Abstract

An effort was conducted to numerically determine, by the nonlinear Schrödinger split-step Fourier method, whether using cross-phase modulation (XPM) could cause temporal soliton pulse propagation in a silicon slow-light photonic crystal waveguide (PhCWG) shorter than a millimeter. The simulations demonstrated that, because of the higher powers and shorter scales of photonic crystals, two-photon absorption (TPA) would cause an optical soliton pulse to be extremely dissipative. The model demonstrated, however, that by utilizing XPM, it is possible to sustain a compressed soliton pulse within a silicon PhCWG subjected to TPA over longer relative distances.

© 2013 Optical Society of America

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2012 (1)

T. Gu, N. Petrone, J. F. McMillan, A. Van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6, 554–559 (2012).
[CrossRef]

2011 (2)

C. A. Husko, A. De Rossi, and C. W. Wong, “Effect of multi-photon absorption and free carriers on self-phase modulation in slow-light photonic crystals,” Opt. Lett. 36, 2239–2241 (2011).
[CrossRef]

N. C. Panoiu, J. F. McMillan, and C. W. Wong, “Influence of the group-velocity on the pulse propagation in 1D silicon photonic crystal waveguides,” Appl. Phys. A 103, 835–838 (2011).
[CrossRef]

2010 (5)

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

W. Ding, A. V. Gorbach, W. J. Wadswarth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, and R. M. De La Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef]

R. S. Tucker, “The role of optics in computing,” Nat. Photonics 4, 405 (2010).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observations of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18, 15484–15497 (2010).
[CrossRef]

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

2007 (3)

I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 1135–1146 (2007).
[CrossRef]

X. Yang and C. W. Wong, “Coupled-mode theory for stimulated Raman scattering in high-Q/Vm photonic bandgap defect cavity lasers,” Opt. Express 15, 4763–4780 (2007).
[CrossRef]

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]

2006 (1)

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. B 39, 2737–2746 (2006).

2004 (1)

M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. Ryu, “Waveguides, resonators and their coupled elements in photonic crystal slabs,” Opt. Express 12, 1551–1561 (2004).
[CrossRef]

2003 (1)

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

Agrawal, G. P.

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]

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

Chen, X.

I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 1135–1146 (2007).
[CrossRef]

Colman, P.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Combrié, S.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Dadap, J. I.

I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 1135–1146 (2007).
[CrossRef]

De La Rue, R. M.

W. Ding, A. V. Gorbach, W. J. Wadswarth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, and R. M. De La Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef]

De Rossi, A.

C. A. Husko, A. De Rossi, and C. W. Wong, “Effect of multi-photon absorption and free carriers on self-phase modulation in slow-light photonic crystals,” Opt. Lett. 36, 2239–2241 (2011).
[CrossRef]

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Ding, W.

W. Ding, A. V. Gorbach, W. J. Wadswarth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, and R. M. De La Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef]

Dinu, M.

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

Fainman, Y.

D. Tan, P. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun.116 (2010).

Foster, M. A.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

Gaeta, A. L.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

Garcia, H.

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. B 39, 2737–2746 (2006).

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

Gorbach, A. V.

W. Ding, A. V. Gorbach, W. J. Wadswarth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, and R. M. De La Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef]

Gu, T.

T. Gu, N. Petrone, J. F. McMillan, A. Van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6, 554–559 (2012).
[CrossRef]

Haberman, R.

R. Haberman, Applied Partial Differential Equations, with Fourier Series and Boundary Value Problems, 4th ed. (Pearson Prentice-Hall, 2004).

Hone, J.

T. Gu, N. Petrone, J. F. McMillan, A. Van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6, 554–559 (2012).
[CrossRef]

Hsieh, I-W.

I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 1135–1146 (2007).
[CrossRef]

Husko, C.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Husko, C. A.

C. A. Husko, A. De Rossi, and C. W. Wong, “Effect of multi-photon absorption and free carriers on self-phase modulation in slow-light photonic crystals,” Opt. Lett. 36, 2239–2241 (2011).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Kalyanaraman, R.

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. B 39, 2737–2746 (2006).

Kim, T.

T.-C. Poon and T. Kim, Engineering Optics with MATLAB (World Scientific, 2006).

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2004).

Knight, J. C.

W. Ding, A. V. Gorbach, W. J. Wadswarth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, and R. M. De La Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef]

Kuramochi, E.

M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. Ryu, “Waveguides, resonators and their coupled elements in photonic crystal slabs,” Opt. Express 12, 1551–1561 (2004).
[CrossRef]

Kwong, D. L.

T. Gu, N. Petrone, J. F. McMillan, A. Van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6, 554–559 (2012).
[CrossRef]

Kwong, D.-L.

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observations of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18, 15484–15497 (2010).
[CrossRef]

Levy, J. S.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

Lin, Q.

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]

Lipson, M.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

Lo, G. Q.

T. Gu, N. Petrone, J. F. McMillan, A. Van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6, 554–559 (2012).
[CrossRef]

McMillan, J. F.

T. Gu, N. Petrone, J. F. McMillan, A. Van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6, 554–559 (2012).
[CrossRef]

N. C. Panoiu, J. F. McMillan, and C. W. Wong, “Influence of the group-velocity on the pulse propagation in 1D silicon photonic crystal waveguides,” Appl. Phys. A 103, 835–838 (2011).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observations of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18, 15484–15497 (2010).
[CrossRef]

McNab, S. J.

I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 1135–1146 (2007).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Mitsugi, S.

M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. Ryu, “Waveguides, resonators and their coupled elements in photonic crystal slabs,” Opt. Express 12, 1551–1561 (2004).
[CrossRef]

Nagle, R. K.

R. K. Nagle, E. B. Saff, and A. D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, 5th ed. (Addison Wesley, 1999).

Notomi, M.

M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. Ryu, “Waveguides, resonators and their coupled elements in photonic crystal slabs,” Opt. Express 12, 1551–1561 (2004).
[CrossRef]

Osgood, R. M.

I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 1135–1146 (2007).
[CrossRef]

Painter, O. J.

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]

Panoiu, N. C.

N. C. Panoiu, J. F. McMillan, and C. W. Wong, “Influence of the group-velocity on the pulse propagation in 1D silicon photonic crystal waveguides,” Appl. Phys. A 103, 835–838 (2011).
[CrossRef]

I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 1135–1146 (2007).
[CrossRef]

Petrone, N.

T. Gu, N. Petrone, J. F. McMillan, A. Van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6, 554–559 (2012).
[CrossRef]

Poitras, C. B.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

Poon, T.-C.

T.-C. Poon and T. Kim, Engineering Optics with MATLAB (World Scientific, 2006).

Quochi, F.

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

Ryu, H.

M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. Ryu, “Waveguides, resonators and their coupled elements in photonic crystal slabs,” Opt. Express 12, 1551–1561 (2004).
[CrossRef]

Sadiku, M.

M. Sadiku, Numerical Techniques in Electromagnetics, 2nd ed. (CRC Press, 2001).

Saff, E. B.

R. K. Nagle, E. B. Saff, and A. D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, 5th ed. (Addison Wesley, 1999).

Sagnes, I.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley-Interscience, 2007).

Salem, R.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

Shinya, A.

M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. Ryu, “Waveguides, resonators and their coupled elements in photonic crystal slabs,” Opt. Express 12, 1551–1561 (2004).
[CrossRef]

Skryabin, D. V.

W. Ding, A. V. Gorbach, W. J. Wadswarth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, and R. M. De La Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef]

Slusher, E.

E. Slusher, Nonlinear Photonic Crystals (Springer, 2003).

Snider, A. D.

R. K. Nagle, E. B. Saff, and A. D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, 5th ed. (Addison Wesley, 1999).

Sorel, M.

W. Ding, A. V. Gorbach, W. J. Wadswarth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, and R. M. De La Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef]

Strain, M. J.

W. Ding, A. V. Gorbach, W. J. Wadswarth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, and R. M. De La Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef]

Sun, P.

D. Tan, P. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun.116 (2010).

Tan, D.

D. Tan, P. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun.116 (2010).

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley-Interscience, 2007).

Tucker, R. S.

R. S. Tucker, “The role of optics in computing,” Nat. Photonics 4, 405 (2010).
[CrossRef]

Turner-Foster, A. C.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

Van der Zande, A.

T. Gu, N. Petrone, J. F. McMillan, A. Van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6, 554–559 (2012).
[CrossRef]

Vlasov, Y. A.

I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 1135–1146 (2007).
[CrossRef]

Wadswarth, W. J.

W. Ding, A. V. Gorbach, W. J. Wadswarth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, and R. M. De La Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Wong, C. W.

T. Gu, N. Petrone, J. F. McMillan, A. Van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6, 554–559 (2012).
[CrossRef]

N. C. Panoiu, J. F. McMillan, and C. W. Wong, “Influence of the group-velocity on the pulse propagation in 1D silicon photonic crystal waveguides,” Appl. Phys. A 103, 835–838 (2011).
[CrossRef]

C. A. Husko, A. De Rossi, and C. W. Wong, “Effect of multi-photon absorption and free carriers on self-phase modulation in slow-light photonic crystals,” Opt. Lett. 36, 2239–2241 (2011).
[CrossRef]

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observations of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18, 15484–15497 (2010).
[CrossRef]

X. Yang and C. W. Wong, “Coupled-mode theory for stimulated Raman scattering in high-Q/Vm photonic bandgap defect cavity lasers,” Opt. Express 15, 4763–4780 (2007).
[CrossRef]

Yang, X.

X. Yang and C. W. Wong, “Coupled-mode theory for stimulated Raman scattering in high-Q/Vm photonic bandgap defect cavity lasers,” Opt. Express 15, 4763–4780 (2007).
[CrossRef]

Yu, M.

T. Gu, N. Petrone, J. F. McMillan, A. Van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6, 554–559 (2012).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observations of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18, 15484–15497 (2010).
[CrossRef]

Appl. Phys. A (1)

N. C. Panoiu, J. F. McMillan, and C. W. Wong, “Influence of the group-velocity on the pulse propagation in 1D silicon photonic crystal waveguides,” Appl. Phys. A 103, 835–838 (2011).
[CrossRef]

Appl. Phys. Lett. (1)

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

J. Phys. B (1)

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. B 39, 2737–2746 (2006).

Nat. Photonics (3)

T. Gu, N. Petrone, J. F. McMillan, A. Van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6, 554–559 (2012).
[CrossRef]

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

R. S. Tucker, “The role of optics in computing,” Nat. Photonics 4, 405 (2010).
[CrossRef]

Opt. Express (7)

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observations of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18, 15484–15497 (2010).
[CrossRef]

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]

W. Ding, A. V. Gorbach, W. J. Wadswarth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, and R. M. De La Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. Ryu, “Waveguides, resonators and their coupled elements in photonic crystal slabs,” Opt. Express 12, 1551–1561 (2004).
[CrossRef]

X. Yang and C. W. Wong, “Coupled-mode theory for stimulated Raman scattering in high-Q/Vm photonic bandgap defect cavity lasers,” Opt. Express 15, 4763–4780 (2007).
[CrossRef]

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

I-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 1135–1146 (2007).
[CrossRef]

Opt. Lett. (1)

C. A. Husko, A. De Rossi, and C. W. Wong, “Effect of multi-photon absorption and free carriers on self-phase modulation in slow-light photonic crystals,” Opt. Lett. 36, 2239–2241 (2011).
[CrossRef]

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M. Sadiku, Numerical Techniques in Electromagnetics, 2nd ed. (CRC Press, 2001).

T.-C. Poon and T. Kim, Engineering Optics with MATLAB (World Scientific, 2006).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

D. Tan, P. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun.116 (2010).

R. K. Nagle, E. B. Saff, and A. D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, 5th ed. (Addison Wesley, 1999).

R. Haberman, Applied Partial Differential Equations, with Fourier Series and Boundary Value Problems, 4th ed. (Pearson Prentice-Hall, 2004).

C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2004).

E. Slusher, Nonlinear Photonic Crystals (Springer, 2003).

“Synchronously pumped OPO,” PP Automatic. OPO PP Auto Manual No. 122970 [Angewandte Physik and Elektronik (APE) GmbH].

R. Paschotta, “Optical parametric oscillators,” RP Photonics Encyclopedia, http://www.rp-photonics.com/optical_parametric_oscillators.html .

Coherent, Operator’s Manual, The Coherent Mira Optima 900-P Laser.

“Two-photon absorption,” RP Photonics Encyclopedia, http://www.rp-photonics.com/two_photon_absorption.html .

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