16(12), 2601–2603 (2004).
[CrossRef]

J. Zhou, J. Chen, X. Li, G. Wu, and Y. Wang, “Exact analytical solution for Raman fiber lasers,” IEEE Photon. Technol. Lett.18(9), 1097–1099 (2006).
[CrossRef]

J. Lightwave Technol. (2)

J. Optoelectron. Adv. Mater. (1)

X. Liu, X. Sang, B. Yan, K. Wang, C. Yu, and W. Dou, “Influences of pump-to-Stokes RIN transfer on the single order silicon Raman lasers,” J. Optoelectron. Adv. Mater.4, 1284–1288 (2010).

Nat. Photonics (4)

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics4(8), 495–497 (2010).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4(8), 557–560 (2010).
[CrossRef]

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics2(3), 170–174 (2008).
[CrossRef]

Nature (1)

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Opt. Commun. (4)

M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-to-Stokes RIN transfer in Raman fiber lasers and its impact on the performance of co-pumped Raman amplifiers,” Opt. Commun.260(2), 656–661 (2006).
[CrossRef]

S. A. Babin, D. V. Churkin, and E. V. Podivilov, “Intensity interactions in cascades of a two-stage Raman fiber laser,” Opt. Commun.226(1-6), 329–335 (2003).
[CrossRef]

C. Huang, Z. Cai, C. Ye, H. Xu, and Z. Luo, “Optimization of dual-wavelength cascaded Raman fiber lasers using an analytic approach,” Opt. Commun.272(2), 414–419 (2007).
[CrossRef]

K. Huang, X. Zhou, Z. Qin, H. Wu, and Z. Zhou, “A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution,” Opt. Commun.271(1), 257–262 (2007).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Proc. SPIE (1)

A. Liu, L. Liao, and H. Rong, “Recent development in silicon photonics: 2.5 Gb/s silicon optical modulator and silicon Raman laser,” Proc. SPIE5730, 80–93 (2005).
[CrossRef]

Other (1)

M. Krause, H. Renner, and E. Brinkmeyer, “Theory of silicon Raman amplifiers and lasers,” in Silicon Photonics for Telecommunications and Biomedicine, S. Fathpour and B. Jalali, eds. (CRC Press, 2012), pp.131–200.

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of the studied mid-IR silicon Raman laser; (b) Optical mode profile (TE) at pump (top) and the Stokes (bottom) wavelengths in the SOS waveguide with air top-cladding having rib width of 2 µm, rib height of 2 µm and slab height of 1µm. The calculations are obtained from a commercial numerical mode solver (BeamPROP by RSoft).

Fig. 2
Fig. 2

(a) Intensity distributions of pump and Stokes waves with Iin = 200 MW/cm2. Rpl = Rpr = Rsl = Rsr = 30%, αp = αs = 0.5 dB/cm and L = 2 cm were assumed. The inset shows the input-output characteristics of the Raman laser. (b) Threshold intensity versus cavity length for various output facet reflectivities and propagation losses and for Rpl = 10%, Rpr = Rsl = 90%.

Fig. 3
Fig. 3

Conversion efficiency versus cavity length L and output facet reflectivity Rsr for two propagation loss values and two pump intensities.

Fig. 4
Fig. 4

Maximum conversion efficiency versus pump intensity for four different propagation loss values.

Fig. 5
Fig. 5

(a) RIN transfer spectra for mid-IR SRLs pumped at 50, 75, 100 and 200 MW/cm2 and (b) the devices’ low frequency RIN transfer versus pump intensity for four propagation loss values. Modal parameter: L = 1.20 cm, Rsr = 38%, α = 0.5 dB/cm (optimized design for Iin = 100 MW/cm2), D = ̶ 120 ps/(nm·km).

Equations (32)

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

± d I p ± I p ± dz = α p Γ g R λ s λ p ( I s + + I s ),
± d I s ± I s ± dz = α s +Γ g R ( I p + + I p )
I p + (0)=(1 R pl ) I in + R pl I p (0), I p (L)= R pr I p + (L), I s + (0)= R sl I s (0), I s (L)= R sr I s + (L),
G p (z)= G p (0)+z[ G p (L) G p (0)]/L.
I th = α δ s (1 R pl e 2 δ p )( e δ p R pl e δ p ) g R (1 R pl )(1 e αL )(1+ R pr e αL ) ,
δ p =αL+1/2ln(1/ R pr ),
δ s =αL+1/2ln(1/ R sl R sr )
L p,s (z)=L sinh[ G p,s (z)]sinh[ G p,s (0)] G p,s (L) G p,s (0) ,
I ¯ p 1/2 = δ 1 /[2 g R L p (L)].
I ¯ s 1/2 = λ p [ G p (0) δ 0 ]/[2 g R λ s L s (L)],
G s (z)= G s (0)αz+2 g R I ¯ p 1/2 L p (z).
I p,s ± (z)= I ¯ p,s 1/2 exp[± G p,s (z)],
I out =(1 R sr ) I s + (L).
I p ± (z,t)= I ¯ p ± (z)[1+ m p ± (z)exp(iΩt)],
I s ± (z,t)= I ¯ s ± (z)[1+ m s ± (z)exp(iΩt)],
± I p ± z + 1 v p I p ± t = α p I p ± g R λ s λ p ( I s + + I s ) I p ± ,
± I s ± z + 1 v s I s ± t = α s I s ± + g R ( I p + + I p ) I s ± .
d m p ± dz = iΩ v p m p ± g R λ s λ p ( I ¯ s + m s + + I ¯ s m s ),
d m s ± dz = iΩ v p m s ± ± g R ( I ¯ p + m p + + I ¯ p m p ),
I ¯ p + (0) m p + (0)=(1 R pl ) I ¯ in m in + R pl I ¯ p (0) m p (0), m p (L)= m p + (L), m s + (0)= m s (0), m s (L)= m s + (L).
T RIN (Ω)= | m s + (L,Ω) | 2 m in 2 .
d I ¯ p dz = I ¯ p + d I ¯ p dz + d I ¯ p + dz I ¯ p = I ¯ p + [ α p + g R λ s λ p ( I s + + I s )] I ¯ p +[ α p g R λ s λ p ( I s + + I s )] I ¯ p + I ¯ p =0.
d G p dz =α2 g R λ s λ p I ¯ s cosh( G s )
d G s dz =α+2 g R I ¯ p cosh( G p )
G p (0)=ln I in (1 R pl )+ I in 2 (1 R pl ) 2 +4 R pl I ¯ p 2 I ¯ p G p (L)= 1 2 ln 1 R pr , G s (0)= 1 2 ln 1 R sl , G s (L)= 1 2 ln 1 R sr .
G p (0)= δ p + g R λ s λ p 0 L [2 I ¯ s cosh( G s )] dz,
g R 0 L [2 I ¯ p cosh( G p )] dz= δ s .
G p (z)= δ p αz.
I ¯ p = I in (1 R pl ) exp( δ p ) R pl exp( δ p ) .
0 L cosh[ G p (z)] dz=L sinh[ G p (z)]sinh[ G p (0)] G p (L) G p (0) = L p (z).
δ s =2 g R I ¯ p L p (L).
I ¯ p = I th (1 R pl ) exp( δ p ) R pl exp( δ p ) = δ s 2 g R L p (L) .

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