Abstract

Competing nonlinear optical effects that act on femtosecond laser pulses propagating in a self-generated light filament may give rise to a pronounced radial beam deformation, similar to the z-pinch contraction of pulsed high-current discharges. This self-generated spatial beam contraction is accompanied by a pulse break-up that can be beneficially exploited for on-axis temporal compression of the pulse. The pinching mechanism therefore explains the recently observed self-compression and the complicated spatio-temporal shapes typical for filament propagation experiments.

© 2009 Optical Society of America

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  1. V. F. D’Yachenko and V. S. Imshenik, "Magnetohydrodynamic Theory of the Pinch Effect in a Dense High-Temperature Plasma (dense Plasma Focus)," Rev. Plasma. Phys. 5, 447-495 (1970).
  2. J. B. Taylor, "Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields," Phys. Rev. Lett. 33, 1139-1141 (1974).
    [CrossRef]
  3. E. B. Treacy, "Optical pulse compression with diffraction gratings," IEEE J. Quantum Electron. 5, 454-458 (1969).
    [CrossRef]
  4. C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761-763 (1982).
    [CrossRef]
  5. M. Nisoli, S. DeSilvestri, O. Svelto, R. Szipocs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, "Compression of high-energy laser pulses below 5 fs," Opt. Lett. 22, 522-524 (1997).
    [CrossRef] [PubMed]
  6. G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, "Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament," Opt. Lett. 31, 274-276 (2006).
    [CrossRef] [PubMed]
  7. S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, "Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74, 056604 (2006).
    [CrossRef]
  8. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, "Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient," Opt. Lett. 30, 2657-2659 (2005).
    [CrossRef] [PubMed]
  9. L. T. Vuong, R. B. Lopez-Martens, C. P. Hauri, and A. L. Gaeta, "Spectral reshaping and pulse compression via sequential filamentation in gases," Opt. Express 16, 390-401 (2008).
    [CrossRef] [PubMed]
  10. R. Fedele and P. K. Shukla, "Self-consistent interaction between the plasma wake field and the driving relativistic electron-beam," Phys. Rev. A 45, 4045-4049 (1992).
    [CrossRef] [PubMed]
  11. T. Passot and P. L. Sulem, "Alfven wave filamentation: from Hall-MHD to kinetic theory," Physica Scripta T113, 89-91 (2004).
  12. N. L. Wagner, E. A. Gibson, T. Popmintchev, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Selfcompression of ultrashort pulses through ionization-induced spatiotemporal reshaping," Phys. Rev. Lett. 93, 173902 (2004).
    [CrossRef] [PubMed]
  13. L. Bergé and A. Couairon, "Gas-induced solitons," Phys. Rev. Lett. 86, 1003-1006 (2001).
    [CrossRef] [PubMed]
  14. A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, "Ionization of atoms in an alternating electric field," Sov. Phys. JETP 23, 924-934 (1966).
  15. L. Bergé and A. Couairon, "Nonlinear propagation of self-guided ultra-short pulses in ionized gases," Phys. Plasmas 7, 210-230 (2000).
    [CrossRef]
  16. M. A. Darwish, "On integral equations of Urysohn-Volterra type," Appl. Math. Comput. 136, 93-98 (2003).
    [CrossRef]
  17. E. Babolian, F. Fattahzadeh, and E. Golpar Raboky, "A Chebyshev approximation for solving nonlinear integral equations of Hammerstein type," Appl. Math. Comput. 189, 641-646 (2007).
    [CrossRef]
  18. C. W. Clenshaw and A. R. Curtis, "A method for numerical integration on an automatic computer," Numer. Math. 2, 197-205 (1960).
    [CrossRef]
  19. C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
    [CrossRef] [PubMed]
  20. A. Couairon, E. Gaižauskas, 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]
  21. M. Mlejnek, E. M. Wright, and J. V. Moloney, "Dynamic spatial replenishment of femtosecond pulses propagating in air," Opt. Lett. 23, 382-384 (1997).
    [CrossRef]
  22. S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, "Spectrogram representation of pulse self compression by filamentation," Opt. Express 16, 17626-17636 (2008)
    [CrossRef] [PubMed]
  23. S. Akturk, C. D’Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "Pulse shortening, spatial mode cleaning, and intense terahertz generation by filamentation in xenon," Phys. Rev. A 76, 063819 (2007).
    [CrossRef]
  24. S. L. Chin, Y. Chen, O. Kosareva, V. P. Kandidov, and F. Théberge, "What is a filament?" Laser Phys. 18, 962-964 (2008).
    [CrossRef]
  25. A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5394-5405 (2007).
    [CrossRef] [PubMed]

2008 (3)

2007 (3)

A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5394-5405 (2007).
[CrossRef] [PubMed]

S. Akturk, C. D’Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "Pulse shortening, spatial mode cleaning, and intense terahertz generation by filamentation in xenon," Phys. Rev. A 76, 063819 (2007).
[CrossRef]

E. Babolian, F. Fattahzadeh, and E. Golpar Raboky, "A Chebyshev approximation for solving nonlinear integral equations of Hammerstein type," Appl. Math. Comput. 189, 641-646 (2007).
[CrossRef]

2006 (3)

A. Couairon, E. Gaižauskas, 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]

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, "Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74, 056604 (2006).
[CrossRef]

G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, "Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament," Opt. Lett. 31, 274-276 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (2)

T. Passot and P. L. Sulem, "Alfven wave filamentation: from Hall-MHD to kinetic theory," Physica Scripta T113, 89-91 (2004).

N. L. Wagner, E. A. Gibson, T. Popmintchev, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Selfcompression of ultrashort pulses through ionization-induced spatiotemporal reshaping," Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

2003 (2)

M. A. Darwish, "On integral equations of Urysohn-Volterra type," Appl. Math. Comput. 136, 93-98 (2003).
[CrossRef]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef] [PubMed]

2001 (1)

L. Bergé and A. Couairon, "Gas-induced solitons," Phys. Rev. Lett. 86, 1003-1006 (2001).
[CrossRef] [PubMed]

2000 (1)

L. Bergé and A. Couairon, "Nonlinear propagation of self-guided ultra-short pulses in ionized gases," Phys. Plasmas 7, 210-230 (2000).
[CrossRef]

1997 (2)

1992 (1)

R. Fedele and P. K. Shukla, "Self-consistent interaction between the plasma wake field and the driving relativistic electron-beam," Phys. Rev. A 45, 4045-4049 (1992).
[CrossRef] [PubMed]

1982 (1)

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761-763 (1982).
[CrossRef]

1974 (1)

J. B. Taylor, "Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields," Phys. Rev. Lett. 33, 1139-1141 (1974).
[CrossRef]

1970 (1)

V. F. D’Yachenko and V. S. Imshenik, "Magnetohydrodynamic Theory of the Pinch Effect in a Dense High-Temperature Plasma (dense Plasma Focus)," Rev. Plasma. Phys. 5, 447-495 (1970).

1969 (1)

E. B. Treacy, "Optical pulse compression with diffraction gratings," IEEE J. Quantum Electron. 5, 454-458 (1969).
[CrossRef]

1966 (1)

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, "Ionization of atoms in an alternating electric field," Sov. Phys. JETP 23, 924-934 (1966).

1960 (1)

C. W. Clenshaw and A. R. Curtis, "A method for numerical integration on an automatic computer," Numer. Math. 2, 197-205 (1960).
[CrossRef]

Akturk, S.

S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, "Spectrogram representation of pulse self compression by filamentation," Opt. Express 16, 17626-17636 (2008)
[CrossRef] [PubMed]

S. Akturk, C. D’Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "Pulse shortening, spatial mode cleaning, and intense terahertz generation by filamentation in xenon," Phys. Rev. A 76, 063819 (2007).
[CrossRef]

Babolian, E.

E. Babolian, F. Fattahzadeh, and E. Golpar Raboky, "A Chebyshev approximation for solving nonlinear integral equations of Hammerstein type," Appl. Math. Comput. 189, 641-646 (2007).
[CrossRef]

Bergé, L.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, "Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74, 056604 (2006).
[CrossRef]

L. Bergé and A. Couairon, "Gas-induced solitons," Phys. Rev. Lett. 86, 1003-1006 (2001).
[CrossRef] [PubMed]

L. Bergé and A. Couairon, "Nonlinear propagation of self-guided ultra-short pulses in ionized gases," Phys. Plasmas 7, 210-230 (2000).
[CrossRef]

Biegert, J.

Chen, Y.

S. L. Chin, Y. Chen, O. Kosareva, V. P. Kandidov, and F. Théberge, "What is a filament?" Laser Phys. 18, 962-964 (2008).
[CrossRef]

Chin, S. L.

S. L. Chin, Y. Chen, O. Kosareva, V. P. Kandidov, and F. Théberge, "What is a filament?" Laser Phys. 18, 962-964 (2008).
[CrossRef]

Christov, I. P.

N. L. Wagner, E. A. Gibson, T. Popmintchev, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Selfcompression of ultrashort pulses through ionization-induced spatiotemporal reshaping," Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

Clenshaw, C. W.

C. W. Clenshaw and A. R. Curtis, "A method for numerical integration on an automatic computer," Numer. Math. 2, 197-205 (1960).
[CrossRef]

Conti, C.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef] [PubMed]

Couairon, A.

S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, "Spectrogram representation of pulse self compression by filamentation," Opt. Express 16, 17626-17636 (2008)
[CrossRef] [PubMed]

S. Akturk, C. D’Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "Pulse shortening, spatial mode cleaning, and intense terahertz generation by filamentation in xenon," Phys. Rev. A 76, 063819 (2007).
[CrossRef]

A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15, 5394-5405 (2007).
[CrossRef] [PubMed]

A. Couairon, E. Gaižauskas, 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]

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, "Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient," Opt. Lett. 30, 2657-2659 (2005).
[CrossRef] [PubMed]

L. Bergé and A. Couairon, "Gas-induced solitons," Phys. Rev. Lett. 86, 1003-1006 (2001).
[CrossRef] [PubMed]

L. Bergé and A. Couairon, "Nonlinear propagation of self-guided ultra-short pulses in ionized gases," Phys. Plasmas 7, 210-230 (2000).
[CrossRef]

Curtis, A. R.

C. W. Clenshaw and A. R. Curtis, "A method for numerical integration on an automatic computer," Numer. Math. 2, 197-205 (1960).
[CrossRef]

D’Amico, C.

S. Akturk, C. D’Amico, M. Franco, A. Couairon, and A. Mysyrowicz, "Pulse shortening, spatial mode cleaning, and intense terahertz generation by filamentation in xenon," Phys. Rev. A 76, 063819 (2007).
[CrossRef]

D’Yachenko, V. F.

V. F. D’Yachenko and V. S. Imshenik, "Magnetohydrodynamic Theory of the Pinch Effect in a Dense High-Temperature Plasma (dense Plasma Focus)," Rev. Plasma. Phys. 5, 447-495 (1970).

Darwish, M. A.

M. A. Darwish, "On integral equations of Urysohn-Volterra type," Appl. Math. Comput. 136, 93-98 (2003).
[CrossRef]

DeSilvestri, S.

Di Trapani, P.

A. Couairon, E. Gaižauskas, 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]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef] [PubMed]

Dubietis, A.

A. Couairon, E. Gaižauskas, 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]

Faccio, D.

A. Couairon, E. Gaižauskas, 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]

Fattahzadeh, F.

E. Babolian, F. Fattahzadeh, and E. Golpar Raboky, "A Chebyshev approximation for solving nonlinear integral equations of Hammerstein type," Appl. Math. Comput. 189, 641-646 (2007).
[CrossRef]

Fedele, R.

R. Fedele and P. K. Shukla, "Self-consistent interaction between the plasma wake field and the driving relativistic electron-beam," Phys. Rev. A 45, 4045-4049 (1992).
[CrossRef] [PubMed]

Ferencz, K.

Fork, R. L.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761-763 (1982).
[CrossRef]

Franco, M.

Gaeta, A. L.

Gaižauskas, E.

A. Couairon, E. Gaižauskas, 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]

Gallmann, L.

Gibson, E. A.

N. L. Wagner, E. A. Gibson, T. Popmintchev, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Selfcompression of ultrashort pulses through ionization-induced spatiotemporal reshaping," Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

Golpar Raboky, E.

E. Babolian, F. Fattahzadeh, and E. Golpar Raboky, "A Chebyshev approximation for solving nonlinear integral equations of Hammerstein type," Appl. Math. Comput. 189, 641-646 (2007).
[CrossRef]

Guandalini, A.

Hauri, C. P.

Holler, M.

Imshenik, V. S.

V. F. D’Yachenko and V. S. Imshenik, "Magnetohydrodynamic Theory of the Pinch Effect in a Dense High-Temperature Plasma (dense Plasma Focus)," Rev. Plasma. Phys. 5, 447-495 (1970).

Jedrkiewicz, O.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef] [PubMed]

Kandidov, V. P.

S. L. Chin, Y. Chen, O. Kosareva, V. P. Kandidov, and F. Théberge, "What is a filament?" Laser Phys. 18, 962-964 (2008).
[CrossRef]

Kapteyn, H. C.

N. L. Wagner, E. A. Gibson, T. Popmintchev, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Selfcompression of ultrashort pulses through ionization-induced spatiotemporal reshaping," Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

Keller, U.

Kosareva, O.

S. L. Chin, Y. Chen, O. Kosareva, V. P. Kandidov, and F. Théberge, "What is a filament?" Laser Phys. 18, 962-964 (2008).
[CrossRef]

Krausz, F.

Lederer, F.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, "Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74, 056604 (2006).
[CrossRef]

Lopez-Martens, R. B.

Mlejnek, M.

Moloney, J. V.

Murnane, M. M.

N. L. Wagner, E. A. Gibson, T. Popmintchev, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Selfcompression of ultrashort pulses through ionization-induced spatiotemporal reshaping," Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

Mysyrowicz, A.

Nisoli, M.

Passot, T.

T. Passot and P. L. Sulem, "Alfven wave filamentation: from Hall-MHD to kinetic theory," Physica Scripta T113, 89-91 (2004).

Perelomov, A. M.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, "Ionization of atoms in an alternating electric field," Sov. Phys. JETP 23, 924-934 (1966).

Piskarskas, A.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef] [PubMed]

Popmintchev, T.

N. L. Wagner, E. A. Gibson, T. Popmintchev, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Selfcompression of ultrashort pulses through ionization-induced spatiotemporal reshaping," Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

Popov, V. S.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, "Ionization of atoms in an alternating electric field," Sov. Phys. JETP 23, 924-934 (1966).

Sartania, S.

Schapper, F.

Schnuerer, M.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, "Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74, 056604 (2006).
[CrossRef]

Shank, C. V.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761-763 (1982).
[CrossRef]

Shukla, P. K.

R. Fedele and P. K. Shukla, "Self-consistent interaction between the plasma wake field and the driving relativistic electron-beam," Phys. Rev. A 45, 4045-4049 (1992).
[CrossRef] [PubMed]

Skupin, S.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, "Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74, 056604 (2006).
[CrossRef]

Sokollik, T.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, "Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74, 056604 (2006).
[CrossRef]

Spielmann, C.

Steinmeyer, G.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, "Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74, 056604 (2006).
[CrossRef]

G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, "Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament," Opt. Lett. 31, 274-276 (2006).
[CrossRef] [PubMed]

Stibenz, G.

G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, "Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament," Opt. Lett. 31, 274-276 (2006).
[CrossRef] [PubMed]

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnuerer, N. Zhavoronkov, and G. Steinmeyer, "Selfcompression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74, 056604 (2006).
[CrossRef]

Stolen, R. H.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761-763 (1982).
[CrossRef]

Sulem, P. L.

T. Passot and P. L. Sulem, "Alfven wave filamentation: from Hall-MHD to kinetic theory," Physica Scripta T113, 89-91 (2004).

Svelto, O.

Szipocs, R.

Taylor, J. B.

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[CrossRef]

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Théberge, F.

S. L. Chin, Y. Chen, O. Kosareva, V. P. Kandidov, and F. Théberge, "What is a filament?" Laser Phys. 18, 962-964 (2008).
[CrossRef]

Tomlinson, W. J.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761-763 (1982).
[CrossRef]

Treacy, E. B.

E. B. Treacy, "Optical pulse compression with diffraction gratings," IEEE J. Quantum Electron. 5, 454-458 (1969).
[CrossRef]

Trillo, S.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef] [PubMed]

Trull, J.

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef] [PubMed]

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C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef] [PubMed]

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Wagner, N. L.

N. L. Wagner, E. A. Gibson, T. Popmintchev, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Selfcompression of ultrashort pulses through ionization-induced spatiotemporal reshaping," Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

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C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761-763 (1982).
[CrossRef]

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C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761-763 (1982).
[CrossRef]

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[CrossRef]

A. Couairon, E. Gaižauskas, 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]

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J. B. Taylor, "Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields," Phys. Rev. Lett. 33, 1139-1141 (1974).
[CrossRef]

N. L. Wagner, E. A. Gibson, T. Popmintchev, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, "Selfcompression of ultrashort pulses through ionization-induced spatiotemporal reshaping," Phys. Rev. Lett. 93, 173902 (2004).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear electromagnetic X waves," Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef] [PubMed]

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A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, "Ionization of atoms in an alternating electric field," Sov. Phys. JETP 23, 924-934 (1966).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Spectrum of solutions I(t) of Eq. (5). (b) Spatio-temporal representation of the solution of Eq. (5) marked in red [see (a)], obtained by rotating the line segment generated by R (t)=P(t)/πI(t) around the t-axis. Color corresponds to on-axis intensity.

Fig. 2.
Fig. 2.

(a) Evolution of the on-axis temporal intensity profile along z for the reduced numerical model governed by Eq. (1). (b) Same for the simulation of the full model equations [7].

Fig. 3.
Fig. 3.

(a) Pulse sequence illustrating the two-stage self-compression mechanism. Shown are the on-axis intensity profiles for z=1.5m (solid line), z=1.55m (dashed line) and z=1.7m (dashed-dotted line). (b) Self-compressed few-cycle pulse at z=2.5m. (c) Spatiotemporal characteristics of the double-spiked structure at z=1.55 m. (d) Same for the fewcycle pulse at z=2.5m.

Fig. 4.
Fig. 4.

Sequence of pulses illustrating temporal self-compression due to Kerr-induced spatial self-pinching in the variational model corresponding to (a) z = 1.7m, (b) z = 1.9m, (c) z = 2.1m and (d) z = 2.3m.

Equations (6)

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z𝓔=i2k0r r r r𝓔+iω0cn2𝓔2𝓔iω02n0cρcρ(I)𝓔,
ρ(I)=ρnt(1exp(tdtW[I(t)])).
𝓔=PπR2exp[r22R2+ik0r2zR2R].
z20r3𝓔2dr=2k02 0r r𝓔2 d r
2n2n00r 𝓔4 d r 1n02ρc 0𝓔2r2 r ρ d r .
0=1P(t)Pcr +μP2(t)tdtIN*+1(t)P(t)1(I(t)+N*I(t)P(t)P(t))2 ,

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