Abstract

We show experimentally for ultrashort laser pulses propagating in air, that the collapse/filamentation distance of intense laser pulses in the atmosphere can be extended and controlled with a simple double-lens setup. We derive a simple formula for the filamentation distance, and confirm its agreement with the experimental results. We also observe that delaying the onset of filamentation increases the filament length.

© 2006 Optical Society of America

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  1. L. Wöste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronnenberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp," Laser und Optoelektronik 29,51-53 (1997).
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  7. S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Breakup and Fusion of Self- Guided Femtosecond Light Pulses in Air," Phys. Rev. Lett. 86,5470-5473 (2001).
    [CrossRef] [PubMed]
  8. Z. Jin, J. Zhang, M.H. Xu, X. Lu, Y.T. Li, Z.H. Wang, Z.Y. Wei, X.H. Yuan, and W. Yu, "Control of filaments induced by femtosecond laser pulses propagating in air," Opt. Express 13,10424-30 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  18. W. Liu, Q. Luo, F. Théberge, H.L. Xu, S.A. Hosseini, S.M. Sarifi, S.L. Chin, "The influence of divergence on filament length during the propagation of intense ultra-short laser pulses," Appl. Phys. B 82,373-376 (2006).
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    [CrossRef]

2006 (1)

W. Liu, Q. Luo, F. Théberge, H.L. Xu, S.A. Hosseini, S.M. Sarifi, S.L. Chin, "The influence of divergence on filament length during the propagation of intense ultra-short laser pulses," Appl. Phys. B 82,373-376 (2006).
[CrossRef]

2005 (6)

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

Q. Luo, S.A. Hosseini, W. Liu, J.˜F. Gravel, O.G. Kosareva, N.A. Panov, N. Aközbek, V.P. Kandidov, G. Roy, S.L. Chin, "Effect of beam diameter on the propagation of intense femtosecond lase pulses," Appl. Phys. B 80,35-38 (2005).
[CrossRef]

S.L. Chin, S.A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V.P. Kandidov, O.G. Kosareva, and H. Schroeder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83,863-905 (2005).
[CrossRef]

G. Fibich, S. Eisenmann, B. Ilan, Y. Erlich, M. Fraenkel, Z. Henis, A.L. Gaeta, and A. Zigler, "Self-focusing distance of very high power laser pulses," Opt. Express 13,5897-5903 (2005).
[CrossRef] [PubMed]

Z. Jin, J. Zhang, M.H. Xu, X. Lu, Y.T. Li, Z.H. Wang, Z.Y. Wei, X.H. Yuan, and W. Yu, "Control of filaments induced by femtosecond laser pulses propagating in air," Opt. Express 13,10424-30 (2005).
[CrossRef] [PubMed]

R. Nuter, S. Skupin, and L. Bergé, "Chirp-induced dynamics of femtosecond filaments in air," Opt. Lett. 30,917-9 (2005).
[CrossRef] [PubMed]

2004 (2)

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

A. Dubietis, E. Gaizauskas, G. Tamošauskas, P. Di Trapani, "Light filaments without self-channeling," Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef] [PubMed]

2003 (3)

A. Couairon "Filamentation length of powerful laser pulses," Appl. Phys. B 76,789-792 (2003).
[CrossRef]

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

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

2002 (1)

P. Sprangle, J.R . Peñano and B . Hafizi, "Propagation of intense short laser pulses in the atmosphere," Phys. Rev. E 66,046418, 2002.
[CrossRef]

2001 (1)

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Breakup and Fusion of Self- Guided Femtosecond Light Pulses in Air," Phys. Rev. Lett. 86,5470-5473 (2001).
[CrossRef] [PubMed]

1999 (1)

M. Mlejnek, E.M. Wright, and J.V. Moloney, "Moving-Focus Versus Self-Waveguiding Model for Long-Distance Propagation of Femtosecond Pulses in Air," IEEE J. Quantum Eelecton. 35,1771 (1999).
[CrossRef]

1997 (1)

L. Wöste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronnenberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp," Laser und Optoelektronik 29,51-53 (1997).

1970 (1)

V.I. Talanov, "Focusing of light in cubic media," JETP Lett. 11,199-201 (1970).

Andre, Y.-B.

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

Andre;, Y.-B.

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

Berg´e, L.

R. Nuter, S. Skupin, and L. Bergé, "Chirp-induced dynamics of femtosecond filaments in air," Opt. Lett. 30,917-9 (2005).
[CrossRef] [PubMed]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Breakup and Fusion of Self- Guided Femtosecond Light Pulses in Air," Phys. Rev. Lett. 86,5470-5473 (2001).
[CrossRef] [PubMed]

Chin, S.L.

W. Liu, Q. Luo, F. Théberge, H.L. Xu, S.A. Hosseini, S.M. Sarifi, S.L. Chin, "The influence of divergence on filament length during the propagation of intense ultra-short laser pulses," Appl. Phys. B 82,373-376 (2006).
[CrossRef]

S.L. Chin, S.A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V.P. Kandidov, O.G. Kosareva, and H. Schroeder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83,863-905 (2005).
[CrossRef]

Couairon, A.

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

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

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

A. Couairon "Filamentation length of powerful laser pulses," Appl. Phys. B 76,789-792 (2003).
[CrossRef]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Breakup and Fusion of Self- Guided Femtosecond Light Pulses in Air," Phys. Rev. Lett. 86,5470-5473 (2001).
[CrossRef] [PubMed]

D’Amico, C.

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

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

Di Trapani, P.

A. Dubietis, E. Gaizauskas, G. Tamošauskas, P. Di Trapani, "Light filaments without self-channeling," Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef] [PubMed]

Dubietis, A.

A. Dubietis, E. Gaizauskas, G. Tamošauskas, P. Di Trapani, "Light filaments without self-channeling," Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef] [PubMed]

Eisenmann, S.

Erlich, Y.

Fibich, G.

Fraenkel, M.

Franco, M.

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

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

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Breakup and Fusion of Self- Guided Femtosecond Light Pulses in Air," Phys. Rev. Lett. 86,5470-5473 (2001).
[CrossRef] [PubMed]

Gaeta, A.L.

Gai?zauskas, E.

A. Dubietis, E. Gaizauskas, G. Tamošauskas, P. Di Trapani, "Light filaments without self-channeling," Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef] [PubMed]

Hafizi, B

P. Sprangle, J.R . Peñano and B . Hafizi, "Propagation of intense short laser pulses in the atmosphere," Phys. Rev. E 66,046418, 2002.
[CrossRef]

Henis, Z.

Hosseini, S.A.

W. Liu, Q. Luo, F. Théberge, H.L. Xu, S.A. Hosseini, S.M. Sarifi, S.L. Chin, "The influence of divergence on filament length during the propagation of intense ultra-short laser pulses," Appl. Phys. B 82,373-376 (2006).
[CrossRef]

S.L. Chin, S.A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V.P. Kandidov, O.G. Kosareva, and H. Schroeder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83,863-905 (2005).
[CrossRef]

Q. Luo, S.A. Hosseini, W. Liu, J.˜F. Gravel, O.G. Kosareva, N.A. Panov, N. Aközbek, V.P. Kandidov, G. Roy, S.L. Chin, "Effect of beam diameter on the propagation of intense femtosecond lase pulses," Appl. Phys. B 80,35-38 (2005).
[CrossRef]

Ilan, B.

Jin, Z.

Li, Y.T.

Liu, W.

W. Liu, Q. Luo, F. Théberge, H.L. Xu, S.A. Hosseini, S.M. Sarifi, S.L. Chin, "The influence of divergence on filament length during the propagation of intense ultra-short laser pulses," Appl. Phys. B 82,373-376 (2006).
[CrossRef]

Q. Luo, S.A. Hosseini, W. Liu, J.˜F. Gravel, O.G. Kosareva, N.A. Panov, N. Aközbek, V.P. Kandidov, G. Roy, S.L. Chin, "Effect of beam diameter on the propagation of intense femtosecond lase pulses," Appl. Phys. B 80,35-38 (2005).
[CrossRef]

S.L. Chin, S.A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V.P. Kandidov, O.G. Kosareva, and H. Schroeder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83,863-905 (2005).
[CrossRef]

Lu, X.

Luo, Q.

W. Liu, Q. Luo, F. Théberge, H.L. Xu, S.A. Hosseini, S.M. Sarifi, S.L. Chin, "The influence of divergence on filament length during the propagation of intense ultra-short laser pulses," Appl. Phys. B 82,373-376 (2006).
[CrossRef]

S.L. Chin, S.A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V.P. Kandidov, O.G. Kosareva, and H. Schroeder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83,863-905 (2005).
[CrossRef]

Q. Luo, S.A. Hosseini, W. Liu, J.˜F. Gravel, O.G. Kosareva, N.A. Panov, N. Aközbek, V.P. Kandidov, G. Roy, S.L. Chin, "Effect of beam diameter on the propagation of intense femtosecond lase pulses," Appl. Phys. B 80,35-38 (2005).
[CrossRef]

Mechain, G.

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

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

Mlejnek, M.

M. Mlejnek, E.M. Wright, and J.V. Moloney, "Moving-Focus Versus Self-Waveguiding Model for Long-Distance Propagation of Femtosecond Pulses in Air," IEEE J. Quantum Eelecton. 35,1771 (1999).
[CrossRef]

Moloney, J.V.

M. Mlejnek, E.M. Wright, and J.V. Moloney, "Moving-Focus Versus Self-Waveguiding Model for Long-Distance Propagation of Femtosecond Pulses in Air," IEEE J. Quantum Eelecton. 35,1771 (1999).
[CrossRef]

Mysyrowicz, A.

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

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

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Breakup and Fusion of Self- Guided Femtosecond Light Pulses in Air," Phys. Rev. Lett. 86,5470-5473 (2001).
[CrossRef] [PubMed]

Nuter, R.

Peñano, J.R

P. Sprangle, J.R . Peñano and B . Hafizi, "Propagation of intense short laser pulses in the atmosphere," Phys. Rev. E 66,046418, 2002.
[CrossRef]

Prade, B.

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

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

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Breakup and Fusion of Self- Guided Femtosecond Light Pulses in Air," Phys. Rev. Lett. 86,5470-5473 (2001).
[CrossRef] [PubMed]

Salmon, E.

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

Sarifi, S.M.

W. Liu, Q. Luo, F. Théberge, H.L. Xu, S.A. Hosseini, S.M. Sarifi, S.L. Chin, "The influence of divergence on filament length during the propagation of intense ultra-short laser pulses," Appl. Phys. B 82,373-376 (2006).
[CrossRef]

Sauerbrey, R.

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

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

Skupin, S.

Sprangle, P.

P. Sprangle, J.R . Peñano and B . Hafizi, "Propagation of intense short laser pulses in the atmosphere," Phys. Rev. E 66,046418, 2002.
[CrossRef]

Talanov, V.I.

V.I. Talanov, "Focusing of light in cubic media," JETP Lett. 11,199-201 (1970).

Tamošauskas, G.

A. Dubietis, E. Gaizauskas, G. Tamošauskas, P. Di Trapani, "Light filaments without self-channeling," Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef] [PubMed]

Th´eberge, F.

W. Liu, Q. Luo, F. Théberge, H.L. Xu, S.A. Hosseini, S.M. Sarifi, S.L. Chin, "The influence of divergence on filament length during the propagation of intense ultra-short laser pulses," Appl. Phys. B 82,373-376 (2006).
[CrossRef]

Théberge, F.

S.L. Chin, S.A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V.P. Kandidov, O.G. Kosareva, and H. Schroeder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83,863-905 (2005).
[CrossRef]

Tzortzakis, S.

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

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

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Breakup and Fusion of Self- Guided Femtosecond Light Pulses in Air," Phys. Rev. Lett. 86,5470-5473 (2001).
[CrossRef] [PubMed]

Wang, Z.H.

Wei, Z.Y.

Wright, E.M.

M. Mlejnek, E.M. Wright, and J.V. Moloney, "Moving-Focus Versus Self-Waveguiding Model for Long-Distance Propagation of Femtosecond Pulses in Air," IEEE J. Quantum Eelecton. 35,1771 (1999).
[CrossRef]

Xu, H.L.

W. Liu, Q. Luo, F. Théberge, H.L. Xu, S.A. Hosseini, S.M. Sarifi, S.L. Chin, "The influence of divergence on filament length during the propagation of intense ultra-short laser pulses," Appl. Phys. B 82,373-376 (2006).
[CrossRef]

Xu, M.H.

Yu, W.

Yuan, X.H.

Zhang, J.

Zigler, A.

App. Phys. B (1)

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

Appl. Phys. B (3)

Q. Luo, S.A. Hosseini, W. Liu, J.˜F. Gravel, O.G. Kosareva, N.A. Panov, N. Aközbek, V.P. Kandidov, G. Roy, S.L. Chin, "Effect of beam diameter on the propagation of intense femtosecond lase pulses," Appl. Phys. B 80,35-38 (2005).
[CrossRef]

W. Liu, Q. Luo, F. Théberge, H.L. Xu, S.A. Hosseini, S.M. Sarifi, S.L. Chin, "The influence of divergence on filament length during the propagation of intense ultra-short laser pulses," Appl. Phys. B 82,373-376 (2006).
[CrossRef]

A. Couairon "Filamentation length of powerful laser pulses," Appl. Phys. B 76,789-792 (2003).
[CrossRef]

Can. J. Phys. (1)

S.L. Chin, S.A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V.P. Kandidov, O.G. Kosareva, and H. Schroeder, "The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges," Can. J. Phys. 83,863-905 (2005).
[CrossRef]

Eur. Phys. J. D. (1)

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

IEEE J. Quantum Eelecton. (1)

M. Mlejnek, E.M. Wright, and J.V. Moloney, "Moving-Focus Versus Self-Waveguiding Model for Long-Distance Propagation of Femtosecond Pulses in Air," IEEE J. Quantum Eelecton. 35,1771 (1999).
[CrossRef]

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V.I. Talanov, "Focusing of light in cubic media," JETP Lett. 11,199-201 (1970).

Laser und Optoelektronik (1)

L. Wöste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronnenberger, H. Schillinger, and R. Sauerbrey, "Femtosecond atmospheric lamp," Laser und Optoelektronik 29,51-53 (1997).

Opt. Commun. (1)

G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, "Range of plasma filaments created in air by a multi-terawatt femtosecond laser," Opt. Commun. 247,171-180 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. E (1)

P. Sprangle, J.R . Peñano and B . Hafizi, "Propagation of intense short laser pulses in the atmosphere," Phys. Rev. E 66,046418, 2002.
[CrossRef]

Phys. Rev. Lett. (2)

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Breakup and Fusion of Self- Guided Femtosecond Light Pulses in Air," Phys. Rev. Lett. 86,5470-5473 (2001).
[CrossRef] [PubMed]

A. Dubietis, E. Gaizauskas, G. Tamošauskas, P. Di Trapani, "Light filaments without self-channeling," Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef] [PubMed]

Science (1)

A.L. Gaeta, "Collapsing light really shines," Science 301,54-55 (2003).
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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, 61-64 (2003).
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Figures (7)

Fig. 1.
Fig. 1.

Control of the location of the blowup point zcF with a defocusing length with focal length F.

Fig. 2.
Fig. 2.

Dynamics of the on-axis intensity of the solution of the NLS (3) with various defocusing lenses. (a) F=-∞; (b) -F=1.18zc ; (c) -F=1.0034zc ; (d) -F=0.9975zc .

Fig. 3.
Fig. 3.

Experimental data extracted from Fig. 8 in [8]. Filamentation distance in air as a function of divergence angle θ. Input power is P=300GW (black, squares), P=350GW (red, circles), and P=400GW (green, triangles).

Fig. 4.
Fig. 4.

The filamentation distance as a function of the distance between the two lenses (d) for the double lens system with F 1=-0.5F 2<0.

Fig. 5.
Fig. 5.

Experimental setup of the double-lens system and filamentation distance measurement.

Fig. 6.
Fig. 6.

Experimental data (stars) and theoretical prediction (solid line) of the filamentation distance as a function of the distance between the lenses. (a) P≈660Pc and zc =11m; (b) P≈780Pc and zc =8.2m.

Fig. 7.
Fig. 7.

Filament length as a function of the filamentation distance, for the experimental data of Fig. 6 (b).

Equations (12)

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

1 z c F = 1 z c + 1 F .
z c F 1 , F 2 ( d ) = d + F 2 z c ( F 1 d ) d F 1 ( F 1 + F 2 ) z c + F 1 F 2 d ( z c + F 1 ) ,
i A z ( z , x , y ) + 2 A + A 2 A = 0 .
L ( z ) = 1 z F ,
ξ = x L ( z ) , η = y L ( z ) , ζ ( z ) = 0 z 1 L 2 .
1 ζ = 1 z + 1 F ,
1 z c F = 1 z c + 1 F .
z c Jin ( θ ) 2 ( p 1 ) + r m 2 tan 2 θ + tan θ 2 ( p 1 ) tan 2 θ ,
1 z c ( θ ) = 1 r 0 tan θ + 1 z c .
L ( z = d ) = ( 1 d F 1 )
z F 1 , F 2 = d + F 2 z F 1 d z d F 1 ( F 1 + F 2 d ) z + F 1 F 2 d F 1 .
z c F 1 , F 2 = d + F 2 z c ( F 1 d ) d F 1 ) ( F 1 + F 2 ) z c + F 1 F 2 d ( z c + F 1 ) .

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