Abstract

We describe generalized nonlinear envelope equation modeling of sub-cycle dynamics on the underlying electric field carrier during one-dimensional propagation in fused silica. Generalized envelope equation simulations are shown to be in excellent quantitative agreement with the numerical integration of Maxwell’s equations, even in the presence of shock dynamics and carrier steepening on a sub-50 attosecond timescale. In addition, by separating the effects of self-phase modulation and third harmonic generation, we examine the relative contribution of these effects in supercontinuum generation in fused silica nanowire waveguides.

© 2007 Optical Society of America

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  1. J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78,1135-1184 (2006).
    [CrossRef]
  2. M. A. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, "Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires," Opt. Express 13,6848-6855 (2005).
    [CrossRef] [PubMed]
  3. V. P. Kalosha and J. Herrmann, "Self-phase modulation and compression of few-optical-cycle pulses," Phys. Rev. A 62,011804(R) (2000).
    [CrossRef]
  4. N. Karasawa, "Computer simulations of nonlinear propagation of an optical pulse using a finite-difference in the frequency-domain method," IEEE J. Quantum Electron. 38,626-629 (2002).
    [CrossRef]
  5. K. J. Blow and D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25,2665-2673 (1989).
    [CrossRef]
  6. T. Brabec and F. Krausz, "Nonlinear optical pulse propagation in the single-cycle regime," Phys. Rev. Lett. 78,3282-3285 (1997).
    [CrossRef]
  7. N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata, R. Morita, H. Shigekawa, and M. Yamashita, "Comparison between theory and experiment of nonlinear propagation for a-few-cycle and ultrabroadband optical pulses in a fused-silica fiber," IEEE J. Quantum Electron. 37,398-404 (2001).
    [CrossRef]
  8. P. Kinsler and G.H.C. New, " Wideband pulse propagation: single-field and multi-field approaches to Raman interactions,"Phys.Rev. A 72, 033804 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
  10. A. V. Husakou and J. Herrmann, "Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers," J. Opt. Soc. Am. B 19,2171-2182 (2002).
    [CrossRef]
  11. M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70,036604 (2004).
    [CrossRef]
  12. M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85,531-538 (2006).
    [CrossRef]
  13. Y. Mizuta, M. Nagasawa, M. Ohtani, and M. Yamashita, "Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond pulse compression and carrier envelope phase effect," Phys. Rev. A 72,063802 (2005).
    [CrossRef]
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    [CrossRef]
  16. M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional optical pulse propagation equation," Phys. Rev. Lett. 89,283902 (2002).
    [CrossRef]
  17. P. Kinsler, S. B. P. Radnor, and G. H. C. New, "Theory of directional pulse propagation," Phys. Rev. A 72,063807 (2005).
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    [CrossRef]
  20. G. Rosen, "Electromagnetic shocks and the self-annihilation of intense linearly polarized radiation in an ideal dielectric material," Phys. Rev. A 139,A539- A543 (1965).
  21. R. G. Flesch, A. Pushkarev, and J. V. Moloney, "Carrier wave shocking of femtosecond optical pulses," Phys. Rev. Lett. 76,2488-2491 (1996).
    [CrossRef] [PubMed]
  22. L. Gilles, J. V. Moloney, and L. Vazquez, "Electromagnetic shocks on the optical cycle of ultrashort pulses in triple-resonance lorentz dielectric media with subfemtosecond nonlinear electronic debye relaxation," Phys. Rev. E 60,1051-1059 (1999).
    [CrossRef]
  23. 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. 52,973-986 (2005).
    [CrossRef]
  24. P. Kinsler, G. H. C. New and J.C.A. Tyrrell, "Phase sensitivity of nonlinear interactions", arXiv.org/physics/0611213.
  25. P. Kinsler, S. B. P. Radnor, J. Tyrrell, and G. H. C. New, "Optical carrier wave shocking and the effect of dispersion," Phys. Rev. E, submitted (2007).
    [CrossRef]
  26. M. A. Foster, J.M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B 81,363-367 (2005).
    [CrossRef]

2007

P. Kinsler, S. B. P. Radnor, J. Tyrrell, and G. H. C. New, "Optical carrier wave shocking and the effect of dispersion," Phys. Rev. E, submitted (2007).
[CrossRef]

2006

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85,531-538 (2006).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78,1135-1184 (2006).
[CrossRef]

2005

P. Kinsler and G.H.C. New, " Wideband pulse propagation: single-field and multi-field approaches to Raman interactions,"Phys.Rev. A 72, 033804 (2005).
[CrossRef]

M. A. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, "Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires," Opt. Express 13,6848-6855 (2005).
[CrossRef] [PubMed]

Y. Mizuta, M. Nagasawa, M. Ohtani, and M. Yamashita, "Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond pulse compression and carrier envelope phase effect," Phys. Rev. A 72,063802 (2005).
[CrossRef]

A. Ferrando, M. Zacares, P. F. de Cordoba, D. Binosi, and A. Montero, "Forward-backward equations for nonlinear propagation in axially invariant optical systems," Phys. Rev. E 71,016601 (2005).
[CrossRef]

P. Kinsler, S. B. P. Radnor, and G. H. C. New, "Theory of directional pulse propagation," Phys. Rev. A 72,063807 (2005).
[CrossRef]

B. Kibler, J. M. Dudley, and S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area," Appl. Phys. B 81,337-342 (2005).
[CrossRef]

M. A. Foster, J.M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B 81,363-367 (2005).
[CrossRef]

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. 52,973-986 (2005).
[CrossRef]

2004

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70,036604 (2004).
[CrossRef]

2002

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional optical pulse propagation equation," Phys. Rev. Lett. 89,283902 (2002).
[CrossRef]

N. Karasawa, "Computer simulations of nonlinear propagation of an optical pulse using a finite-difference in the frequency-domain method," IEEE J. Quantum Electron. 38,626-629 (2002).
[CrossRef]

A. V. Husakou and J. Herrmann, "Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers," J. Opt. Soc. Am. B 19,2171-2182 (2002).
[CrossRef]

2001

A. V. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87,203901 (2001).
[CrossRef] [PubMed]

N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata, R. Morita, H. Shigekawa, and M. Yamashita, "Comparison between theory and experiment of nonlinear propagation for a-few-cycle and ultrabroadband optical pulses in a fused-silica fiber," IEEE J. Quantum Electron. 37,398-404 (2001).
[CrossRef]

1999

L. Gilles, J. V. Moloney, and L. Vazquez, "Electromagnetic shocks on the optical cycle of ultrashort pulses in triple-resonance lorentz dielectric media with subfemtosecond nonlinear electronic debye relaxation," Phys. Rev. E 60,1051-1059 (1999).
[CrossRef]

1997

T. Brabec and F. Krausz, "Nonlinear optical pulse propagation in the single-cycle regime," Phys. Rev. Lett. 78,3282-3285 (1997).
[CrossRef]

1996

R. G. Flesch, A. Pushkarev, and J. V. Moloney, "Carrier wave shocking of femtosecond optical pulses," Phys. Rev. Lett. 76,2488-2491 (1996).
[CrossRef] [PubMed]

1989

K. J. Blow and D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25,2665-2673 (1989).
[CrossRef]

1965

G. Rosen, "Electromagnetic shocks and the self-annihilation of intense linearly polarized radiation in an ideal dielectric material," Phys. Rev. A 139,A539- A543 (1965).

Becker, A.

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85,531-538 (2006).
[CrossRef]

Binosi, D.

A. Ferrando, M. Zacares, P. F. de Cordoba, D. Binosi, and A. Montero, "Forward-backward equations for nonlinear propagation in axially invariant optical systems," Phys. Rev. E 71,016601 (2005).
[CrossRef]

Blow, K. J.

K. J. Blow and D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25,2665-2673 (1989).
[CrossRef]

Brabec, T.

T. Brabec and F. Krausz, "Nonlinear optical pulse propagation in the single-cycle regime," Phys. Rev. Lett. 78,3282-3285 (1997).
[CrossRef]

Cao, Q.

M. A. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, "Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires," Opt. Express 13,6848-6855 (2005).
[CrossRef] [PubMed]

M. A. Foster, J.M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B 81,363-367 (2005).
[CrossRef]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78,1135-1184 (2006).
[CrossRef]

B. Kibler, J. M. Dudley, and S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area," Appl. Phys. B 81,337-342 (2005).
[CrossRef]

de Cordoba, P. F.

A. Ferrando, M. Zacares, P. F. de Cordoba, D. Binosi, and A. Montero, "Forward-backward equations for nonlinear propagation in axially invariant optical systems," Phys. Rev. E 71,016601 (2005).
[CrossRef]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78,1135-1184 (2006).
[CrossRef]

B. Kibler, J. M. Dudley, and S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area," Appl. Phys. B 81,337-342 (2005).
[CrossRef]

Dudley, J.M.

M. A. Foster, J.M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B 81,363-367 (2005).
[CrossRef]

Ferrando, A.

A. Ferrando, M. Zacares, P. F. de Cordoba, D. Binosi, and A. Montero, "Forward-backward equations for nonlinear propagation in axially invariant optical systems," Phys. Rev. E 71,016601 (2005).
[CrossRef]

Flesch, R. G.

R. G. Flesch, A. Pushkarev, and J. V. Moloney, "Carrier wave shocking of femtosecond optical pulses," Phys. Rev. Lett. 76,2488-2491 (1996).
[CrossRef] [PubMed]

Foster, M. A.

M. A. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, "Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires," Opt. Express 13,6848-6855 (2005).
[CrossRef] [PubMed]

M. A. Foster, J.M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B 81,363-367 (2005).
[CrossRef]

Gaeta, A. L.

M. A. Foster, J.M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B 81,363-367 (2005).
[CrossRef]

M. A. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, "Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires," Opt. Express 13,6848-6855 (2005).
[CrossRef] [PubMed]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78,1135-1184 (2006).
[CrossRef]

Gilles, L.

L. Gilles, J. V. Moloney, and L. Vazquez, "Electromagnetic shocks on the optical cycle of ultrashort pulses in triple-resonance lorentz dielectric media with subfemtosecond nonlinear electronic debye relaxation," Phys. Rev. E 60,1051-1059 (1999).
[CrossRef]

Herrmann, J.

A. V. Husakou and J. Herrmann, "Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers," J. Opt. Soc. Am. B 19,2171-2182 (2002).
[CrossRef]

A. V. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87,203901 (2001).
[CrossRef] [PubMed]

Husakou, A. V.

A. V. Husakou and J. Herrmann, "Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers," J. Opt. Soc. Am. B 19,2171-2182 (2002).
[CrossRef]

A. V. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87,203901 (2001).
[CrossRef] [PubMed]

Karasawa, N.

N. Karasawa, "Computer simulations of nonlinear propagation of an optical pulse using a finite-difference in the frequency-domain method," IEEE J. Quantum Electron. 38,626-629 (2002).
[CrossRef]

N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata, R. Morita, H. Shigekawa, and M. Yamashita, "Comparison between theory and experiment of nonlinear propagation for a-few-cycle and ultrabroadband optical pulses in a fused-silica fiber," IEEE J. Quantum Electron. 37,398-404 (2001).
[CrossRef]

Kibler, B.

B. Kibler, J. M. Dudley, and S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area," Appl. Phys. B 81,337-342 (2005).
[CrossRef]

M. A. Foster, J.M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B 81,363-367 (2005).
[CrossRef]

Kinsler, P.

P. Kinsler, S. B. P. Radnor, J. Tyrrell, and G. H. C. New, "Optical carrier wave shocking and the effect of dispersion," Phys. Rev. E, submitted (2007).
[CrossRef]

P. Kinsler and G.H.C. New, " Wideband pulse propagation: single-field and multi-field approaches to Raman interactions,"Phys.Rev. A 72, 033804 (2005).
[CrossRef]

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. 52,973-986 (2005).
[CrossRef]

P. Kinsler, S. B. P. Radnor, and G. H. C. New, "Theory of directional pulse propagation," Phys. Rev. A 72,063807 (2005).
[CrossRef]

Kolesik, M.

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85,531-538 (2006).
[CrossRef]

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70,036604 (2004).
[CrossRef]

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional optical pulse propagation equation," Phys. Rev. Lett. 89,283902 (2002).
[CrossRef]

Krausz, F.

T. Brabec and F. Krausz, "Nonlinear optical pulse propagation in the single-cycle regime," Phys. Rev. Lett. 78,3282-3285 (1997).
[CrossRef]

Lee, D.

M. A. Foster, J.M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B 81,363-367 (2005).
[CrossRef]

Mizuta, Y.

Y. Mizuta, M. Nagasawa, M. Ohtani, and M. Yamashita, "Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond pulse compression and carrier envelope phase effect," Phys. Rev. A 72,063802 (2005).
[CrossRef]

Mlejnek, M.

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional optical pulse propagation equation," Phys. Rev. Lett. 89,283902 (2002).
[CrossRef]

Moloney, J. V.

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85,531-538 (2006).
[CrossRef]

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70,036604 (2004).
[CrossRef]

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional optical pulse propagation equation," Phys. Rev. Lett. 89,283902 (2002).
[CrossRef]

L. Gilles, J. V. Moloney, and L. Vazquez, "Electromagnetic shocks on the optical cycle of ultrashort pulses in triple-resonance lorentz dielectric media with subfemtosecond nonlinear electronic debye relaxation," Phys. Rev. E 60,1051-1059 (1999).
[CrossRef]

R. G. Flesch, A. Pushkarev, and J. V. Moloney, "Carrier wave shocking of femtosecond optical pulses," Phys. Rev. Lett. 76,2488-2491 (1996).
[CrossRef] [PubMed]

Montero, A.

A. Ferrando, M. Zacares, P. F. de Cordoba, D. Binosi, and A. Montero, "Forward-backward equations for nonlinear propagation in axially invariant optical systems," Phys. Rev. E 71,016601 (2005).
[CrossRef]

Morita, R.

N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata, R. Morita, H. Shigekawa, and M. Yamashita, "Comparison between theory and experiment of nonlinear propagation for a-few-cycle and ultrabroadband optical pulses in a fused-silica fiber," IEEE J. Quantum Electron. 37,398-404 (2001).
[CrossRef]

Nagasawa, M.

Y. Mizuta, M. Nagasawa, M. Ohtani, and M. Yamashita, "Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond pulse compression and carrier envelope phase effect," Phys. Rev. A 72,063802 (2005).
[CrossRef]

Nakagawa, N.

N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata, R. Morita, H. Shigekawa, and M. Yamashita, "Comparison between theory and experiment of nonlinear propagation for a-few-cycle and ultrabroadband optical pulses in a fused-silica fiber," IEEE J. Quantum Electron. 37,398-404 (2001).
[CrossRef]

Nakamura, S.

N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata, R. Morita, H. Shigekawa, and M. Yamashita, "Comparison between theory and experiment of nonlinear propagation for a-few-cycle and ultrabroadband optical pulses in a fused-silica fiber," IEEE J. Quantum Electron. 37,398-404 (2001).
[CrossRef]

New, G. H. C.

P. Kinsler, S. B. P. Radnor, J. Tyrrell, and G. H. C. New, "Optical carrier wave shocking and the effect of dispersion," Phys. Rev. E, submitted (2007).
[CrossRef]

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. 52,973-986 (2005).
[CrossRef]

P. Kinsler, S. B. P. Radnor, and G. H. C. New, "Theory of directional pulse propagation," Phys. Rev. A 72,063807 (2005).
[CrossRef]

New, G.H.C.

P. Kinsler and G.H.C. New, " Wideband pulse propagation: single-field and multi-field approaches to Raman interactions,"Phys.Rev. A 72, 033804 (2005).
[CrossRef]

Ohtani, M.

Y. Mizuta, M. Nagasawa, M. Ohtani, and M. Yamashita, "Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond pulse compression and carrier envelope phase effect," Phys. Rev. A 72,063802 (2005).
[CrossRef]

Pushkarev, A.

R. G. Flesch, A. Pushkarev, and J. V. Moloney, "Carrier wave shocking of femtosecond optical pulses," Phys. Rev. Lett. 76,2488-2491 (1996).
[CrossRef] [PubMed]

Radnor, S. B. P.

P. Kinsler, S. B. P. Radnor, J. Tyrrell, and G. H. C. New, "Optical carrier wave shocking and the effect of dispersion," Phys. Rev. E, submitted (2007).
[CrossRef]

P. Kinsler, S. B. P. Radnor, and G. H. C. New, "Theory of directional pulse propagation," Phys. Rev. A 72,063807 (2005).
[CrossRef]

Rosen, G.

G. Rosen, "Electromagnetic shocks and the self-annihilation of intense linearly polarized radiation in an ideal dielectric material," Phys. Rev. A 139,A539- A543 (1965).

Shibata, M.

N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata, R. Morita, H. Shigekawa, and M. Yamashita, "Comparison between theory and experiment of nonlinear propagation for a-few-cycle and ultrabroadband optical pulses in a fused-silica fiber," IEEE J. Quantum Electron. 37,398-404 (2001).
[CrossRef]

Shigekawa, H.

N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata, R. Morita, H. Shigekawa, and M. Yamashita, "Comparison between theory and experiment of nonlinear propagation for a-few-cycle and ultrabroadband optical pulses in a fused-silica fiber," IEEE J. Quantum Electron. 37,398-404 (2001).
[CrossRef]

Trebino, R.

M. A. Foster, J.M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B 81,363-367 (2005).
[CrossRef]

M. A. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, "Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires," Opt. Express 13,6848-6855 (2005).
[CrossRef] [PubMed]

Tyrrell, J.

P. Kinsler, S. B. P. Radnor, J. Tyrrell, and G. H. C. New, "Optical carrier wave shocking and the effect of dispersion," Phys. Rev. E, submitted (2007).
[CrossRef]

Tyrrell, J. C. A.

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. 52,973-986 (2005).
[CrossRef]

Vazquez, L.

L. Gilles, J. V. Moloney, and L. Vazquez, "Electromagnetic shocks on the optical cycle of ultrashort pulses in triple-resonance lorentz dielectric media with subfemtosecond nonlinear electronic debye relaxation," Phys. Rev. E 60,1051-1059 (1999).
[CrossRef]

Wood, D.

K. J. Blow and D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25,2665-2673 (1989).
[CrossRef]

Wright, E. M.

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85,531-538 (2006).
[CrossRef]

Yamashita, M.

Y. Mizuta, M. Nagasawa, M. Ohtani, and M. Yamashita, "Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond pulse compression and carrier envelope phase effect," Phys. Rev. A 72,063802 (2005).
[CrossRef]

N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata, R. Morita, H. Shigekawa, and M. Yamashita, "Comparison between theory and experiment of nonlinear propagation for a-few-cycle and ultrabroadband optical pulses in a fused-silica fiber," IEEE J. Quantum Electron. 37,398-404 (2001).
[CrossRef]

Zacares, M.

A. Ferrando, M. Zacares, P. F. de Cordoba, D. Binosi, and A. Montero, "Forward-backward equations for nonlinear propagation in axially invariant optical systems," Phys. Rev. E 71,016601 (2005).
[CrossRef]

Appl. Phys. B

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85,531-538 (2006).
[CrossRef]

B. Kibler, J. M. Dudley, and S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area," Appl. Phys. B 81,337-342 (2005).
[CrossRef]

M. A. Foster, J.M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B 81,363-367 (2005).
[CrossRef]

IEEE J. Quantum Electron.

N. Karasawa, "Computer simulations of nonlinear propagation of an optical pulse using a finite-difference in the frequency-domain method," IEEE J. Quantum Electron. 38,626-629 (2002).
[CrossRef]

K. J. Blow and D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25,2665-2673 (1989).
[CrossRef]

N. Karasawa, S. Nakamura, N. Nakagawa, M. Shibata, R. Morita, H. Shigekawa, and M. Yamashita, "Comparison between theory and experiment of nonlinear propagation for a-few-cycle and ultrabroadband optical pulses in a fused-silica fiber," IEEE J. Quantum Electron. 37,398-404 (2001).
[CrossRef]

J. Mod. Opt.

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. 52,973-986 (2005).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Phys. Rev. A

G. Rosen, "Electromagnetic shocks and the self-annihilation of intense linearly polarized radiation in an ideal dielectric material," Phys. Rev. A 139,A539- A543 (1965).

P. Kinsler, S. B. P. Radnor, and G. H. C. New, "Theory of directional pulse propagation," Phys. Rev. A 72,063807 (2005).
[CrossRef]

Y. Mizuta, M. Nagasawa, M. Ohtani, and M. Yamashita, "Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond pulse compression and carrier envelope phase effect," Phys. Rev. A 72,063802 (2005).
[CrossRef]

Phys. Rev. E

A. Ferrando, M. Zacares, P. F. de Cordoba, D. Binosi, and A. Montero, "Forward-backward equations for nonlinear propagation in axially invariant optical systems," Phys. Rev. E 71,016601 (2005).
[CrossRef]

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70,036604 (2004).
[CrossRef]

L. Gilles, J. V. Moloney, and L. Vazquez, "Electromagnetic shocks on the optical cycle of ultrashort pulses in triple-resonance lorentz dielectric media with subfemtosecond nonlinear electronic debye relaxation," Phys. Rev. E 60,1051-1059 (1999).
[CrossRef]

P. Kinsler, S. B. P. Radnor, J. Tyrrell, and G. H. C. New, "Optical carrier wave shocking and the effect of dispersion," Phys. Rev. E, submitted (2007).
[CrossRef]

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A. V. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87,203901 (2001).
[CrossRef] [PubMed]

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P. Kinsler and G.H.C. New, " Wideband pulse propagation: single-field and multi-field approaches to Raman interactions,"Phys.Rev. A 72, 033804 (2005).
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J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78,1135-1184 (2006).
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Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).

V. P. Kalosha and J. Herrmann, "Self-phase modulation and compression of few-optical-cycle pulses," Phys. Rev. A 62,011804(R) (2000).
[CrossRef]

P. Kinsler, G. H. C. New and J.C.A. Tyrrell, "Phase sensitivity of nonlinear interactions", arXiv.org/physics/0611213.

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Figures (3)

Fig. 1.
Fig. 1.

GNEE results neglecting dispersion. (a) Temporal feld profile and (b) detail of carrier shock. (c) Spectral amplitude. Solid lines and circles show GNEE and PSSD simulation results respectively. (d) Detail of first spectral minima comparing results with initial CEO phase set to zero (solid line) and π/2 as indicated. For the latter case, dashed lines and circles show GNEE and PSSD simulation results respectively.

Fig. 2.
Fig. 2.

Results with dispersion: (a) Field profile, (b) detail near center (c) spectral amplitude. Solid lines and circles in (b) and (c) show GNEE and PSSD results respectively.

Fig. 3.
Fig. 3.

SC generation in a fused silica nanowire modelled using GNEE with: the full χ(3) response including THG (solid line), and without THG (dashed line).

Equations (4)

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

z 2 E ˜ ( z , ω ) + β 2 ( ω ) E ˜ ( z , ω ) = β 2 ( ω ) [ 𝒩 ˜ E ˜ ( z , ω ) ] .
[ z ] E ˜ = 2 [ 𝒩 ˜ ( E ˜ + + E ˜ ) ] .
[ z ] A ˜ ± = ± 2 [ 𝒩 ˜ A ˜ ± ] .
U z + α 2 U k 0 i k + 1 k ! β k k U t k = i γ ( 1 + ss t ) × ( ( 1 f R ) [ U 2 + 1 3 e i 2 ω 0 t U 2 ] U + f R g ( z , t , U ) )

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