Abstract

We numerically simulated the nonlinear propagation of high-power subpicosecond laser radiation at 10.6 μm carrier wavelength in air under conditions of pulse Kerr self-focusing and single and multiple filamentation. For the first time, to the best of our knowledge, we show that in contrast to the well-known femtosecond pulse filamentation in the near-infrared domain (800 nm), the self-action of mid-infrared radiation is characterized by the formation of millimeter-wide filaments accompanied by nearly continuous along the propagation direction and elongated plasma columns. The physical cause is the change of the air ionization regime by the CO2-laser pulse in favor of impact ionization and electron avalanche development. This alters the character of plasma influence on the laser radiation by enhancing the role of physical processes attributed to the liberated hot electrons.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  33. E. P. Silaeva, S. A. Shlenov, and V. P. Kandidov, “Multifilamentation of high-power femtosecond laser pulse in turbulent atmosphere with aerosol,” Appl. Phys. B 101, 393–401 (2010).
    [CrossRef]
  34. L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
    [CrossRef]

2013

M. N. Polyanskiy, M. Babzien, I. Pogorelsky, and V. Yakimenko, “Ultrashort-pulse CO2 lasers: ready for the race to petawatt?” Proc. SPIE 8677, 86770G (2013).
[CrossRef]

L. Berge, J. Rolle, and C. Kohler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013).
[CrossRef]

D. Kartashov, S. Ališauskas, A. Pugžlys, A. Voronin, A. Zheltikov, M. Petrarca, P. Béjot, J. Kasparian, J.-P. Wolf, and A. Baltuška, “Mid-infrared laser filamentation in molecular gases,” Opt. Lett. 38, 3194–3196 (2013).
[CrossRef]

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of a gaseous medium in the regime of atom stabilization in a strong radiation field,” J. Exp. Theor. Phys. 116, 372–380 (2013).
[CrossRef]

C. Kohler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Berge, and S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[CrossRef]

2012

2011

B. Shim, S. E. Schrauth, and A. L. Gaeta, “Filamentation in air with ultrashort mid-infrared pulses,” Opt. Express 19, 9118–9126 (2011).
[CrossRef]

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

2010

2009

V. M. Gordienko, V. T. Platonenko, and A. F. Sterzhantov, “Self-action of a high-power 10  μm laser radiation in gases: control of the pulse duration and generation of hot electrons,” Quantum Electron. 39, 663–668 (2009).
[CrossRef]

V. P. Kandidov, S. A. Shlenov, and O. G. Kosareva, “Filamentation of high-power femtosecond laser radiation,” Quantum Electron. 39, 205–228 (2009).
[CrossRef]

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B 96, 175–183 (2009).
[CrossRef]

2007

L. Bergé, S. Skupin, R. Nuter, 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. Couairon and A. Myzyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

2004

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Phys. Usp. 47, 855–885 (2004).
[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]

2003

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

1999

1998

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382–384 (1998).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: a pressure dependence study,” Phys. Rev. E 58, 4903–4910 (1998).
[CrossRef]

1997

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

1976

1966

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in alternating electric field,” Zh. Teor. Eksp. Fiz. 50, 1393–1397 (1966).

1965

L. V. Keldysh, “Ionization in the field of strong electromagnetic wave,” Sov. Phys. JETP 20, 1307 (1965).

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1997).

Ališauskas, S.

André, Y.-B.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Apollonov, V. V.

V. V. Apollonov and N. V. Pletnev, “Formation of extended conducting channels in atmosphere,” Quantum Electron. 42, 130–139 (2012).
[CrossRef]

Babzien, M.

M. N. Polyanskiy, M. Babzien, I. Pogorelsky, and V. Yakimenko, “Ultrashort-pulse CO2 lasers: ready for the race to petawatt?” Proc. SPIE 8677, 86770G (2013).
[CrossRef]

M. N. Polyanskiy and M. Babzien, “Ultrashort pulses,” in CO2 Laser—Optimization and Application, D. C. Dumitras, ed. (InTech, 2012), pp. 139–162.

Baltuška, A.

Bandrauk, A. D.

C. Kohler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Berge, and S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[CrossRef]

Béjot, P.

Berge, L.

C. Kohler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Berge, and S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[CrossRef]

L. Berge, J. Rolle, and C. Kohler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013).
[CrossRef]

Bergé, L.

L. Bergé, S. Skupin, R. Nuter, 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]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

Bourayou, R.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Brabec, T.

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

Bravy, B. G.

Chelkowski, S.

C. Kohler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Berge, and S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[CrossRef]

Chernyshev, Y. A.

Chin, S. L.

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

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1997).

Couairon, A.

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

Daigle, J.-F.

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

Eislöffel, J.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Ettoumi, W.

Faucher, O.

Frey, S.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Gaeta, A. L.

Gebhardt, F. G.

Giesen, A.

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B 96, 175–183 (2009).
[CrossRef]

Gordienko, V. M.

B. G. Bravy, Y. A. Chernyshev, V. M. Gordienko, E. F. Makarov, V. Y. Panchenko, V. T. Platonenko, and G. K. Vasil’ev, “Multi-terawatt picoseconds 10  μm CO2 laser system: design and parameters’ control,” Opt. Express 20, 25536–25544 (2012).
[CrossRef]

V. M. Gordienko, V. T. Platonenko, and A. F. Sterzhantov, “Self-action of a high-power 10  μm laser radiation in gases: control of the pulse duration and generation of hot electrons,” Quantum Electron. 39, 663–668 (2009).
[CrossRef]

Guichard, R.

C. Kohler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Berge, and S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[CrossRef]

Haberberger, D.

Hatzes, A. P.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Hertz, E.

Hosseini, S.

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

Joshi, C.

Kandidov, V. P.

E. P. Silaeva, S. A. Shlenov, and V. P. Kandidov, “Multifilamentation of high-power femtosecond laser pulse in turbulent atmosphere with aerosol,” Appl. Phys. B 101, 393–401 (2010).
[CrossRef]

V. P. Kandidov, S. A. Shlenov, and O. G. Kosareva, “Filamentation of high-power femtosecond laser radiation,” Quantum Electron. 39, 205–228 (2009).
[CrossRef]

Kartashov, D.

Kasparian, J.

D. Kartashov, S. Ališauskas, A. Pugžlys, A. Voronin, A. Zheltikov, M. Petrarca, P. Béjot, J. Kasparian, J.-P. Wolf, and A. Baltuška, “Mid-infrared laser filamentation in molecular gases,” Opt. Lett. 38, 3194–3196 (2013).
[CrossRef]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, “Generalized Miller formulae,” Opt. Express 18, 6613–6620 (2010).
[CrossRef]

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

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Kawasaki, Z.

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of strong electromagnetic wave,” Sov. Phys. JETP 20, 1307 (1965).

Kohler, C.

C. Kohler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Berge, and S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[CrossRef]

L. Berge, J. Rolle, and C. Kohler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013).
[CrossRef]

Kopytin, Y. D.

V. E. Zuev, A. A. Zemlyanov, Y. D. Kopytin, and A. V. Kuzikovskii, High-Power Laser Radiation in Atmospheric Aerosols (Reidel, 1984).

Kosareva, O.

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

Kosareva, O. G.

V. P. Kandidov, S. A. Shlenov, and O. G. Kosareva, “Filamentation of high-power femtosecond laser radiation,” Quantum Electron. 39, 205–228 (2009).
[CrossRef]

Krausz, F.

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

Kuzikovskii, A. V.

V. E. Zuev, A. A. Zemlyanov, Y. D. Kopytin, and A. V. Kuzikovskii, High-Power Laser Radiation in Atmospheric Aerosols (Reidel, 1984).

Laux, U.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Lavorel, B.

Lederer, F.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

Lorin, E.

C. Kohler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Berge, and S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[CrossRef]

Loriot, V.

Makarov, E. F.

Méjean, G.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Mlejnek, M.

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382–384 (1998).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: a pressure dependence study,” Phys. Rev. E 58, 4903–4910 (1998).
[CrossRef]

Moloney, J. V.

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382–384 (1998).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: a pressure dependence study,” Phys. Rev. E 58, 4903–4910 (1998).
[CrossRef]

Motokoshi, S.

Mysyrowicz, A.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Myzyrowicz, A.

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

Nuter, R.

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

Panchenko, V. Y.

Panov, N.

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

Paunescu, G.

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B 96, 175–183 (2009).
[CrossRef]

Perelomov, A. M.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in alternating electric field,” Zh. Teor. Eksp. Fiz. 50, 1393–1397 (1966).

Petit, Y.

Petrarca, M.

Platonenko, V. T.

B. G. Bravy, Y. A. Chernyshev, V. M. Gordienko, E. F. Makarov, V. Y. Panchenko, V. T. Platonenko, and G. K. Vasil’ev, “Multi-terawatt picoseconds 10  μm CO2 laser system: design and parameters’ control,” Opt. Express 20, 25536–25544 (2012).
[CrossRef]

V. M. Gordienko, V. T. Platonenko, and A. F. Sterzhantov, “Self-action of a high-power 10  μm laser radiation in gases: control of the pulse duration and generation of hot electrons,” Quantum Electron. 39, 663–668 (2009).
[CrossRef]

Pletnev, N. V.

V. V. Apollonov and N. V. Pletnev, “Formation of extended conducting channels in atmosphere,” Quantum Electron. 42, 130–139 (2012).
[CrossRef]

Pogorelsky, I.

M. N. Polyanskiy, M. Babzien, I. Pogorelsky, and V. Yakimenko, “Ultrashort-pulse CO2 lasers: ready for the race to petawatt?” Proc. SPIE 8677, 86770G (2013).
[CrossRef]

Polyanskiy, M. N.

M. N. Polyanskiy, M. Babzien, I. Pogorelsky, and V. Yakimenko, “Ultrashort-pulse CO2 lasers: ready for the race to petawatt?” Proc. SPIE 8677, 86770G (2013).
[CrossRef]

M. N. Polyanskiy and M. Babzien, “Ultrashort pulses,” in CO2 Laser—Optimization and Application, D. C. Dumitras, ed. (InTech, 2012), pp. 139–162.

Popov, A. M.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of a gaseous medium in the regime of atom stabilization in a strong radiation field,” J. Exp. Theor. Phys. 116, 372–380 (2013).
[CrossRef]

Popov, V. S.

V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Phys. Usp. 47, 855–885 (2004).
[CrossRef]

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in alternating electric field,” Zh. Teor. Eksp. Fiz. 50, 1393–1397 (1966).

Pugžlys, A.

Raizer, Y. P.

Y. P. Raizer, Gas Discharge Physics (Springer, 1991).

Riede, W.

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B 96, 175–183 (2009).
[CrossRef]

Rodriguez, M.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Rolle, J.

L. Berge, J. Rolle, and C. Kohler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013).
[CrossRef]

Roy, G.

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

Salmon, E.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Sauerbrey, R.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Scholz, A.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Schrauth, S. E.

Schröder, H.

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B 96, 175–183 (2009).
[CrossRef]

Shim, B.

Shimada, Y.

Shlenov, S. A.

E. P. Silaeva, S. A. Shlenov, and V. P. Kandidov, “Multifilamentation of high-power femtosecond laser pulse in turbulent atmosphere with aerosol,” Appl. Phys. B 101, 393–401 (2010).
[CrossRef]

V. P. Kandidov, S. A. Shlenov, and O. G. Kosareva, “Filamentation of high-power femtosecond laser radiation,” Quantum Electron. 39, 205–228 (2009).
[CrossRef]

Silaeva, E. P.

E. P. Silaeva, S. A. Shlenov, and V. P. Kandidov, “Multifilamentation of high-power femtosecond laser pulse in turbulent atmosphere with aerosol,” Appl. Phys. B 101, 393–401 (2010).
[CrossRef]

Skupin, S.

C. Kohler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Berge, and S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[CrossRef]

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

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

Spindler, G.

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B 96, 175–183 (2009).
[CrossRef]

Stecklum, B.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Sterzhantov, A. F.

V. M. Gordienko, V. T. Platonenko, and A. F. Sterzhantov, “Self-action of a high-power 10  μm laser radiation in gases: control of the pulse duration and generation of hot electrons,” Quantum Electron. 39, 663–668 (2009).
[CrossRef]

Terent’ev, M. V.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in alternating electric field,” Zh. Teor. Eksp. Fiz. 50, 1393–1397 (1966).

Tikhonova, O. V.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of a gaseous medium in the regime of atom stabilization in a strong radiation field,” J. Exp. Theor. Phys. 116, 372–380 (2013).
[CrossRef]

Tochitsky, S.

Tsubakimoto, K.

Uchida, S.

Vasil’ev, G. K.

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 a gaseous medium in the regime of atom stabilization in a strong radiation field,” J. Exp. Theor. Phys. 116, 372–380 (2013).
[CrossRef]

Voronin, A.

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1997).

Wang, T.-J.

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

Wille, H.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Wolf, J. P.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

Wolf, J.-P.

D. Kartashov, S. Ališauskas, A. Pugžlys, A. Voronin, A. Zheltikov, M. Petrarca, P. Béjot, J. Kasparian, J.-P. Wolf, and A. Baltuška, “Mid-infrared laser filamentation in molecular gases,” Opt. Lett. 38, 3194–3196 (2013).
[CrossRef]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, “Generalized Miller formulae,” Opt. Express 18, 6613–6620 (2010).
[CrossRef]

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

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Woste, L.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Wöste, L.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Wright, E. M.

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: a pressure dependence study,” Phys. Rev. E 58, 4903–4910 (1998).
[CrossRef]

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382–384 (1998).
[CrossRef]

Yakimenko, V.

M. N. Polyanskiy, M. Babzien, I. Pogorelsky, and V. Yakimenko, “Ultrashort-pulse CO2 lasers: ready for the race to petawatt?” Proc. SPIE 8677, 86770G (2013).
[CrossRef]

Yamanaka, C.

Yamanaka, T.

Yasuda, H.

Yu, J.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Yuanc, S.

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

Zemlyanov, A. A.

V. E. Zuev, A. A. Zemlyanov, Y. D. Kopytin, and A. V. Kuzikovskii, High-Power Laser Radiation in Atmospheric Aerosols (Reidel, 1984).

Zheltikov, A.

Zuev, V. E.

V. E. Zuev, A. A. Zemlyanov, Y. D. Kopytin, and A. V. Kuzikovskii, High-Power Laser Radiation in Atmospheric Aerosols (Reidel, 1984).

Appl. Opt.

Appl. Phys. B

G. Paunescu, G. Spindler, W. Riede, H. Schröder, and A. Giesen, “Multifilamentation of femtosecond laser pulses induced by small-scale air turbulence,” Appl. Phys. B 96, 175–183 (2009).
[CrossRef]

E. P. Silaeva, S. A. Shlenov, and V. P. Kandidov, “Multifilamentation of high-power femtosecond laser pulse in turbulent atmosphere with aerosol,” Appl. Phys. B 101, 393–401 (2010).
[CrossRef]

J. Exp. Theor. Phys.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of a gaseous medium in the regime of atom stabilization in a strong radiation field,” J. Exp. Theor. Phys. 116, 372–380 (2013).
[CrossRef]

J. Opt. Technol.

Opt. Commun.

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

Opt. Express

Opt. Lett.

Phys. Rep.

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

Phys. Rev. A

L. Berge, J. Rolle, and C. Kohler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013).
[CrossRef]

C. Kohler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Berge, and S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[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]

Phys. Rev. E

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: a pressure dependence study,” Phys. Rev. E 58, 4903–4910 (1998).
[CrossRef]

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[CrossRef]

Phys. Rev. Lett.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[CrossRef]

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

Phys. Usp.

V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Phys. Usp. 47, 855–885 (2004).
[CrossRef]

Proc. SPIE

M. N. Polyanskiy, M. Babzien, I. Pogorelsky, and V. Yakimenko, “Ultrashort-pulse CO2 lasers: ready for the race to petawatt?” Proc. SPIE 8677, 86770G (2013).
[CrossRef]

Quantum Electron.

V. M. Gordienko, V. T. Platonenko, and A. F. Sterzhantov, “Self-action of a high-power 10  μm laser radiation in gases: control of the pulse duration and generation of hot electrons,” Quantum Electron. 39, 663–668 (2009).
[CrossRef]

V. P. Kandidov, S. A. Shlenov, and O. G. Kosareva, “Filamentation of high-power femtosecond laser radiation,” Quantum Electron. 39, 205–228 (2009).
[CrossRef]

V. V. Apollonov and N. V. Pletnev, “Formation of extended conducting channels in atmosphere,” Quantum Electron. 42, 130–139 (2012).
[CrossRef]

Rep. Prog. Phys.

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

Science

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef]

Sov. Phys. JETP

L. V. Keldysh, “Ionization in the field of strong electromagnetic wave,” Sov. Phys. JETP 20, 1307 (1965).

Zh. Teor. Eksp. Fiz.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in alternating electric field,” Zh. Teor. Eksp. Fiz. 50, 1393–1397 (1966).

Other

Y. P. Raizer, Gas Discharge Physics (Springer, 1991).

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1997).

M. N. Polyanskiy and M. Babzien, “Ultrashort pulses,” in CO2 Laser—Optimization and Application, D. C. Dumitras, ed. (InTech, 2012), pp. 139–162.

V. E. Zuev, A. A. Zemlyanov, Y. D. Kopytin, and A. V. Kuzikovskii, High-Power Laser Radiation in Atmospheric Aerosols (Reidel, 1984).

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Figures (8)

Fig. 1.
Fig. 1.

Rate of free electron generation δtρe through field or impact ionization of oxygen atoms by laser radiation with (a) λ0=0.8μm and (b) 10.6 μm. Calculations for impact ionization rate were performed at ρe0=1013cm3 and 1016cm3 as indicated in the figure.

Fig. 2.
Fig. 2.

Trace profiles of (a) laser beam radius Rw and (b) peak intensity Imax for nIR and mIR pulses with η=5; dashed lines are for pure Kerr-focusing model (no HOKE).

Fig. 3.
Fig. 3.

Fluence spatial distribution of laser pulses at (a) λ0=0.8 and (b), (c) 10.6 μm. (c) is for tp=500fs, and (d) shows the vertical fluence profile.

Fig. 4.
Fig. 4.

Axial pulse intensity profile and nonlinear absorption coefficient αN of plasma as a function of time for (a) λ0=0.8 and (b) 10.6 μm (tp=500fs).

Fig. 5.
Fig. 5.

Normalized radiation spectrum of 200 fs pulse after propagation to the distance z=200m for λ0=800nm and 10.6 μm radiation; shaded areas are for the initial spectrum of pulses.

Fig. 6.
Fig. 6.

Shaded-relief images of x-integrated laser intensity during laser radiation propagation in air with η=20 and (a) λ0=800nm, (b) 10.6 μm.

Fig. 7.
Fig. 7.

Transverse intensity profiles of laser radiation with η=20 and λ0=800nm (upper panel) and 10.6 μm (lower panel) propagating in air to the different distances (a), (f) z=1m; (b), (g) 17 m; (c), (h) 24 m; (d), (i) 60 m; and (e), (j) 150 m. Imax values (TW/cm2) are shown by numbers in the right lower corner of the images.

Fig. 8.
Fig. 8.

(a) Maximal laser intensity and (b) maximal electron density versus propagation distance of laser pulses with different carrier wavelengths.

Equations (10)

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{zi2n0k0T^2+ikω22t2}Uik0T^(n2+nHOKET^2np)U+αN+αL2U=0.
αN=σcρe+WI(I)I1ΔEi(ρntρe),
np=σcτccρe/2n0,
ρe/t=WI(I)(ρntρe)+νiρeIνrρe2(νatt+νdiff)ρe,
σc=e2τc/[cme0(ω2τc2+1)].
ρe/t=WI(I)(ρntρe)+νiρeI.
Ri=νc1+νc2/ω2(1+2γi2)1,
U(r,z,t)=U0u(r,z)
ρ¯e(t¯)=(2νrρnt)1{Rtanh(0.5Rt0[t¯+C])(WIνi|u|2)},
{zi42im=1MLRL2m|u|2m+12LRLWW¯I(|u|2)(1B)|u|2+i2LRLpl(1iω0τc)B+LRαL2}u=0.

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