Abstract

Laser filamentation is understood to be self-channeling of intense ultrashort laser pulses achieved when the self-focusing because of the Kerr nonlinearity is balanced by ionization-induced defocusing. Here, we show that, right behind the ionized region of a laser filament, ultrashort laser pulses can couple into a much longer light channel, where a stable self-guiding spatial mode is sustained by the saturable self-focusing nonlinearity. In the limiting regime of negligibly low ionization, this post-filamentation beam dynamics converges to a large-scale beam self-trapping scenario known since the pioneering work on saturable self-focusing nonlinearities.

© 2014 Optical Society of America

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2011 (2)

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef]

J.-F. Daigle, T.-J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, Appl. Opt. 50, 6234 (2011).
[CrossRef]

2010 (1)

P. Bejot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

2009 (1)

2008 (1)

Y. Chen, F. Théberge, C. Marceau, H. Xu, N. Aközbek, O. Kosareva, and S. L. Chin, Appl. Phys. B 91, 219 (2008).
[CrossRef]

2007 (2)

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

2005 (1)

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

2004 (3)

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (2004).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

2003 (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, Science 301, 61 (2003).
[CrossRef]

1995 (1)

1992 (1)

M. Karlsson, Phys. Rev. A 46, 2726 (1992).
[CrossRef]

1991 (1)

1990 (1)

1974 (1)

A. H. Piekara, J. S. Moore, and M. S. Field, Phys. Rev. A 9, 1403 (1974).
[CrossRef]

1969 (1)

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

1968 (1)

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

1965 (2)

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965) [Zh. Eksp. Teor. Fiz. 47, 1945 (1965)].

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

1962 (1)

G. A. Askar’yan, Sov. Phys. JETP 15, 1088 (1962) [Zh. Eksp. Teor. Fiz. 42, 1657 (1961)].

Aközbek, N.

Y. Chen, F. Théberge, C. Marceau, H. Xu, N. Aközbek, O. Kosareva, and S. L. Chin, Appl. Phys. B 91, 219 (2008).
[CrossRef]

André, Y.-B.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (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, Science 301, 61 (2003).
[CrossRef]

Askar’yan, G. A.

G. A. Askar’yan, Sov. Phys. JETP 15, 1088 (1962) [Zh. Eksp. Teor. Fiz. 42, 1657 (1961)].

Bejot, P.

P. Bejot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

Berge, L.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Biegert, J.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[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, Science 301, 61 (2003).
[CrossRef]

Brown, A.

Chen, Y.

Y. Chen, F. Théberge, C. Marceau, H. Xu, N. Aközbek, O. Kosareva, and S. L. Chin, Appl. Phys. B 91, 219 (2008).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Chin, S. L.

J.-F. Daigle, T.-J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, Appl. Opt. 50, 6234 (2011).
[CrossRef]

Y. Chen, F. Théberge, C. Marceau, H. Xu, N. Aközbek, O. Kosareva, and S. L. Chin, Appl. Phys. B 91, 219 (2008).
[CrossRef]

Couairon, A.

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (2004).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

D’Amico, C.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (2004).
[CrossRef]

Daigle, J.-F.

Di Trapani, P.

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef]

Du, D.

Dubietis, A.

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef]

Faucher, O.

P. Bejot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef]

Field, M. S.

A. H. Piekara, J. S. Moore, and M. S. Field, Phys. Rev. A 9, 1403 (1974).
[CrossRef]

Franco, M.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (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, Science 301, 61 (2003).
[CrossRef]

Gaižauskas, E.

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Gustafson, T. K.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Hauri, C. P.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Haus, H. A.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

Heinrich, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Helbing, F. W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Henin, S.

P. Bejot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

Hertz, E.

P. Bejot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef]

Hosseini, S.

Karlsson, M.

M. Karlsson, Phys. Rev. A 46, 2726 (1992).
[CrossRef]

Kasparian, J.

P. Bejot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (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, Science 301, 61 (2003).
[CrossRef]

Kean, P. N.

Keldysh, L. V.

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965) [Zh. Eksp. Teor. Fiz. 47, 1945 (1965)].

Keller, U.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Kelley, P. L.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Kolesik, M.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef]

Korn, G.

Kornelis, W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Kosareva, O.

Y. Chen, F. Théberge, C. Marceau, H. Xu, N. Aközbek, O. Kosareva, and S. L. Chin, Appl. Phys. B 91, 219 (2008).
[CrossRef]

Lavorel, B.

P. Bejot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef]

Lifsitz, J. R.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Liu, X.

Loriot, V.

P. Bejot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef]

Marburger, J. H.

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

Marceau, C.

Y. Chen, F. Théberge, C. Marceau, H. Xu, N. Aközbek, O. Kosareva, and S. L. Chin, Appl. Phys. B 91, 219 (2008).
[CrossRef]

Méchain, G.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (2004).
[CrossRef]

Méjean, G.

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, Science 301, 61 (2003).
[CrossRef]

Moloney, J. V.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef]

Moore, J. S.

A. H. Piekara, J. S. Moore, and M. S. Field, Phys. Rev. A 9, 1403 (1974).
[CrossRef]

Mourou, G.

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (2004).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (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, Science 301, 61 (2003).
[CrossRef]

Nuter, R.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Piekara, A. H.

A. H. Piekara, J. S. Moore, and M. S. Field, Phys. Rev. A 9, 1403 (1974).
[CrossRef]

Polynkin, P.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef]

Prade, B.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (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, Science 301, 61 (2003).
[CrossRef]

Roy, G.

Salmon, E.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[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, Science 301, 61 (2003).
[CrossRef]

Sauerbrey, R.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (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, Science 301, 61 (2003).
[CrossRef]

Shen, Y. R.

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

Sibbett, W.

Silberberg, Y.

Skupin, S.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Spence, D. E.

Squier, J.

Tamošauskas, G.

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef]

Taran, J. P.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, Phys. Rev. 177, 306 (1969).
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G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
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G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (2004).
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Vieillard, T.

P. Bejot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
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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, Science 301, 61 (2003).
[CrossRef]

Wolf, J.-P.

P. Bejot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
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[CrossRef]

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, Science 301, 61 (2003).
[CrossRef]

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Y. Chen, F. Théberge, C. Marceau, H. Xu, N. Aközbek, O. Kosareva, and S. L. Chin, Appl. Phys. B 91, 219 (2008).
[CrossRef]

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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, Science 301, 61 (2003).
[CrossRef]

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Appl. Opt. (1)

Appl. Phys. B (3)

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (2004).
[CrossRef]

Y. Chen, F. Théberge, C. Marceau, H. Xu, N. Aközbek, O. Kosareva, and S. L. Chin, Appl. Phys. B 91, 219 (2008).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
[CrossRef]

Opt. Commun. (1)

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

Phys. Rev. (2)

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Phys. Rev. A (2)

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[CrossRef]

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[CrossRef]

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P. Bejot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef]

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

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[CrossRef]

Rep. Prog. Phys. (1)

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[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, Science 301, 61 (2003).
[CrossRef]

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Other (1)

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

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Figures (3)

Fig. 1.
Fig. 1.

(a) Supercontinuum spectra generated by 1030-nm, 200-fs Yb-laser pulses behind the self-channeling region at z=4.6m: (solid line) experiments and (dashed line) simulations. The energy of the input pulse is indicated in the panels. The input spectrum is shown by shading. (b) The experimental SHG FROG trace, (c) the Wigner spectrogram, (d) temporal envelope (solid line) and the phase (dashed line), and (e) the spectrum (solid line) and spectral phase (dashed line) of the laser pulse with τ0200fs and W04mJ behind the self-channeling region at z=4.6m. (f) The experimental SHG FROG trace and (g) temporal envelope (solid line) and the phase (dashed line) of the same laser pulse behind the self-channeling region following a partial chirp compensation with a 6-cm-thick silica block.

Fig. 2.
Fig. 2.

(a) Map of the field intensity (on the color-coded dB scale) integrated over the entire pulse with the FWHM beam radius rFWHM (blue curve) and rms beam radius r0 (rose curve), (b) the on-axis electron density along the beam propagation path, (c) the spatiotemporal map of beam self-trapping, and (d) evolution of the spectrum along the propagation path. (e) Spectrum of the laser pulse behind the self-channeling region at z=4.6m calculated with the full model (curve 2), with the Raman effect disabled (fR=0) for z>2.8m (curve 3), and with self-steepening disabled for z>2.8m (curve 1, shading); and (f) the spectrum of the laser pulse behind the self-channeling region at z=4.6m: (curve 1, shading) experiments, simulations with the full, three-dimensional model (curve 2), and calculations with a one-dimensional model (curve 3).

Fig. 3.
Fig. 3.

(a)–(d) Maps of the field intensity (on the color-coded dB scale) integrated over the entire pulse with the FWHM beam radius rFWHM (blue curve) and rms beam radius r0 (rose curve) calculated using the full model (a), with ionization disabled (b), with the n4 term in Eq. (1) disabled (c), and (d) with a 350-μm-radius circular pinhole (white line) placed at z=3m. (e) Pulse evolution along the propagation path. The initial beam diameter is 11 mm, τ0200fs, and W04mJ.

Equations (1)

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A/z=iω0n2T˜c1[δ(η)(1fR)]I+fRR(ηη)I(η,r,z)dη]A,

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