Abstract

We investigate experimentally the role that the initial temporal profile of ultrashort laser pulses has on the self-focusing dynamics in the anomalous group-velocity dispersion (GVD) regime. We observe that pulse-splitting occurs for super-Gaussian pulses, but not for Gaussian pulses. The splitting does not occur for either pulse shape when the GVD is near-zero. These observations agree with predictions based on the nonlinear Schrödinger equation, and can be understood intuitively using the method of nonlinear geometrical optics.

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  1. R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
    [CrossRef]
  2. N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, “Multiple fractionation of wave structure in a nonlinear medium,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 13–17 (1986).
  3. S. N. Vlasov, L. V. Piskunova, and V. I. Talanov, “Three-dimensional wave collapse in the nonlinear Schrödinger equation model,” Zh. Eksp. Teor. Fiz. 95, 1945–1950 (1989).
  4. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000).
    [CrossRef] [PubMed]
  5. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
    [CrossRef]
  6. J. E. Rothenberg, “Pulse splitting during self-focusing in normally dispersive media,” Opt. Lett. 17, 583–585 (1992).
    [CrossRef] [PubMed]
  7. G. Fibich, V. M. Malkin, and G. C. Papanicolaou, “Beam self-focusing in the presence of a small normal time dispersion,” Phys. Rev. A 52, 4218–4228 (1995).
    [CrossRef] [PubMed]
  8. J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
    [CrossRef] [PubMed]
  9. S. A. Diddams, H. K. Eaton, A. A. Zozulya, and T. S. Clement, “Amplitude and phase measurements of femtosecond pulse splitting in nonlinear dispersive media,” Opt. Lett. 23, 379–381 (1998).
    [CrossRef]
  10. A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).
    [CrossRef]
  11. A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).
    [CrossRef]
  12. S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
    [CrossRef] [PubMed]
  13. K. D. Moll and A. L. Gaeta, “Role of dispersion in multiple-collapse dynamics,” Opt. Lett. 29, 995–997 (2004).
    [CrossRef] [PubMed]
  14. M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791–4803 (1998).
    [CrossRef]
  15. S. Skupin and L. Bergé, “Self-guiding of femtosecond light pulses in condensed media: Plasma generation versus chromatic dispersion,” Physica D 220, 14–30 (2006).
    [CrossRef]
  16. J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006).
    [CrossRef]
  17. G. Fibich, N. Gavish, and X. Wang, “Singular ring solutions of critical and supercritical nonlinear Schrödinger equations,” Physica D 231, 55–86 (2007).
    [CrossRef]
  18. N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: a nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
    [CrossRef]
  19. T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian beams,” Opt. Express 14, 5468–5475 (2006).
    [CrossRef] [PubMed]
  20. A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1998).
    [CrossRef]
  21. J. K. Ranka, A. L. Gaeta, A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, “Autocorrelation measurement of 6-fs pulses based on the two-photon-induced photocurrent in a GaAsP photodiode,” Opt. Lett. 22, 1344–1346 (1997).
    [CrossRef]

2008

N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: a nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
[CrossRef]

2007

G. Fibich, N. Gavish, and X. Wang, “Singular ring solutions of critical and supercritical nonlinear Schrödinger equations,” Physica D 231, 55–86 (2007).
[CrossRef]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

2006

S. Skupin and L. Bergé, “Self-guiding of femtosecond light pulses in condensed media: Plasma generation versus chromatic dispersion,” Physica D 220, 14–30 (2006).
[CrossRef]

J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006).
[CrossRef]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian beams,” Opt. Express 14, 5468–5475 (2006).
[CrossRef] [PubMed]

2004

2001

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

2000

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000).
[CrossRef] [PubMed]

1999

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).
[CrossRef]

1998

A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).
[CrossRef]

S. A. Diddams, H. K. Eaton, A. A. Zozulya, and T. S. Clement, “Amplitude and phase measurements of femtosecond pulse splitting in nonlinear dispersive media,” Opt. Lett. 23, 379–381 (1998).
[CrossRef]

M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791–4803 (1998).
[CrossRef]

A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1998).
[CrossRef]

1997

1996

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[CrossRef] [PubMed]

1995

G. Fibich, V. M. Malkin, and G. C. Papanicolaou, “Beam self-focusing in the presence of a small normal time dispersion,” Phys. Rev. A 52, 4218–4228 (1995).
[CrossRef] [PubMed]

1992

1989

S. N. Vlasov, L. V. Piskunova, and V. I. Talanov, “Three-dimensional wave collapse in the nonlinear Schrödinger equation model,” Zh. Eksp. Teor. Fiz. 95, 1945–1950 (1989).

1986

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, “Multiple fractionation of wave structure in a nonlinear medium,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 13–17 (1986).

1964

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[CrossRef]

Baltuska, A.

Band, Y. B.

M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791–4803 (1998).
[CrossRef]

Bergé, L.

S. Skupin and L. Bergé, “Self-guiding of femtosecond light pulses in condensed media: Plasma generation versus chromatic dispersion,” Physica D 220, 14–30 (2006).
[CrossRef]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[CrossRef]

Clement, T. S.

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).
[CrossRef]

A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).
[CrossRef]

S. A. Diddams, H. K. Eaton, A. A. Zozulya, and T. S. Clement, “Amplitude and phase measurements of femtosecond pulse splitting in nonlinear dispersive media,” Opt. Lett. 23, 379–381 (1998).
[CrossRef]

Couairon, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

Diddams, S. A.

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).
[CrossRef]

S. A. Diddams, H. K. Eaton, A. A. Zozulya, and T. S. Clement, “Amplitude and phase measurements of femtosecond pulse splitting in nonlinear dispersive media,” Opt. Lett. 23, 379–381 (1998).
[CrossRef]

A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).
[CrossRef]

Eaton, H. K.

Fibich, G.

N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: a nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
[CrossRef]

G. Fibich, N. Gavish, and X. Wang, “Singular ring solutions of critical and supercritical nonlinear Schrödinger equations,” Physica D 231, 55–86 (2007).
[CrossRef]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian beams,” Opt. Express 14, 5468–5475 (2006).
[CrossRef] [PubMed]

G. Fibich, V. M. Malkin, and G. C. Papanicolaou, “Beam self-focusing in the presence of a small normal time dispersion,” Phys. Rev. A 52, 4218–4228 (1995).
[CrossRef] [PubMed]

Franco, M.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

Gaeta, A. L.

N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: a nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
[CrossRef]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian beams,” Opt. Express 14, 5468–5475 (2006).
[CrossRef] [PubMed]

K. D. Moll and A. L. Gaeta, “Role of dispersion in multiple-collapse dynamics,” Opt. Lett. 29, 995–997 (2004).
[CrossRef] [PubMed]

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000).
[CrossRef] [PubMed]

J. K. Ranka, A. L. Gaeta, A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, “Autocorrelation measurement of 6-fs pulses based on the two-photon-induced photocurrent in a GaAsP photodiode,” Opt. Lett. 22, 1344–1346 (1997).
[CrossRef]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[CrossRef] [PubMed]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[CrossRef]

Gavish, N.

N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: a nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
[CrossRef]

G. Fibich, N. Gavish, and X. Wang, “Singular ring solutions of critical and supercritical nonlinear Schrödinger equations,” Physica D 231, 55–86 (2007).
[CrossRef]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian beams,” Opt. Express 14, 5468–5475 (2006).
[CrossRef] [PubMed]

Grow, T. D.

Heritage, J. P.

Ishaaya, A. A.

Kirschner, E. M.

Li, R.

J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006).
[CrossRef]

Litvak, A. G.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, “Multiple fractionation of wave structure in a nonlinear medium,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 13–17 (1986).

Liu, J.

J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006).
[CrossRef]

Malkin, V. M.

G. Fibich, V. M. Malkin, and G. C. Papanicolaou, “Beam self-focusing in the presence of a small normal time dispersion,” Phys. Rev. A 52, 4218–4228 (1995).
[CrossRef] [PubMed]

Moll, K. D.

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

Papanicolaou, G. C.

G. Fibich, V. M. Malkin, and G. C. Papanicolaou, “Beam self-focusing in the presence of a small normal time dispersion,” Phys. Rev. A 52, 4218–4228 (1995).
[CrossRef] [PubMed]

Petrova, T. A.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, “Multiple fractionation of wave structure in a nonlinear medium,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 13–17 (1986).

Piskunova, L. V.

S. N. Vlasov, L. V. Piskunova, and V. I. Talanov, “Three-dimensional wave collapse in the nonlinear Schrödinger equation model,” Zh. Eksp. Teor. Fiz. 95, 1945–1950 (1989).

Prade, B.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

Pshenichnikov, M. S.

Ranka, J. K.

Rothenberg, J. E.

Schirmer, R. W.

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[CrossRef] [PubMed]

Sergeev, A. M.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, “Multiple fractionation of wave structure in a nonlinear medium,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 13–17 (1986).

Skupin, S.

S. Skupin and L. Bergé, “Self-guiding of femtosecond light pulses in condensed media: Plasma generation versus chromatic dispersion,” Physica D 220, 14–30 (2006).
[CrossRef]

Sudrie, L.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

Talanov, V. I.

S. N. Vlasov, L. V. Piskunova, and V. I. Talanov, “Three-dimensional wave collapse in the nonlinear Schrödinger equation model,” Zh. Eksp. Teor. Fiz. 95, 1945–1950 (1989).

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[CrossRef]

Trippenbach, M.

M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791–4803 (1998).
[CrossRef]

Tzortzakis, S.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

Van Engen, A. G.

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).
[CrossRef]

Vlasov, S. N.

S. N. Vlasov, L. V. Piskunova, and V. I. Talanov, “Three-dimensional wave collapse in the nonlinear Schrödinger equation model,” Zh. Eksp. Teor. Fiz. 95, 1945–1950 (1989).

Vuong, L. T.

N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: a nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
[CrossRef]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian beams,” Opt. Express 14, 5468–5475 (2006).
[CrossRef] [PubMed]

Wang, X.

G. Fibich, N. Gavish, and X. Wang, “Singular ring solutions of critical and supercritical nonlinear Schrödinger equations,” Physica D 231, 55–86 (2007).
[CrossRef]

Weiner, A. M.

Wiersma, D. A.

Xu, Z.

J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006).
[CrossRef]

Yunakovskii, A. D.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, “Multiple fractionation of wave structure in a nonlinear medium,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 13–17 (1986).

Zharova, N. A.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, “Multiple fractionation of wave structure in a nonlinear medium,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 13–17 (1986).

Zozulya, A. A.

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).
[CrossRef]

S. A. Diddams, H. K. Eaton, A. A. Zozulya, and T. S. Clement, “Amplitude and phase measurements of femtosecond pulse splitting in nonlinear dispersive media,” Opt. Lett. 23, 379–381 (1998).
[CrossRef]

A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rep.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

Phys. Rev. A

G. Fibich, V. M. Malkin, and G. C. Papanicolaou, “Beam self-focusing in the presence of a small normal time dispersion,” Phys. Rev. A 52, 4218–4228 (1995).
[CrossRef] [PubMed]

M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791–4803 (1998).
[CrossRef]

A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).
[CrossRef]

N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: a nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
[CrossRef]

J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006).
[CrossRef]

Phys. Rev. Lett.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-guided propagation of ultrashort IR laser pulses in fused silica,” Phys. Rev. Lett. 87, 213902 (2001).
[CrossRef] [PubMed]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[CrossRef] [PubMed]

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).
[CrossRef]

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000).
[CrossRef] [PubMed]

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[CrossRef]

Physica D

S. Skupin and L. Bergé, “Self-guiding of femtosecond light pulses in condensed media: Plasma generation versus chromatic dispersion,” Physica D 220, 14–30 (2006).
[CrossRef]

G. Fibich, N. Gavish, and X. Wang, “Singular ring solutions of critical and supercritical nonlinear Schrödinger equations,” Physica D 231, 55–86 (2007).
[CrossRef]

Pis’ma Zh. Eksp. Teor. Fiz.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, “Multiple fractionation of wave structure in a nonlinear medium,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 13–17 (1986).

Zh. Eksp. Teor. Fiz.

S. N. Vlasov, L. V. Piskunova, and V. I. Talanov, “Three-dimensional wave collapse in the nonlinear Schrödinger equation model,” Zh. Eksp. Teor. Fiz. 95, 1945–1950 (1989).

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Figures (4)

Fig. 1
Fig. 1

Comparison of simulation results for Gaussian temporal profile (top) and super-Gaussian temporal profile (bottom), for input power of 2Pcr [(a) and (c)], 3Pcr [(b) and (d)], wavelength of 1550 nm, and β 2 of −279 fs2/cm. The input spatial profiles for all simulations are Gaussian. The spatio-temporal profiles are taken from the propagation point at which the beam is collapsing and before the intensity becomes sufficiently high that higher order effects change the dynamics.

Fig. 2
Fig. 2

Comparison of simulation results for a super-Gaussian temporal profile. The top (a) is the on-axis temporal profile found by directly integrating the NLSE in the anomalous (a) with input power 3Pcr , wavelength of 1550 nm, and β 2 of −279 fs2/cm. The bottom (b) is found using the 1-D building block of the NGO method. Although the profiles are slightly diffrerent, the peaks of the split pulses occur at ±0.2 for both direct integration and the NGO method.

Fig. 3
Fig. 3

Autocorrelation traces after propagation through 30 mm of fused silica at a wavelength of 1510 nm. The top plot (a) is for a temporal Gaussian input profile with peak power increasing from bottom to top (P = 15.7 MW, 24.7 MW, 33.7 MW, 41.5 MW, 49.4 MW, 62.8 MW). The lower plot (b) is for a temporal super-Gaussian input profile with peak power increasing from bottom to top (P = 11.2 MW, 14.6 MW, 18.0 MW, 21.8 MW, 26.9 MW). For the super-Gaussian case the pulse-splitting is pronounced as the power is increased.

Fig. 4
Fig. 4

Pulse autocorrelation traces after propagation through 30-mm of fused-silica at wavelength of 1275 nm. The top plot (a) is for a temporal Gaussian input profile with power increasing from bottom to top (P = 33.8 MW, 50.7 MW, 67.6 MW, 84.5 MW). The lower plot (b) is for a temporal super-Gaussian input profile with power increasing from bottom to top (P = 19.7 MW, 29.6 MW, 45.1 MW). Pulse-splitting does not occur in either case.

Equations (3)

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A ζ = i 4 ( 2 η 2 + 2 ξ 2 ) A i sgn ( β 2 ) L d f 2 L d s 2 A τ 2 + i L d f L n l | A | 2 A ,
d T ( z ) d z = 2 z d d T | ψ 0 ( T ) | 2 ,
d C ( z ) d z = C [ T ( z ) ] z d 2 d T 2 | ψ 0 ( T ) | 2 ,

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