Abstract

The observation of discrete lines in the white spectrum at the initial stage of filamentation of powerful femtosecond laser pulses, propagating in silica glasses, as well as the filamentation without plasma channels observed in the experiments in air, pushed us to look for other nonlinear mechanisms for describing these effects. In this paper, we present a new parametric conversion mechanism for asymmetric spectrum broadening of femtosecond laser pulses towards higher frequencies in isotropic media. This mechanism includes cascade generation with THz spectral shift for solids and GHz shift for gases. The process works simultaneously with the four-photon parametric wave mixing. The theoretical model proposed agrees well with the experimental data.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  22. S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
    [Crossref] [PubMed]
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    [Crossref]
  24. L. Bergé, S. Mauger, and S. Skupin, “Multifilamentation of powerful optical pulses in silica,” Phys. Rev. A 81(1), 013817 (2010).
    [Crossref]
  25. D. Georgieva, L. Kovachev, and N. Nedyalkov, “Avalanche parametric conversion in the initial moment of filamentation,” Proc. SPIE 10226, 102261G (2017).
    [Crossref]
  26. www.refractiveindex.info

2017 (1)

D. Georgieva, L. Kovachev, and N. Nedyalkov, “Avalanche parametric conversion in the initial moment of filamentation,” Proc. SPIE 10226, 102261G (2017).
[Crossref]

2015 (1)

L. M. Kovachev, D. A. Georgieva, and A. M. Dakova, “Influence of the four-photon parametric processes and cross-phase modulation on the relative motion of optical filaments,” Laser Phys. 25(10), 105402 (2015).
[Crossref]

2014 (2)

O. Lahav, L. Levi, I. Orr, R. A. Nemirovsky, J. Nemirovsky, I. Kaminer, M. Segev, and O. Cohen, “Long-lived waveguides and sound-wave generation by laser filamentation,” Phys. Rev. A 90(2), 021801 (2014).
[Crossref]

J. K. Wahlstrand, N. Jhajj, E. W. Rosenthal, S. Zahedpour, and H. M. Milchberg, “Direct imaging of the acoustic waves generated by femtosecond filaments in air,” Opt. Lett. 39(5), 1290–1293 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (1)

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

2011 (1)

J.-F. Daigle, O. Kosareva, N. Panov, T. -J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, “Formation and evolution of intense, postfilamentation, ionization-free low divergence beams,” Opt. Commun. 284(14), 3601–3606 (2011).
[Crossref]

2010 (3)

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[Crossref] [PubMed]

O. Kosareva, N. Panov, V. Makarov, I. Perezhogin, C. Marceau, Y. Chen, S. Yuan, T. Wang, H. Zeng, A. Savel’ev, and S. L. Chin, “Polarization rotation due to femtosecond filamentation in an atomic gas,” Opt. Lett. 35(17), 2904–2906 (2010).
[Crossref] [PubMed]

L. Bergé, S. Mauger, and S. Skupin, “Multifilamentation of powerful optical pulses in silica,” Phys. Rev. A 81(1), 013817 (2010).
[Crossref]

2008 (1)

2007 (3)

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Coherent and incoherent radial THz radiation emission from femtosecond filaments in air,” Opt. Express 15(23), 15274–15279 (2007).
[Crossref] [PubMed]

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2–4), 47–189 (2007).
[Crossref]

2006 (2)

S. Skupin and L. Bergé, “Self-guiding of femtosecond light pulses in condensed media: Plasma: generation versus chromatic dispersion,” Physica D 220(1), 14–30 (2006).
[Crossref]

N. T. Nguyen, A. Saliminia, S. L. Chin, and R. Vallée, “Control of femtosecond laser written waveguides in silica glass,” Appl. Phys. B 85(1), 145–148 (2006).
[Crossref]

2005 (2)

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[Crossref]

S. Champeaux and L. Bergé, “Postionization regimes of femtosecond laser pulses self-channeling in air,” Phys. Rev. E. 71(4), 046604 (2005).
[Crossref] [PubMed]

2004 (2)

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long-range self-channeling of infrared laser pulses in air: a new regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

2002 (1)

2001 (2)

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[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(24), 5470–5473 (2001).
[Crossref] [PubMed]

1997 (1)

1995 (1)

André, Y.-B.

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long-range self-channeling of infrared laser pulses in air: a new regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, Y.-B. André, B. Prade, M. Franco, A. Mysyrowicz, J.-M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, “Coherent Subterahertz Radiation from Femtosecond Infrared Filaments in Air,” Opt. Lett. 27(21), 1944–1946 (2002).
[Crossref] [PubMed]

Azarm, A.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Beaudin, G.

Berge, L.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Bergé, L.

L. Bergé, S. Mauger, and S. Skupin, “Multifilamentation of powerful optical pulses in silica,” Phys. Rev. A 81(1), 013817 (2010).
[Crossref]

S. Skupin and L. Bergé, “Self-guiding of femtosecond light pulses in condensed media: Plasma: generation versus chromatic dispersion,” Physica D 220(1), 14–30 (2006).
[Crossref]

S. Champeaux and L. Bergé, “Postionization regimes of femtosecond laser pulses self-channeling in air,” Phys. Rev. E. 71(4), 046604 (2005).
[Crossref] [PubMed]

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[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(24), 5470–5473 (2001).
[Crossref] [PubMed]

L. Bergé, M. R. Schmidt, J. Juul Rasmussen, P. L. Christiansen, and K. Rasmussen, “Amalgamation of interacting light beamlets in Kerr-type media,” J. Opt. Soc. Am. B 14(10), 2550–2562 (1997).
[Crossref]

Bourayou, R.

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

Braun, A.

Cao, Y.

Champeaux, S.

S. Champeaux and L. Bergé, “Postionization regimes of femtosecond laser pulses self-channeling in air,” Phys. Rev. E. 71(4), 046604 (2005).
[Crossref] [PubMed]

Chen, S.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[Crossref] [PubMed]

Chen, Y.

Chen, Y. P.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Chin, S. L.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

J.-F. Daigle, O. Kosareva, N. Panov, T. -J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, “Formation and evolution of intense, postfilamentation, ionization-free low divergence beams,” Opt. Commun. 284(14), 3601–3606 (2011).
[Crossref]

O. Kosareva, N. Panov, V. Makarov, I. Perezhogin, C. Marceau, Y. Chen, S. Yuan, T. Wang, H. Zeng, A. Savel’ev, and S. L. Chin, “Polarization rotation due to femtosecond filamentation in an atomic gas,” Opt. Lett. 35(17), 2904–2906 (2010).
[Crossref] [PubMed]

N. T. Nguyen, A. Saliminia, S. L. Chin, and R. Vallée, “Control of femtosecond laser written waveguides in silica glass,” Appl. Phys. B 85(1), 145–148 (2006).
[Crossref]

Christiansen, P. L.

Cohen, O.

O. Lahav, L. Levi, I. Orr, R. A. Nemirovsky, J. Nemirovsky, I. Kaminer, M. Segev, and O. Cohen, “Long-lived waveguides and sound-wave generation by laser filamentation,” Phys. Rev. A 90(2), 021801 (2014).
[Crossref]

Couairon, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2–4), 47–189 (2007).
[Crossref]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long-range self-channeling of infrared laser pulses in air: a new regime without ionization,” Appl. Phys. B 79(3), 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(24), 5470–5473 (2001).
[Crossref] [PubMed]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[Crossref] [PubMed]

D’Amico, C.

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Coherent and incoherent radial THz radiation emission from femtosecond filaments in air,” Opt. Express 15(23), 15274–15279 (2007).
[Crossref] [PubMed]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long-range self-channeling of infrared laser pulses in air: a new regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

Daigle, J.-F.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

J.-F. Daigle, O. Kosareva, N. Panov, T. -J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, “Formation and evolution of intense, postfilamentation, ionization-free low divergence beams,” Opt. Commun. 284(14), 3601–3606 (2011).
[Crossref]

Dakova, A. M.

L. M. Kovachev, D. A. Georgieva, and A. M. Dakova, “Influence of the four-photon parametric processes and cross-phase modulation on the relative motion of optical filaments,” Laser Phys. 25(10), 105402 (2015).
[Crossref]

Ding, P.

Du, D.

Durand, M.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[Crossref] [PubMed]

Encrenaz, P.

Forestier, B.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[Crossref] [PubMed]

Franco, M.

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Coherent and incoherent radial THz radiation emission from femtosecond filaments in air,” Opt. Express 15(23), 15274–15279 (2007).
[Crossref] [PubMed]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long-range self-channeling of infrared laser pulses in air: a new regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, Y.-B. André, B. Prade, M. Franco, A. Mysyrowicz, J.-M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, “Coherent Subterahertz Radiation from Femtosecond Infrared Filaments in Air,” Opt. Lett. 27(21), 1944–1946 (2002).
[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(24), 5470–5473 (2001).
[Crossref] [PubMed]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[Crossref] [PubMed]

Georgieva, D.

D. Georgieva, L. Kovachev, and N. Nedyalkov, “Avalanche parametric conversion in the initial moment of filamentation,” Proc. SPIE 10226, 102261G (2017).
[Crossref]

Georgieva, D. A.

L. M. Kovachev, D. A. Georgieva, and A. M. Dakova, “Influence of the four-photon parametric processes and cross-phase modulation on the relative motion of optical filaments,” Laser Phys. 25(10), 105402 (2015).
[Crossref]

Gheudin, M.

Guo, Z.

Hosseini, S.

J.-F. Daigle, O. Kosareva, N. Panov, T. -J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, “Formation and evolution of intense, postfilamentation, ionization-free low divergence beams,” Opt. Commun. 284(14), 3601–3606 (2011).
[Crossref]

Houard, A.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[Crossref] [PubMed]

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Coherent and incoherent radial THz radiation emission from femtosecond filaments in air,” Opt. Express 15(23), 15274–15279 (2007).
[Crossref] [PubMed]

Hu, B.

Jhajj, N.

Juul Rasmussen, J.

Kamata, M.

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[Crossref]

Kaminer, I.

O. Lahav, L. Levi, I. Orr, R. A. Nemirovsky, J. Nemirovsky, I. Kaminer, M. Segev, and O. Cohen, “Long-lived waveguides and sound-wave generation by laser filamentation,” Phys. Rev. A 90(2), 021801 (2014).
[Crossref]

Kasparian, J.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

Kolesik, M.

Korn, G.

Kosareva, O.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

J.-F. Daigle, O. Kosareva, N. Panov, T. -J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, “Formation and evolution of intense, postfilamentation, ionization-free low divergence beams,” Opt. Commun. 284(14), 3601–3606 (2011).
[Crossref]

O. Kosareva, N. Panov, V. Makarov, I. Perezhogin, C. Marceau, Y. Chen, S. Yuan, T. Wang, H. Zeng, A. Savel’ev, and S. L. Chin, “Polarization rotation due to femtosecond filamentation in an atomic gas,” Opt. Lett. 35(17), 2904–2906 (2010).
[Crossref] [PubMed]

Kovachev, L.

D. Georgieva, L. Kovachev, and N. Nedyalkov, “Avalanche parametric conversion in the initial moment of filamentation,” Proc. SPIE 10226, 102261G (2017).
[Crossref]

Kovachev, L. M.

L. M. Kovachev, D. A. Georgieva, and A. M. Dakova, “Influence of the four-photon parametric processes and cross-phase modulation on the relative motion of optical filaments,” Laser Phys. 25(10), 105402 (2015).
[Crossref]

Lahav, O.

O. Lahav, L. Levi, I. Orr, R. A. Nemirovsky, J. Nemirovsky, I. Kaminer, M. Segev, and O. Cohen, “Long-lived waveguides and sound-wave generation by laser filamentation,” Phys. Rev. A 90(2), 021801 (2014).
[Crossref]

Lederer, F.

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

Levi, L.

O. Lahav, L. Levi, I. Orr, R. A. Nemirovsky, J. Nemirovsky, I. Kaminer, M. Segev, and O. Cohen, “Long-lived waveguides and sound-wave generation by laser filamentation,” Phys. Rev. A 90(2), 021801 (2014).
[Crossref]

Li, R.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Liu, J. S.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Liu, W. W.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Liu, X.

Liu, Y.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[Crossref] [PubMed]

Makarov, V.

Marceau, C.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

O. Kosareva, N. Panov, V. Makarov, I. Perezhogin, C. Marceau, Y. Chen, S. Yuan, T. Wang, H. Zeng, A. Savel’ev, and S. L. Chin, “Polarization rotation due to femtosecond filamentation in an atomic gas,” Opt. Lett. 35(17), 2904–2906 (2010).
[Crossref] [PubMed]

Mauger, S.

L. Bergé, S. Mauger, and S. Skupin, “Multifilamentation of powerful optical pulses in silica,” Phys. Rev. A 81(1), 013817 (2010).
[Crossref]

Méchain, G.

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long-range self-channeling of infrared laser pulses in air: a new regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, Y.-B. André, B. Prade, M. Franco, A. Mysyrowicz, J.-M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, “Coherent Subterahertz Radiation from Femtosecond Infrared Filaments in Air,” Opt. Lett. 27(21), 1944–1946 (2002).
[Crossref] [PubMed]

Méjean, G.

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

Milchberg, H. M.

Moloney, J. V.

Mourou, G.

Munier, J.-M.

Mysyrowicz, A.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[Crossref] [PubMed]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2–4), 47–189 (2007).
[Crossref]

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Coherent and incoherent radial THz radiation emission from femtosecond filaments in air,” Opt. Express 15(23), 15274–15279 (2007).
[Crossref] [PubMed]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long-range self-channeling of infrared laser pulses in air: a new regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, Y.-B. André, B. Prade, M. Franco, A. Mysyrowicz, J.-M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, “Coherent Subterahertz Radiation from Femtosecond Infrared Filaments in Air,” Opt. Lett. 27(21), 1944–1946 (2002).
[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(24), 5470–5473 (2001).
[Crossref] [PubMed]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[Crossref] [PubMed]

Nedyalkov, N.

D. Georgieva, L. Kovachev, and N. Nedyalkov, “Avalanche parametric conversion in the initial moment of filamentation,” Proc. SPIE 10226, 102261G (2017).
[Crossref]

Nemirovsky, J.

O. Lahav, L. Levi, I. Orr, R. A. Nemirovsky, J. Nemirovsky, I. Kaminer, M. Segev, and O. Cohen, “Long-lived waveguides and sound-wave generation by laser filamentation,” Phys. Rev. A 90(2), 021801 (2014).
[Crossref]

Nemirovsky, R. A.

O. Lahav, L. Levi, I. Orr, R. A. Nemirovsky, J. Nemirovsky, I. Kaminer, M. Segev, and O. Cohen, “Long-lived waveguides and sound-wave generation by laser filamentation,” Phys. Rev. A 90(2), 021801 (2014).
[Crossref]

Nguyen, N. T.

N. T. Nguyen, A. Saliminia, S. L. Chin, and R. Vallée, “Control of femtosecond laser written waveguides in silica glass,” Appl. Phys. B 85(1), 145–148 (2006).
[Crossref]

Nuter, R.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Obara, M.

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[Crossref]

Orr, I.

O. Lahav, L. Levi, I. Orr, R. A. Nemirovsky, J. Nemirovsky, I. Kaminer, M. Segev, and O. Cohen, “Long-lived waveguides and sound-wave generation by laser filamentation,” Phys. Rev. A 90(2), 021801 (2014).
[Crossref]

Panov, N.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

J.-F. Daigle, O. Kosareva, N. Panov, T. -J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, “Formation and evolution of intense, postfilamentation, ionization-free low divergence beams,” Opt. Commun. 284(14), 3601–3606 (2011).
[Crossref]

O. Kosareva, N. Panov, V. Makarov, I. Perezhogin, C. Marceau, Y. Chen, S. Yuan, T. Wang, H. Zeng, A. Savel’ev, and S. L. Chin, “Polarization rotation due to femtosecond filamentation in an atomic gas,” Opt. Lett. 35(17), 2904–2906 (2010).
[Crossref] [PubMed]

Patalano, G.

Perezhogin, I.

Peschel, U.

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

Prade, B.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[Crossref] [PubMed]

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Coherent and incoherent radial THz radiation emission from femtosecond filaments in air,” Opt. Express 15(23), 15274–15279 (2007).
[Crossref] [PubMed]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long-range self-channeling of infrared laser pulses in air: a new regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, Y.-B. André, B. Prade, M. Franco, A. Mysyrowicz, J.-M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, “Coherent Subterahertz Radiation from Femtosecond Infrared Filaments in Air,” Opt. Lett. 27(21), 1944–1946 (2002).
[Crossref] [PubMed]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[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(24), 5470–5473 (2001).
[Crossref] [PubMed]

Rasmussen, K.

Richardson, M.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Rodriguez, M.

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

Rosenthal, E. W.

Roy, G.

J.-F. Daigle, O. Kosareva, N. Panov, T. -J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, “Formation and evolution of intense, postfilamentation, ionization-free low divergence beams,” Opt. Commun. 284(14), 3601–3606 (2011).
[Crossref]

Saliminia, A.

N. T. Nguyen, A. Saliminia, S. L. Chin, and R. Vallée, “Control of femtosecond laser written waveguides in silica glass,” Appl. Phys. B 85(1), 145–148 (2006).
[Crossref]

Salmon, E.

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

Sauerbrey, R.

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long-range self-channeling of infrared laser pulses in air: a new regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

Savel’ev, A.

Schmidt, M. R.

Segev, M.

O. Lahav, L. Levi, I. Orr, R. A. Nemirovsky, J. Nemirovsky, I. Kaminer, M. Segev, and O. Cohen, “Long-lived waveguides and sound-wave generation by laser filamentation,” Phys. Rev. A 90(2), 021801 (2014).
[Crossref]

Seideman, T.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Shi, Y.

Skupin, S.

L. Bergé, S. Mauger, and S. Skupin, “Multifilamentation of powerful optical pulses in silica,” Phys. Rev. A 81(1), 013817 (2010).
[Crossref]

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

S. Skupin and L. Bergé, “Self-guiding of femtosecond light pulses in condensed media: Plasma: generation versus chromatic dispersion,” Physica D 220(1), 14–30 (2006).
[Crossref]

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

Squier, J.

Sudrie, L.

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[Crossref] [PubMed]

Sun, M.

Sun, S.

Toratani, E.

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[Crossref]

Tzortzakis, S.

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long-range self-channeling of infrared laser pulses in air: a new regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

S. Tzortzakis, G. Méchain, G. Patalano, Y.-B. André, B. Prade, M. Franco, A. Mysyrowicz, J.-M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, “Coherent Subterahertz Radiation from Femtosecond Infrared Filaments in Air,” Opt. Lett. 27(21), 1944–1946 (2002).
[Crossref] [PubMed]

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[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(24), 5470–5473 (2001).
[Crossref] [PubMed]

Vallée, R.

N. T. Nguyen, A. Saliminia, S. L. Chin, and R. Vallée, “Control of femtosecond laser written waveguides in silica glass,” Appl. Phys. B 85(1), 145–148 (2006).
[Crossref]

Wahlstrand, J. K.

Wang, T.

Wang, T. -J.

J.-F. Daigle, O. Kosareva, N. Panov, T. -J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, “Formation and evolution of intense, postfilamentation, ionization-free low divergence beams,” Opt. Commun. 284(14), 3601–3606 (2011).
[Crossref]

Wang, T.-J.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Wang, X.

Wolf, J. P.

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

Wolf, J.-P.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Wöste, L.

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

Wu, J.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Xu, Z. Z.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Yu, J.

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

Yuan, S.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

J.-F. Daigle, O. Kosareva, N. Panov, T. -J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, “Formation and evolution of intense, postfilamentation, ionization-free low divergence beams,” Opt. Commun. 284(14), 3601–3606 (2011).
[Crossref]

O. Kosareva, N. Panov, V. Makarov, I. Perezhogin, C. Marceau, Y. Chen, S. Yuan, T. Wang, H. Zeng, A. Savel’ev, and S. L. Chin, “Polarization rotation due to femtosecond filamentation in an atomic gas,” Opt. Lett. 35(17), 2904–2906 (2010).
[Crossref] [PubMed]

Zahedpour, S.

Zeng, H.

Zeng, H. P.

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Zhao, P.

Appl. Phys. B (2)

G. Méchain, A. Couairon, Y.-B. André, C. D’Amico, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, “Long-range self-channeling of infrared laser pulses in air: a new regime without ionization,” Appl. Phys. B 79(3), 379–382 (2004).
[Crossref]

N. T. Nguyen, A. Saliminia, S. L. Chin, and R. Vallée, “Control of femtosecond laser written waveguides in silica glass,” Appl. Phys. B 85(1), 145–148 (2006).
[Crossref]

Appl. Phys. Lett. (1)

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett. 87(17), 171103 (2005).
[Crossref]

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

Laser Phys. (2)

L. M. Kovachev, D. A. Georgieva, and A. M. Dakova, “Influence of the four-photon parametric processes and cross-phase modulation on the relative motion of optical filaments,” Laser Phys. 25(10), 105402 (2015).
[Crossref]

S. L. Chin, T.-J. Wang, C. Marceau, J. Wu, J. S. Liu, O. Kosareva, N. Panov, Y. P. Chen, J.-F. Daigle, S. Yuan, A. Azarm, W. W. Liu, T. Seideman, H. P. Zeng, M. Richardson, R. Li, and Z. Z. Xu, “Advances in Intense Femtosecond Laser Filamentation in Air,” Laser Phys. 22(1), 1–53 (2012).
[Crossref]

Opt. Commun. (1)

J.-F. Daigle, O. Kosareva, N. Panov, T. -J. Wang, S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, “Formation and evolution of intense, postfilamentation, ionization-free low divergence beams,” Opt. Commun. 284(14), 3601–3606 (2011).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2–4), 47–189 (2007).
[Crossref]

Phys. Rev. A (2)

L. Bergé, S. Mauger, and S. Skupin, “Multifilamentation of powerful optical pulses in silica,” Phys. Rev. A 81(1), 013817 (2010).
[Crossref]

O. Lahav, L. Levi, I. Orr, R. A. Nemirovsky, J. Nemirovsky, I. Kaminer, M. Segev, and O. Cohen, “Long-lived waveguides and sound-wave generation by laser filamentation,” Phys. Rev. A 90(2), 021801 (2014).
[Crossref]

Phys. Rev. E. (2)

S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters,” Phys. Rev. E. 70(4), 046602 (2004).
[Crossref] [PubMed]

S. Champeaux and L. Bergé, “Postionization regimes of femtosecond laser pulses self-channeling in air,” Phys. Rev. E. 71(4), 046604 (2005).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and L. Bergé, “Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica,” Phys. Rev. Lett. 87(21), 213902 (2001).
[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(24), 5470–5473 (2001).
[Crossref] [PubMed]

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[Crossref] [PubMed]

Physica D (1)

S. Skupin and L. Bergé, “Self-guiding of femtosecond light pulses in condensed media: Plasma: generation versus chromatic dispersion,” Physica D 220(1), 14–30 (2006).
[Crossref]

Proc. SPIE (1)

D. Georgieva, L. Kovachev, and N. Nedyalkov, “Avalanche parametric conversion in the initial moment of filamentation,” Proc. SPIE 10226, 102261G (2017).
[Crossref]

Rep. Prog. Phys. (1)

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[Crossref]

Other (1)

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Figures (10)

Fig. 1
Fig. 1 Experimental setup for observation of the initial filamentation in glass. 1- Ti-sapphire fs laser, 2- reflecting mirror, 3- attenuator, 4- focusing lens, 5- BK7 glass sample or fused silica plate, 6- spectrometer.
Fig. 2
Fig. 2 (a) A white spot with a red ring obtained with the infrared pulse propagating through the BK7 glass sample. (b) The spectrum of the narrow-band pulse propagating through the glass. Discrete spectral components from 450 to 870 nm are seen: the typical asymmetric conversion towards the short wavelengths shows that we observe the initial stage of the filamentation process.
Fig. 3
Fig. 3 (a) The observed white spot with intensive broad blue and red rings of the pulse propagating through the fused silica sample. (b) The initial pulse spectrum (in red) compared with the spectrum of the pulse propagating through the material (in black). The spectrum modification significantly smoother with small and less resolved spectral maxima, see also Fig. 6.
Fig. 4
Fig. 4 (a) The nonlinear frequency shift for BK7 glass Δ ω nl BK7 =3 ω cep =3 k 0 ( v ph v gr )in the region 780 nm to 2 µm. The frequency shift at 800 nm is Δ ω nl BK7 ( 800nm )=48.78THz. (b) The nonlinear frequency shift for fused silica in the region 780 nm to 2 µm. The frequency shift at 800 nm is Δ ω nl silica ( 800nm )=45.8THz.
Fig. 5
Fig. 5 Comparison of the calculated shifts Δ λ ij = n λ j 2 2πc Δ ω nl ( λ j ) towards the short wavelengths obtained from the physical model (colored vertical lines) with the experimental spectrum for BK7 glass (black line).
Fig. 6
Fig. 6 Comparison between the calculated spectral shifts Δ λ ij obtained from the physical model (colored vertical lines) with the experimental spectrum for fused silica (black line).
Fig. 7
Fig. 7 Evolution of the spectrum and generation of signal waves from an initial 150 fs pulse in BK7 glass. The results are obtained by numerical calculation of the system of Eqs. (17)-(18) under initial conditions (19)-(20). The total spectrum of the pulse becomes asymmetrical with spectral maxima at distances Δλ25nm. The spectral maxima are well resolved, compare with Fig. 2(b) and Fig. 5.
Fig. 8
Fig. 8 Evolution of the spectra of each of the seven pulses in the process of nonlinear interaction in BK7 glass. The initial pulse A1 yields (by THz synchronism) the generation of a blue-shifted wave A2. The combined action of A1 and A2 leads to the generation of a red-shifted A3 wave, by the FPP process. Further on, A2 yields a blue-shifted A4 wave, due to the THz synchronism, while A3 is reduced, since it transfers its energy by the THz synchronism to a position, which in our model coincides with the position of A1. The generation of signal waves with THz shift combined with the FPP processes leads to significant increase of the pulses situated to the short wavelengths.
Fig. 9
Fig. 9 The calculated energies of each signal wave during the process of interaction: (a) even indexed waves, i.e., the waves generated to the shorter wavelengths with respect to the pump; (b) energy transfer of the odd indexed waves, i.e. the waves generated to the longer wavelengths with respect to the pump. A significant energy transfer to the short wavelengths is observed:
Fig. 10
Fig. 10 The spectral evolution and generation of signal waves from the broadband 30 fs pulse at different distances for fused silica. The total spectrum of the pulse becomes asymmetrical. The shape of the spectrum at 10 mm reveals the same overlapping of the spectral lines as in the real experiment, compare with Fig. 3(b) and Fig. 6.

Equations (20)

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2i k 0 ( A z + 1 v gr A t )= k 0 k" 2 A t 2 + k 0 2 n ˜ 2 | A | 2 A,
χ xxxx ( 3 ) ( 3ω=ω+ω+ω )and χ xxxx ( 3 ) ( ω=ω+ωω ).
2i k 0 [ A z + 1 v gr A t ]= 2 A z 2 ( 1+β v gr 2 ) 2 A t 2 + k 0 2 n 2 ( | A | 2 A+3 A 3 e 2i( k 0 z ω 0 t) ).
2i k 0 v gr A x t =β 2 A x z 2 + k 0 2 n ˜ 2 [ 1 3 A x 3 exp( 2i k 0 ( z( v ph v gr )t ) )+ | A x | 2 A x ],
ω nl =3 k 0 ( v ph v gr )=3 ω CEF .
Δ ω nl BK7 (800nm)=3 k 0 ( v ph v gr )=48.78THz.
Δ λ 10 BK7 = n λ 0 2 2πc Δ ω nl ( λ 0 )=25.1nm.
Δ ω nl silica (800nm)=3 k 0 ( v ph v gr )=45.8THz,
Δ λ 10 silica = n λ 0 2 2πc Δ ω nl ( λ 0 )=22.6nm.
χ xxxx ( 3 ) ( 3 ω 1 = ω 1 + ω 1 + ω 1 ), χ xxxx ( 3 ) ( ω 1 = ω 1 + ω 2 ω 2 ), χ xxxx ( 3 ) ( ω 1 = ω 1 + ω 1 ω 1 ), χ xxxx ( 3 ) ( 3 ω 2 = ω 2 + ω 2 + ω 2 ), χ xxxx ( 3 ) ( ω 2 = ω 2 + ω 1 ω 1 ), χ xxxx ( 3 ) ( ω 2 = ω 2 + ω 2 ω 2 ).
i A 1 t = β 1 2 A 1 z 2 + γ 1 ( | A 1 | 2 A 1 +2 | A 2 | 2 A 1 + A 1 *2 A 2 exp(iδkz) ), i A 2 t = β 2 2 A 2 z 2 + γ 2 ( | A 2 | 2 A 2 +2 | A 1 | 2 A 2 + A 1 3 exp(iδkz)+ A 2 3 exp(iδKz) ),
i A 1 t = β 1 2 A 1 z 2 + γ 1 ( | A 1 | 2 A 1 +2 | A 2 | 2 A 1 + A 1 *2 A 2 exp(iδkz) ) i A 2 t = β 2 2 A 2 z 2 + γ 2 ( | A 2 | 2 A 2 +2 | A 1 | 2 A 2 + A 1 3 exp(iδkz) ),
λ 6 Δ λ 4 Δ λ 2 Δ λ 1 Δ λ 3 Δ λ 5 Δ λ 7 ,
ω 1 +Δ ω nl = ω 2 , ω 2 +Δ ω nl = ω 4 , ω 4 +Δ ω nl = ω 6 , ω 3 +Δ ω nl = ω 1 , ω 5 +Δ ω nl = ω 3 , ω 7 +Δ ω nl = ω 5 .
ω i + ω j =2 ω k .
ω i + ω j = ω k + ω l .
i A j t = β j 2 A j z 2 + γ j P nl j ,j=17,
P nl j =( | A j | 2 + kj 7 2 | A k | 2 ) A j + 1 3 A jΔ 3 exp(iδkz)+ A j * 2 A j+Δ exp(iδkz) +2 A j * A j+Δ A jΔ exp(iδkz)+2 A j * A j+2Δ A j2Δ exp(2iδkz)+2 A j * A j+3Δ A j3Δ exp(3iδkz) + A j±1Δ 2 A j±2Δ * exp(iδkz)+ A j±2Δ 2 A j±4Δ * exp(i2δkz)+ A j+Δ * A jΔ A j+2Δ exp(iδkz) + A jΔ * A j+Δ A j2Δ exp(iδkz)+ A j+3Δ * A j+Δ A j+2Δ exp(iδkz)+ A j3Δ * A jΔ A j2Δ exp(iδkz) + A j+2Δ * A j2Δ A j+4Δ exp(iδkz)+ A j2Δ * A j+2Δ A j4Δ exp(iδkz)+ A j+6Δ * A j+4Δ A j+2Δ exp(iδkz) + A j6Δ * A j4Δ A j2Δ exp(iδkz),j=17.
A j = A 0j exp( i ϕ j )exp( iΔ k j z )exp( z 2 /2 z 0j 2 ),j=17,
A 01 =1, A 02 = A 03 =0.01, A 04 = A 05 =0.01, A 06 = A 07 =0.005, z 01 =1, z 02 = z 03 =15,δk=0.001 Δ λ 1 =0,Δ λ 2 =2.5,Δ λ 3 =2.5;Δ λ 4 =5,Δ λ 5 =5,Δ λ 6 =7.5,Δ λ 7 =7.5.

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