Abstract

The description of ultrashort laser pulse filamentation in condensed media as a spontaneous formation of X waves is shown to apply also to filaments generated in air. Within this framework, a simple explanation is brought for several features of the filament such as the subdiffractive propagation and the energy flux from the weakly localized tails of the X-waves to the intense core.

© 2008 Optical Society of America

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References

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  1. A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 (2007).
    [CrossRef]
  2. F. Théberge, N. Aközbek, W. Liu, A. Becker, and S. L. Chin, "Tunable Ultrashort Laser Pulses Generated through Filamentation in Gases," Phys. Rev. lett. 97, 023904 (2006)
    [CrossRef] [PubMed]
  3. A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Selfcompression of ultra-short laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
    [CrossRef]
  4. S. Tzortzakis, M.A. Franco, Y.B. André, A. Chiron, B. Lamouroux, B.S. Prade, and A. Mysyrowicz, "Formation of a conducting channel in air by self-guided femtosecond laser pulses," Phys. Rev. E 60, 3505-3508 (1999)
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    [CrossRef]
  9. B. La Fontaine, D. Comtois, C.-Y. Chien, A. Desparois, F. Génin, G. Jarry, T. Johnston, J.-C. Kieffer, F. Martin, R. Mawassi, H. Pépin, F. A. M. Rizk, F. Vidal, C. Potvin, P. Couture and H. P. Mercure, "Guiding large-scale spark discharges with ultrashort pulse laser filaments," J. Appl. Phys. 88, 610-615 (2000)
    [CrossRef]
  10. 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. 98235002 (2007)
    [CrossRef] [PubMed]
  11. G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Long-range self-channeling of infrared laser pulses in air: a new propagation regime without ionization," Appl. Phys. B 79, 379-382 (2004)
    [CrossRef]
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    [CrossRef] [PubMed]
  15. D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72037601 (2005)
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    [CrossRef] [PubMed]
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    [CrossRef]
  20. 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 (2003)
    [CrossRef] [PubMed]
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    [CrossRef]
  23. D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J.V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13079-13095 (2007)
    [CrossRef]
  24. S. Champeaux and L. Bergé, "Postionization regimes of femtosecond laser pulses self-channeling in air," Phys. Rev. E 71, 046604 (2005)
    [CrossRef]
  25. F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Mejèan, J. Yu, and. J.P. Wolf, "Light filaments transmitted through clouds," Appl. Phys. Lett. 83, 213-215 (2003)
    [CrossRef]
  26. M. Kolesik and J.V. Moloney, "Self-healing femtosecond light filaments," Opt. Lett. 29, 590-592 (2004)
    [CrossRef] [PubMed]

2007 (4)

A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 (2007).
[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. 98235002 (2007)
[CrossRef] [PubMed]

S. Eisenmann, A. Pukhov, and A. Zigler, "Fine Structure of a Laser-Plasma Filament in Air," Phys. Rev. Lett. 98, 155002 (2007)
[CrossRef] [PubMed]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J.V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13079-13095 (2007)
[CrossRef]

2006 (5)

D. Faccio, A. Averchi, A. Couairon, A. Dubietis, R. Piskarskas, A. Matijosius, F. Bragheri, M.A. Porras, A. Piskarskas, and P. Di Trapani, "Competition between phase-matching and stationarity in Kerr-driven optical pulse filamentation," Phys. Rev. E 74, 047603 (2006)
[CrossRef]

A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis and P. Di Trapani, Nonlinear X-wave formation by femtosecond filamentation in Kerr media, Phys. Rev. E 73, 016608 (2006).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

F. Théberge, N. Aközbek, W. Liu, A. Becker, and S. L. Chin, "Tunable Ultrashort Laser Pulses Generated through Filamentation in Gases," Phys. Rev. lett. 97, 023904 (2006)
[CrossRef] [PubMed]

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Selfcompression of ultra-short laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

2005 (4)

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72037601 (2005)
[CrossRef]

D. Faccio, P. Di Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, A. Matijosius, "Far-field spectral characterization of conical emission and filamentation in Kerr media," J. Opt. Soc. Am. B 22, 862-869 (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]

S. Champeaux and L. Bergé, "Postionization regimes of femtosecond laser pulses self-channeling in air," Phys. Rev. E 71, 046604 (2005)
[CrossRef]

2004 (3)

M. Kolesik and J.V. Moloney, "Self-healing femtosecond light filaments," Opt. Lett. 29, 590-592 (2004)
[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 (2004).
[CrossRef] [PubMed]

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Long-range self-channeling of infrared laser pulses in air: a new propagation regime without ionization," Appl. Phys. B 79, 379-382 (2004)
[CrossRef]

2003 (2)

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Mejèan, J. Yu, and. J.P. Wolf, "Light filaments transmitted through clouds," Appl. Phys. Lett. 83, 213-215 (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 (2003)
[CrossRef] [PubMed]

2001 (1)

S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, "Femtosecond laser-guided electric discharge in air," Phys. Rev. E 64, 057401 (2001)
[CrossRef]

2000 (1)

B. La Fontaine, D. Comtois, C.-Y. Chien, A. Desparois, F. Génin, G. Jarry, T. Johnston, J.-C. Kieffer, F. Martin, R. Mawassi, H. Pépin, F. A. M. Rizk, F. Vidal, C. Potvin, P. Couture and H. P. Mercure, "Guiding large-scale spark discharges with ultrashort pulse laser filaments," J. Appl. Phys. 88, 610-615 (2000)
[CrossRef]

1999 (1)

S. Tzortzakis, M.A. Franco, Y.B. André, A. Chiron, B. Lamouroux, B.S. Prade, and A. Mysyrowicz, "Formation of a conducting channel in air by self-guided femtosecond laser pulses," Phys. Rev. E 60, 3505-3508 (1999)
[CrossRef]

1998 (1)

1995 (1)

1994 (1)

1993 (1)

X.M. Zhao and J.C. Diels, "Femtosecond pulses to divert lightning," Laser Focus World 29, 113-123 (1993)

1972 (1)

Appl. Phys. B (1)

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Long-range self-channeling of infrared laser pulses in air: a new propagation regime without ionization," Appl. Phys. B 79, 379-382 (2004)
[CrossRef]

Appl. Phys. Lett. (1)

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Mejèan, J. Yu, and. J.P. Wolf, "Light filaments transmitted through clouds," Appl. Phys. Lett. 83, 213-215 (2003)
[CrossRef]

J. Appl. Phys. (1)

B. La Fontaine, D. Comtois, C.-Y. Chien, A. Desparois, F. Génin, G. Jarry, T. Johnston, J.-C. Kieffer, F. Martin, R. Mawassi, H. Pépin, F. A. M. Rizk, F. Vidal, C. Potvin, P. Couture and H. P. Mercure, "Guiding large-scale spark discharges with ultrashort pulse laser filaments," J. Appl. Phys. 88, 610-615 (2000)
[CrossRef]

J. Mod. Opt. (1)

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Selfcompression of ultra-short laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Laser Focus World (1)

X.M. Zhao and J.C. Diels, "Femtosecond pulses to divert lightning," Laser Focus World 29, 113-123 (1993)

Opt. Express (2)

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]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J.V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13079-13095 (2007)
[CrossRef]

Opt. Lett. (4)

Phys. Rep. (1)

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

Phys. Rev. E (6)

S. Tzortzakis, M.A. Franco, Y.B. André, A. Chiron, B. Lamouroux, B.S. Prade, and A. Mysyrowicz, "Formation of a conducting channel in air by self-guided femtosecond laser pulses," Phys. Rev. E 60, 3505-3508 (1999)
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, "Femtosecond laser-guided electric discharge in air," Phys. Rev. E 64, 057401 (2001)
[CrossRef]

D. Faccio, A. Averchi, A. Couairon, A. Dubietis, R. Piskarskas, A. Matijosius, F. Bragheri, M.A. Porras, A. Piskarskas, and P. Di Trapani, "Competition between phase-matching and stationarity in Kerr-driven optical pulse filamentation," Phys. Rev. E 74, 047603 (2006)
[CrossRef]

S. Champeaux and L. Bergé, "Postionization regimes of femtosecond laser pulses self-channeling in air," Phys. Rev. E 71, 046604 (2005)
[CrossRef]

A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis and P. Di Trapani, Nonlinear X-wave formation by femtosecond filamentation in Kerr media, Phys. Rev. E 73, 016608 (2006).
[CrossRef]

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72037601 (2005)
[CrossRef]

Phys. Rev. Lett. (5)

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. 98235002 (2007)
[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 (2003)
[CrossRef] [PubMed]

S. Eisenmann, A. Pukhov, and A. Zigler, "Fine Structure of a Laser-Plasma Filament in Air," Phys. Rev. Lett. 98, 155002 (2007)
[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 (2004).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

F. Théberge, N. Aközbek, W. Liu, A. Becker, and S. L. Chin, "Tunable Ultrashort Laser Pulses Generated through Filamentation in Gases," Phys. Rev. lett. 97, 023904 (2006)
[CrossRef] [PubMed]

Supplementary Material (1)

» Media 1: MOV (604 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

Measured (θ,λ) spectra of filaments in air generated using a 2 m lens (a) and of a 10 m lens (b). (c) shows the numerically calculated spectrum for the experimental settings of (b). The white lines in all graphs show the best fits obtained with the X Wave relation Eq. (1). The filament appears as a white spot surrounded by colored rings when viewed on piece of paper a few meters after the end of the self-induced plasma string (d).

Fig. 2.
Fig. 2.

(a) The solid lines shows the calculated FWHM of the filament generated with a 10 m focal length lens. The circles show the same quantity as measured experimentally while the contour plot represents the calculated plasma density in 1/cm3 within the filament. (b) shows the calculated FWHM evolution of the filament when, at a distance of z=7 m, all nonlinear effects are switched off. The blue-dashed line indicates the expected FWHM of a linearly diffracting beam. Sub-diffractive propagation is observed in this linear regime over a 4 m distance (red solid line). The spatial far-field spectrum shows two peaks, a distinct feature of conical propagation (c).

Fig. 3.
Fig. 3.

Calculated transverse energy flux (in arbitrary units) for the same filament in Fig. 2(a) at a distance z=7 m. The leading intensity peak clearly shows and X shaped profile the reflects the profile of the optical pulse. The leading X tail has an inward flux while the trailing tails has an outward flux. The diagram exemplifies this situation: plane waves propagating at an angle (i.e. along a cone) will give an X shaped energy flux in the region in which they overlap followed by an outgoing flux at the end of this region.[Media 1]

Equations (1)

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k = k 2 k z 2   with k z = k 0 + Ω ν g ,

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