Abstract

We present a theoretical investigation of the self-focusing dynamics of femtosecond pulses in a hollow waveguide. We show that transverse effects play an important role in these dynamics, even for pulses that are significantly below the critical power for self-focusing in free space, and that excitation of higher-order modes of the waveguide results in the spreading of the pulse in time. Inclusion of self-steepening and space–time focusing in our model is necessary for properly capturing the pulse dynamics.

© 2000 Optical Society of America

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References

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  1. M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); Opt. Lett. 22, 522 (1997); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997).
    [CrossRef]
  2. C. G. Durfee, S. Backus, M. M. Murnane, and H. C. Kapteyn, Opt. Lett. 22, 1565 (1997); C. G. Durfee, S. Backus, H. C. Kapteyn, and M. M. Murnane, Opt. Lett. 4, 697 (1999).
    [CrossRef]
  3. Y. Tamaki, K. Midorikawa, and M. Obara, Appl. Phys. B 67, 59 (1999).
    [CrossRef]
  4. A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
    [CrossRef] [PubMed]
  5. M. Schnürer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, Appl. Phys. B 67, 263 (1998).
    [CrossRef]
  6. Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, Phys. Rev. A 59, 4041 (1999).
    [CrossRef]
  7. G. Tempea and T. Brabec, Opt. Lett. 23, 762 (1998).
    [CrossRef]
  8. G. Tempea and T. Brabec, Opt. Lett. 23, 1286 (1998).
    [CrossRef]
  9. T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3283 (1997).
    [CrossRef]
  10. J. K. Ranka and A. L. Gaeta, Opt. Lett. 23, 534 (1998).
    [CrossRef]
  11. E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
    [CrossRef]
  12. J. E. Rothenburg, Opt. Lett. 17, 1340 (1992).
    [CrossRef]
  13. G. Yang and Y. R. Shen, Opt. Lett. 9, 510 (1984).
    [CrossRef] [PubMed]
  14. G. Fibich and A. L. Gaeta, Opt. Lett. 25, 335 (2000).
    [CrossRef]
  15. There is a typo in Ref. 7. The oscillation period should read 2LP rather than 4LP.
  16. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

2000 (1)

1999 (2)

Y. Tamaki, K. Midorikawa, and M. Obara, Appl. Phys. B 67, 59 (1999).
[CrossRef]

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, Phys. Rev. A 59, 4041 (1999).
[CrossRef]

1998 (5)

G. Tempea and T. Brabec, Opt. Lett. 23, 762 (1998).
[CrossRef]

G. Tempea and T. Brabec, Opt. Lett. 23, 1286 (1998).
[CrossRef]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

M. Schnürer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, Appl. Phys. B 67, 263 (1998).
[CrossRef]

J. K. Ranka and A. L. Gaeta, Opt. Lett. 23, 534 (1998).
[CrossRef]

1997 (2)

1996 (1)

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); Opt. Lett. 22, 522 (1997); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997).
[CrossRef]

1992 (1)

1984 (1)

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

Backus, S.

Brabec, T.

M. Schnürer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, Appl. Phys. B 67, 263 (1998).
[CrossRef]

G. Tempea and T. Brabec, Opt. Lett. 23, 762 (1998).
[CrossRef]

G. Tempea and T. Brabec, Opt. Lett. 23, 1286 (1998).
[CrossRef]

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

Chang, Z.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Cheng, Z.

M. Schnürer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, Appl. Phys. B 67, 263 (1998).
[CrossRef]

De Silvestri, S.

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); Opt. Lett. 22, 522 (1997); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997).
[CrossRef]

Durfee, C. G.

Fibich, G.

Gaeta, A. L.

Hentschel, M.

M. Schnürer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, Appl. Phys. B 67, 263 (1998).
[CrossRef]

Herne, C.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Kapteyn, H. C.

Krausz, F.

M. Schnürer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, Appl. Phys. B 67, 263 (1998).
[CrossRef]

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

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Midorikawa, K.

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, Phys. Rev. A 59, 4041 (1999).
[CrossRef]

Y. Tamaki, K. Midorikawa, and M. Obara, Appl. Phys. B 67, 59 (1999).
[CrossRef]

Murnane, M. M.

Nagata, Y.

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, Phys. Rev. A 59, 4041 (1999).
[CrossRef]

Nisoli, M.

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); Opt. Lett. 22, 522 (1997); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997).
[CrossRef]

Obara, M.

Y. Tamaki, K. Midorikawa, and M. Obara, Appl. Phys. B 67, 59 (1999).
[CrossRef]

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, Phys. Rev. A 59, 4041 (1999).
[CrossRef]

Ranka, J. K.

Rothenburg, J. E.

Rundquist, A.

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Sartania, S.

M. Schnürer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, Appl. Phys. B 67, 263 (1998).
[CrossRef]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Schnürer, M.

M. Schnürer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, Appl. Phys. B 67, 263 (1998).
[CrossRef]

Shen, Y. R.

Svelto, O.

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); Opt. Lett. 22, 522 (1997); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997).
[CrossRef]

Tamaki, Y.

Y. Tamaki, K. Midorikawa, and M. Obara, Appl. Phys. B 67, 59 (1999).
[CrossRef]

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, Phys. Rev. A 59, 4041 (1999).
[CrossRef]

Tempea, G.

M. Schnürer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, Appl. Phys. B 67, 263 (1998).
[CrossRef]

G. Tempea and T. Brabec, Opt. Lett. 23, 762 (1998).
[CrossRef]

G. Tempea and T. Brabec, Opt. Lett. 23, 1286 (1998).
[CrossRef]

Yang, G.

Appl. Phys. B (2)

Y. Tamaki, K. Midorikawa, and M. Obara, Appl. Phys. B 67, 59 (1999).
[CrossRef]

M. Schnürer, Z. Cheng, S. Sartania, M. Hentschel, G. Tempea, T. Brabec, and F. Krausz, Appl. Phys. B 67, 263 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

M. Nisoli, S. De Silvestri, and O. Svelto, Appl. Phys. Lett. 68, 2793 (1996); Opt. Lett. 22, 522 (1997); M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, and F. Krausz, Appl. Phys. B 65, 189 (1997).
[CrossRef]

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. A (1)

Y. Tamaki, Y. Nagata, M. Obara, and K. Midorikawa, Phys. Rev. A 59, 4041 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

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

Science (1)

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Other (2)

There is a typo in Ref. 7. The oscillation period should read 2LP rather than 4LP.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

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Figures (4)

Fig. 1
Fig. 1

Peak intensity versus propagation distance.

Fig. 2
Fig. 2

Temporal profiles for ωτp=100, P/Pcr=0.53, and (a) ξ=11.2, (b) ξ=14.4, (c) ξ=17.6; (d) frequency chirp for ξ=17.6. For clarity, we plot the frequency chirp only over the region in which significant energy is present in the pulse.

Fig. 3
Fig. 3

Temporal profile for ωτp=20, P/Pcr=0.53, and ξ=2.4.

Fig. 4
Fig. 4

Spectrum for P/Pcr=0.53 and ωτp=100 with ξ=0 and ξ=17.6.

Equations (1)

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uξ=i41+iωτpτ-12u-i2LdfLds2τ2u+i1+iωτpτLdfLnlu2u,

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