Abstract

We investigate the reversibility of laser filamentation, a self-sustained, non-linear propagation regime including dissipation and time-retarded effects. We show that even losses related to ionization marginally affect the possibility of reverse propagating ultrashort pulses back to the initial conditions, although they make it prone to finite-distance blow-up susceptible to prevent backward propagation.

© 2014 Optical Society of America

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  1. A. Ben-Artzi, I. Gohberg, and M. A. Kaashoek, “Invertibility and dichotomy of differential operators on a half-line,” J. Dyn. Diff. Eq. 5, 1–36 (1993).
    [Crossref]
  2. M. K. Chernyshov, “Invertibility of first-order linear differential operators,” Math. Notes 64, 688–693 (1998).
    [Crossref]
  3. M. Fliess, “A note on the invertibility of nonlinear input-output differential systems,” Syst. Control Lett. 8, 147–151 (1986).
    [Crossref]
  4. M. Tsang, D. Psaltis, and F. Omenetto, “Reverse propagation of femtosecond pulses in optical fibers,” Opt. Lett. 28, 1873–1875 (2003).
    [Crossref] [PubMed]
  5. A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802 (2011).
    [Crossref]
  6. C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photon. 3, 211 (2009).
    [Crossref]
  7. C. Wang, R. Martini, and C. P. Search, “Time-reversing light pulses by adiabatic coupling modulation in coupled-resonator optical waveguides,” Phys. Rev. A 86, 063832 (2012).
    [Crossref]
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    [Crossref]
  10. 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]
  11. L. Bergé, S. Skupin, R. Nuter R, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly-ionized, optically-transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
    [Crossref]
  12. N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: A nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
    [Crossref]
  13. E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
    [Crossref]
  14. F. Morales, M. Richter, S. Patchkovskii, and O. Smirnova, “Imaging the Kramers-Henneberger atom,” Proc. Natl. Acad. Sci. U.S.A. 187, 16906–16911 (2011).
    [Crossref]
  15. M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
    [Crossref]
  16. P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “On quantum mechanical origin of higher-order Kerr effect in gases: induced resonances and channel closure,” Phys. Rev. Lett. 110, 043902 (2013).
    [Crossref]
  17. J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
    [Crossref]
  18. J. F. Daigle, A. Jaron-Becker, S. Hosseini, T. J. Wang, Y. Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
    [Crossref]
  19. F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215 (2003).
    [Crossref]
  20. W. Liu, F. Théberge, E. Arévalo, J.-F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005).
    [Crossref] [PubMed]
  21. B. Prade, M. Franco, A. Mysyrowicz, A. Couairon, H. Buersing, B. Eberle, M. Krenz, D. Seiffer, and O. Vasseur, “Spatial mode cleaning by femtosecond filamentation in air,” Opt. Lett. 31, 2601–2603 (2006).
    [Crossref] [PubMed]
  22. B. G. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
    [Crossref] [PubMed]
  23. A. Vinçotte and L. Bergé, “χ(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,” Phys. Rev. A 70, 061802(R) (2004).
    [Crossref]
  24. G. Fibich, “Self-focusing in the damped nonlinear Schrödinger equation,” J. Appl. Math. 61, 1680–1705 (2001).
  25. M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
    [Crossref]
  26. M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
    [Crossref]
  27. M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in 02, N2 and CO2,” Chem. Phys. Lett. 209, 1–9 (1993).
    [Crossref]
  28. C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J.-P. McTague, “Birefringence arising from the reorientation of the polarizability anisotropy of molecnles in collisionless gases,” Phys. Rev. A 13, 813–829 (1976).
    [Crossref]
  29. N. Berti, P. Béjot, J. P. Wolf, and O. Faucher, “Molecular alignment and filamentation: comparison between weak and strong field models,” Submitted to Phys. Rev. A, arXiv:1407.3952.
  30. H. Stapelfeldt and T. Seideman, “Colloquium: Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 534–557 (2003).
    [Crossref]
  31. P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
    [Crossref] [PubMed]
  32. P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “Transition from plasma- to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011)
    [Crossref]
  33. M. Scheller, M. S. Mills, M.-A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photon. 8, 297–301 (2014).
    [Crossref]

2014 (1)

M. Scheller, M. S. Mills, M.-A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photon. 8, 297–301 (2014).
[Crossref]

2013 (2)

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “On quantum mechanical origin of higher-order Kerr effect in gases: induced resonances and channel closure,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

2012 (2)

B. G. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

C. Wang, R. Martini, and C. P. Search, “Time-reversing light pulses by adiabatic coupling modulation in coupled-resonator optical waveguides,” Phys. Rev. A 86, 063832 (2012).
[Crossref]

2011 (4)

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802 (2011).
[Crossref]

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
[Crossref]

F. Morales, M. Richter, S. Patchkovskii, and O. Smirnova, “Imaging the Kramers-Henneberger atom,” Proc. Natl. Acad. Sci. U.S.A. 187, 16906–16911 (2011).
[Crossref]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “Transition from plasma- to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011)
[Crossref]

2010 (2)

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

J. F. Daigle, A. Jaron-Becker, S. Hosseini, T. J. Wang, Y. Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[Crossref]

2009 (1)

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photon. 3, 211 (2009).
[Crossref]

2008 (1)

N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: A nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
[Crossref]

2007 (2)

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

L. Bergé, S. Skupin, R. Nuter R, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly-ionized, optically-transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

2006 (1)

2005 (2)

W. Liu, F. Théberge, E. Arévalo, J.-F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005).
[Crossref] [PubMed]

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]

2004 (2)

A. Vinçotte and L. Bergé, “χ(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,” Phys. Rev. A 70, 061802(R) (2004).
[Crossref]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[Crossref]

2003 (3)

H. Stapelfeldt and T. Seideman, “Colloquium: Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 534–557 (2003).
[Crossref]

M. Tsang, D. Psaltis, and F. Omenetto, “Reverse propagation of femtosecond pulses in optical fibers,” Opt. Lett. 28, 1873–1875 (2003).
[Crossref] [PubMed]

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

2002 (1)

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[Crossref]

2001 (1)

G. Fibich, “Self-focusing in the damped nonlinear Schrödinger equation,” J. Appl. Math. 61, 1680–1705 (2001).

2000 (1)

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[Crossref]

1998 (1)

M. K. Chernyshov, “Invertibility of first-order linear differential operators,” Math. Notes 64, 688–693 (1998).
[Crossref]

1995 (1)

1993 (2)

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in 02, N2 and CO2,” Chem. Phys. Lett. 209, 1–9 (1993).
[Crossref]

A. Ben-Artzi, I. Gohberg, and M. A. Kaashoek, “Invertibility and dichotomy of differential operators on a half-line,” J. Dyn. Diff. Eq. 5, 1–36 (1993).
[Crossref]

1986 (1)

M. Fliess, “A note on the invertibility of nonlinear input-output differential systems,” Syst. Control Lett. 8, 147–151 (1986).
[Crossref]

1976 (1)

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J.-P. McTague, “Birefringence arising from the reorientation of the polarizability anisotropy of molecnles in collisionless gases,” Phys. Rev. A 13, 813–829 (1976).
[Crossref]

Aközbek, N.

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]

Arévalo, E.

Barsi, C.

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photon. 3, 211 (2009).
[Crossref]

Becker, A.

J. F. Daigle, A. Jaron-Becker, S. Hosseini, T. J. Wang, Y. Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[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]

W. Liu, F. Théberge, E. Arévalo, J.-F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005).
[Crossref] [PubMed]

Béjot, P.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “On quantum mechanical origin of higher-order Kerr effect in gases: induced resonances and channel closure,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “Transition from plasma- to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011)
[Crossref]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

N. Berti, P. Béjot, J. P. Wolf, and O. Faucher, “Molecular alignment and filamentation: comparison between weak and strong field models,” Submitted to Phys. Rev. A, arXiv:1407.3952.

Ben-Artzi, A.

A. Ben-Artzi, I. Gohberg, and M. A. Kaashoek, “Invertibility and dichotomy of differential operators on a half-line,” J. Dyn. Diff. Eq. 5, 1–36 (1993).
[Crossref]

Bergé, L.

L. Bergé, S. Skupin, R. Nuter R, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly-ionized, optically-transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

A. Vinçotte and L. Bergé, “χ(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,” Phys. Rev. A 70, 061802(R) (2004).
[Crossref]

Berti, N.

N. Berti, P. Béjot, J. P. Wolf, and O. Faucher, “Molecular alignment and filamentation: comparison between weak and strong field models,” Submitted to Phys. Rev. A, arXiv:1407.3952.

Blackwell, M.

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in 02, N2 and CO2,” Chem. Phys. Lett. 209, 1–9 (1993).
[Crossref]

Boutou, V.

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

Braun, A.

Buersing, H.

Chen, Y.

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in 02, N2 and CO2,” Chem. Phys. Lett. 209, 1–9 (1993).
[Crossref]

Cheng, W.

M. Scheller, M. S. Mills, M.-A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photon. 8, 297–301 (2014).
[Crossref]

Chernyshov, M. K.

M. K. Chernyshov, “Invertibility of first-order linear differential operators,” Math. Notes 64, 688–693 (1998).
[Crossref]

Chiao, R. Y.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J.-P. McTague, “Birefringence arising from the reorientation of the polarizability anisotropy of molecnles in collisionless gases,” Phys. Rev. A 13, 813–829 (1976).
[Crossref]

Chin, S. L.

J. F. Daigle, A. Jaron-Becker, S. Hosseini, T. J. Wang, Y. Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[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]

W. Liu, F. Théberge, E. Arévalo, J.-F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005).
[Crossref] [PubMed]

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[Crossref]

Christodoulides, D. N.

M. Scheller, M. S. Mills, M.-A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photon. 8, 297–301 (2014).
[Crossref]

Cormier, E.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “On quantum mechanical origin of higher-order Kerr effect in gases: induced resonances and channel closure,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

Couairon, A.

Courvoisier, F.

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

Daigle, J. F.

J. F. Daigle, A. Jaron-Becker, S. Hosseini, T. J. Wang, Y. Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[Crossref]

Du, D.

Eberle, B.

Faucher, O.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “On quantum mechanical origin of higher-order Kerr effect in gases: induced resonances and channel closure,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “Transition from plasma- to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011)
[Crossref]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

N. Berti, P. Béjot, J. P. Wolf, and O. Faucher, “Molecular alignment and filamentation: comparison between weak and strong field models,” Submitted to Phys. Rev. A, arXiv:1407.3952.

Fibich, G.

B. G. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: A nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
[Crossref]

G. Fibich, “Self-focusing in the damped nonlinear Schrödinger equation,” J. Appl. Math. 61, 1680–1705 (2001).

Fleischer, J. W.

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photon. 3, 211 (2009).
[Crossref]

Fliess, M.

M. Fliess, “A note on the invertibility of nonlinear input-output differential systems,” Syst. Control Lett. 8, 147–151 (1986).
[Crossref]

Franco, M.

Gaeta, A. L.

B. G. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: A nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
[Crossref]

Gavish, N.

N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: A nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
[Crossref]

Gohberg, I.

A. Ben-Artzi, I. Gohberg, and M. A. Kaashoek, “Invertibility and dichotomy of differential operators on a half-line,” J. Dyn. Diff. Eq. 5, 1–36 (1993).
[Crossref]

Goy, A.

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802 (2011).
[Crossref]

Gravel, J.-F.

Gustafson, T. K.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J.-P. McTague, “Birefringence arising from the reorientation of the polarizability anisotropy of molecnles in collisionless gases,” Phys. Rev. A 13, 813–829 (1976).
[Crossref]

Henin, S.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

Heritage, J. P.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J.-P. McTague, “Birefringence arising from the reorientation of the polarizability anisotropy of molecnles in collisionless gases,” Phys. Rev. A 13, 813–829 (1976).
[Crossref]

Hertz, E.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “On quantum mechanical origin of higher-order Kerr effect in gases: induced resonances and channel closure,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “Transition from plasma- to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011)
[Crossref]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

Hosseini, S.

J. F. Daigle, A. Jaron-Becker, S. Hosseini, T. J. Wang, Y. Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[Crossref]

Hosseini, S. A.

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]

Hunziker, L.

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in 02, N2 and CO2,” Chem. Phys. Lett. 209, 1–9 (1993).
[Crossref]

Ivanov, M.

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

Jaron-Becker, A.

J. F. Daigle, A. Jaron-Becker, S. Hosseini, T. J. Wang, Y. Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[Crossref]

Kaashoek, M. A.

A. Ben-Artzi, I. Gohberg, and M. A. Kaashoek, “Invertibility and dichotomy of differential operators on a half-line,” J. Dyn. Diff. Eq. 5, 1–36 (1993).
[Crossref]

Kamali, Y.

J. F. Daigle, A. Jaron-Becker, S. Hosseini, T. J. Wang, Y. Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[Crossref]

Kandidov, V. P.

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]

Kasparian, J.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “On quantum mechanical origin of higher-order Kerr effect in gases: induced resonances and channel closure,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “Transition from plasma- to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011)
[Crossref]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

L. Bergé, S. Skupin, R. Nuter R, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly-ionized, optically-transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

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

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[Crossref]

Klein, M.

B. G. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

Kolesik, M.

M. Scheller, M. S. Mills, M.-A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photon. 8, 297–301 (2014).
[Crossref]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[Crossref]

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[Crossref]

Korn, G.

Kosareva, O. G.

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]

Krenz, M.

Lavorel, B.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “On quantum mechanical origin of higher-order Kerr effect in gases: induced resonances and channel closure,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “Transition from plasma- to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011)
[Crossref]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

Lin, C. H.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J.-P. McTague, “Birefringence arising from the reorientation of the polarizability anisotropy of molecnles in collisionless gases,” Phys. Rev. A 13, 813–829 (1976).
[Crossref]

Liu, W.

W. Liu, F. Théberge, E. Arévalo, J.-F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005).
[Crossref] [PubMed]

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]

Liu, X.

Loriot, V.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

Ludowise, P.

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in 02, N2 and CO2,” Chem. Phys. Lett. 209, 1–9 (1993).
[Crossref]

Luo, Q.

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]

Martini, R.

C. Wang, R. Martini, and C. P. Search, “Time-reversing light pulses by adiabatic coupling modulation in coupled-resonator optical waveguides,” Phys. Rev. A 86, 063832 (2012).
[Crossref]

McTague, J.-P.

C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao, and J.-P. McTague, “Birefringence arising from the reorientation of the polarizability anisotropy of molecnles in collisionless gases,” Phys. Rev. A 13, 813–829 (1976).
[Crossref]

Méjean, G.

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

Mills, M. S.

M. Scheller, M. S. Mills, M.-A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photon. 8, 297–301 (2014).
[Crossref]

Miri, M.-A.

M. Scheller, M. S. Mills, M.-A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photon. 8, 297–301 (2014).
[Crossref]

Mlejnek, M.

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[Crossref]

Moloney, J. V.

M. Scheller, M. S. Mills, M.-A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photon. 8, 297–301 (2014).
[Crossref]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[Crossref]

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[Crossref]

Morales, F.

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

F. Morales, M. Richter, S. Patchkovskii, and O. Smirnova, “Imaging the Kramers-Henneberger atom,” Proc. Natl. Acad. Sci. U.S.A. 187, 16906–16911 (2011).
[Crossref]

Morgen, M.

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in 02, N2 and CO2,” Chem. Phys. Lett. 209, 1–9 (1993).
[Crossref]

Mourou, G.

Mysyrowicz, A.

Nuter R, R.

L. Bergé, S. Skupin, R. Nuter R, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly-ionized, optically-transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Omenetto, F.

Patchkovskii, S.

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

F. Morales, M. Richter, S. Patchkovskii, and O. Smirnova, “Imaging the Kramers-Henneberger atom,” Proc. Natl. Acad. Sci. U.S.A. 187, 16906–16911 (2011).
[Crossref]

Polynkin, P.

M. Scheller, M. S. Mills, M.-A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photon. 8, 297–301 (2014).
[Crossref]

Popov, A. M.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
[Crossref]

Prade, B.

Price, W.

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in 02, N2 and CO2,” Chem. Phys. Lett. 209, 1–9 (1993).
[Crossref]

Psaltis, D.

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802 (2011).
[Crossref]

M. Tsang, D. Psaltis, and F. Omenetto, “Reverse propagation of femtosecond pulses in optical fibers,” Opt. Lett. 28, 1873–1875 (2003).
[Crossref] [PubMed]

Richter, M.

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

F. Morales, M. Richter, S. Patchkovskii, and O. Smirnova, “Imaging the Kramers-Henneberger atom,” Proc. Natl. Acad. Sci. U.S.A. 187, 16906–16911 (2011).
[Crossref]

Roy, G.

J. F. Daigle, A. Jaron-Becker, S. Hosseini, T. J. Wang, Y. Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[Crossref]

Salmon, E.

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

Sauerbrey, R.

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[Crossref]

Scheller, M.

M. Scheller, M. S. Mills, M.-A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photon. 8, 297–301 (2014).
[Crossref]

Schrauth, S. E.

B. G. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

Schroeder, H.

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]

Search, C. P.

C. Wang, R. Martini, and C. P. Search, “Time-reversing light pulses by adiabatic coupling modulation in coupled-resonator optical waveguides,” Phys. Rev. A 86, 063832 (2012).
[Crossref]

Seideman, T.

H. Stapelfeldt and T. Seideman, “Colloquium: Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 534–557 (2003).
[Crossref]

Seiffer, D.

Shim, B. G.

B. G. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref] [PubMed]

Skupin, S.

L. Bergé, S. Skupin, R. Nuter R, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly-ionized, optically-transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Smirnova, O.

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[Crossref]

F. Morales, M. Richter, S. Patchkovskii, and O. Smirnova, “Imaging the Kramers-Henneberger atom,” Proc. Natl. Acad. Sci. U.S.A. 187, 16906–16911 (2011).
[Crossref]

Squier, J.

Stapelfeldt, H.

H. Stapelfeldt and T. Seideman, “Colloquium: Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 534–557 (2003).
[Crossref]

Théberge, F.

W. Liu, F. Théberge, E. Arévalo, J.-F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005).
[Crossref] [PubMed]

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]

Tikhonova, O. V.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
[Crossref]

Tsang, M.

Vasseur, O.

Vieillard, T.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

Vinçotte, A.

A. Vinçotte and L. Bergé, “χ(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,” Phys. Rev. A 70, 061802(R) (2004).
[Crossref]

Volkova, E. A.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
[Crossref]

Vuong, L. T.

N. Gavish, G. Fibich, L. T. Vuong, and A. L. Gaeta, “Predicting the filamentation of high-power beams and pulses without numerical integration: A nonlinear geometrical optics method,” Phys. Rev. A 78043807 (2008).
[Crossref]

Wan, W.

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photon. 3, 211 (2009).
[Crossref]

Wang, C.

C. Wang, R. Martini, and C. P. Search, “Time-reversing light pulses by adiabatic coupling modulation in coupled-resonator optical waveguides,” Phys. Rev. A 86, 063832 (2012).
[Crossref]

Wang, T. J.

J. F. Daigle, A. Jaron-Becker, S. Hosseini, T. J. Wang, Y. Kamali, G. Roy, A. Becker, and S. L. Chin, “Intensity clamping measurement of laser filaments in air at 400 and 800 nm,” Phys. Rev. A 82, 023405 (2010).
[Crossref]

Wolf, J. P.

N. Berti, P. Béjot, J. P. Wolf, and O. Faucher, “Molecular alignment and filamentation: comparison between weak and strong field models,” Submitted to Phys. Rev. A, arXiv:1407.3952.

Wolf, J.-P.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “On quantum mechanical origin of higher-order Kerr effect in gases: induced resonances and channel closure,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “Transition from plasma- to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011)
[Crossref]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104, 103903 (2010).
[Crossref] [PubMed]

L. Bergé, S. Skupin, R. Nuter R, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly-ionized, optically-transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

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

Yu, J.

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

Appl. Phys. B (1)

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[Crossref]

Appl. Phys. Lett. (1)

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215 (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]

Chem. Phys. Lett. (1)

M. Morgen, W. Price, L. Hunziker, P. Ludowise, M. Blackwell, and Y. Chen, “Femtosecond Raman-induced polarization spectroscopy studies of rotational coherence in 02, N2 and CO2,” Chem. Phys. Lett. 209, 1–9 (1993).
[Crossref]

J. Appl. Math. (1)

G. Fibich, “Self-focusing in the damped nonlinear Schrödinger equation,” J. Appl. Math. 61, 1680–1705 (2001).

J. Dyn. Diff. Eq. (1)

A. Ben-Artzi, I. Gohberg, and M. A. Kaashoek, “Invertibility and dichotomy of differential operators on a half-line,” J. Dyn. Diff. Eq. 5, 1–36 (1993).
[Crossref]

JETP Lett. (1)

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
[Crossref]

Math. Notes (1)

M. K. Chernyshov, “Invertibility of first-order linear differential operators,” Math. Notes 64, 688–693 (1998).
[Crossref]

Nat. Photon. (2)

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photon. 3, 211 (2009).
[Crossref]

M. Scheller, M. S. Mills, M.-A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refuelled optical filaments,” Nat. Photon. 8, 297–301 (2014).
[Crossref]

New J. Phys. (1)

M. Richter, S. Patchkovskii, F. Morales, O. Smirnova, and M. Ivanov, “The role of the Kramers-Henneberger atom in the higher-order Kerr effect,” New J. Phys. 15, 083012 (2013).
[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. A (6)

C. Wang, R. Martini, and C. P. Search, “Time-reversing light pulses by adiabatic coupling modulation in coupled-resonator optical waveguides,” Phys. Rev. A 86, 063832 (2012).
[Crossref]

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802 (2011).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 Back-propagation of a laser filament within the frame of the cubic-quintic model. (a) On-axis intensity and (b) spectrum of the initial (red solid line), propagated (blue dash-dotted line) and back-propagated pulses (black dashed line); (c) Relative error on intensity between the initial and back-propagated pulses; (d) Fluence distribution along the propagation distance. The solid white line indicates the beam radius.
Fig. 2
Fig. 2 Back-propagation of a laser filament in argon when including ionization in the model. (a) On-axis intensity and (b) spectrum of the initial (red solid line), propagated (blue dash-dotted line), back-propagated pulses (black dashed line) and at z = 97 cm (green solid line); (c) Relative error on intensity between the initial and back-propagated pulses; (d) Fluence distribution along the propagation distance. The solid white line indicates the beam radius.
Fig. 3
Fig. 3 Back-propagation of a laser filament in nitrogen, taking into account ionization as well as molecular alignment. (a) On-axis intensity and (b) spectrum of the initial (red solid line), propagated (blue dash-dotted line) and back-propagated pulses (black dashed line); (c) Relative error on intensity between the initial and back-propagated pulses; (d) Fluence distribution along the propagation distance. The solid white line indicates the beam radius.

Equations (9)

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i z ε + Δ ε + f ( | ε | 2 ) ε = 0 ,
i z ε * + Δ ε * + f ( | ε | 2 ) ε * = 0 ,
i z ε + Δ ε + f ( | ε | 2 ) ε + i δ ε = 0 .
i z ε * + Δ ε * + f ( | ε | 2 ) ε * i δ ε * = 0 ,
z ε ˜ = i ( k z ω v g ) ε ˜ + i ω 2 c 2 k z j = 1 2 n 2 j | ε | 2 j ε ˜ ,
ε ˜ ( k , z , ω ) = r J 0 ( k r ) ε ( r , z , t ) e i ω t d t d r .
z ε ˜ = i ( k z ω v g ) ε ˜ + ω c 2 k z [ i ω ( n 2 | ε | 2 ε ˜ + Δ n r ( t ) ( ε ) ˜ ) e 2 2 ε 0 m e τ ( ω ) ρ ε ˜ ] L [ ε ] ˜ ,
L [ ε ] = U i W ( | ε | 2 ) 2 | ε | 2 ( ρ at ρ ) ε .
ρ ( t ) = ρ at t σ K | ε | 2 K d t

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