Abstract

The field of optical filament formation from initial ultrashort laser pulses in bulk dielectric media has now reached a high state of maturity, and has been studied in all three phases of matter, including long distance propagation in air, also termed light string propagation, water, and glass. From the earliest studies of light string propagation in air it was observed that conical emission, namely colored light emission off-axis from the filament, was a byproduct that accompanied the filamentation process.Since then several other byproducts accompanying optical filamentation have been studied, namely, white light or supercontinuum (SC) generation, third-harmonic (TH) generation, and X- and O-waves. Our goal in this paper is to review the theory and simulation of the byproducts accompanying optical filamentation, and to show that a unified approach is possible. Employing the angularly resolved spectrum, or K - Ω spectrum, a notion that has been used to great effect in the area of nonlinear conical waves, we demonstrate that a unified approach to the byproducts accompanying optical filamentation can be achieved using the twin notions of the Effective Three-Wave-Mixing (ETWM) picture of wave-mixing in the presence of filaments, which determines the locus of phase-matched wave generation in the angularly resolved spectrum, and the first-Born approximation to determine the profile of the angularly resolved spectrum. We summarize results of previous works and show that unlike the essentially non-perturbative core of the filament, several byproducts of filamentation can be treated as perturbative effects that have negligible feed-back effects on the filament itself. This should be of great utility for future studies of optimization of the yield of a given byproduct.

© 2008 Optical Society of America

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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. E. Garmire, R. Y. Chiao, and C. H. Townes, "Dynamics and characteristics of the self-trapping of intense light beams," Phys. Rev. Lett. 16, 347-349 (1966).
    [CrossRef]
  3. P. L. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1008 (1965).
    [CrossRef]
  4. P. Lallemand and N. Bloembergen, "Self-focusing of laser beams and stimulated Raman gain in liquids," Phys. Rev. Lett. 15, 1010-1012 (1965).
    [CrossRef]
  5. Y. R. Shen and Y. J. Shaham, "Beam deterioration and stimulated Raman effect," Phys. Rev. Lett. 15, 1008-1010 (1965).
    [CrossRef]
  6. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, "Self-channeling of high-peak-power femtosecond laser pulses in air," Opt. Lett. 20, 73-75 (1995).
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  7. L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).
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  11. A. L. Gaeta, "Catastrophic collapse of ultrashort pulses," Phys. Rev. Lett. 84, 3582-3585 (2000).
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  12. N. Akozbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, "Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses," Phys. Rev. Lett. 89, 143901-4 (2002).
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  13. S. Tzortzakis, G. Mechain, G. Patalano, Y. B. Andre, B. Prade, M. Franco, A. Mysyrowicz, J. M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, "Coherent subterahertz radiation from femtosecond infrared filaments in air," Opt. Lett. 27, 1944-1946 (2002).
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  14. C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon. and V. T. Tikhonchuk, " Conical forward THz emission from femtosecond-laser-beam filamentation in air, " Phys. Rev. Lett. 98, 235002-4 (2007).
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  15. P. DiTrapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904-7 (2003).
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  17. D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. DiTrapani, "Conical emission, pulse splitting, and X-Wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901-4 (2006).
    [CrossRef] [PubMed]
  18. M. A. Porras, A. Parola, and P. DiTrapani, "Nonlinear unbalanced O-waves: nonsolitary, conical light bullets in nonlinear dissipative media," J. Opt. Soc. Am. B 22, 1406-1413 (2005).
    [CrossRef]
  19. M. A. Porras, A. Dubietis, E. Kucinskas, F. Bragheri, V. Degiorgio, A. Couairon, D. Faccio, and P. DiTrapani, "From X- to O-shaped spatiotemporal spectra of light filaments in water," Opt. Lett. 30, 3398-3400 (2005).
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  20. A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Physics Reports 441, 47-189 (2007).
    [CrossRef]
  21. J. Kasparian, and J.-P. Wolf, "Physics and applications of atmospheric nonlinear optics and filamentation," Opt. Express 16, 466-493 (2008).
    [CrossRef] [PubMed]
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  23. S. N. Vlasov, V. A. Petrishschev, and V. I. Talanov, "Averaged description of wave beams in linear and nonlinear media (the method of moments)," Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofyzika 14, 1353-1363 (1971) (in Russian).
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    [CrossRef] [PubMed]
  27. G. G. Luther, A. C. Newell, and J. V. Moloney, "The effects of normal dispersion on collapse events," Physica D 74, 59-74 (1994).
    [CrossRef]
  28. M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, " Light-filament dynamics and the spatiotemporal instability of the Townes profile, " Phys. Rev. A 76, 011803-4 (2007).
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  29. D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. DiTrapani, "Near- and far-field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601-4 (2005).
    [CrossRef]
  30. M. Kolesik, E. M. Wright, and J. V. Moloney, "Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media," Opt. Express 13, 10729-10741 (2005).
    [CrossRef] [PubMed]
  31. M. Kolesik, E. M. Wright, and J. V. Moloney, "Supercontinuum and third-harmonic generation accompanying optical filamentation as first-order scattering processes," Opt. Lett. 32, 2816-2818 (2007).
    [CrossRef] [PubMed]
  32. M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional optical pulse propagation equation," Phys. Rev. Lett. 89, 28392-5 (2002).
    [CrossRef]
  33. M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604-14 (2004).
    [CrossRef]
  34. A. Couairon and L. Berge, "Modeling the filamentation of the ultra-short pulses in ionizing media," Phys. Plasmas 7, 193-209 (2000).
    [CrossRef]
  35. L. Berge and A. Couairon, "Nonlinear propagation of self-guided ultra-short pulses in ionized gases," Phys. Plasmas 7, 210-230 (2000).
    [CrossRef]
  36. F. Theberge, N. Akozbek, W. Liu, J. F. Gravel, and S. L. Chin, "Third harmonic beam profile generated in atmospheric air using femtosecond laser pulses," Opt. Commun. 245, 399-405 (2005).
    [CrossRef]
  37. L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, "Supercontinuum emission and enhanced self-guiding of infrared femtosecond filaments sustained by third-harmonic generation in air," Phys. Rev. E 71, 016602-14 (2005).
    [CrossRef]
  38. M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85, 531-538 (2006).
    [CrossRef]
  39. M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, "Theory and simulation of supercontinuum generation in transparent bulk media," Appl. Phys. B 77, 185-195 (2003).
    [CrossRef]
  40. M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, "Physical factors limiting the spectral extent and band gap dependence of supercontinuum generation," Phys. Rev. Lett. 91, 043905-4 (2003).
    [CrossRef] [PubMed]
  41. D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. DiTrapani, and A. Couairon, "Stimulated Raman X-waves in ultrashort optical pulse filamentation," Opt. Lett. 32, 184-186 (2007).
    [CrossRef]
  42. D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. DiTrapani, "Spatio-temporal reshaping and X-Wave dynamics in optical filaments," Opt. Express 15, 13077-95 (2007).
    [CrossRef] [PubMed]

2008 (1)

2007 (6)

D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. DiTrapani, and A. Couairon, "Stimulated Raman X-waves in ultrashort optical pulse filamentation," Opt. Lett. 32, 184-186 (2007).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Supercontinuum and third-harmonic generation accompanying optical filamentation as first-order scattering processes," Opt. Lett. 32, 2816-2818 (2007).
[CrossRef] [PubMed]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. DiTrapani, "Spatio-temporal reshaping and X-Wave dynamics in optical filaments," Opt. Express 15, 13077-95 (2007).
[CrossRef] [PubMed]

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon. and V. T. Tikhonchuk, " Conical forward THz emission from femtosecond-laser-beam filamentation in air, " Phys. Rev. Lett. 98, 235002-4 (2007).
[CrossRef] [PubMed]

A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Physics Reports 441, 47-189 (2007).
[CrossRef]

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, " Light-filament dynamics and the spatiotemporal instability of the Townes profile, " Phys. Rev. A 76, 011803-4 (2007).
[CrossRef]

2006 (2)

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85, 531-538 (2006).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. DiTrapani, "Conical emission, pulse splitting, and X-Wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901-4 (2006).
[CrossRef] [PubMed]

2005 (6)

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. DiTrapani, "Near- and far-field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601-4 (2005).
[CrossRef]

F. Theberge, N. Akozbek, W. Liu, J. F. Gravel, and S. L. Chin, "Third harmonic beam profile generated in atmospheric air using femtosecond laser pulses," Opt. Commun. 245, 399-405 (2005).
[CrossRef]

L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, "Supercontinuum emission and enhanced self-guiding of infrared femtosecond filaments sustained by third-harmonic generation in air," Phys. Rev. E 71, 016602-14 (2005).
[CrossRef]

M. A. Porras, A. Parola, and P. DiTrapani, "Nonlinear unbalanced O-waves: nonsolitary, conical light bullets in nonlinear dissipative media," J. Opt. Soc. Am. B 22, 1406-1413 (2005).
[CrossRef]

M. A. Porras, A. Dubietis, E. Kucinskas, F. Bragheri, V. Degiorgio, A. Couairon, D. Faccio, and P. DiTrapani, "From X- to O-shaped spatiotemporal spectra of light filaments in water," Opt. Lett. 30, 3398-3400 (2005).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media," Opt. Express 13, 10729-10741 (2005).
[CrossRef] [PubMed]

2004 (2)

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604-14 (2004).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Dynamic nonlinear X-Waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901-4 (2004).
[CrossRef] [PubMed]

2003 (4)

K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes profile," Phys. Rev. Lett. 90, 203902-5 (2003).
[CrossRef] [PubMed]

P. DiTrapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904-7 (2003).
[CrossRef]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, "Theory and simulation of supercontinuum generation in transparent bulk media," Appl. Phys. B 77, 185-195 (2003).
[CrossRef]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, "Physical factors limiting the spectral extent and band gap dependence of supercontinuum generation," Phys. Rev. Lett. 91, 043905-4 (2003).
[CrossRef] [PubMed]

2002 (3)

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional optical pulse propagation equation," Phys. Rev. Lett. 89, 28392-5 (2002).
[CrossRef]

N. Akozbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, "Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses," Phys. Rev. Lett. 89, 143901-4 (2002).
[CrossRef] [PubMed]

S. Tzortzakis, G. Mechain, G. Patalano, Y. B. Andre, B. Prade, M. Franco, A. Mysyrowicz, J. M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, "Coherent subterahertz radiation from femtosecond infrared filaments in air," Opt. Lett. 27, 1944-1946 (2002).
[CrossRef]

2000 (4)

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

A. Couairon and L. Berge, "Modeling the filamentation of the ultra-short pulses in ionizing media," Phys. Plasmas 7, 193-209 (2000).
[CrossRef]

L. Berge and A. Couairon, "Nonlinear propagation of self-guided ultra-short pulses in ionized gases," Phys. Plasmas 7, 210-230 (2000).
[CrossRef]

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. P. Wolf, Y. B. Andre, M. A. Franco, B. S. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Woste, "Infrared extension of the supercontinuum generated by femtosecond terrawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-99 (2000).
[CrossRef]

1998 (1)

1997 (2)

C. Sulem and P.-L. Sulem, "Focusing nonlinear Schrodinger equation and wave-packet collapse," Nonlinear Anal.-Theory Methods Appl. 30, 833-844 (1997).
[CrossRef]

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).

1996 (1)

1995 (1)

1994 (1)

G. G. Luther, A. C. Newell, and J. V. Moloney, "The effects of normal dispersion on collapse events," Physica D 74, 59-74 (1994).
[CrossRef]

1972 (1)

V. E. Zakharov and A. B. Shabat, "Exact theory of 2-dimensional self-focusing and one-dimensional selfmodulation of waves in nonlinear media," Sov. Phys. JETP 34, 62-69 (1972).

1971 (1)

S. N. Vlasov, V. A. Petrishschev, and V. I. Talanov, "Averaged description of wave beams in linear and nonlinear media (the method of moments)," Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofyzika 14, 1353-1363 (1971) (in Russian).

1966 (1)

E. Garmire, R. Y. Chiao, and C. H. Townes, "Dynamics and characteristics of the self-trapping of intense light beams," Phys. Rev. Lett. 16, 347-349 (1966).
[CrossRef]

1965 (3)

P. L. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1008 (1965).
[CrossRef]

P. Lallemand and N. Bloembergen, "Self-focusing of laser beams and stimulated Raman gain in liquids," Phys. Rev. Lett. 15, 1010-1012 (1965).
[CrossRef]

Y. R. Shen and Y. J. Shaham, "Beam deterioration and stimulated Raman effect," Phys. Rev. Lett. 15, 1008-1010 (1965).
[CrossRef]

1964 (1)

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

Akozbek, N.

F. Theberge, N. Akozbek, W. Liu, J. F. Gravel, and S. L. Chin, "Third harmonic beam profile generated in atmospheric air using femtosecond laser pulses," Opt. Commun. 245, 399-405 (2005).
[CrossRef]

N. Akozbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, "Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses," Phys. Rev. Lett. 89, 143901-4 (2002).
[CrossRef] [PubMed]

Andre, Y. B.

Averchi, A.

Beaudin, G.

Becker, A.

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85, 531-538 (2006).
[CrossRef]

N. Akozbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, "Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses," Phys. Rev. Lett. 89, 143901-4 (2002).
[CrossRef] [PubMed]

Berge, L.

L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, "Supercontinuum emission and enhanced self-guiding of infrared femtosecond filaments sustained by third-harmonic generation in air," Phys. Rev. E 71, 016602-14 (2005).
[CrossRef]

A. Couairon and L. Berge, "Modeling the filamentation of the ultra-short pulses in ionizing media," Phys. Plasmas 7, 193-209 (2000).
[CrossRef]

L. Berge and A. Couairon, "Nonlinear propagation of self-guided ultra-short pulses in ionized gases," Phys. Plasmas 7, 210-230 (2000).
[CrossRef]

Bloembergen, N.

P. Lallemand and N. Bloembergen, "Self-focusing of laser beams and stimulated Raman gain in liquids," Phys. Rev. Lett. 15, 1010-1012 (1965).
[CrossRef]

Bowden, C. M.

N. Akozbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, "Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses," Phys. Rev. Lett. 89, 143901-4 (2002).
[CrossRef] [PubMed]

Bragheri, F.

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. DiTrapani, "Conical emission, pulse splitting, and X-Wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901-4 (2006).
[CrossRef] [PubMed]

M. A. Porras, A. Dubietis, E. Kucinskas, F. Bragheri, V. Degiorgio, A. Couairon, D. Faccio, and P. DiTrapani, "From X- to O-shaped spatiotemporal spectra of light filaments in water," Opt. Lett. 30, 3398-3400 (2005).
[CrossRef]

Braun, A.

Chiao, R. Y.

E. Garmire, R. Y. Chiao, and C. H. Townes, "Dynamics and characteristics of the self-trapping of intense light beams," Phys. Rev. Lett. 16, 347-349 (1966).
[CrossRef]

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

Chin, S. L.

F. Theberge, N. Akozbek, W. Liu, J. F. Gravel, and S. L. Chin, "Third harmonic beam profile generated in atmospheric air using femtosecond laser pulses," Opt. Commun. 245, 399-405 (2005).
[CrossRef]

N. Akozbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, "Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses," Phys. Rev. Lett. 89, 143901-4 (2002).
[CrossRef] [PubMed]

Conti, C.

P. DiTrapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904-7 (2003).
[CrossRef]

Couairon, A.

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M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, " Light-filament dynamics and the spatiotemporal instability of the Townes profile, " Phys. Rev. A 76, 011803-4 (2007).
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C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon. and V. T. Tikhonchuk, " Conical forward THz emission from femtosecond-laser-beam filamentation in air, " Phys. Rev. Lett. 98, 235002-4 (2007).
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D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. DiTrapani, "Near- and far-field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601-4 (2005).
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M. A. Porras, A. Dubietis, E. Kucinskas, F. Bragheri, V. Degiorgio, A. Couairon, D. Faccio, and P. DiTrapani, "From X- to O-shaped spatiotemporal spectra of light filaments in water," Opt. Lett. 30, 3398-3400 (2005).
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M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, " Light-filament dynamics and the spatiotemporal instability of the Townes profile, " Phys. Rev. A 76, 011803-4 (2007).
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D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. DiTrapani, and A. Couairon, "Stimulated Raman X-waves in ultrashort optical pulse filamentation," Opt. Lett. 32, 184-186 (2007).
[CrossRef]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. DiTrapani, "Spatio-temporal reshaping and X-Wave dynamics in optical filaments," Opt. Express 15, 13077-95 (2007).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. DiTrapani, "Conical emission, pulse splitting, and X-Wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901-4 (2006).
[CrossRef] [PubMed]

M. A. Porras, A. Parola, and P. DiTrapani, "Nonlinear unbalanced O-waves: nonsolitary, conical light bullets in nonlinear dissipative media," J. Opt. Soc. Am. B 22, 1406-1413 (2005).
[CrossRef]

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. DiTrapani, "Near- and far-field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601-4 (2005).
[CrossRef]

M. A. Porras, A. Dubietis, E. Kucinskas, F. Bragheri, V. Degiorgio, A. Couairon, D. Faccio, and P. DiTrapani, "From X- to O-shaped spatiotemporal spectra of light filaments in water," Opt. Lett. 30, 3398-3400 (2005).
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P. DiTrapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904-7 (2003).
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Dubietis, A.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. DiTrapani, "Spatio-temporal reshaping and X-Wave dynamics in optical filaments," Opt. Express 15, 13077-95 (2007).
[CrossRef] [PubMed]

D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. DiTrapani, and A. Couairon, "Stimulated Raman X-waves in ultrashort optical pulse filamentation," Opt. Lett. 32, 184-186 (2007).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. DiTrapani, "Conical emission, pulse splitting, and X-Wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901-4 (2006).
[CrossRef] [PubMed]

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. DiTrapani, "Near- and far-field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601-4 (2005).
[CrossRef]

M. A. Porras, A. Dubietis, E. Kucinskas, F. Bragheri, V. Degiorgio, A. Couairon, D. Faccio, and P. DiTrapani, "From X- to O-shaped spatiotemporal spectra of light filaments in water," Opt. Lett. 30, 3398-3400 (2005).
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Faccio, D.

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, " Light-filament dynamics and the spatiotemporal instability of the Townes profile, " Phys. Rev. A 76, 011803-4 (2007).
[CrossRef]

D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. DiTrapani, and A. Couairon, "Stimulated Raman X-waves in ultrashort optical pulse filamentation," Opt. Lett. 32, 184-186 (2007).
[CrossRef]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. DiTrapani, "Spatio-temporal reshaping and X-Wave dynamics in optical filaments," Opt. Express 15, 13077-95 (2007).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. DiTrapani, "Conical emission, pulse splitting, and X-Wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901-4 (2006).
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D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. DiTrapani, "Near- and far-field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601-4 (2005).
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M. A. Porras, A. Dubietis, E. Kucinskas, F. Bragheri, V. Degiorgio, A. Couairon, D. Faccio, and P. DiTrapani, "From X- to O-shaped spatiotemporal spectra of light filaments in water," Opt. Lett. 30, 3398-3400 (2005).
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C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon. and V. T. Tikhonchuk, " Conical forward THz emission from femtosecond-laser-beam filamentation in air, " Phys. Rev. Lett. 98, 235002-4 (2007).
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K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes profile," Phys. Rev. Lett. 90, 203902-5 (2003).
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C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon. and V. T. Tikhonchuk, " Conical forward THz emission from femtosecond-laser-beam filamentation in air, " Phys. Rev. Lett. 98, 235002-4 (2007).
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P. DiTrapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904-7 (2003).
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M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, "Physical factors limiting the spectral extent and band gap dependence of supercontinuum generation," Phys. Rev. Lett. 91, 043905-4 (2003).
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M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, "Theory and simulation of supercontinuum generation in transparent bulk media," Appl. Phys. B 77, 185-195 (2003).
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D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. DiTrapani, "Spatio-temporal reshaping and X-Wave dynamics in optical filaments," Opt. Express 15, 13077-95 (2007).
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M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85, 531-538 (2006).
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M. Kolesik, E. M. Wright, and J. V. Moloney, "Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media," Opt. Express 13, 10729-10741 (2005).
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M. Kolesik, E. M. Wright, and J. V. Moloney, "Dynamic nonlinear X-Waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901-4 (2004).
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M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, "Theory and simulation of supercontinuum generation in transparent bulk media," Appl. Phys. B 77, 185-195 (2003).
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D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. DiTrapani, "Near- and far-field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601-4 (2005).
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Mejean, G.

L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, "Supercontinuum emission and enhanced self-guiding of infrared femtosecond filaments sustained by third-harmonic generation in air," Phys. Rev. E 71, 016602-14 (2005).
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K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes profile," Phys. Rev. Lett. 90, 203902-5 (2003).
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D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. DiTrapani, "Spatio-temporal reshaping and X-Wave dynamics in optical filaments," Opt. Express 15, 13077-95 (2007).
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M. Kolesik, E. M. Wright, and J. V. Moloney, "Supercontinuum and third-harmonic generation accompanying optical filamentation as first-order scattering processes," Opt. Lett. 32, 2816-2818 (2007).
[CrossRef] [PubMed]

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[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media," Opt. Express 13, 10729-10741 (2005).
[CrossRef] [PubMed]

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M. Kolesik, E. M. Wright, and J. V. Moloney, "Dynamic nonlinear X-Waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901-4 (2004).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, " Light-filament dynamics and the spatiotemporal instability of the Townes profile, " Phys. Rev. A 76, 011803-4 (2007).
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D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. DiTrapani, "Spatio-temporal reshaping and X-Wave dynamics in optical filaments," Opt. Express 15, 13077-95 (2007).
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D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. DiTrapani, and A. Couairon, "Stimulated Raman X-waves in ultrashort optical pulse filamentation," Opt. Lett. 32, 184-186 (2007).
[CrossRef]

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. DiTrapani, "Near- and far-field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601-4 (2005).
[CrossRef]

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[CrossRef]

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D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. DiTrapani, "Near- and far-field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601-4 (2005).
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M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, " Light-filament dynamics and the spatiotemporal instability of the Townes profile, " Phys. Rev. A 76, 011803-4 (2007).
[CrossRef]

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[CrossRef] [PubMed]

M. A. Porras, A. Parola, and P. DiTrapani, "Nonlinear unbalanced O-waves: nonsolitary, conical light bullets in nonlinear dissipative media," J. Opt. Soc. Am. B 22, 1406-1413 (2005).
[CrossRef]

M. A. Porras, A. Dubietis, E. Kucinskas, F. Bragheri, V. Degiorgio, A. Couairon, D. Faccio, and P. DiTrapani, "From X- to O-shaped spatiotemporal spectra of light filaments in water," Opt. Lett. 30, 3398-3400 (2005).
[CrossRef]

Prade, B.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon. and V. T. Tikhonchuk, " Conical forward THz emission from femtosecond-laser-beam filamentation in air, " Phys. Rev. Lett. 98, 235002-4 (2007).
[CrossRef] [PubMed]

S. Tzortzakis, G. Mechain, G. Patalano, Y. B. Andre, B. Prade, M. Franco, A. Mysyrowicz, J. M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, "Coherent subterahertz radiation from femtosecond infrared filaments in air," Opt. Lett. 27, 1944-1946 (2002).
[CrossRef]

Prade, B. S.

Rairoux, P.

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).

Rodriguez, M.

Ronneberger, F.

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).

Salin, F.

Salmon, E.

L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, "Supercontinuum emission and enhanced self-guiding of infrared femtosecond filaments sustained by third-harmonic generation in air," Phys. Rev. E 71, 016602-14 (2005).
[CrossRef]

Sauerbrey, R.

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. P. Wolf, Y. B. Andre, M. A. Franco, B. S. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Woste, "Infrared extension of the supercontinuum generated by femtosecond terrawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-99 (2000).
[CrossRef]

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).

Scalora, M.

N. Akozbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, "Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses," Phys. Rev. Lett. 89, 143901-4 (2002).
[CrossRef] [PubMed]

Schillinger, H.

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, "Exact theory of 2-dimensional self-focusing and one-dimensional selfmodulation of waves in nonlinear media," Sov. Phys. JETP 34, 62-69 (1972).

Shaham, Y. J.

Y. R. Shen and Y. J. Shaham, "Beam deterioration and stimulated Raman effect," Phys. Rev. Lett. 15, 1008-1010 (1965).
[CrossRef]

Shen, Y. R.

Y. R. Shen and Y. J. Shaham, "Beam deterioration and stimulated Raman effect," Phys. Rev. Lett. 15, 1008-1010 (1965).
[CrossRef]

Skupin, S.

L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, "Supercontinuum emission and enhanced self-guiding of infrared femtosecond filaments sustained by third-harmonic generation in air," Phys. Rev. E 71, 016602-14 (2005).
[CrossRef]

Squier, J.

Stein, B.

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).

Sulem, C.

C. Sulem and P.-L. Sulem, "Focusing nonlinear Schrodinger equation and wave-packet collapse," Nonlinear Anal.-Theory Methods Appl. 30, 833-844 (1997).
[CrossRef]

Sulem, P.-L.

C. Sulem and P.-L. Sulem, "Focusing nonlinear Schrodinger equation and wave-packet collapse," Nonlinear Anal.-Theory Methods Appl. 30, 833-844 (1997).
[CrossRef]

Talanov, V. I.

S. N. Vlasov, V. A. Petrishschev, and V. I. Talanov, "Averaged description of wave beams in linear and nonlinear media (the method of moments)," Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofyzika 14, 1353-1363 (1971) (in Russian).

Tamosauskas, G.

Theberge, F.

F. Theberge, N. Akozbek, W. Liu, J. F. Gravel, and S. L. Chin, "Third harmonic beam profile generated in atmospheric air using femtosecond laser pulses," Opt. Commun. 245, 399-405 (2005).
[CrossRef]

Tikhonchuk, V. T.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon. and V. T. Tikhonchuk, " Conical forward THz emission from femtosecond-laser-beam filamentation in air, " Phys. Rev. Lett. 98, 235002-4 (2007).
[CrossRef] [PubMed]

Townes, C. H.

E. Garmire, R. Y. Chiao, and C. H. Townes, "Dynamics and characteristics of the self-trapping of intense light beams," Phys. Rev. Lett. 16, 347-349 (1966).
[CrossRef]

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

Trillo, S.

P. DiTrapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904-7 (2003).
[CrossRef]

Trull, J.

P. DiTrapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904-7 (2003).
[CrossRef]

Tzortzakis, S.

Valiulis, G.

P. DiTrapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904-7 (2003).
[CrossRef]

Varanavicius, A.

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. DiTrapani, "Near- and far-field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601-4 (2005).
[CrossRef]

Vlasov, S. N.

S. N. Vlasov, V. A. Petrishschev, and V. I. Talanov, "Averaged description of wave beams in linear and nonlinear media (the method of moments)," Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofyzika 14, 1353-1363 (1971) (in Russian).

Wedekind, C.

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).

Werner, C.

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).

Wille, H.

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. P. Wolf, Y. B. Andre, M. A. Franco, B. S. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Woste, "Infrared extension of the supercontinuum generated by femtosecond terrawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-99 (2000).
[CrossRef]

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).

Wolf, J. P.

L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, "Supercontinuum emission and enhanced self-guiding of infrared femtosecond filaments sustained by third-harmonic generation in air," Phys. Rev. E 71, 016602-14 (2005).
[CrossRef]

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. P. Wolf, Y. B. Andre, M. A. Franco, B. S. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Woste, "Infrared extension of the supercontinuum generated by femtosecond terrawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-99 (2000).
[CrossRef]

Wolf, J.-P.

Woste, L.

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. P. Wolf, Y. B. Andre, M. A. Franco, B. S. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Woste, "Infrared extension of the supercontinuum generated by femtosecond terrawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-99 (2000).
[CrossRef]

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).

Wright, E. M.

M. Kolesik, E. M. Wright, and J. V. Moloney, "Supercontinuum and third-harmonic generation accompanying optical filamentation as first-order scattering processes," Opt. Lett. 32, 2816-2818 (2007).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85, 531-538 (2006).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media," Opt. Express 13, 10729-10741 (2005).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Dynamic nonlinear X-Waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901-4 (2004).
[CrossRef] [PubMed]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, "Physical factors limiting the spectral extent and band gap dependence of supercontinuum generation," Phys. Rev. Lett. 91, 043905-4 (2003).
[CrossRef] [PubMed]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, "Theory and simulation of supercontinuum generation in transparent bulk media," Appl. Phys. B 77, 185-195 (2003).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, "Dynamic spatial replenishment of femtosecond pulses propagating in air," Opt. Lett. 23, 382-384 (1998).
[CrossRef]

Yu, J.

L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, "Supercontinuum emission and enhanced self-guiding of infrared femtosecond filaments sustained by third-harmonic generation in air," Phys. Rev. E 71, 016602-14 (2005).
[CrossRef]

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. P. Wolf, Y. B. Andre, M. A. Franco, B. S. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Woste, "Infrared extension of the supercontinuum generated by femtosecond terrawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-99 (2000).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, "Exact theory of 2-dimensional self-focusing and one-dimensional selfmodulation of waves in nonlinear media," Sov. Phys. JETP 34, 62-69 (1972).

Appl. Phys. B (2)

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, "Simulation of third-harmonic and supercontinuum generation for femtosecond pulses in air," Appl. Phys. B 85, 531-538 (2006).
[CrossRef]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, "Theory and simulation of supercontinuum generation in transparent bulk media," Appl. Phys. B 77, 185-195 (2003).
[CrossRef]

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

Laser und Optoelectronik (1)

L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp." AT-Fachverlag, Stuttgart, Laser und Optoelectronik 29, 51-53 (1997).

Opt. Commun. (1)

F. Theberge, N. Akozbek, W. Liu, J. F. Gravel, and S. L. Chin, "Third harmonic beam profile generated in atmospheric air using femtosecond laser pulses," Opt. Commun. 245, 399-405 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (8)

D. Faccio, A. Averchi, A. Dubietis, P. Polesana, A. Piskarskas, P. DiTrapani, and A. Couairon, "Stimulated Raman X-waves in ultrashort optical pulse filamentation," Opt. Lett. 32, 184-186 (2007).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Supercontinuum and third-harmonic generation accompanying optical filamentation as first-order scattering processes," Opt. Lett. 32, 2816-2818 (2007).
[CrossRef] [PubMed]

M. A. Porras, A. Dubietis, E. Kucinskas, F. Bragheri, V. Degiorgio, A. Couairon, D. Faccio, and P. DiTrapani, "From X- to O-shaped spatiotemporal spectra of light filaments in water," Opt. Lett. 30, 3398-3400 (2005).
[CrossRef]

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, "Self-channeling of high-peak-power femtosecond laser pulses in air," Opt. Lett. 20, 73-75 (1995).
[CrossRef] [PubMed]

M. Mlejnek, E. M. Wright, and J. V. Moloney, "Dynamic spatial replenishment of femtosecond pulses propagating in air," Opt. Lett. 23, 382-384 (1998).
[CrossRef]

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, "Conical emission from self-guided femtosecond pulses in air," Opt. Lett. 21, 62-64 (1996).
[CrossRef] [PubMed]

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. P. Wolf, Y. B. Andre, M. A. Franco, B. S. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Woste, "Infrared extension of the supercontinuum generated by femtosecond terrawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-99 (2000).
[CrossRef]

S. Tzortzakis, G. Mechain, G. Patalano, Y. B. Andre, B. Prade, M. Franco, A. Mysyrowicz, J. M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, "Coherent subterahertz radiation from femtosecond infrared filaments in air," Opt. Lett. 27, 1944-1946 (2002).
[CrossRef]

Phys. Plasmas (2)

A. Couairon and L. Berge, "Modeling the filamentation of the ultra-short pulses in ionizing media," Phys. Plasmas 7, 193-209 (2000).
[CrossRef]

L. Berge and A. Couairon, "Nonlinear propagation of self-guided ultra-short pulses in ionized gases," Phys. Plasmas 7, 210-230 (2000).
[CrossRef]

Phys. Rev. A (1)

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, " Light-filament dynamics and the spatiotemporal instability of the Townes profile, " Phys. Rev. A 76, 011803-4 (2007).
[CrossRef]

Phys. Rev. E (3)

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. DiTrapani, "Near- and far-field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601-4 (2005).
[CrossRef]

L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, "Supercontinuum emission and enhanced self-guiding of infrared femtosecond filaments sustained by third-harmonic generation in air," Phys. Rev. E 71, 016602-14 (2005).
[CrossRef]

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604-14 (2004).
[CrossRef]

Phys. Rev. Lett. (14)

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, "Physical factors limiting the spectral extent and band gap dependence of supercontinuum generation," Phys. Rev. Lett. 91, 043905-4 (2003).
[CrossRef] [PubMed]

M. Kolesik, J. V. Moloney, and M. Mlejnek, "Unidirectional optical pulse propagation equation," Phys. Rev. Lett. 89, 28392-5 (2002).
[CrossRef]

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon. and V. T. Tikhonchuk, " Conical forward THz emission from femtosecond-laser-beam filamentation in air, " Phys. Rev. Lett. 98, 235002-4 (2007).
[CrossRef] [PubMed]

P. DiTrapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, "Spontaneously generated X-shaped light bullets," Phys. Rev. Lett. 91, 093904-7 (2003).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, "Dynamic nonlinear X-Waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901-4 (2004).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. DiTrapani, "Conical emission, pulse splitting, and X-Wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901-4 (2006).
[CrossRef] [PubMed]

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

N. Akozbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, "Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses," Phys. Rev. Lett. 89, 143901-4 (2002).
[CrossRef] [PubMed]

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

E. Garmire, R. Y. Chiao, and C. H. Townes, "Dynamics and characteristics of the self-trapping of intense light beams," Phys. Rev. Lett. 16, 347-349 (1966).
[CrossRef]

P. L. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1008 (1965).
[CrossRef]

P. Lallemand and N. Bloembergen, "Self-focusing of laser beams and stimulated Raman gain in liquids," Phys. Rev. Lett. 15, 1010-1012 (1965).
[CrossRef]

Y. R. Shen and Y. J. Shaham, "Beam deterioration and stimulated Raman effect," Phys. Rev. Lett. 15, 1008-1010 (1965).
[CrossRef]

K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes profile," Phys. Rev. Lett. 90, 203902-5 (2003).
[CrossRef] [PubMed]

Physica D (1)

G. G. Luther, A. C. Newell, and J. V. Moloney, "The effects of normal dispersion on collapse events," Physica D 74, 59-74 (1994).
[CrossRef]

Physics Reports (1)

A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Physics Reports 441, 47-189 (2007).
[CrossRef]

Radiofyzika (1)

S. N. Vlasov, V. A. Petrishschev, and V. I. Talanov, "Averaged description of wave beams in linear and nonlinear media (the method of moments)," Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofyzika 14, 1353-1363 (1971) (in Russian).

Sov. Phys. JETP (1)

V. E. Zakharov and A. B. Shabat, "Exact theory of 2-dimensional self-focusing and one-dimensional selfmodulation of waves in nonlinear media," Sov. Phys. JETP 34, 62-69 (1972).

Theory Methods Appl. (1)

C. Sulem and P.-L. Sulem, "Focusing nonlinear Schrodinger equation and wave-packet collapse," Nonlinear Anal.-Theory Methods Appl. 30, 833-844 (1997).
[CrossRef]

Other (1)

C. Sulem and P.-L. Sulem, The Nonlinear Schr¨odinger Equation: Self-focusing and wave collapse, (Springer Series on Applied Mathematical Sciences, 1999) Vol. 139.

Supplementary Material (1)

» Media 1: MPG (1530 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Femtosecond pulse’s self-similar collapse in water. On the left, the maximal amplitude of the pulse is shown as a function of the propagation distance in the water sample. The symbols show the simulated increase of amplitude as the collapse distance is approached. The line represents the analytic prediction of the self-similar collapsing solution in the pure NLS equation. The scaling plot on the right shows comparison of the Townes profile, i.e. of the expected transverse shape of the collapsing beam, with the simulation data obtained in the region indicated in the left panel. Different symbol colors correspond to different propagation distances. The fact that the scaled data collapses closely on the Townes profile corroborates the expectation that even in the non-idealized system, the collapse as predicted by the NLS equation still governs the evolution of the filament core.

Fig. 2.
Fig. 2.

Supercontinuum and third-harmonic generation in air. The right panel shows angle-integrated spectrum. The weak feature above the high-frequency background is due to third harmonic generation. The angularly resolved spectrum on the left reveals angular separation between the supercontinuum and third harmonic radiation parts of the spectrum.

Fig. 3.
Fig. 3.

Profiles of the intensity (left) and nonlinear modification of the local susceptibility (right) as functions of radius and time in the frame co-moving with the pulse. This is a typical picture shortly after pulse splitting that creates two daughter pulses that propagate with velocities somewhat larger (front) and smaller (back) than the group velocity of the original pulse. Both pulses leave strong signature in the nonlinear response. The dip in the susceptibility located between the peaks and behind the trailing peak is due to the generated plasma.

Fig. 4.
Fig. 4.

Angularly resolved spectrum generated in water by combination of two ultrashort pulses centered at 1100 (ω≈1.7×1015s-1) and 527 nm (ω≈3.7 ×1015s-1) wavelengths. The resulting spectrum spans both the region of anomalous and normal GVD. The anomalous regime is manifested through the oval-shaped core of the spectrum (so called O-wave) around ω≈1.7×1015s-1. The structure characteristic for the normal GVD regime is the X-wave “arm” (conical emission) originating at ω ≈2.5×1015s-1 and extending to wide angles and high frequencies. The narrow, weak, extended structures are due to four-wave mixing processes in which supercontinuum beats against either pump or seed.

Fig. 5.
Fig. 5.

Angularly resolved spectrum generated in water by combination of two ultrashortpulses centered at 1100 (ω≈1.7×1015s-1) and 527 nm (ω≈3.7×1015s-1) wavelengths. White lines mark loci of effective phase matching for three and four wave mixing processes described in the text. In the left panel, the top white line is given by Eq. (14) and represents scattering of the seed-pulse photon off the nonlinear response peak. The lower white line represents the process of pump-photon scattering on the nonlinear response peak according to Eq. (13). The right hand side panel shows phase matching loci corresponding to Eq. (18) (upper line) and Eq. (17) (lower line), respectively. Note that all the phase-matched loci are controlled by a single parameter, namely the propagation speed of the nonlinear response peak.

Fig. 6.
Fig. 6.

Log plot of the angularly resolved power spectrum |A(k, ω)|2 for SC generation in the normal GVD regime in water. Left panel: full simulation. Right panel: first Born approximation.

Fig. 7.
Fig. 7.

Log plot of the angular resolved power spectrum for SC and TH generation in air. Left panel: full simulation. Right panel: first Born approximation.

Fig. 8.
Fig. 8.

“Scattering potentials” for supercontinuum and third-harmonic generation. On the left, the on-axis E 2 profile of a pulse is shown shortly after pulse splitting. Its shape is essentially the shape of the scattering potential that enters the first-Born approximation formula. The scattering potential is decomposed into AC (right) and DC (middle) components that cause production of third-harmonic and supercontinuum spectral components, respectively.

Fig. 9.
Fig. 9.

Animation comparing evolution, with the propagation distance in the water sample,of the far-field spectrum (left) and its first-Born approximation (right) in a femtosecond pulse propagating in water. [Media 1]

Equations (20)

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ψ ( r , z ) = 1 z * z R ( r z * z ) exp ir 2 4 ( z * z )
Δ R R + R 3 = 0 , R ( 0 ) = 0 , R ( ) 0 .
E ( z , r , t ) = k , ω A ( z , k , ω ) e i ω t + i k · r + iK ( ω , k ) z ,
z A ( z , k , ω ) = i ω 2 μ 0 2 K ( ω , k ) e i [ ω t k . r K ( ω , k ) z ] P ( r , z , t ) d 2 r d t .
P = ε 0 Δ χ E
Δ χ = 2 n b n 2 [ ( 1 f ) E 2 + f 0 ( τ ) E 2 ( t τ ) d τ ] + ρ Δ χ e
A ( z , k , ω ) = dtd 2 rE ( z , r , t ) e + i ω t i k · r iK ( ω , k ) z .
S ( ω ) d 2 kA ( z , k , ω ) .
P ( z , r , t ) = Δ χ ( z , r , t ) E ( z , r , t ) Δ χ ( z , r , t ) exp [ i ω 0 t + iK ( ω 0 , 0 ) z ] .
Δ χ ( z , r , t ) p peaks Δ χ p ( z , r , t z ν P ) .
A ( k , ω ) ω c p peaks d 2 r d τ d z × e i [ ( ω ω 0 ) τ k · r ( K ( ω , k ) K ( ω 0 , 0 ) ) z + ( ω ω 0 ) z ν p ] Δ χ p ( z , r , τ ) .
K ( ω , k ) + K ( ω 0 , 0 ) + ω ω 0 ν P = 0
K ( ω , k ) + K ( ω 0 , 0 ) + ω ω 0 ν P = 0 ,
K ( ω , k ) + K ( ω S , 0 ) + ω ω S ν P = 0 .
K ( ω , k ) 2 K ( ω 0 , 0 ) K ( ω X , k X ) , ω 2 ω 0 ω X
K ( ω X , k X ) = K ( ω S , 0 ) ω S ω X ν P
K ( ω , k ) 2 K ( ω 0 , 0 ) + K ( ω S , 0 ) ω S 2 ω 0 + ω ν P = 0
K ( ω , k ) 2 K ( ω S , 0 ) + K ( ω 0 , 0 ) ω 0 2 ω S + ω ν P = 0
P ( z , r , t ) Δ χ ( z , r , t ) exp [ i ω 0 t + iK ( ω 0 , 0 ) z ] .
A ( k , ω ) ω c d 2 r d t d z × e i [ ( ω ω 0 ) t k · r ( K ( ω , k ) K ( ω 0 , 0 ) ) z ] Δ χ ( z , r , t ) .

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