Abstract

A theoretical investigation of the propagation of femtosecond pulses under conditions similar to those of recent experiments in which a white-light continuum was generated in a microstructured fiber is presented. It is found that higher-order dispersion primarily determines the shape and width of the generated spectrum and that the fine spectral substructure exhibits extreme sensitivity to the initial pulse energy.

© 2002 Optical Society of America

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References

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  1. J. K. Ranka, R. S. Windeler, and A. J. Stentz, Opt. Lett. 25, 25 (2000).
    [CrossRef]
  2. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, Opt. Lett. 26, 608 (2001).
    [CrossRef]
  3. See, for example, D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
    [CrossRef] [PubMed]
  4. See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
    [CrossRef] [PubMed]
  5. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (2000).
    [CrossRef]
  6. G. P. Agrawal and M. J. Potasek, Phys. Rev. A 33, 1765 (1986).
    [CrossRef] [PubMed]
  7. P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
    [CrossRef]
  8. V. Yanofsky and F. W. Wise, Opt. Lett. 19, 1547 (1994).
    [CrossRef]
  9. G. Boyer, Opt. Lett. 24, 945 (1999).
    [CrossRef]
  10. X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. (to be published).
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    [CrossRef] [PubMed]
  12. T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3283 (1997).
    [CrossRef]
  13. See, for example, G. P. Agrawal, Nonlinear Fiber Optics, 3rd. ed. (Academic, San Diego, Calif., 2001), Chap. 1.
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    [CrossRef] [PubMed]
  15. R. H. Stolen, J. P. Gordon, W. J. Tomilson, and H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
    [CrossRef]
  16. R. H. Stolen and W. J. Tomilson, J. Opt. Soc. Am. B 9, 565 (1992).
    [CrossRef]
  17. J. K. Ranka, R. S. Windeler, and A. J. Stentz, in Conference on Lasers and Electro-Optics, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper CD-8.
  18. J. C. Knight, J. Arriga, T. A. Birks, A. Ortigasa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
    [CrossRef]

2001 (1)

2000 (5)

See, for example, D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (2000).
[CrossRef]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, Opt. Lett. 25, 25 (2000).
[CrossRef]

J. C. Knight, J. Arriga, T. A. Birks, A. Ortigasa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

1999 (1)

1997 (1)

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3283 (1997).
[CrossRef]

1994 (1)

1992 (1)

1990 (1)

1989 (1)

1987 (1)

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[CrossRef]

1986 (1)

G. P. Agrawal and M. J. Potasek, Phys. Rev. A 33, 1765 (1986).
[CrossRef] [PubMed]

1984 (1)

Agrawal, G. P.

G. P. Agrawal and M. J. Potasek, Phys. Rev. A 33, 1765 (1986).
[CrossRef] [PubMed]

See, for example, G. P. Agrawal, Nonlinear Fiber Optics, 3rd. ed. (Academic, San Diego, Calif., 2001), Chap. 1.

Arriga, J.

J. C. Knight, J. Arriga, T. A. Birks, A. Ortigasa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Beaud, P.

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[CrossRef]

Birks, T. A.

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (2000).
[CrossRef]

J. C. Knight, J. Arriga, T. A. Birks, A. Ortigasa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Boyer, G.

Brabec, T.

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3283 (1997).
[CrossRef]

Chernikov, S. V.

Chudoba, C.

Cundiff, S. T.

See, for example, D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

Diddams, S. A.

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

See, for example, D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Fujimoto, J. G.

Ghanta, R. K.

Gordon, J. P.

Gu, X.

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. (to be published).

Hall, J. L.

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

See, for example, D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Hänsch, T.

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

Hartl, I.

Haus, H. A.

Hodel, W.

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[CrossRef]

Holzwarth, R.

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

Jones, D. J.

See, for example, D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

Kimmel, M.

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. (to be published).

Knight, J. C.

J. C. Knight, J. Arriga, T. A. Birks, A. Ortigasa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Ko, T. H.

Krausz, F.

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3283 (1997).
[CrossRef]

Li, X. D.

Mamyshev, P. V.

O’Shea, P.

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. (to be published).

Ortigasa-Blanch, A.

J. C. Knight, J. Arriga, T. A. Birks, A. Ortigasa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Potasek, M. J.

G. P. Agrawal and M. J. Potasek, Phys. Rev. A 33, 1765 (1986).
[CrossRef] [PubMed]

Ranka, J. K.

I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, Opt. Lett. 26, 608 (2001).
[CrossRef]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, Opt. Lett. 25, 25 (2000).
[CrossRef]

See, for example, D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, in Conference on Lasers and Electro-Optics, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper CD-8.

Russell, P. St. J.

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (2000).
[CrossRef]

J. C. Knight, J. Arriga, T. A. Birks, A. Ortigasa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Shen, Y. R.

Shreenath, A. P.

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. (to be published).

Stentz, A.

See, for example, D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Stentz, A. J.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, Opt. Lett. 25, 25 (2000).
[CrossRef]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, in Conference on Lasers and Electro-Optics, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper CD-8.

Stolen, R. H.

Tomilson, W. J.

Trebino, R.

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. (to be published).

Udem, T.

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

Wadsworth, W. J.

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (2000).
[CrossRef]

J. C. Knight, J. Arriga, T. A. Birks, A. Ortigasa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Weber, H. P.

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[CrossRef]

Windeler, R. S.

I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, Opt. Lett. 26, 608 (2001).
[CrossRef]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, Opt. Lett. 25, 25 (2000).
[CrossRef]

See, for example, D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. (to be published).

J. K. Ranka, R. S. Windeler, and A. J. Stentz, in Conference on Lasers and Electro-Optics, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper CD-8.

Wise, F. W.

Xu, L.

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. (to be published).

Yang, G.

Yanofsky, V.

Ye, J.

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

Zeek, E.

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. (to be published).

Zysset, B.

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, IEEE J. Quantum Electron. QE-23, 1938 (1987).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. C. Knight, J. Arriga, T. A. Birks, A. Ortigasa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (7)

Phys. Rev. A (1)

G. P. Agrawal and M. J. Potasek, Phys. Rev. A 33, 1765 (1986).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3283 (1997).
[CrossRef]

See also S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. Hänsch, Phys. Rev. Lett. 84, 5102 (2000).
[CrossRef] [PubMed]

Science (1)

See, for example, D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Other (3)

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. (to be published).

See, for example, G. P. Agrawal, Nonlinear Fiber Optics, 3rd. ed. (Academic, San Diego, Calif., 2001), Chap. 1.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, in Conference on Lasers and Electro-Optics, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), postdeadline paper CD-8.

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Figures (3)

Fig. 1
Fig. 1

(a), (c) Spectra and (b), (d) temporal profiles (solid curves) and frequency chirp (dotted curves) of the initially 100-fs τp=60 fs pulse at two propagation distances ζ inside the fiber for the case in which the input power is 1 kW. In (a) and (c), full scale Ωτp=100 corresponds to 2.65×1014 Hz.

Fig. 2
Fig. 2

Plots of the output spectrum of the transmitted pulse for increasing peak input power P: (a) P=2 kW, (b) P=4 kW, and (c) P=8 kW.

Fig. 3
Fig. 3

(a) Output spectrum for an input peak power P=16 kW and propagation distance ζ=0.5. (b) Same as (a) but with 0.1% higher peak power. (c) High-resolution window of the spectra in (a) (solid curve) and (b) (dotted curve).

Equations (2)

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uξ=-in=2Ldsn!Ldsnnuτn+i1+iω0τpτpnl,
pnlζ,τ=LdsLnl1-fuζ,τ2+f-τdτRτ-τuζ,τ2uζ,τ,

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