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).

C. 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]

D. Tan, P. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun. 1, 116 (2011).

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]

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 21, 862–868 (2010).

A. C. Peacock, “Soliton propagation in tapered silicon core fibers,” Opt. Lett. 35, 3697–3699 (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]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on-insulator photonic wires,” Opt. Express 16, 3310–3319 (2008).

[Crossref]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, “Optical solitons in a silicon waveguide,” Opt. Express 15, 7682–7688 (2007).

[Crossref]

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32, 391–393 (2007).

[Crossref]

W. Hseih, X. Chen, J. Dadap, N. Panoiu, and R. Osgood, “Cross-phase modulation-induced spectral and teporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 3310–3319 (2007).

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

J. C. A. Tyrrell, P. Kinsler, and G. H. C. New, “Pseudospectral spatial-domain: a new method for nonlinear pulse propagation in the few-cycle regime with arbitrary dispersion,” J. Mod. Opt. 52, 973 (2005).

[Crossref]

C.-F. Chen, S. Chi, and B. Luo, “Femtosecond soliton propagation in an optical fiber,” Optik 113, 267–271 (2002).

[Crossref]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, “Optical solitons in a silicon waveguide,” Opt. Express 15, 7682–7688 (2007).

[Crossref]

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32, 391–393 (2007).

[Crossref]

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295–1297 (2006).

[Crossref]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on-insulator photonic wires,” Opt. Express 16, 3310–3319 (2008).

[Crossref]

C.-F. Chen, S. Chi, and B. Luo, “Femtosecond soliton propagation in an optical fiber,” Optik 113, 267–271 (2002).

[Crossref]

W. Hseih, X. Chen, J. Dadap, N. Panoiu, and R. Osgood, “Cross-phase modulation-induced spectral and teporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 3310–3319 (2007).

C.-F. Chen, S. Chi, and B. Luo, “Femtosecond soliton propagation in an optical fiber,” Optik 113, 267–271 (2002).

[Crossref]

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 21, 862–868 (2010).

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 21, 862–868 (2010).

W. Hseih, X. Chen, J. Dadap, N. Panoiu, and R. Osgood, “Cross-phase modulation-induced spectral and teporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 3310–3319 (2007).

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]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on-insulator photonic wires,” Opt. Express 16, 3310–3319 (2008).

[Crossref]

C. 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. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 21, 862–868 (2010).

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]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on-insulator photonic wires,” Opt. Express 16, 3310–3319 (2008).

[Crossref]

S. Eggleton, Nonlinear Photonic Crystals (Springer, 2003).

D. Tan, P. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun. 1, 116 (2011).

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on-insulator photonic wires,” Opt. Express 16, 3310–3319 (2008).

[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]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on-insulator photonic wires,” Opt. Express 16, 3310–3319 (2008).

[Crossref]

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

W. Hseih, X. Chen, J. Dadap, N. Panoiu, and R. Osgood, “Cross-phase modulation-induced spectral and teporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 3310–3319 (2007).

C. 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. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 21, 862–868 (2010).

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

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

R. Nagle, E. Kent, B. Saff, and A. D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, 3rd ed. (Addison Wesley, 2000).

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

J. C. A. Tyrrell, P. Kinsler, and G. H. C. New, “Pseudospectral spatial-domain: a new method for nonlinear pulse propagation in the few-cycle regime with arbitrary dispersion,” J. Mod. Opt. 52, 973 (2005).

[Crossref]

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

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]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on-insulator photonic wires,” Opt. Express 16, 3310–3319 (2008).

[Crossref]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, “Optical solitons in a silicon waveguide,” Opt. Express 15, 7682–7688 (2007).

[Crossref]

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32, 391–393 (2007).

[Crossref]

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

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295–1297 (2006).

[Crossref]

C.-F. Chen, S. Chi, and B. Luo, “Femtosecond soliton propagation in an optical fiber,” Optik 113, 267–271 (2002).

[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).

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]

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

R. Nagle, E. Kent, B. Saff, and A. D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, 3rd ed. (Addison Wesley, 2000).

J. C. A. Tyrrell, P. Kinsler, and G. H. C. New, “Pseudospectral spatial-domain: a new method for nonlinear pulse propagation in the few-cycle regime with arbitrary dispersion,” J. Mod. Opt. 52, 973 (2005).

[Crossref]

W. Hseih, X. Chen, J. Dadap, N. Panoiu, and R. Osgood, “Cross-phase modulation-induced spectral and teporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 3310–3319 (2007).

W. Hseih, X. Chen, J. Dadap, N. Panoiu, and R. Osgood, “Cross-phase modulation-induced spectral and teporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 3310–3319 (2007).

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).

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

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

R. Nagle, E. Kent, B. Saff, and A. D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, 3rd ed. (Addison Wesley, 2000).

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 21, 862–868 (2010).

B. Saleh and M. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

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]

C. J. Benton and D. V. Skryabin, “Coupling induced anomalous group velocity dispersion in nonlinear arrays of silicon photonic wires,” Opt. Express 17, 5879–5884 (2009).

[Crossref]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on-insulator photonic wires,” Opt. Express 16, 3310–3319 (2008).

[Crossref]

R. Nagle, E. Kent, B. Saff, and A. D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, 3rd ed. (Addison Wesley, 2000).

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]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on-insulator photonic wires,” Opt. Express 16, 3310–3319 (2008).

[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]

G. Strang, Linear Algebra and its Applications, 3rd ed. (Brooks/Cole, 1988).

D. Tan, P. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun. 1, 116 (2011).

D. Tan, P. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun. 1, 116 (2011).

B. Saleh and M. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

J. C. A. Tyrrell, P. Kinsler, and G. H. C. New, “Pseudospectral spatial-domain: a new method for nonlinear pulse propagation in the few-cycle regime with arbitrary dispersion,” J. Mod. Opt. 52, 973 (2005).

[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]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on-insulator photonic wires,” Opt. Express 16, 3310–3319 (2008).

[Crossref]

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

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).

C. 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]

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]

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 21, 862–868 (2010).

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32, 391–393 (2007).

[Crossref]

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295–1297 (2006).

[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).

J. C. A. Tyrrell, P. Kinsler, and G. H. C. New, “Pseudospectral spatial-domain: a new method for nonlinear pulse propagation in the few-cycle regime with arbitrary dispersion,” J. Mod. Opt. 52, 973 (2005).

[Crossref]

D. Tan, P. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun. 1, 116 (2011).

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 21, 862–868 (2010).

W. Hseih, X. Chen, J. Dadap, N. Panoiu, and R. Osgood, “Cross-phase modulation-induced spectral and teporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15, 3310–3319 (2007).

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]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, “Optical solitons in a silicon waveguide,” Opt. Express 15, 7682–7688 (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]

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

C. J. Benton and D. V. Skryabin, “Coupling induced anomalous group velocity dispersion in nonlinear arrays of silicon photonic wires,” Opt. Express 17, 5879–5884 (2009).

[Crossref]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on-insulator photonic wires,” Opt. Express 16, 3310–3319 (2008).

[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]

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32, 391–393 (2007).

[Crossref]

C. 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]

A. C. Peacock, “Soliton propagation in tapered silicon core fibers,” Opt. Lett. 35, 3697–3699 (2010).

[Crossref]

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295–1297 (2006).

[Crossref]

C.-F. Chen, S. Chi, and B. Luo, “Femtosecond soliton propagation in an optical fiber,” Optik 113, 267–271 (2002).

[Crossref]

R. Nagle, E. Kent, B. Saff, and A. D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, 3rd ed. (Addison Wesley, 2000).

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

R. Paschotta, “Transform limit,” http://www.rp-photonics.com/transform_limit.html .

R. Paschotta, “Timebandwidth product,” http://www.rp-photonics.com/time_bandwidth_product.html .

G. Strang, Linear Algebra and its Applications, 3rd ed. (Brooks/Cole, 1988).

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

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

S. Eggleton, Nonlinear Photonic Crystals (Springer, 2003).

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

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

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

B. Saleh and M. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).