Abstract

The influence mechanism of higher-order Kerr effect on the propagation of laser beam is investigated by a modified model, which indicates that a collapsing wave will transform into a universe blowup profile. The analysis of higher-order terms of the nonlinear refractive index shows that the filamentation process can be induced by Kerr self-focusing without the occurrence of the ionization effect. The determining role of the combination of self-focusing and spontaneous defocusing and the energy reservoir in formation of lengthy filament is confirmed visually.

© 2010 OSA

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References

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  1. 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(1), 73–75 (1995).
    [Crossref] [PubMed]
  2. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
    [Crossref]
  3. A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett. 100(25), 255006 (2008).
    [Crossref] [PubMed]
  4. A. Couairon, S. C. Himadri, and B. G. Mette, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77(5), 053814 (2008).
    [Crossref]
  5. J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
    [Crossref] [PubMed]
  6. J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
    [Crossref]
  7. W. Liu, J.-F. Gravel, F. Th’eberge, A. Becker, and S. L. Chin, “Background reservoir its crucial role for longdistance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80(7), 857–860 (2005).
    [Crossref]
  8. E. P. Silaeva and V. P. Kandidov, “Propagation of a High-Power Femtosecond Pulse Filament through a Layer of Aerosol,” Atmos. Oceanic Opt. 22(1), 26–34 (2009).
    [Crossref]
  9. A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett. 22(5), 304–306 (1997).
    [Crossref] [PubMed]
  10. M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
    [Crossref]
  11. G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
    [Crossref]
  12. C. Ruiz, J. San Román, C. Méndez, V. Díaz, L. Plaja, I. Arias, and L. Roso, “Observation of spontaneous self-channeling of light in air below the collapse threshold,” Phys. Rev. Lett. 95(5), 053905 (2005).
    [Crossref] [PubMed]
  13. G. Fibich, N. Gavish, and X. P. Wang, “New singular solutions of the nonlinear Schrödinger equation,” Physica D 211(3-4), 193–220 (2005).
    [Crossref]
  14. V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components,” Opt. Express 17(16), 13429–13434 (2009) (Erratum in Opt. Express 18, 3011 ) (2010).
    [Crossref] [PubMed]
  15. T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
    [Crossref] [PubMed]
  16. V. P. Kandidov, O. G. Kosareva, I. S. Golubstov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media(or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
    [Crossref]
  17. M. B. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: diagnostics and application,” Phys. Rev. Lett. 103(4), 043901 (2009).
    [Crossref] [PubMed]

2009 (3)

E. P. Silaeva and V. P. Kandidov, “Propagation of a High-Power Femtosecond Pulse Filament through a Layer of Aerosol,” Atmos. Oceanic Opt. 22(1), 26–34 (2009).
[Crossref]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components,” Opt. Express 17(16), 13429–13434 (2009) (Erratum in Opt. Express 18, 3011 ) (2010).
[Crossref] [PubMed]

M. B. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: diagnostics and application,” Phys. Rev. Lett. 103(4), 043901 (2009).
[Crossref] [PubMed]

2008 (2)

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett. 100(25), 255006 (2008).
[Crossref] [PubMed]

A. Couairon, S. C. Himadri, and B. G. Mette, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77(5), 053814 (2008).
[Crossref]

2007 (2)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[Crossref]

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

2006 (1)

2005 (3)

C. Ruiz, J. San Román, C. Méndez, V. Díaz, L. Plaja, I. Arias, and L. Roso, “Observation of spontaneous self-channeling of light in air below the collapse threshold,” Phys. Rev. Lett. 95(5), 053905 (2005).
[Crossref] [PubMed]

G. Fibich, N. Gavish, and X. P. Wang, “New singular solutions of the nonlinear Schrödinger equation,” Physica D 211(3-4), 193–220 (2005).
[Crossref]

W. Liu, J.-F. Gravel, F. Th’eberge, A. Becker, and S. L. Chin, “Background reservoir its crucial role for longdistance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80(7), 857–860 (2005).
[Crossref]

2004 (1)

G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

2003 (2)

V. P. Kandidov, O. G. Kosareva, I. S. Golubstov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media(or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

1999 (1)

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

1997 (1)

1995 (1)

Akozbek, N.

V. P. Kandidov, O. G. Kosareva, I. S. Golubstov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media(or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

Amico, C. D.

G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

Andr’e, Y.-B.

G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

André, Y.-B.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Arias, I.

C. Ruiz, J. San Román, C. Méndez, V. Díaz, L. Plaja, I. Arias, and L. Roso, “Observation of spontaneous self-channeling of light in air below the collapse threshold,” Phys. Rev. Lett. 95(5), 053905 (2005).
[Crossref] [PubMed]

Azarm, A.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

Becker, A.

W. Liu, J.-F. Gravel, F. Th’eberge, A. Becker, and S. L. Chin, “Background reservoir its crucial role for longdistance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80(7), 857–860 (2005).
[Crossref]

V. P. Kandidov, O. G. Kosareva, I. S. Golubstov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media(or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

Bernardt, J.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

Bourayou, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Bowden, C. M.

V. P. Kandidov, O. G. Kosareva, I. S. Golubstov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media(or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

Braun, A.

Brodeur, A.

Chien, C. Y.

Chin, S. L.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

W. Liu, J.-F. Gravel, F. Th’eberge, A. Becker, and S. L. Chin, “Background reservoir its crucial role for longdistance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80(7), 857–860 (2005).
[Crossref]

V. P. Kandidov, O. G. Kosareva, I. S. Golubstov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media(or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett. 22(5), 304–306 (1997).
[Crossref] [PubMed]

Couairon, A.

M. B. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: diagnostics and application,” Phys. Rev. Lett. 103(4), 043901 (2009).
[Crossref] [PubMed]

A. Couairon, S. C. Himadri, and B. G. Mette, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77(5), 053814 (2008).
[Crossref]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[Crossref]

G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

Daigle, J.-F.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

Díaz, V.

C. Ruiz, J. San Román, C. Méndez, V. Díaz, L. Plaja, I. Arias, and L. Roso, “Observation of spontaneous self-channeling of light in air below the collapse threshold,” Phys. Rev. Lett. 95(5), 053905 (2005).
[Crossref] [PubMed]

Du, D.

Faucher, O.

Fibich, G.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[Crossref] [PubMed]

G. Fibich, N. Gavish, and X. P. Wang, “New singular solutions of the nonlinear Schrödinger equation,” Physica D 211(3-4), 193–220 (2005).
[Crossref]

Franco, M.

G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

Frey, S.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Gaarde, M. B.

M. B. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: diagnostics and application,” Phys. Rev. Lett. 103(4), 043901 (2009).
[Crossref] [PubMed]

Gaeta, A. L.

Gavish, N.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[Crossref] [PubMed]

G. Fibich, N. Gavish, and X. P. Wang, “New singular solutions of the nonlinear Schrödinger equation,” Physica D 211(3-4), 193–220 (2005).
[Crossref]

Golubstov, I. S.

V. P. Kandidov, O. G. Kosareva, I. S. Golubstov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media(or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

Gravel, J.-F.

W. Liu, J.-F. Gravel, F. Th’eberge, A. Becker, and S. L. Chin, “Background reservoir its crucial role for longdistance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80(7), 857–860 (2005).
[Crossref]

Grow, T. D.

Hertz, E.

Himadri, S. C.

A. Couairon, S. C. Himadri, and B. G. Mette, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77(5), 053814 (2008).
[Crossref]

Houard, A.

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett. 100(25), 255006 (2008).
[Crossref] [PubMed]

Ilkov, F. A.

Ishaaya, A. A.

Kamali, Y.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

Kandidov, V. P.

E. P. Silaeva and V. P. Kandidov, “Propagation of a High-Power Femtosecond Pulse Filament through a Layer of Aerosol,” Atmos. Oceanic Opt. 22(1), 26–34 (2009).
[Crossref]

V. P. Kandidov, O. G. Kosareva, I. S. Golubstov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media(or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett. 22(5), 304–306 (1997).
[Crossref] [PubMed]

Kasparian, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Kolesik, M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

Korn, G.

Kosareva, O. G.

V. P. Kandidov, O. G. Kosareva, I. S. Golubstov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media(or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett. 22(5), 304–306 (1997).
[Crossref] [PubMed]

Lavorel, B.

Liu, W.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

W. Liu, J.-F. Gravel, F. Th’eberge, A. Becker, and S. L. Chin, “Background reservoir its crucial role for longdistance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80(7), 857–860 (2005).
[Crossref]

V. P. Kandidov, O. G. Kosareva, I. S. Golubstov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media(or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

Liu, X.

Liu, Y.

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett. 100(25), 255006 (2008).
[Crossref] [PubMed]

Loriot, V.

M’ejean, G.

G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

Mathieu, P.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

Méjean, G.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Méndez, C.

C. Ruiz, J. San Román, C. Méndez, V. Díaz, L. Plaja, I. Arias, and L. Roso, “Observation of spontaneous self-channeling of light in air below the collapse threshold,” Phys. Rev. Lett. 95(5), 053905 (2005).
[Crossref] [PubMed]

Mette, B. G.

A. Couairon, S. C. Himadri, and B. G. Mette, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77(5), 053814 (2008).
[Crossref]

Mlejnek, M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

Moloney, J. V.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

Mourou, G.

Mysyrowicz, A.

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett. 100(25), 255006 (2008).
[Crossref] [PubMed]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[Crossref]

G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Plaja, L.

C. Ruiz, J. San Román, C. Méndez, V. Díaz, L. Plaja, I. Arias, and L. Roso, “Observation of spontaneous self-channeling of light in air below the collapse threshold,” Phys. Rev. Lett. 95(5), 053905 (2005).
[Crossref] [PubMed]

Prade, B.

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett. 100(25), 255006 (2008).
[Crossref] [PubMed]

G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

Rodriguez, M.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Roso, L.

C. Ruiz, J. San Román, C. Méndez, V. Díaz, L. Plaja, I. Arias, and L. Roso, “Observation of spontaneous self-channeling of light in air below the collapse threshold,” Phys. Rev. Lett. 95(5), 053905 (2005).
[Crossref] [PubMed]

Roy, G.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

Ruiz, C.

C. Ruiz, J. San Román, C. Méndez, V. Díaz, L. Plaja, I. Arias, and L. Roso, “Observation of spontaneous self-channeling of light in air below the collapse threshold,” Phys. Rev. Lett. 95(5), 053905 (2005).
[Crossref] [PubMed]

Salmon, E.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

San Román, J.

C. Ruiz, J. San Román, C. Méndez, V. Díaz, L. Plaja, I. Arias, and L. Roso, “Observation of spontaneous self-channeling of light in air below the collapse threshold,” Phys. Rev. Lett. 95(5), 053905 (2005).
[Crossref] [PubMed]

Sauerbrey, R.

G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Silaeva, E. P.

E. P. Silaeva and V. P. Kandidov, “Propagation of a High-Power Femtosecond Pulse Filament through a Layer of Aerosol,” Atmos. Oceanic Opt. 22(1), 26–34 (2009).
[Crossref]

Simard, J. R.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

Squier, J.

Sun, A.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

Th’eberge, F.

W. Liu, J.-F. Gravel, F. Th’eberge, A. Becker, and S. L. Chin, “Background reservoir its crucial role for longdistance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80(7), 857–860 (2005).
[Crossref]

Théberge, F.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

Tikhonchuk, V. T.

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett. 100(25), 255006 (2008).
[Crossref] [PubMed]

Tzortzakis, S.

G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

Vuong, L. T.

Wang, X. P.

G. Fibich, N. Gavish, and X. P. Wang, “New singular solutions of the nonlinear Schrödinger equation,” Physica D 211(3-4), 193–220 (2005).
[Crossref]

Wille, H.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Wolf, J.-P.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Wöste, L.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Wright, E. M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

Xu, H. L.

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

Yu, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

Appl. Phys. B (4)

J.-F. Daigle, G. Méjean, W. Liu, F. Théberge, H. L. Xu, Y. Kamali, J. Bernardt, A. Azarm, A. Sun, P. Mathieu, G. Roy, J. R. Simard, and S. L. Chin, “Long range trace detection in aqueous aerosol using remotefilament-induced breakdown spectroscopy,” Appl. Phys. B 87(4), 749–754 (2007).
[Crossref]

W. Liu, J.-F. Gravel, F. Th’eberge, A. Becker, and S. L. Chin, “Background reservoir its crucial role for longdistance propagation of femtosecond laser pulses in air,” Appl. Phys. B 80(7), 857–860 (2005).
[Crossref]

G. M’ejean, A. Couairon, Y.-B. Andr’e, C. D. Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long range self-channeling of infrared laser pulses in air a new propagation regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

V. P. Kandidov, O. G. Kosareva, I. S. Golubstov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media(or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

Atmos. Oceanic Opt. (1)

E. P. Silaeva and V. P. Kandidov, “Propagation of a High-Power Femtosecond Pulse Filament through a Layer of Aerosol,” Atmos. Oceanic Opt. 22(1), 26–34 (2009).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[Crossref]

Phys. Rev. A (1)

A. Couairon, S. C. Himadri, and B. G. Mette, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77(5), 053814 (2008).
[Crossref]

Phys. Rev. Lett. (4)

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett. 100(25), 255006 (2008).
[Crossref] [PubMed]

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83(15), 2938–2941 (1999).
[Crossref]

M. B. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: diagnostics and application,” Phys. Rev. Lett. 103(4), 043901 (2009).
[Crossref] [PubMed]

C. Ruiz, J. San Román, C. Méndez, V. Díaz, L. Plaja, I. Arias, and L. Roso, “Observation of spontaneous self-channeling of light in air below the collapse threshold,” Phys. Rev. Lett. 95(5), 053905 (2005).
[Crossref] [PubMed]

Physica D (1)

G. Fibich, N. Gavish, and X. P. Wang, “New singular solutions of the nonlinear Schrödinger equation,” Physica D 211(3-4), 193–220 (2005).
[Crossref]

Science (1)

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003).
[Crossref] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(Color online) Calculated transverse peak intensity profiles for the laser beam at the different z positions. (a-f) z = 9.57, 9.8, 10.8, 11.2, 11.35, 11.5 m, respectively. The narrow, weak, extended structures are due to self-focusing process in which the higher-order Kerr terms play a dominant role to be self-defocusing balance mechanism.

Fig. 2
Fig. 2

(Color online) The intensity profile of the beam at (a) z = 12.7 m and (b) z = 14.1m, showing the presence of a narrow core surrounded by a weaker ring. It is shown that the robustness of the filament comes from the transverse low-intensity pedestal that controls the formation of the central hot spot.

Fig. 3
Fig. 3

(Color online) (a) The energy fluence distribution in the filament along the propagation axis z; (b) On-axis peak intensity vs propagation distance, and(c) Iso-intensity (iso = 0.5) distribution of the filament.

Equations (1)

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E z = i 2 k 0 ( 2 x 2 + 2 y 2 ) E i k ' ' 2 2 t 2 E + i k 0 n 2 n 0 | E | 2 E + i k 0 n 0 ( j = 2 5 n 2 * j | E | 2 * j ) E β ( K ) 2 | E | ( 2 K 2 ) E

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