Abstract

We present a theoretical model capable of describing the evolution of pulse parameters when stimulated Raman scattering under continuous-wave pumping is employed for amplifying them inside a silicon waveguide. In our approach, pulse evolution is described analytically by a set of coupled equations derived using a variational formalism. Optical losses resulting from linear absorption or scattering, two-photon absorption, and free-carrier absorption are included by introducing the Rayleigh dissipation function. The influence of gain dispersion originated from a relatively narrow Raman-gain bandwidth is also considered. The role of initial pulse width and chirp is studied extensively because of its practical applications. To ensure the validity of the variational technique, all analytical results are compared with the numerical data obtained with the split-step Fourier algorithm.

© 2008 Optical Society of America

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2008 (1)

2007 (6)

2006 (8)

2005 (6)

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

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four wave mixing in silicon wire waveguides,” Opt. Express 13, 4629-4637 (2005).
[CrossRef] [PubMed]

R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 15, 519-525 (2005).
[CrossRef]

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

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

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, 071115 (2005).
[CrossRef]

2004 (9)

T. K. Liang and H. K. Tsang, “Nonlinear absorption and Raman scattering in silicon-on-insulator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 10, 1149-1153 (2004).
[CrossRef]

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

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

P. Spirito, S. Daliento, A. Sanseverino, L. Gialanella, M. Romano, B. Limata, R. Carta, and L. Bellemo, “Characterization of recombination center in Si epilayers after He implantation by direct measurement of local lifetime distribution with the AC lifetime pro-filing technique,” IEEE. Elec. Dev. Lett. 25, 602-604 (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, 2745-2747 (2004).
[CrossRef]

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

Ö. Boyraz, P. Koonath, V. Ranghanathan, and B. Jalali, “All optical switching and continuous generation in silicon waveguides,” Opt. Express 12, 4094-4102 (2004).
[CrossRef] [PubMed]

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12, 4261-4267 (2004).
[CrossRef] [PubMed]

M. Krause, H. Renner, and E. Brinkmeyer, “Analysis of Raman lasing characteristics in silicon-on-insulator waveguides,” Opt. Express 12, 5703-5710 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

H. K. Tsang, C. S. Wong, and T. K. Liang, “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]

1983 (1)

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135-3145 (1983).
[CrossRef]

Agrawal, G. P.

Almeida, V. R.

Anderson, D.

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135-3145 (1983).
[CrossRef]

Bellemo, L.

P. Spirito, S. Daliento, A. Sanseverino, L. Gialanella, M. Romano, B. Limata, R. Carta, and L. Bellemo, “Characterization of recombination center in Si epilayers after He implantation by direct measurement of local lifetime distribution with the AC lifetime pro-filing technique,” IEEE. Elec. Dev. Lett. 25, 602-604 (2004).
[CrossRef]

Bhadra, S. K.

Boyraz, O.

Boyraz, Ö.

Brinkmeyer, E.

Carta, R.

P. Spirito, S. Daliento, A. Sanseverino, L. Gialanella, M. Romano, B. Limata, R. Carta, and L. Bellemo, “Characterization of recombination center in Si epilayers after He implantation by direct measurement of local lifetime distribution with the AC lifetime pro-filing technique,” IEEE. Elec. Dev. Lett. 25, 602-604 (2004).
[CrossRef]

Chen, X.

X. Chen, N. C. Panoiu, and M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguide,” Int. J. Quantum Chem. 42, 160-170 (2006).

Claps, R.

Cohen, O.

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

V. Sih, S. Xu, Y. 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, 357-362 (2007).
[CrossRef] [PubMed]

A. Liu, H. Rong, R. Jones, O. Cohen, D. Hak, and M. J. Paniccia, “Optical amplification and lasing by stimulated Raman scattering in silicon waveguide,” J. Lightwave Technol. 24, 1440-1448 (2006).
[CrossRef]

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

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

R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 15, 519-525 (2005).
[CrossRef]

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

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12, 4261-4267 (2004).
[CrossRef] [PubMed]

Daliento, S.

P. Spirito, S. Daliento, A. Sanseverino, L. Gialanella, M. Romano, B. Limata, R. Carta, and L. Bellemo, “Characterization of recombination center in Si epilayers after He implantation by direct measurement of local lifetime distribution with the AC lifetime pro-filing technique,” IEEE. Elec. Dev. Lett. 25, 602-604 (2004).
[CrossRef]

Dekker, R.

Dimitropoulos, D.

Driessen, A.

Fang, A. W.

R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 15, 519-525 (2005).
[CrossRef]

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

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

Fathpour, S.

Fauchet, P. M.

Först, M.

Fukuda, H.

Gialanella, L.

P. Spirito, S. Daliento, A. Sanseverino, L. Gialanella, M. Romano, B. Limata, R. Carta, and L. Bellemo, “Characterization of recombination center in Si epilayers after He implantation by direct measurement of local lifetime distribution with the AC lifetime pro-filing technique,” IEEE. Elec. Dev. Lett. 25, 602-604 (2004).
[CrossRef]

Goldstein, H.

H. Goldstein, Classical Mechanics, 2nd ed. (Narosa Publishing House, 2001).

Hak, D.

A. Liu, H. Rong, R. Jones, O. Cohen, D. Hak, and M. J. Paniccia, “Optical amplification and lasing by stimulated Raman scattering in silicon waveguide,” J. Lightwave Technol. 24, 1440-1448 (2006).
[CrossRef]

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

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

R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 15, 519-525 (2005).
[CrossRef]

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

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12, 4261-4267 (2004).
[CrossRef] [PubMed]

Han, Y.

Itabashi, S.

Jalali, B.

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, 071115 (2005).
[CrossRef]

Jones, R.

A. Liu, H. Rong, R. Jones, O. Cohen, D. Hak, and M. J. Paniccia, “Optical amplification and lasing by stimulated Raman scattering in silicon waveguide,” J. Lightwave Technol. 24, 1440-1448 (2006).
[CrossRef]

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

R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 15, 519-525 (2005).
[CrossRef]

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

Koonath, P.

Krause, M.

Kuo, Y.

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,” Nature Photonics 1, 232-237 (2007).
[CrossRef]

Leonardis, F. D.

Liang, T. K.

T. K. Liang and H. K. Tsang, “Efficient Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 85, 3343-3345 (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, 2745-2747 (2004).
[CrossRef]

T. K. Liang and H. K. Tsang, “Nonlinear absorption and Raman scattering in silicon-on-insulator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 10, 1149-1153 (2004).
[CrossRef]

H. K. Tsang, C. S. Wong, and T. K. Liang, “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]

Limata, B.

P. Spirito, S. Daliento, A. Sanseverino, L. Gialanella, M. Romano, B. Limata, R. Carta, and L. Bellemo, “Characterization of recombination center in Si epilayers after He implantation by direct measurement of local lifetime distribution with the AC lifetime pro-filing technique,” IEEE. Elec. Dev. Lett. 25, 602-604 (2004).
[CrossRef]

Lin, Q.

Lipson, M.

Liu, A.

A. Liu, H. Rong, R. Jones, O. Cohen, D. Hak, and M. J. Paniccia, “Optical amplification and lasing by stimulated Raman scattering in silicon waveguide,” J. Lightwave Technol. 24, 1440-1448 (2006).
[CrossRef]

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

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

R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 15, 519-525 (2005).
[CrossRef]

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

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12, 4261-4267 (2004).
[CrossRef] [PubMed]

Liu, Y.

Moormann, C.

Nicolaescu, R.

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

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

Niehusmann, J.

Osgood, M.

X. Chen, N. C. Panoiu, and M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguide,” Int. J. Quantum Chem. 42, 160-170 (2006).

Painter, O. J.

Paniccia, M.

V. Sih, S. Xu, Y. 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, 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,” Nature Photonics 1, 232-237 (2007).
[CrossRef]

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

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12, 4261-4267 (2004).
[CrossRef] [PubMed]

Paniccia, M. J.

A. Liu, H. Rong, R. Jones, O. Cohen, D. Hak, and M. J. Paniccia, “Optical amplification and lasing by stimulated Raman scattering in silicon waveguide,” J. Lightwave Technol. 24, 1440-1448 (2006).
[CrossRef]

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

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

R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 15, 519-525 (2005).
[CrossRef]

Panoiu, N. C.

X. Chen, N. C. Panoiu, and M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguide,” Int. J. Quantum Chem. 42, 160-170 (2006).

Passaro, V.

Qian, F.

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,” Nature Photonics 1, 232-237 (2007).
[CrossRef]

V. Sih, S. Xu, Y. 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, 357-362 (2007).
[CrossRef] [PubMed]

Raghunathan, V.

Ranghanathan, V.

Renner, H.

Romano, M.

P. Spirito, S. Daliento, A. Sanseverino, L. Gialanella, M. Romano, B. Limata, R. Carta, and L. Bellemo, “Characterization of recombination center in Si epilayers after He implantation by direct measurement of local lifetime distribution with the AC lifetime pro-filing technique,” IEEE. Elec. Dev. Lett. 25, 602-604 (2004).
[CrossRef]

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,” Nature Photonics 1, 232-237 (2007).
[CrossRef]

V. Sih, S. Xu, Y. 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, 357-362 (2007).
[CrossRef] [PubMed]

A. Liu, H. Rong, R. Jones, O. Cohen, D. Hak, and M. J. Paniccia, “Optical amplification and lasing by stimulated Raman scattering in silicon waveguide,” J. Lightwave Technol. 24, 1440-1448 (2006).
[CrossRef]

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

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

R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 15, 519-525 (2005).
[CrossRef]

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

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12, 4261-4267 (2004).
[CrossRef] [PubMed]

Roy, S.

Sanseverino, A.

P. Spirito, S. Daliento, A. Sanseverino, L. Gialanella, M. Romano, B. Limata, R. Carta, and L. Bellemo, “Characterization of recombination center in Si epilayers after He implantation by direct measurement of local lifetime distribution with the AC lifetime pro-filing technique,” IEEE. Elec. Dev. Lett. 25, 602-604 (2004).
[CrossRef]

Shoji, T.

Sih, V.

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

V. Sih, S. Xu, Y. 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, 357-362 (2007).
[CrossRef] [PubMed]

Spirito, P.

P. Spirito, S. Daliento, A. Sanseverino, L. Gialanella, M. Romano, B. Limata, R. Carta, and L. Bellemo, “Characterization of recombination center in Si epilayers after He implantation by direct measurement of local lifetime distribution with the AC lifetime pro-filing technique,” IEEE. Elec. Dev. Lett. 25, 602-604 (2004).
[CrossRef]

Takahashi, J.

Takahashi, M.

Tien, E.

Tsang, H. K.

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

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

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, 2745-2747 (2004).
[CrossRef]

T. K. Liang and H. K. Tsang, “Nonlinear absorption and Raman scattering in silicon-on-insulator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 10, 1149-1153 (2004).
[CrossRef]

H. K. Tsang, C. S. Wong, and T. K. Liang, “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]

Tsuchizawa, T.

Wahlbrink, T.

Watanabe, T.

Wong, C. S.

H. K. Tsang, C. S. Wong, and T. K. Liang, “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]

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, 071115 (2005).
[CrossRef]

Xu, Q.

Xu, S.

V. Sih, S. Xu, Y. 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, 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,” Nature Photonics 1, 232-237 (2007).
[CrossRef]

Yamada, K.

Yin, L.

Yuksek, N. S.

Zhang, J.

Appl. Phys. Lett. (5)

H. K. Tsang, C. S. Wong, and T. K. Liang, “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]

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

T. K. Liang and H. K. Tsang, “Efficient Raman amplification in silicon-on-insulator waveguides,” Appl. Phys. Lett. 85, 3343-3345 (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, 2745-2747 (2004).
[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, 071115 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

T. K. Liang and H. K. Tsang, “Nonlinear absorption and Raman scattering in silicon-on-insulator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 10, 1149-1153 (2004).
[CrossRef]

IEEE. Elec. Dev. Lett. (1)

P. Spirito, S. Daliento, A. Sanseverino, L. Gialanella, M. Romano, B. Limata, R. Carta, and L. Bellemo, “Characterization of recombination center in Si epilayers after He implantation by direct measurement of local lifetime distribution with the AC lifetime pro-filing technique,” IEEE. Elec. Dev. Lett. 25, 602-604 (2004).
[CrossRef]

Int. J. Quantum Chem. (1)

X. Chen, N. C. Panoiu, and M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguide,” Int. J. Quantum Chem. 42, 160-170 (2006).

J. Lightwave Technol. (4)

Nature (2)

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

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

Nature Photonics (1)

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

Opt. Express (12)

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguide,” Opt. Express 11, 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, 2774-2780 (2004).
[CrossRef] [PubMed]

Ö. Boyraz, P. Koonath, V. Ranghanathan, and B. Jalali, “All optical switching and continuous generation in silicon waveguides,” Opt. Express 12, 4094-4102 (2004).
[CrossRef] [PubMed]

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, “Net optical gain in low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 12, 4261-4267 (2004).
[CrossRef] [PubMed]

M. Krause, H. Renner, and E. Brinkmeyer, “Analysis of Raman lasing characteristics in silicon-on-insulator waveguides,” Opt. Express 12, 5703-5710 (2004).
[CrossRef] [PubMed]

R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 15, 519-525 (2005).
[CrossRef]

E. Tien, N. S. Yuksek, F. Qian, and O. Boyraz, “Pulse compression and modelocking by using TPA in silicon waveguides,” Opt. Express 15, 6500-6506 (2007).
[CrossRef] [PubMed]

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

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four wave mixing in silicon wire waveguides,” Opt. Express 13, 4629-4637 (2005).
[CrossRef] [PubMed]

L. Yin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express 14, 4786-4799 (2006).
[CrossRef]

R. Dekker, A. Driessen, T. Wahlbrink, C. Moormann, J. Niehusmann, and M. Först, “Ultrafast Kerr--induced all-optical waveguide conversion in silicon waveguides using1.55 μm femtosecond pulses,” Opt. Express 14, 8336-8346 (2006).
[CrossRef] [PubMed]

V. Sih, S. Xu, Y. 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, 357-362 (2007).
[CrossRef] [PubMed]

Opt. Lett. (5)

Phys. Rev. A (1)

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135-3145 (1983).
[CrossRef]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

H. Goldstein, Classical Mechanics, 2nd ed. (Narosa Publishing House, 2001).

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Figures (8)

Fig. 1
Fig. 1

Evolution of the peak power, pulse width, and chirp as a 10 ps wide signal pulse is amplified through SRS inside a silicon waveguide with parameters listed in Table 1. The gain dispersion effect is neglected for solid curves and is considered for dotted curves ( T 2 = 3 ps ) . The pump power decreases in the same fashion in both cases. The open circles represent the numerical data based on the SSF algorithm.

Fig. 2
Fig. 2

Effect of different input pulse width on pulse parameters is represented. Open circles represent the corresponding numerical data based on the SSF algorithm. Parameters used are listed in Table 1.

Fig. 3
Fig. 3

Amplification factor, G s = P s ( L ) P s ( 0 ) , plotted as a function of the input pulse width for three different values of τ c . Open circles represent the corresponding numerical data based on the SSF algorithm.

Fig. 4
Fig. 4

Evolution of the peak signal power along the waveguide during amplification, for three different values of the carrier lifetime. In (a) gain dispersion is considered where as in (b) it is absent. Open circles represent the corresponding values obtained numerically with the SSF algorithm.

Fig. 5
Fig. 5

Evolution of pump power along the waveguide length for different values of τ c ranging from 50 ps to 10 ns .

Fig. 6
Fig. 6

The amplification factor, G s = P s ( L ) P s ( 0 ) , plotted as a function of the pump power for three different values of τ c . Solid curves represent the amount of gain considering infinite gain band width whereas dashed curves signify the same for finite bandwidth.

Fig. 7
Fig. 7

The amplification factor, G s = P s ( L ) P s ( 0 ) , plotted as a function of input chirp for three different values of τ c . Open circles represent the corresponding values obtained numerically with the SSF algorithm.

Fig. 8
Fig. 8

Evolution of normalized pulse width for different initial chirping. Open circles represent the corresponding values obtained numerically with the SSF algorithm.

Tables (1)

Tables Icon

Table 1 Values of the Parameters Used for Numerical Calculations

Equations (21)

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E s z + i β 2 2 2 E s t 2 = i k s n 2 ( 1 + i r ) ( E s 2 + 2 E p 2 ) E s σ s 2 ( 1 + i μ ) N c E s α s 2 E s + g R 2 [ 1 + T 2 2 2 t 2 ] E p 2 E s ,
d E p d z = i k p n 2 ( 1 + i r ) E p 2 E p σ p 2 ( 1 + i μ ) N c E p α p 2 E p .
d P p d z = 2 a eff Re [ E p * d E p d z ] = [ 2 k p n 2 r a eff P p 2 + σ p N c P p + α p P p ] .
d N c d t = β TPA 2 h ν p a eff 2 P p 2 N c τ c ,
N c ( z ) = β TPA τ c P p 2 ( z ) 2 h ν p a eff 2 .
N ¯ c = β TPA τ c P ¯ p 2 2 h ν p a eff 2 , P ¯ p = 1 L 0 L P p ( z ) d z .
L = 1 2 ( E s E s z * E s * E s z ) + i β 2 s 2 E s t 2 + i k s n 2 2 E s 4 + 2 i k s n 2 P p a eff E s 2 i σ s μ 2 N c E s 2 ,
R = β TPA [ 1 2 E s 2 + P p a eff ] ( E s E s z * E s * E s z ) + [ σ s 2 N c + α s 2 g R 2 a eff P p ] ( E s E s z * E s * E s z ) g R P p T 2 2 2 a eff ( E s t t E s z * E s t t * E s z ) ,
E s ( z , t ) = A s exp [ ( 1 i c s ) t 2 2 T s 2 + i φ s ] ,
L g = L d t , R g = R d t .
L g = i A s 2 T s π [ φ s z + 1 4 c s z c s 2 T s T s z ] + i β 2 s π 4 T s A s 2 [ 1 + c s 2 ] + i k s n 2 2 2 π A s 4 T s + 2 i k s n 2 a eff P p A s 2 T s π i σ μ 2 { β TPA τ c P p 2 2 h ν p a eff 2 } A s 2 T s π ,
R g = i ( β TPA 2 ) π A s 4 T s [ φ s z + 1 8 c s z c s 4 T s T s z ] 2 i A s 2 T s π [ φ s z + 1 4 c s z c s 2 T s T s z ] [ β TPA a eff P p + σ s 2 { β TPA τ c P p 2 2 h ν p a eff 2 } + α s 2 g R 2 a eff P p ] 2 i g R P p T 2 2 2 a eff A s 2 π t s [ 1 2 φ z ( 1 + c s 2 ) + 1 8 c s z ( 3 c s 2 1 ) 3 4 c s t s ( c s 2 + 1 ) ] ,
d d z ( L g q z ) L g q + R g q z = 0 ,
A s z = A s [ g R 2 a eff P p ( 1 T 2 2 T s 2 ) + β 2 s c s 2 T s 2 α s 2 β TPA a eff P p σ s 2 β TPA τ c P p 2 2 h ν p a eff 2 ] 5 β TPA 8 2 A s 3 ,
T s z = β 2 s c s T s + β TPA 4 2 A s 2 T s + g R 2 a eff P p T 2 2 T s ( 1 c s 2 ) ,
c s z = β 2 s T s 2 ( 1 + c s 2 ) k s n 2 A s 2 2 + 1 2 2 β TPA A s 2 c s g R a eff P p T 2 2 T s 2 ( 1 + c s 2 ) c s ,
φ s z = β 2 s 2 T s 2 + 5 k s n 2 4 2 A s 2 + 2 k s n 2 P p a eff σ s μ 2 [ β TPA τ c P p 2 2 h ν p a eff 2 ] + g R P p 2 a eff T 2 2 T s 2 c s .
d P p d z = α p P p β TPA a eff P p 2 ( σ p β TPA τ c 2 h ν p a eff 2 ) P p 3 ,
P s z = P s [ g R a eff P p ( 1 T 2 2 T s 2 ) + β 2 s c s T s 2 α s 2 β TPA a eff P p σ s β TPA τ c P p 2 2 h ν p a eff 2 ] 5 4 2 β TPA P s 2 a eff .
( c s β 2 s T s 2 α s ) + [ g R ( 1 T 2 2 T s 2 ) 2 β TPA ] P p a eff σ s β TPA τ c P p 2 2 h ν p a eff 2 > 0 .
τ c < [ g R ( 1 T 2 2 T s 2 ) 2 β TPA ] 2 h ν p 2 σ s β TPA ( α s β 2 s c s T s 2 ) τ th .

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