Abstract

By directly solving Maxwell’s equations including higher-order gas polarization and by using a semi-analytical method for pulse propagation, we study the generation of plasma by high-irradiance laser pulses propagating in a neutral gas and determine the effect of initial focusing on the blueshift of the laser pulse. By varying the initial focusing length, we find that longer than a specific focusing length the blueshift is nearly fixed and shorter than the specific focusing length that the shift changes with the initial focusing length.

© 2009 Optical Society of America

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  2. A. M. A. Couairon, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47-189 (2007).
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  3. J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
    [CrossRef]
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    [CrossRef]
  6. Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
    [CrossRef]
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  19. G. Fibich and B. Ilan, “Self-focusing of elliptic beams: an example of the failure of the aberrationless approximation,” J. Opt. Soc. Am. B 17, 1749-1758 (2000).
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  21. N. C. Kothari and T. Kobayashi, “Growth rate and diameter of filaments in self-focusing media,” Phys. Rev. Lett. 50, 160-163 (1983).
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  22. S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212-2215 (1989).
    [CrossRef] [PubMed]
  23. A. Javan and P. L. Kelley, “Possibility of self-focusing due to intensity-dependent anomalous dispersion,” IEEE J. Quantum Electron. QE-2, 470-473 (1966).
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    [CrossRef]
  26. D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, “Angular and chromatic dispersion in Kerr-driven conical emission,” Opt. Commun. 265, 672-677 (2006).
    [CrossRef]
  27. D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, “Spatio-temporal reshaping and x wave dynamics in optical filaments,” Opt. Express 15, 13077-13095 (2007).
    [CrossRef] [PubMed]
  28. S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46, 1084-1090 (1992).
    [CrossRef] [PubMed]
  29. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307-1314 (1965).
  30. H. Press, T. Teukolsky, T. Vetterling, and P. Flannery, Numerical Recipes (Cambridge University Press, 1992).
  31. E. Esarey, G. Joyce, and P. Sprangle, “Frequency up-shifting of laser pulses by copropagating ionization fronts,” Phys. Rev. A 44, 3908-3911 (1991).
    [CrossRef] [PubMed]
  32. K. Nagashima, J. Koga, and M. Kando, “Numerical study of laser wake field generated by two colliding laser beams,” Phys. Rev. E 64, 066403-1-066403-4 (2001).
    [CrossRef]
  33. W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, “Intensity clamping of a femtosecond laser pulse in condensed matter,” Opt. Commun. 202, 189-197 (2002).
    [CrossRef]

2007

2006

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, “Angular and chromatic dispersion in Kerr-driven conical emission,” Opt. Commun. 265, 672-677 (2006).
[CrossRef]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406-1-036406-7 (2006).
[CrossRef]

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

2004

J. Koga, “Observation of supercontinuum generation in the direct simulation of an intense laser pulse propagating in a neutral gas,” Phys. Rev. E 70, 056404-1-056404-5 (2004).
[CrossRef]

2003

A. L. Gaeta, “Collapsing light really shines,” Science 301, 54-55 (2003).
[CrossRef] [PubMed]

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behavior of a focused femtosecond laser pulse in fused silica,” J. Opt. A 5, 102-107 (2003).
[CrossRef]

A. Couairon, “Light bullets from femtosecond filamentation,” Eur. Phys. J. D 27, 159-167 (2003).
[CrossRef]

2002

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, “Intensity clamping of a femtosecond laser pulse in condensed matter,” Opt. Commun. 202, 189-197 (2002).
[CrossRef]

2001

K. Nagashima, J. Koga, and M. Kando, “Numerical study of laser wake field generated by two colliding laser beams,” Phys. Rev. E 64, 066403-1-066403-4 (2001).
[CrossRef]

2000

G. Fibich and B. Ilan, “Self-focusing of elliptic beams: an example of the failure of the aberrationless approximation,” J. Opt. Soc. Am. B 17, 1749-1758 (2000).
[CrossRef]

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540-4549 (2000).
[CrossRef]

J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
[CrossRef]

1999

1998

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611-1613 (1998).
[CrossRef]

1996

P. Sprangle, E. Esarey, and J. Krall, “Self-guiding and stability of intense optical beams in gases undergoing ionization,” Phys. Rev. E 54, 4211-4232 (1996).
[CrossRef]

1995

1992

S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46, 1084-1090 (1992).
[CrossRef] [PubMed]

1991

E. Esarey, G. Joyce, and P. Sprangle, “Frequency up-shifting of laser pulses by copropagating ionization fronts,” Phys. Rev. A 44, 3908-3911 (1991).
[CrossRef] [PubMed]

J. H. Eberly, J. Javanainen, and K. Rzażwski, “Above-threshold ionization,” Phys. Rep. 204, 331-383 (1991).
[CrossRef]

1989

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212-2215 (1989).
[CrossRef] [PubMed]

1983

N. C. Kothari and T. Kobayashi, “Growth rate and diameter of filaments in self-focusing media,” Phys. Rev. Lett. 50, 160-163 (1983).
[CrossRef]

1975

E. L. Lindman, “'Free-space' boundary conditions for the time-dependent wave equation,” J. Comput. Phys. 18, 66-78 (1975).
[CrossRef]

J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35-l10 (1975).
[CrossRef]

1968

W. G. Wagner, H. A. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beams in the paraxial ray approximation,” Phys. Rev. 175, 256-266 (1968).
[CrossRef]

1966

A. Javan and P. L. Kelley, “Possibility of self-focusing due to intensity-dependent anomalous dispersion,” IEEE J. Quantum Electron. QE-2, 470-473 (1966).
[CrossRef]

1965

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307-1314 (1965).

Agostini, P.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611-1613 (1998).
[CrossRef]

Aközbek, N.

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, “Intensity clamping of a femtosecond laser pulse in condensed matter,” Opt. Commun. 202, 189-197 (2002).
[CrossRef]

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540-4549 (2000).
[CrossRef]

Augst, S.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212-2215 (1989).
[CrossRef] [PubMed]

Averchi, A.

Becker, A.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406-1-036406-7 (2006).
[CrossRef]

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, “Intensity clamping of a femtosecond laser pulse in condensed matter,” Opt. Commun. 202, 189-197 (2002).
[CrossRef]

Bowden, C. M.

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, “Intensity clamping of a femtosecond laser pulse in condensed matter,” Opt. Commun. 202, 189-197 (2002).
[CrossRef]

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540-4549 (2000).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Braun, A.

Breger, P.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611-1613 (1998).
[CrossRef]

Bulanov, S. V.

J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
[CrossRef]

Burnett, K.

S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46, 1084-1090 (1992).
[CrossRef] [PubMed]

Chin, S. L.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406-1-036406-7 (2006).
[CrossRef]

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, “Intensity clamping of a femtosecond laser pulse in condensed matter,” Opt. Commun. 202, 189-197 (2002).
[CrossRef]

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540-4549 (2000).
[CrossRef]

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212-2215 (1989).
[CrossRef] [PubMed]

Chiron, A.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611-1613 (1998).
[CrossRef]

Couairon, A.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, “Spatio-temporal reshaping and x wave dynamics in optical filaments,” Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, “Angular and chromatic dispersion in Kerr-driven conical emission,” Opt. Commun. 265, 672-677 (2006).
[CrossRef]

A. Couairon, “Light bullets from femtosecond filamentation,” Eur. Phys. J. D 27, 159-167 (2003).
[CrossRef]

Couairon, A. M. A.

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

Dewa, H.

J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
[CrossRef]

Di Trapani, P.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, “Spatio-temporal reshaping and x wave dynamics in optical filaments,” Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, “Angular and chromatic dispersion in Kerr-driven conical emission,” Opt. Commun. 265, 672-677 (2006).
[CrossRef]

Du, D.

Dubietis, A.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, “Spatio-temporal reshaping and x wave dynamics in optical filaments,” Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, “Angular and chromatic dispersion in Kerr-driven conical emission,” Opt. Commun. 265, 672-677 (2006).
[CrossRef]

Eberly, J. H.

J. H. Eberly, J. Javanainen, and K. Rzażwski, “Above-threshold ionization,” Phys. Rep. 204, 331-383 (1991).
[CrossRef]

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212-2215 (1989).
[CrossRef] [PubMed]

Esarey, E.

P. Sprangle, E. Esarey, and J. Krall, “Self-guiding and stability of intense optical beams in gases undergoing ionization,” Phys. Rev. E 54, 4211-4232 (1996).
[CrossRef]

E. Esarey, G. Joyce, and P. Sprangle, “Frequency up-shifting of laser pulses by copropagating ionization fronts,” Phys. Rev. A 44, 3908-3911 (1991).
[CrossRef] [PubMed]

Faccio, D.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, “Spatio-temporal reshaping and x wave dynamics in optical filaments,” Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, “Angular and chromatic dispersion in Kerr-driven conical emission,” Opt. Commun. 265, 672-677 (2006).
[CrossRef]

Fibich, G.

Flannery, P.

H. Press, T. Teukolsky, T. Vetterling, and P. Flannery, Numerical Recipes (Cambridge University Press, 1992).

Gaeta, A. L.

A. L. Gaeta, “Collapsing light really shines,” Science 301, 54-55 (2003).
[CrossRef] [PubMed]

Gong, Q.

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behavior of a focused femtosecond laser pulse in fused silica,” J. Opt. A 5, 102-107 (2003).
[CrossRef]

Hao, Z.

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

Haus, H. A.

W. G. Wagner, H. A. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beams in the paraxial ray approximation,” Phys. Rev. 175, 256-266 (1968).
[CrossRef]

Ilan, B.

Javan, A.

A. Javan and P. L. Kelley, “Possibility of self-focusing due to intensity-dependent anomalous dispersion,” IEEE J. Quantum Electron. QE-2, 470-473 (1966).
[CrossRef]

Javanainen, J.

J. H. Eberly, J. Javanainen, and K. Rzażwski, “Above-threshold ionization,” Phys. Rep. 204, 331-383 (1991).
[CrossRef]

Jiang, H.

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behavior of a focused femtosecond laser pulse in fused silica,” J. Opt. A 5, 102-107 (2003).
[CrossRef]

Jin, Z.

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

Joyce, G.

E. Esarey, G. Joyce, and P. Sprangle, “Frequency up-shifting of laser pulses by copropagating ionization fronts,” Phys. Rev. A 44, 3908-3911 (1991).
[CrossRef] [PubMed]

Kando, M.

K. Nagashima, J. Koga, and M. Kando, “Numerical study of laser wake field generated by two colliding laser beams,” Phys. Rev. E 64, 066403-1-066403-4 (2001).
[CrossRef]

J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307-1314 (1965).

Kelley, P. L.

A. Javan and P. L. Kelley, “Possibility of self-focusing due to intensity-dependent anomalous dispersion,” IEEE J. Quantum Electron. QE-2, 470-473 (1966).
[CrossRef]

Kobayashi, T.

N. C. Kothari and T. Kobayashi, “Growth rate and diameter of filaments in self-focusing media,” Phys. Rev. Lett. 50, 160-163 (1983).
[CrossRef]

Koga, J.

J. Koga, “Observation of supercontinuum generation in the direct simulation of an intense laser pulse propagating in a neutral gas,” Phys. Rev. E 70, 056404-1-056404-5 (2004).
[CrossRef]

K. Nagashima, J. Koga, and M. Kando, “Numerical study of laser wake field generated by two colliding laser beams,” Phys. Rev. E 64, 066403-1-066403-4 (2001).
[CrossRef]

J. Koga, “Simulation model for the effects of nonlinear polarization on the propagation of intense pulse lasers,” Opt. Lett. 24, 408-410 (1999).
[CrossRef]

Koga, J. K.

J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
[CrossRef]

Kolesik, M.

Korn, G.

Kotaki, H.

J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
[CrossRef]

Kothari, N. C.

N. C. Kothari and T. Kobayashi, “Growth rate and diameter of filaments in self-focusing media,” Phys. Rev. Lett. 50, 160-163 (1983).
[CrossRef]

Krall, J.

P. Sprangle, E. Esarey, and J. Krall, “Self-guiding and stability of intense optical beams in gases undergoing ionization,” Phys. Rev. E 54, 4211-4232 (1996).
[CrossRef]

Kucinskas, E.

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, “Angular and chromatic dispersion in Kerr-driven conical emission,” Opt. Commun. 265, 672-677 (2006).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Butterworth-Heinemann, 1997).

Lange, H. R.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611-1613 (1998).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Butterworth-Heinemann, 1997).

Lindman, E. L.

E. L. Lindman, “'Free-space' boundary conditions for the time-dependent wave equation,” J. Comput. Phys. 18, 66-78 (1975).
[CrossRef]

Liu, W.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406-1-036406-7 (2006).
[CrossRef]

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, “Intensity clamping of a femtosecond laser pulse in condensed matter,” Opt. Commun. 202, 189-197 (2002).
[CrossRef]

Liu, X.

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]

X. Liu and D. Umstadter, “Self-focusing of intense subpicosecond laser pulses in a low pressure gas,” in Vol. 17 of OSA Proceedings on Shortwavelength V, P.B.Corkum and M.D.Perry, eds. (Optical Society of America, 1993), pp. 45-49.

Liu, Y.

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

Lu, X.

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

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J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35-l10 (1975).
[CrossRef]

W. G. Wagner, H. A. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beams in the paraxial ray approximation,” Phys. Rev. 175, 256-266 (1968).
[CrossRef]

Meyerhofer, D. D.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212-2215 (1989).
[CrossRef] [PubMed]

Moloney, J. V.

Mourou, G.

Mysyrowicz, A.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611-1613 (1998).
[CrossRef]

Nagashima, K.

K. Nagashima, J. Koga, and M. Kando, “Numerical study of laser wake field generated by two colliding laser beams,” Phys. Rev. E 64, 066403-1-066403-4 (2001).
[CrossRef]

Nakajima, K.

J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
[CrossRef]

Naumova, N.

J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
[CrossRef]

Petit, S.

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, “Intensity clamping of a femtosecond laser pulse in condensed matter,” Opt. Commun. 202, 189-197 (2002).
[CrossRef]

Piskarskas, A.

Polesana, P.

Porras, M. A.

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, “Angular and chromatic dispersion in Kerr-driven conical emission,” Opt. Commun. 265, 672-677 (2006).
[CrossRef]

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H. Press, T. Teukolsky, T. Vetterling, and P. Flannery, Numerical Recipes (Cambridge University Press, 1992).

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S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46, 1084-1090 (1992).
[CrossRef] [PubMed]

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H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611-1613 (1998).
[CrossRef]

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[CrossRef]

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Y. R. Shen, The Principle of Nonlinear Optics (Wiley-Interscience, 1984).

Simard, P. T.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406-1-036406-7 (2006).
[CrossRef]

Sprangle, P.

P. Sprangle, E. Esarey, and J. Krall, “Self-guiding and stability of intense optical beams in gases undergoing ionization,” Phys. Rev. E 54, 4211-4232 (1996).
[CrossRef]

E. Esarey, G. Joyce, and P. Sprangle, “Frequency up-shifting of laser pulses by copropagating ionization fronts,” Phys. Rev. A 44, 3908-3911 (1991).
[CrossRef] [PubMed]

Squier, J.

Strickland, D.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212-2215 (1989).
[CrossRef] [PubMed]

Tajima, T.

J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
[CrossRef]

Talebpour, A.

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540-4549 (2000).
[CrossRef]

Tamosauskas, G.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, “Spatio-temporal reshaping and x wave dynamics in optical filaments,” Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, “Angular and chromatic dispersion in Kerr-driven conical emission,” Opt. Commun. 265, 672-677 (2006).
[CrossRef]

Teukolsky, T.

H. Press, T. Teukolsky, T. Vetterling, and P. Flannery, Numerical Recipes (Cambridge University Press, 1992).

Théberge, F.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406-1-036406-7 (2006).
[CrossRef]

Tsintsadze, L. N.

J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
[CrossRef]

Umstadter, D.

X. Liu and D. Umstadter, “Self-focusing of intense subpicosecond laser pulses in a low pressure gas,” in Vol. 17 of OSA Proceedings on Shortwavelength V, P.B.Corkum and M.D.Perry, eds. (Optical Society of America, 1993), pp. 45-49.

Vetterling, T.

H. Press, T. Teukolsky, T. Vetterling, and P. Flannery, Numerical Recipes (Cambridge University Press, 1992).

Wagner, W. G.

W. G. Wagner, H. A. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beams in the paraxial ray approximation,” Phys. Rev. 175, 256-266 (1968).
[CrossRef]

Wang, Z.

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

Wu, Z.

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behavior of a focused femtosecond laser pulse in fused silica,” J. Opt. A 5, 102-107 (2003).
[CrossRef]

Yang, H.

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behavior of a focused femtosecond laser pulse in fused silica,” J. Opt. A 5, 102-107 (2003).
[CrossRef]

Yuan, X.

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

Zhang, J.

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

Zhang, Z.

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

Zheng, Z.

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

Zhong, J.

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

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A. Couairon, “Light bullets from femtosecond filamentation,” Eur. Phys. J. D 27, 159-167 (2003).
[CrossRef]

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[CrossRef]

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E. L. Lindman, “'Free-space' boundary conditions for the time-dependent wave equation,” J. Comput. Phys. 18, 66-78 (1975).
[CrossRef]

J. Opt. A

Z. Wu, H. Jiang, H. Yang, and Q. Gong, “The refocusing behavior of a focused femtosecond laser pulse in fused silica,” J. Opt. A 5, 102-107 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. Di Trapani, “Angular and chromatic dispersion in Kerr-driven conical emission,” Opt. Commun. 265, 672-677 (2006).
[CrossRef]

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, “Intensity clamping of a femtosecond laser pulse in condensed matter,” Opt. Commun. 202, 189-197 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Plasmas

J. K. Koga, N. Naumova, M. Kando, L. N. Tsintsadze, K. Nakajima, S. V. Bulanov, H. Dewa, H. Kotaki, and T. Tajima, “Fixed blueshift of high intensity short pulse lasers propagating in gas chambers,” Phys. Plasmas 7, 5223-5231 (2000).
[CrossRef]

Phys. Rep.

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

J. H. Eberly, J. Javanainen, and K. Rzażwski, “Above-threshold ionization,” Phys. Rep. 204, 331-383 (1991).
[CrossRef]

Phys. Rev.

W. G. Wagner, H. A. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beams in the paraxial ray approximation,” Phys. Rev. 175, 256-266 (1968).
[CrossRef]

Phys. Rev. A

E. Esarey, G. Joyce, and P. Sprangle, “Frequency up-shifting of laser pulses by copropagating ionization fronts,” Phys. Rev. A 44, 3908-3911 (1991).
[CrossRef] [PubMed]

S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46, 1084-1090 (1992).
[CrossRef] [PubMed]

Phys. Rev. E

N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, “Femtosecond pulse propagation in air: variational analysis,” Phys. Rev. E 61, 4540-4549 (2000).
[CrossRef]

K. Nagashima, J. Koga, and M. Kando, “Numerical study of laser wake field generated by two colliding laser beams,” Phys. Rev. E 64, 066403-1-066403-4 (2001).
[CrossRef]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406-1-036406-7 (2006).
[CrossRef]

Z. Hao, J. Zhang, Z. Zhang, X. Yuan, Z. Zheng, X. Lu, Z. Jin, Z. Wang, J. Zhong, and Y. Liu, “Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation,” Phys. Rev. E 74, 066402-1-066402-5 (2006).
[CrossRef]

J. Koga, “Observation of supercontinuum generation in the direct simulation of an intense laser pulse propagating in a neutral gas,” Phys. Rev. E 70, 056404-1-056404-5 (2004).
[CrossRef]

P. Sprangle, E. Esarey, and J. Krall, “Self-guiding and stability of intense optical beams in gases undergoing ionization,” Phys. Rev. E 54, 4211-4232 (1996).
[CrossRef]

Phys. Rev. Lett.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611-1613 (1998).
[CrossRef]

N. C. Kothari and T. Kobayashi, “Growth rate and diameter of filaments in self-focusing media,” Phys. Rev. Lett. 50, 160-163 (1983).
[CrossRef]

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, “Tunneling ionization of noble gases in a high-intensity laser field,” Phys. Rev. Lett. 63, 2212-2215 (1989).
[CrossRef] [PubMed]

Prog. Quantum Electron.

J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35-l10 (1975).
[CrossRef]

Science

A. L. Gaeta, “Collapsing light really shines,” Science 301, 54-55 (2003).
[CrossRef] [PubMed]

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L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307-1314 (1965).

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H. Press, T. Teukolsky, T. Vetterling, and P. Flannery, Numerical Recipes (Cambridge University Press, 1992).

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Y. R. Shen, The Principle of Nonlinear Optics (Wiley-Interscience, 1984).

X. Liu and D. Umstadter, “Self-focusing of intense subpicosecond laser pulses in a low pressure gas,” in Vol. 17 of OSA Proceedings on Shortwavelength V, P.B.Corkum and M.D.Perry, eds. (Optical Society of America, 1993), pp. 45-49.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Butterworth-Heinemann, 1997).

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Figures (9)

Fig. 1
Fig. 1

Laser pulse with nearly no initial focusing ( R 0 x f = 3 × 10 10 ) (a) near the initial start position after propagating 0.02 cm and (b) after propagating 0.5 cm . The x and y values are normalized by λ 0 .

Fig. 2
Fig. 2

Laser pulse with strong initial focusing ( R 0 x f = 0.15 ) (a) near the initial start position after propagating 0.02 cm and (b) after propagating 0.1 cm . The x and y values are normalized by λ 0 .

Fig. 3
Fig. 3

Laser spot size w λ 0 as a function of propagation distance (a) x x f , where x f is the self-focusing distance and (b) x x f R , where x f R = x f ( 1 + x f R 0 ) is the lens transformed self-focusing distance [18]. The different initial focusing distances are indicated.

Fig. 4
Fig. 4

Maximum plasma density n p n c , normalized by the critical density as a function of propagation distance x x f , normalized by the laser wavelength and self-focusing length. The different initial focusing lengths are indicated.

Fig. 5
Fig. 5

Two-dimensional spectra of the laser pulse for nearly no initial focusing after propagating (a) 0.02 cm and (b) 0.5 cm , where k 0 is the initial wave number of the laser. Dark areas refer to large amplitudes and light areas to low amplitudes, where legends have been inserted into both plots indicating the amplitudes.

Fig. 6
Fig. 6

Two-dimensional spectra of the laser pulse for strong focusing after propagating (a) 0.02 cm and (b) 0.1 cm , where k 0 is the initial wave number of the laser. Dark areas refer to large amplitudes and light areas to low amplitudes, where legends have been inserted into both plots indicating the amplitudes.

Fig. 7
Fig. 7

Spectra of the laser pulse for different (a) long and (b) short initial focusing lengths, where λ 0 is the initial wavelength of the laser.

Fig. 8
Fig. 8

Laser pulse spot size a a 0 versus the initial focal length f and the propagation distance x, where both are normalized by x f .

Fig. 9
Fig. 9

Change in the laser frequency Δ ω ω 0 versus the initial focal length f x f .

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

2 E t 2 c 2 2 E = 4 π ( J t + 2 P t 2 ) .
J t = q 2 n e m e ( 1 + a l 2 ) 1 2 E ,
2 P t 2 + q 5 n N 3 m e P ( P 0 2 + P 2 ) 3 2 + Γ P t = q 2 n N m e E ,
n e t = ( n N 0 n e ) W ( E ) ,
W ( E ) = 4 ω a ( ϵ i ϵ h ) 5 2 E a E exp [ 2 3 ( ϵ i ϵ h ) 3 2 E a E ] ,
ω R = q 2 m e a S 3 .
P cr = π ( 0.61 ) 2 λ 0 2 8 n 0 n 2 ,
n 0 = 1 + 4 π a S 3 n N ,
n 2 = 12 π 2 n 0 2 c a S 7 n N q 2 ,
x f = π w 0 2 λ 0 0.367 ( P P 2 0.852 ) 2 0.0219 ,
n p n c = 2 [ n 2 I crit ( 1.22 λ 0 ) 2 8 n 0 π w 0 2 ] .
i E x + 1 2 k ( 2 E y 2 + 2 E z 2 ) + Δ n E = 0 ,
Δ n = n 2 k 0 E 2 2 π e 2 n e ( E 2 ) k m e c 2 ,
n e t = n N 0 R ( E 2 ) ,
E ( x , y , z , τ ) = A ( x , τ ) exp [ ( y 2 + z 2 ) a 2 ( x , τ ) ] exp [ i b ( x , τ ) ( y 2 + z 2 ) + i ϕ ( x , τ ) ] ,
1 2 ( a x ) 2 + U ( a ) = 0
U ( a ) = 2 a 2 2 P 0 ( τ ) a 2 + [ 8 γ n k P cr n 2 n 2 n π n ( n + 1 ) ( 2 n + 2 ) a 0 2 n 2 ] P 0 n ( τ ) a 2 n + C ( τ ) ,
C ( τ ) = 2 + 2 P 0 ( τ ) [ 8 γ n k P cr n 2 n 2 n π n ( n + 1 ) ( 2 n + 2 ) a 0 2 n 2 ] P 0 n ( τ ) 2 b 0 2 ,
R ( E 2 ) = A ω 0 ( ϵ i ω 0 ) 3 2 exp { 2 ϵ ̃ i ω 0 + 1 ϵ ̃ i ω 0 ( 1 + e 2 E 2 2 m ω 0 2 ϵ i ) }
Φ { [ 2 ϵ ̃ i ω 0 + 1 2 ϵ ̃ i ω 0 ] 1 2 } ( e 2 E 2 8 m ω 0 2 ϵ i ) ϵ ̃ i ω 0 + 1 ,
Φ ( z ) = 0 z exp ( y 2 z 2 ) d y .
σ ( n ) ω 0 ( n 1 ) 3 2 exp { 2 n ( n 1 ) }
Φ { [ 2 n 2 ( n 1 ) ] 1 2 } ( e 2 8 m ω 0 2 ϵ i ) n .
I ( 2 n 2 n c σ ( n ) τ 0 n N ) 1 ( n 1 ) ,
f crit x f = k a 0 2 2 x f 2 2 P 0 2 [ 8 γ n k P cr n 2 n 2 n π n ( n + 1 ) ( 2 n + 2 ) a 0 2 n 2 ] P 0 n ( τ ) .
ω ( x ) ω 0 = 1 + 0 x d x 1 L 0 ( n p ( x ) n c ) ,
n p ( x ) = { n p 0 ( x ) if τ > 0 n p 0 ( x ) ( 1 + v g τ L 0 ) if L 0 v g < τ < 0 0 if τ < L 0 v g } ,
n p 0 ( x ) = g ( τ ) τ 0 n N σ ( n ) ( 2 P crit π a 0 2 P 0 a 2 ) n ,

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