Abstract

We report numerical investigation of several effects accompanying propagation of femtosecond pulses in air-core photonic crystal fibers.We have found that the strong Raman response of air does not always result in the large soliton self-frequency shift, because it can simultaneously stimulate energy losses into non-solitonic radiation. We demonstrate that the pronounced spectral tails seen in many recent experiments on the short wavelength side of the soliton spectra can be associated with emission of Airy waves by the decelerating solitons. For pulse durations close to 10fs all radiation effects due to Raman response of air become negligible for a special choice of the peak power leading to propagation in the self-induced transparency regime.

© 2008 Optical Society of America

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  1. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Alan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
    [CrossRef] [PubMed]
  2. D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
    [CrossRef] [PubMed]
  3. D. Ouzounov, C. Hensley, A. Gaeta, N. Venkateraman, M. Gallagher, and K. Koch, "Soliton pulse compression in photonic band-gap fibers," Opt. Express 13, 6153-6159 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. A. D. Bessonov and A. M. Zheltikov, "Pulse compression and multimegawatt optical solitons in hollow photoniccrystal fibers," Phys. Rev. E 73, 066618 (2006).
    [CrossRef]
  7. S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
    [CrossRef] [PubMed]
  8. L. Berge, S. Skupin, R. Nuter, J. Kasparian and J-P Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
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    [CrossRef]
  13. E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).
  14. N. Akhmediev, W. Krolikowski, and A. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996); G. Ingledew, N. F. Smyth, and A. L. Worthy, "Raman induced destabilisation of asymmetric coupled solitary waves in nonlinear twin-core fibres," Opt. Commun. 218, 255-271 (2003).
    [CrossRef]
  15. A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature Photonics 1, 653-657 (2007); A. V. Gorbach and D. V. Skryabin, "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A 76, 053803 (2007); A. V. Gorbach and D. V. Skryabin, "Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers," Opt. Express 15, 14560-14565 (2007).
    [CrossRef]
  16. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of Accelerating Airy Beams," Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  17. I. Gabitov, R. A. Indik, N. M. Litchinitser, A. I. Maimistov, V. M. Shalaev, J. E. Soneson, "Double-resonant optical materials with embedded metal nanostructures," J. Opt. Soc. Am. B 23, 535-542 (2006); D. V. Skryabin, A. V. Yulin, A. Maimistov, "Localized polaritons and second harmonic generation in a resonant medium with quadratic nonlinearity," Phys. Rev. Lett. 96, 163904 (2006).
    [CrossRef]
  18. D. V. Skryabin, A. V. Yulin, F. Biancalana, "Nontopological Raman-Kerr self-induced transparency solitons in photonic crystal fibers," Phys. Rev. E 73, 045603 (2006); D. V. Skryabin and A. V. Yulin, "Raman solitons with group velocity dispersion," Phys. Rev. E 74, 046616 (2006).
    [CrossRef]

2007 (4)

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature Photonics 1, 653-657 (2007); A. V. Gorbach and D. V. Skryabin, "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A 76, 053803 (2007); A. V. Gorbach and D. V. Skryabin, "Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers," Opt. Express 15, 14560-14565 (2007).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature Photonics 1, 653-657 (2007); A. V. Gorbach and D. V. Skryabin, "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A 76, 053803 (2007); A. V. Gorbach and D. V. Skryabin, "Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers," Opt. Express 15, 14560-14565 (2007).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature Photonics 1, 653-657 (2007); A. V. Gorbach and D. V. Skryabin, "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A 76, 053803 (2007); A. V. Gorbach and D. V. Skryabin, "Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers," Opt. Express 15, 14560-14565 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of Accelerating Airy Beams," Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

L. Berge, S. Skupin, R. Nuter, J. Kasparian and J-P Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

F. Gerome, K. Cook, A. K. George, W. J. Wadsworth, and J. C. Knight, "Delivery of sub-100fs pulses through 8m of hollow-core fiber using soliton compression," Opt. Express 15, 7126-7131 (2007).
[CrossRef] [PubMed]

2006 (4)

I. Gabitov, R. A. Indik, N. M. Litchinitser, A. I. Maimistov, V. M. Shalaev, J. E. Soneson, "Double-resonant optical materials with embedded metal nanostructures," J. Opt. Soc. Am. B 23, 535-542 (2006); D. V. Skryabin, A. V. Yulin, A. Maimistov, "Localized polaritons and second harmonic generation in a resonant medium with quadratic nonlinearity," Phys. Rev. Lett. 96, 163904 (2006).
[CrossRef]

I. Gabitov, R. A. Indik, N. M. Litchinitser, A. I. Maimistov, V. M. Shalaev, J. E. Soneson, "Double-resonant optical materials with embedded metal nanostructures," J. Opt. Soc. Am. B 23, 535-542 (2006); D. V. Skryabin, A. V. Yulin, A. Maimistov, "Localized polaritons and second harmonic generation in a resonant medium with quadratic nonlinearity," Phys. Rev. Lett. 96, 163904 (2006).
[CrossRef]

D. V. Skryabin, A. V. Yulin, F. Biancalana, "Nontopological Raman-Kerr self-induced transparency solitons in photonic crystal fibers," Phys. Rev. E 73, 045603 (2006); D. V. Skryabin and A. V. Yulin, "Raman solitons with group velocity dispersion," Phys. Rev. E 74, 046616 (2006).
[CrossRef]

D. V. Skryabin, A. V. Yulin, F. Biancalana, "Nontopological Raman-Kerr self-induced transparency solitons in photonic crystal fibers," Phys. Rev. E 73, 045603 (2006); D. V. Skryabin and A. V. Yulin, "Raman solitons with group velocity dispersion," Phys. Rev. E 74, 046616 (2006).
[CrossRef]

A. D. Bessonov and A. M. Zheltikov, "Pulse compression and multimegawatt optical solitons in hollow photoniccrystal fibers," Phys. Rev. E 73, 066618 (2006).
[CrossRef]

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

2005 (1)

2004 (2)

2003 (2)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Alan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

1998 (1)

1996 (1)

N. Akhmediev, W. Krolikowski, and A. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996); G. Ingledew, N. F. Smyth, and A. L. Worthy, "Raman induced destabilisation of asymmetric coupled solitary waves in nonlinear twin-core fibres," Opt. Commun. 218, 255-271 (2003).
[CrossRef]

N. Akhmediev, W. Krolikowski, and A. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996); G. Ingledew, N. F. Smyth, and A. L. Worthy, "Raman induced destabilisation of asymmetric coupled solitary waves in nonlinear twin-core fibres," Opt. Commun. 218, 255-271 (2003).
[CrossRef]

1992 (1)

R. H. Stolen and W. J. Tomlinson, "Effect of the Raman part of the nonlinear refractive index on propagation of ultrashort optical pulses in fibers," J. Opt. Soc. Am B 9, 565-569 (1992).
[CrossRef]

1985 (1)

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Ahmad, F. R.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

Akhmediev, N.

N. Akhmediev, W. Krolikowski, and A. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996); G. Ingledew, N. F. Smyth, and A. L. Worthy, "Raman induced destabilisation of asymmetric coupled solitary waves in nonlinear twin-core fibres," Opt. Commun. 218, 255-271 (2003).
[CrossRef]

Alan, D. C.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Alan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Benabid, F.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

Berge, L.

L. Berge, S. Skupin, R. Nuter, J. Kasparian and J-P Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

Bessonov, A. D.

A. D. Bessonov and A. M. Zheltikov, "Pulse compression and multimegawatt optical solitons in hollow photoniccrystal fibers," Phys. Rev. E 73, 066618 (2006).
[CrossRef]

Bhagwat, A. R.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

Biancalana, F.

D. V. Skryabin, A. V. Yulin, F. Biancalana, "Nontopological Raman-Kerr self-induced transparency solitons in photonic crystal fibers," Phys. Rev. E 73, 045603 (2006); D. V. Skryabin and A. V. Yulin, "Raman solitons with group velocity dispersion," Phys. Rev. E 74, 046616 (2006).
[CrossRef]

Borrelli, N. F.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Alan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of Accelerating Airy Beams," Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Campbell, S.

Christodoulides, D. N.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of Accelerating Airy Beams," Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Cook, K.

Couny, F.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

Dianov, E. M.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of Accelerating Airy Beams," Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Fomichev, A. A.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Franco, M. A.

Gabitov, I.

Gaeta, A.

Gaeta, A. L.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

Gallagher, M.

Gallagher, M. T.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Alan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

George, A. K.

Gerome, F.

Ghosh, S.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

Goh, S.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature Photonics 1, 653-657 (2007); A. V. Gorbach and D. V. Skryabin, "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A 76, 053803 (2007); A. V. Gorbach and D. V. Skryabin, "Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers," Opt. Express 15, 14560-14565 (2007).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature Photonics 1, 653-657 (2007); A. V. Gorbach and D. V. Skryabin, "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A 76, 053803 (2007); A. V. Gorbach and D. V. Skryabin, "Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers," Opt. Express 15, 14560-14565 (2007).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature Photonics 1, 653-657 (2007); A. V. Gorbach and D. V. Skryabin, "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A 76, 053803 (2007); A. V. Gorbach and D. V. Skryabin, "Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers," Opt. Express 15, 14560-14565 (2007).
[CrossRef]

Gordon, J. P.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Grillon, G.

Hensley, C.

Indik, R. A.

Ingledew, G.

N. Akhmediev, W. Krolikowski, and A. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996); G. Ingledew, N. F. Smyth, and A. L. Worthy, "Raman induced destabilisation of asymmetric coupled solitary waves in nonlinear twin-core fibres," Opt. Commun. 218, 255-271 (2003).
[CrossRef]

Karasik, A. Y.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Kasparian, J.

L. Berge, S. Skupin, R. Nuter, J. Kasparian and J-P Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

Kirby, B. J.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

Knight, J.

Knight, J. C.

Koch, K.

Koch, K. W.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Alan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

Krolikowski, W.

N. Akhmediev, W. Krolikowski, and A. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996); G. Ingledew, N. F. Smyth, and A. L. Worthy, "Raman induced destabilisation of asymmetric coupled solitary waves in nonlinear twin-core fibres," Opt. Commun. 218, 255-271 (2003).
[CrossRef]

Light, P. S.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

Litchinitser, N. M.

Lowery, A.

N. Akhmediev, W. Krolikowski, and A. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996); G. Ingledew, N. F. Smyth, and A. L. Worthy, "Raman induced destabilisation of asymmetric coupled solitary waves in nonlinear twin-core fibres," Opt. Commun. 218, 255-271 (2003).
[CrossRef]

Luan, F.

M¨uller, D.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

Maimistov, A.

Maimistov, A. I.

Mamyshev, P. V.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Mangan, B.

Mitschke, F. M.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Mlejnek, M.

Mollenauer, L. F.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Moloney, J. V.

Muller, D.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Alan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Mysyrowicz, A.

Nibbering, E. T. J.

Nuter, R.

L. Berge, S. Skupin, R. Nuter, J. Kasparian and J-P Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

Ouzounov, D.

Ouzounov, D. G.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

Prade, B. S.

Prokhorov, A. M.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Reid, D.

Renshaw, C. K.

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

Roberts, P.

Russell, P.

Serkin, V. N.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Shalaev, V. M.

Silcox, J.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of Accelerating Airy Beams," Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Skryabin, D. V.

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature Photonics 1, 653-657 (2007); A. V. Gorbach and D. V. Skryabin, "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A 76, 053803 (2007); A. V. Gorbach and D. V. Skryabin, "Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers," Opt. Express 15, 14560-14565 (2007).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature Photonics 1, 653-657 (2007); A. V. Gorbach and D. V. Skryabin, "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A 76, 053803 (2007); A. V. Gorbach and D. V. Skryabin, "Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers," Opt. Express 15, 14560-14565 (2007).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature Photonics 1, 653-657 (2007); A. V. Gorbach and D. V. Skryabin, "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A 76, 053803 (2007); A. V. Gorbach and D. V. Skryabin, "Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers," Opt. Express 15, 14560-14565 (2007).
[CrossRef]

D. V. Skryabin, A. V. Yulin, F. Biancalana, "Nontopological Raman-Kerr self-induced transparency solitons in photonic crystal fibers," Phys. Rev. E 73, 045603 (2006); D. V. Skryabin and A. V. Yulin, "Raman solitons with group velocity dispersion," Phys. Rev. E 74, 046616 (2006).
[CrossRef]

D. V. Skryabin, A. V. Yulin, F. Biancalana, "Nontopological Raman-Kerr self-induced transparency solitons in photonic crystal fibers," Phys. Rev. E 73, 045603 (2006); D. V. Skryabin and A. V. Yulin, "Raman solitons with group velocity dispersion," Phys. Rev. E 74, 046616 (2006).
[CrossRef]

I. Gabitov, R. A. Indik, N. M. Litchinitser, A. I. Maimistov, V. M. Shalaev, J. E. Soneson, "Double-resonant optical materials with embedded metal nanostructures," J. Opt. Soc. Am. B 23, 535-542 (2006); D. V. Skryabin, A. V. Yulin, A. Maimistov, "Localized polaritons and second harmonic generation in a resonant medium with quadratic nonlinearity," Phys. Rev. Lett. 96, 163904 (2006).
[CrossRef]

D. V. Skryabin, "Coupled core-surface solitons in photonic crystal fibers," Opt. Express 12, 4841-4846 (2004).
[CrossRef] [PubMed]

Skupin, S.

L. Berge, S. Skupin, R. Nuter, J. Kasparian and J-P Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

Smith, C. M.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Alan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Smyth, N. F.

N. Akhmediev, W. Krolikowski, and A. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996); G. Ingledew, N. F. Smyth, and A. L. Worthy, "Raman induced destabilisation of asymmetric coupled solitary waves in nonlinear twin-core fibres," Opt. Commun. 218, 255-271 (2003).
[CrossRef]

Soneson, J. E.

Stelmakh, M. F.

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Stolen, R. H.

R. H. Stolen and W. J. Tomlinson, "Effect of the Raman part of the nonlinear refractive index on propagation of ultrashort optical pulses in fibers," J. Opt. Soc. Am B 9, 565-569 (1992).
[CrossRef]

Thomas, M. G.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

Tomlinson, W. J.

R. H. Stolen and W. J. Tomlinson, "Effect of the Raman part of the nonlinear refractive index on propagation of ultrashort optical pulses in fibers," J. Opt. Soc. Am B 9, 565-569 (1992).
[CrossRef]

Venkataraman, N.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Alan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

Venkateraman, N.

Wadsworth, W. J.

West, J. A.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Alan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Williams, D.

Wolf, J-P

L. Berge, S. Skupin, R. Nuter, J. Kasparian and J-P Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

Worthy, A. L.

N. Akhmediev, W. Krolikowski, and A. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996); G. Ingledew, N. F. Smyth, and A. L. Worthy, "Raman induced destabilisation of asymmetric coupled solitary waves in nonlinear twin-core fibres," Opt. Commun. 218, 255-271 (2003).
[CrossRef]

Wright, E. M.

Xiao, D.

Yulin, A. V.

I. Gabitov, R. A. Indik, N. M. Litchinitser, A. I. Maimistov, V. M. Shalaev, J. E. Soneson, "Double-resonant optical materials with embedded metal nanostructures," J. Opt. Soc. Am. B 23, 535-542 (2006); D. V. Skryabin, A. V. Yulin, A. Maimistov, "Localized polaritons and second harmonic generation in a resonant medium with quadratic nonlinearity," Phys. Rev. Lett. 96, 163904 (2006).
[CrossRef]

D. V. Skryabin, A. V. Yulin, F. Biancalana, "Nontopological Raman-Kerr self-induced transparency solitons in photonic crystal fibers," Phys. Rev. E 73, 045603 (2006); D. V. Skryabin and A. V. Yulin, "Raman solitons with group velocity dispersion," Phys. Rev. E 74, 046616 (2006).
[CrossRef]

D. V. Skryabin, A. V. Yulin, F. Biancalana, "Nontopological Raman-Kerr self-induced transparency solitons in photonic crystal fibers," Phys. Rev. E 73, 045603 (2006); D. V. Skryabin and A. V. Yulin, "Raman solitons with group velocity dispersion," Phys. Rev. E 74, 046616 (2006).
[CrossRef]

Zheltikov, A. M.

A. D. Bessonov and A. M. Zheltikov, "Pulse compression and multimegawatt optical solitons in hollow photoniccrystal fibers," Phys. Rev. E 73, 066618 (2006).
[CrossRef]

J. Opt. Soc. Am B (1)

R. H. Stolen and W. J. Tomlinson, "Effect of the Raman part of the nonlinear refractive index on propagation of ultrashort optical pulses in fibers," J. Opt. Soc. Am B 9, 565-569 (1992).
[CrossRef]

J. Opt. Soc. Am. B (1)

JETP Lett. (1)

E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, A. A. Fomichev, "Stimulated Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985); F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986); J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

Nature (1)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Alan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Nature Photonics (1)

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity like potentials and expansion of supercontinuum spectra in photonic crystal fibers," Nature Photonics 1, 653-657 (2007); A. V. Gorbach and D. V. Skryabin, "Theory of radiation trapping by the accelerating solitons in optical fibers," Phys. Rev. A 76, 053803 (2007); A. V. Gorbach and D. V. Skryabin, "Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers," Opt. Express 15, 14560-14565 (2007).
[CrossRef]

Opt. Commun. (1)

N. Akhmediev, W. Krolikowski, and A. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996); G. Ingledew, N. F. Smyth, and A. L. Worthy, "Raman induced destabilisation of asymmetric coupled solitary waves in nonlinear twin-core fibres," Opt. Commun. 218, 255-271 (2003).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. E (2)

D. V. Skryabin, A. V. Yulin, F. Biancalana, "Nontopological Raman-Kerr self-induced transparency solitons in photonic crystal fibers," Phys. Rev. E 73, 045603 (2006); D. V. Skryabin and A. V. Yulin, "Raman solitons with group velocity dispersion," Phys. Rev. E 74, 046616 (2006).
[CrossRef]

A. D. Bessonov and A. M. Zheltikov, "Pulse compression and multimegawatt optical solitons in hollow photoniccrystal fibers," Phys. Rev. E 73, 066618 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006); F. Couny, F. Benabid, and P. S. Light, "Subwatt threshold cw raman fiber-gas laser based on H2-filled hollow-core photonic crystal fiber," Phys. Rev. Lett. 99, 143903 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of Accelerating Airy Beams," Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Rep. Prog. Phys. (1)

L. Berge, S. Skupin, R. Nuter, J. Kasparian and J-P Wolf, "Ultrashort filaments of light in weakly ionized, optically transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007).
[CrossRef]

Science (1)

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear fiber Optics (Academic Press, 2001), 3rd ed.

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Figures (6)

Fig. 1.
Fig. 1.

Raman gain functions of air (a) and silica (b) plotted together with spectra of q=2 (180fs FWHM, 0.5MW peak power) and q=20 (60 fs FWHM, 5MW peak power) solitons. Spectrum outside the gray interval is mainly transformed into non-solitonic radiation (spectral cut-off effect), see Section 3 for details.

Fig. 2.
Fig. 2.

Spectrograms (logarithmic scale) showing the effect of the Raman induced spectral cut-off in the air-dominant fiber. Initial soliton parameters are q=20 (60fs FWHM), N=1. Relatively narrow (cf. Fig. 3(b,c)) soliton spectra, indicate strong spectral cut-off and resulting energy loss into non-solitonic radiation.

Fig. 3.
Fig. 3.

The same as Fig. 2 but for the silica-dominant fiber. Relatively broad (cf. Fig. 2(b,c)) soliton spectra, indicate that the spectral cut-off effect is weak and the resulting energy loss into non-solitonic radiation is small.

Fig. 4.
Fig. 4.

Direct comparison of the soliton self-frequency shifts in the air-dominant (AD) and silica-dominant (SD) fibers. (a) shows spectra corresponding to the spectrograms in Fig. 2(c) (black line) and Fig. 3(c) (red line). Thus for q=20 (60fs FWHM) the larger soliton self-frequency shift is achieved in the silica-dominant fiber. (b) shows spectra calculated for q=2 (180fs FWHM) and propagation distance Lz=10m, other parameters are the same as in (a). Thus for q=2 the larger frequency shift is achieved in the air-dominant fiber.

Fig. 5.
Fig. 5.

(a) Spectrogram as in Fig. 2, but calculated for the distance Lz=5m. The difference between the cut-off radiation and Airy tail is obvious. (b) Spectrum corresponding to (a). (c) is the Airy function given by B[x≡2g 1/3(t+q/g)]=Bi[x]+iAi[x] multiplied by the suitable super-gaussian envelope function exp[-(x/w)32] and (d) is its spectrum. Soliton parameters g and q, as well as the envelope function width w are taken from the data in (a): w=30ps.

Fig. 6.
Fig. 6.

(a) XFROG diagram of the output signal after 40cm of propagation for the case of multi-solitonic input condition with N=3 and q=20. Higher order dispersions are neglected. (b) Output spectra after 50cm of propagation for the case of multi-solitonic input pulse with N=1 and N=1.35, q=215.

Equations (3)

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[ z i 1 2 t 2 A i β ( i t ) ] A = i γ a ( 1 f a ) A 2 A + i γ a f a A d t R a ( t ) A ( t t , z ) 2
    + i γ s ( 1 f s ) A 2 A + i γ s f s A d t R s ( t ) A ( t t , z ) 2
R i ( t ) = Θ ( t ) ( τ 1 ( i ) ) 2 + ( τ 2 ( i ) ) 2 τ 1 ( i ) ( τ 2 ( i ) ) 2 exp [ t τ 2 ( i ) ] sin [ t τ 1 ( i ) ] , i = a , s .

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