Abstract

The multiple-collapse dynamics of ultrashort pulses along the propagation direction are investigated under conditions of both normal and anomalous group-velocity dispersion (GVD). In the anomalous-GVD regime we find that collapse events can occur at locations in the medium many diffraction lengths beyond the initial collapse point, in contrast with the normal-GVD regime in which multiple collapse occurs within a diffraction length. Numerical simulations of a modified nonlinear envelope equation are found to be in good qualitative agreement with the observed lengths of the filaments.

© 2004 Optical Society of America

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  1. J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
    [CrossRef]
  2. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, Opt. Lett. 20, 73 (1995).
    [CrossRef] [PubMed]
  3. J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
    [CrossRef] [PubMed]
  4. N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, JETP Lett. 44, 13 (1986).
  5. J. E. Rothenberg, Opt. Lett. 17, 583 (1992).
    [CrossRef] [PubMed]
  6. P. Chernev and V. Petrov, Opt. Lett. 17, 172 (1992).
    [CrossRef]
  7. J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
    [CrossRef] [PubMed]
  8. J. K. Ranka and A. L. Gaeta, Opt. Lett. 23, 534 (1998).
    [CrossRef]
  9. S. A. Diddams, H. K. Eaton, A. A. Zozulya, and T. S. Clement, Opt. Lett. 23, 379 (1998).
    [CrossRef]
  10. A. L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000).
    [CrossRef] [PubMed]
  11. K. D. Moll and A. L. Gaeta, in Postconference Digest, Vol. 43 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 307–308.
  12. Z. X. Wu, H. B. Jiang, L. Luo, H. C. Guo, H. Yang, and Q. H. Gong, Opt. Lett. 27, 448 (2002).
    [CrossRef]
  13. Z. X. Wu, H. B. Jiang, H. Yang, and Q. H. Gong, J. Opt. A 5, 102 (2003).
    [CrossRef]
  14. M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 23, 382 (1998).
    [CrossRef]
  15. A. Talebpour, S. Petit, and S. L. Chin, Opt. Commun. 171, 285 (1999).
    [CrossRef]
  16. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
    [CrossRef] [PubMed]
  17. D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, Opt. Lett. 24, 1311 (1999).
    [CrossRef]
  18. M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
    [CrossRef]
  19. K. K. Thornber, J. Appl. Phys. 52, 279 (1981).
    [CrossRef]
  20. F. Quere, S. Guizard, and P. Martin, Europhys. Lett. 56, 138 (2001).
    [CrossRef]
  21. W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, England, 1989).

2003 (3)

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Z. X. Wu, H. B. Jiang, H. Yang, and Q. H. Gong, J. Opt. A 5, 102 (2003).
[CrossRef]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

2002 (1)

2001 (1)

F. Quere, S. Guizard, and P. Martin, Europhys. Lett. 56, 138 (2001).
[CrossRef]

2000 (1)

A. L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000).
[CrossRef] [PubMed]

1999 (2)

1998 (3)

1996 (2)

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[CrossRef] [PubMed]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
[CrossRef] [PubMed]

1995 (1)

1992 (2)

1986 (1)

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

1981 (1)

K. K. Thornber, J. Appl. Phys. 52, 279 (1981).
[CrossRef]

1975 (1)

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Andre, Y. B.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Borrelli, N. F.

Bourayou, R.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Braun, A.

Chernev, P.

Chin, S. L.

A. Talebpour, S. Petit, and S. L. Chin, Opt. Commun. 171, 285 (1999).
[CrossRef]

Clement, T. S.

Davis, K. M.

Diddams, S. A.

Du, D.

Eaton, H. K.

Flannery, B.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, England, 1989).

Frey, S.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Gaeta, A. L.

A. L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000).
[CrossRef] [PubMed]

D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, Opt. Lett. 24, 1311 (1999).
[CrossRef]

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

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
[CrossRef] [PubMed]

K. D. Moll and A. L. Gaeta, in Postconference Digest, Vol. 43 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 307–308.

Gong, Q. H.

Guizard, S.

F. Quere, S. Guizard, and P. Martin, Europhys. Lett. 56, 138 (2001).
[CrossRef]

Guo, H. C.

Hirao, K.

Homoelle, D.

Jiang, H. B.

Kasparian, J.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Katona, G.

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

Kolesik, M.

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

Korn, G.

Litvak, A. G.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Liu, X.

Luo, L.

Marburger, J. H.

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Martin, P.

F. Quere, S. Guizard, and P. Martin, Europhys. Lett. 56, 138 (2001).
[CrossRef]

Mejean, G.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Miura, K.

Mlejnek, M.

Moll, K. D.

K. D. Moll and A. L. Gaeta, in Postconference Digest, Vol. 43 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 307–308.

Moloney, J. V.

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 23, 382 (1998).
[CrossRef]

Mourou, G.

Mysyrowicz, A.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Petit, S.

A. Talebpour, S. Petit, and S. L. Chin, Opt. Commun. 171, 285 (1999).
[CrossRef]

Petrov, V.

Petrova, T. A.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Press, W.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, England, 1989).

Quere, F.

F. Quere, S. Guizard, and P. Martin, Europhys. Lett. 56, 138 (2001).
[CrossRef]

Ranka, J. K.

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

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
[CrossRef] [PubMed]

Rodriguez, M.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Rothenberg, J. E.

Sauerbrey, R.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Schirmer, R. W.

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
[CrossRef] [PubMed]

Sergeev, A. M.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Smith, C.

Squier, J.

Sugimoto, N.

Talebpour, A.

A. Talebpour, S. Petit, and S. L. Chin, Opt. Commun. 171, 285 (1999).
[CrossRef]

Teukolsky, S.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, England, 1989).

Thornber, K. K.

K. K. Thornber, J. Appl. Phys. 52, 279 (1981).
[CrossRef]

Vetterling, W.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, England, 1989).

Wielandy, S.

Willie, H.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Wolf, J. P.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Woste, L.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Wright, E. M.

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 23, 382 (1998).
[CrossRef]

Wu, Z. X.

Yang, H.

Yu, J.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Yunakovskii, A. D.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Zharova, N. A.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Zozulya, A. A.

Europhys. Lett. (1)

F. Quere, S. Guizard, and P. Martin, Europhys. Lett. 56, 138 (2001).
[CrossRef]

J. Appl. Phys. (1)

K. K. Thornber, J. Appl. Phys. 52, 279 (1981).
[CrossRef]

J. Opt. A (1)

Z. X. Wu, H. B. Jiang, H. Yang, and Q. H. Gong, J. Opt. A 5, 102 (2003).
[CrossRef]

JETP Lett. (1)

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, JETP Lett. 44, 13 (1986).

Opt. Commun. (1)

A. Talebpour, S. Petit, and S. L. Chin, Opt. Commun. 171, 285 (1999).
[CrossRef]

Opt. Lett. (9)

Phys. Rev. Lett. (3)

A. L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000).
[CrossRef] [PubMed]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
[CrossRef] [PubMed]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

Prog. Quantum Electron. (1)

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Science (1)

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, H. Willie, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef] [PubMed]

Other (2)

K. D. Moll and A. L. Gaeta, in Postconference Digest, Vol. 43 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 307–308.

W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, England, 1989).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup to observe the spatial dynamics of a focused laser beam. Light scattered by the sample perpendicular to the propagation direction is imaged through a microscope and recorded by a digital camera.

Fig. 2
Fig. 2

Experimental results of multiple-collapse behavior as a function of input power. In the normal-GVD regime [(a) and (b)], collapse is localized, whereas extended filaments are observed in the anomalous-GVD regime [(c) and (d)]. The distance between the collapse events is also much larger in the anomalous-GVD regime. A more comprehensive series of lineouts depicting the collapse behavor is presented for the (e) normal- and (f) anomalous-GVD regimes. Note that different scales are used in (e) and (f). The light is propagating from left to right.

Fig. 3
Fig. 3

Simulations of multiple-collapse behavior in the normal-GVD regime. As the beam power is increased, the collapse location is observed to move toward the input face, and the second location is observed to grow in strength.

Fig. 4
Fig. 4

Simulation of collapse in the anomalous-GVD regime. The arrest of a single collapse event with a significantly elongated collapse region is in qualitative agreement with the experimentally observed behavior.

Equations (3)

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uξ=i4T-12u-iLdf2Lds2uτ2+iTpnl-jnl,
pnl=LdfLnlu2u+iLdf2Lmpρ/tu2u,
jnl=iLdfLpl1-iωτcu-ωτc/ωτp1-iωτcuτρ,

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