Abstract

We numerically study the filamentation of ultrashort laser pulses at 2 µm carrier wavelength in noble gases (argon, xenon) and in air. Compared with filamentation in the near-visible domain (800 nm), mid-infrared optical sources with durations close to a single cycle can be generically produced at various pressures and powers near the self-focusing threshold. The mechanism by which self-compression takes place mainly involves optical self-focusing, pulse steepening and plasma defocusing. On-axis spectra and spectral phases are discussed. Delivering single-cycled pulses at long wavelengths has important applications in the generation of high-order harmonics and isolated attosecond pulses.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  38. S. Skupin and L. Bergé, "Supercontinuum generation of ulrashort pulses in air at different central wavelengths," Opt. Commun. 280,173-182 (2007).
    [CrossRef]
  39. S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, "(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments," Phys. Rev. E 77,036406 (2008).
    [CrossRef]
  40. A. Talebpour, J. Yang, and S. L. Chin, "Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse," Opt. Commun. 163,29-32 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2008 (12)

J. Kasparian and J.-P. Wolf, "Physics and applications of atmospheric nonlinear optics and filamentation," Opt. Express 16,466-493 (2008).
[CrossRef] [PubMed]

O. G. Kosareva, N. A. Panov, D. S. Uryupina, M. V. Kurilova, A. V. Mazhorova, A. B. Savel’ev, R. V. Volkov, V. P. Kandidov, and S. L. Chin, "Optimization of a femtosecond pulse self-compression region along a filament in air," Appl. Phys. B 91,35-43 (2008).
[CrossRef]

L. Bergé and S. Skupin, "Few-cycle light bullets created by femtosecond filaments," Phys. Rev. Lett. 100,113902 (2008).
[CrossRef] [PubMed]

A. Couairon and H. S. Chakraborty and M. B. Gaarde, "From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases," Phys. Rev. A 77,053814 (2008).
[CrossRef]

E. Goulielmakis, S. Koehler, B. Reiter, M. Schultze, A. J. Verheof, E. E. Serebryannikov, A. M. Zheltikov, and F. Krausz, "Ultrabroadband, coherent light source based on self-channeling of few-cycle pulses in helium," Opt. Lett. 33,1407-1409 (2008).
[CrossRef] [PubMed]

L. Bergé and S. Skupin, "Sub-2 fs pulses generated by self-channeling in the deep ultraviolet," Opt. Lett. 33,750-752 (2008).
[CrossRef] [PubMed]

G. Sansone, E. Benedetti, F. Galegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314,443-446 (2008).
[CrossRef]

D. Faccio, A. Lotti, M. Kolesik, J. V. Moloney, S. Tzortzakis, A. Couairon, and P. Di Trapani, "Spontaneous emergence of pulses with constant carrier-envelope phase in femtosecond filamentation," Opt. Express 16,11103-11114 (2008).
[CrossRef] [PubMed]

C. Vozzi, C. Manzoni, F. Calegari, E. Benedetti, G. Sansone, G. Cerullo, M. Nisoli, S. De Silvestri, and S. Stagira, "Characterization of a high-energy self-phase-stabilized near-infrared parametric source," J. Opt. Soc. Am. B 25,112-117 (2008).
[CrossRef]

D. Brida, G. Cirmi, C. Manzoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, "Sub-two-cycle light pulses at 1.6 m from an optical parametric amplifier," Opt. Lett. 33,741-743 (2008).
[CrossRef] [PubMed]

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, "(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments," Phys. Rev. E 77,036406 (2008).
[CrossRef]

J. Bernhardt, W. Liu, S. L. Chin, and R. Sauerbrey, "Pressure independence of intensity clamping during filamentation: theory and experiment," Appl. Phys. B 91,45-48 (2008).
[CrossRef]

2007 (8)

S. Skupin and L. Bergé, "Supercontinuum generation of ulrashort pulses in air at different central wavelengths," Opt. Commun. 280,173-182 (2007).
[CrossRef]

T. Fuji and T. Suzuki, "Generation of sub-two-cycle mid-infrared pulses by four-wave mixing through filamentation in air," Opt. Lett. 32,3330-3332 (2007).
[CrossRef] [PubMed]

K. D. Schultz, C. I. Blaga, R. Chirla, P. Colosimo, J. Cryan, A. M. March, C. Roedig, E. Sistrunk, J. tate, J. Wheeler, P. Agostini, and L. F. DiMauro, "Strong field physics with long wavelength lasers," J. Mod. Opt. 54,1075-1085 (2007).
[CrossRef]

J. Tate, T. Auguste, H. G. Muller, P. Sali`eres, P. Agostini, and L. F. DiMauro, "Scaling of wave-packet dynamics in an intense midinfrared field," Phys. Rev. Lett. 98,013901 (2007).
[CrossRef] [PubMed]

C. P. Hauri, R. B. Lopez-Martens, C. I. Blaga, K. D. Schultz, J. Cryan, R. Chirla, P. Colosimo, G. Doumy, A. M. March, C. Roedig, E. Sistrunk, J. Tate, J. Wheeler, L. F. DiMauro, and E. P. Power, "Intense self-compressed, self-phase-stabilized few-cycle pulses at 2m from an optical filament," Opt. Lett. 32,868-870 (2007).
[CrossRef] [PubMed]

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

A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 44,47-189 (2007).
[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]

2006 (5)

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

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

R. Nuter and L. Bergé, "Pulse chirping and ionization of O2 molecules for the filamentation of femtosecond laser pulses in air," J. Opt. Soc. Am. B 23,874-884 (2006).
[CrossRef]

N. Ak¨ozbek, S. A. Trushin, A. Baltuška,W. Fuss, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, "Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses," New J. Phys. 8,177 (2006).
[CrossRef]

S. Champeaux and L. Bergé, "Long-range multifilamentation of femtosecond laser pulses versus air pressure," Opt. Lett. 31,1301-1303 (2006).
[CrossRef] [PubMed]

2005 (2)

W. Liu and S. L. Chin, "Direct measurement of the critical power of femtosecond Ti:sapphire laser pulse in air," Opt. Express 13,5750-5755 (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 (1)

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79,673-677 (2004).
[CrossRef]

2003 (3)

S. Champeaux and L. Bergé, "Femtosecond pulse compression in pressure-gas cells filled with argon," Phys. Rev. E 68,066603 (2003).
[CrossRef]

R. Wiehle, B. Witzel, H. Helm, and E. Cormier, "Dynamics of strong-field above-threshold ionization of argon: Comparison between experiment and theory," Phys. Rev. A 67,063405 (2003).
[CrossRef]

E. Cormier, P.-A. Hervieux, R. Wiehle, B. Witzel, and H. Helm, "ATI of complex systems: Ar and C60," Eur. Phys. J. D. 26,83-90 (2003).
[CrossRef]

2001 (3)

B. Shan and Z. Chang, "Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field," Phys. Rev. A 65,011804(R) (2001).
[CrossRef]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292,1689-1692 (2001).
[CrossRef] [PubMed]

N. Ak¨ozbek, M. Scalora, C. M. Bowden, and S. L. Chin, "White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air," Opt. Commun. 191,353-362 (2001).
[CrossRef]

1999 (2)

A. Talebpour, J. Yang, and S. L. Chin, "Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse," Opt. Commun. 163,29-32 (1999).
[CrossRef]

B. Sheehy, J. D. D. Martin, L. F. DiMauro, P. Agostini, K. J. Schafer, M. B. Gaarde, and K. C. Kulander, "High harmonic generation at long wavelengths," Phys. Rev. Lett. 83,5270-5273 (1999).
[CrossRef]

1998 (2)

1997 (2)

1995 (1)

1994 (1)

1990 (1)

D. P. Shelton, "Nonlinear-optical susceptibilities of gases measured at 1064 and 1319 nm," Phys. Rev. A 42,2578-2592 (1990).
[CrossRef] [PubMed]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. JETP 64,1191-1194 (1986).

1983 (1)

D. Anderson and M. Lisak, "Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides," Phys. Rev. A 27,1393-1398 (1983).
[CrossRef]

1972 (1)

1966 (1)

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

1960 (1)

A. Dalgarno and A. E. Kingston, "The refractive indices and Verdet constants of the inert gases," Proc. Royal Soc. London A 259,424-429 (1960).
[CrossRef]

Agostini, P.

K. D. Schultz, C. I. Blaga, R. Chirla, P. Colosimo, J. Cryan, A. M. March, C. Roedig, E. Sistrunk, J. tate, J. Wheeler, P. Agostini, and L. F. DiMauro, "Strong field physics with long wavelength lasers," J. Mod. Opt. 54,1075-1085 (2007).
[CrossRef]

J. Tate, T. Auguste, H. G. Muller, P. Sali`eres, P. Agostini, and L. F. DiMauro, "Scaling of wave-packet dynamics in an intense midinfrared field," Phys. Rev. Lett. 98,013901 (2007).
[CrossRef] [PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292,1689-1692 (2001).
[CrossRef] [PubMed]

B. Sheehy, J. D. D. Martin, L. F. DiMauro, P. Agostini, K. J. Schafer, M. B. Gaarde, and K. C. Kulander, "High harmonic generation at long wavelengths," Phys. Rev. Lett. 83,5270-5273 (1999).
[CrossRef]

Ak¨ozbek, N.

N. Ak¨ozbek, S. A. Trushin, A. Baltuška,W. Fuss, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, "Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses," New J. Phys. 8,177 (2006).
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N. Ak¨ozbek, M. Scalora, C. M. Bowden, and S. L. Chin, "White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air," Opt. Commun. 191,353-362 (2001).
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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).
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G. Sansone, E. Benedetti, F. Galegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314,443-446 (2008).
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M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. JETP 64,1191-1194 (1986).

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P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292,1689-1692 (2001).
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J. Tate, T. Auguste, H. G. Muller, P. Sali`eres, P. Agostini, and L. F. DiMauro, "Scaling of wave-packet dynamics in an intense midinfrared field," Phys. Rev. Lett. 98,013901 (2007).
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G. Sansone, E. Benedetti, F. Galegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314,443-446 (2008).
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P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292,1689-1692 (2001).
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N. Ak¨ozbek, S. A. Trushin, A. Baltuška,W. Fuss, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, "Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses," New J. Phys. 8,177 (2006).
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N. Ak¨ozbek, S. A. Trushin, A. Baltuška,W. Fuss, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, "Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses," New J. Phys. 8,177 (2006).
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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).
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Benedetti, E.

G. Sansone, E. Benedetti, F. Galegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314,443-446 (2008).
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C. Vozzi, C. Manzoni, F. Calegari, E. Benedetti, G. Sansone, G. Cerullo, M. Nisoli, S. De Silvestri, and S. Stagira, "Characterization of a high-energy self-phase-stabilized near-infrared parametric source," J. Opt. Soc. Am. B 25,112-117 (2008).
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Bergé, L.

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, "(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments," Phys. Rev. E 77,036406 (2008).
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R. Nuter and L. Bergé, "Pulse chirping and ionization of O2 molecules for the filamentation of femtosecond laser pulses in air," J. Opt. Soc. Am. B 23,874-884 (2006).
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S. Champeaux and L. Bergé, "Long-range multifilamentation of femtosecond laser pulses versus air pressure," Opt. Lett. 31,1301-1303 (2006).
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S. Skupin, G. Stibenz, and L. Bergé, F. Lederer, T. Sokollik, M. Schnürer, N. Zhavoronkov, and G. Steinmeyer, "Self-compression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74,056604 (2006).
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S. Champeaux and L. Bergé, "Femtosecond pulse compression in pressure-gas cells filled with argon," Phys. Rev. E 68,066603 (2003).
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J. Bernhardt, W. Liu, S. L. Chin, and R. Sauerbrey, "Pressure independence of intensity clamping during filamentation: theory and experiment," Appl. Phys. B 91,45-48 (2008).
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A. Za¨ır, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15,5394-5405 (2007).
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C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79,673-677 (2004).
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Blaga, C. I.

C. P. Hauri, R. B. Lopez-Martens, C. I. Blaga, K. D. Schultz, J. Cryan, R. Chirla, P. Colosimo, G. Doumy, A. M. March, C. Roedig, E. Sistrunk, J. Tate, J. Wheeler, L. F. DiMauro, and E. P. Power, "Intense self-compressed, self-phase-stabilized few-cycle pulses at 2m from an optical filament," Opt. Lett. 32,868-870 (2007).
[CrossRef] [PubMed]

K. D. Schultz, C. I. Blaga, R. Chirla, P. Colosimo, J. Cryan, A. M. March, C. Roedig, E. Sistrunk, J. tate, J. Wheeler, P. Agostini, and L. F. DiMauro, "Strong field physics with long wavelength lasers," J. Mod. Opt. 54,1075-1085 (2007).
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Bloemer, M.

N. Ak¨ozbek, S. A. Trushin, A. Baltuška,W. Fuss, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, "Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses," New J. Phys. 8,177 (2006).
[CrossRef]

Bonora, S.

Bowden, C. M.

N. Ak¨ozbek, M. Scalora, C. M. Bowden, and S. L. Chin, "White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air," Opt. Commun. 191,353-362 (2001).
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Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292,1689-1692 (2001).
[CrossRef] [PubMed]

Brida, D.

Calegari, F.

C. Vozzi, C. Manzoni, F. Calegari, E. Benedetti, G. Sansone, G. Cerullo, M. Nisoli, S. De Silvestri, and S. Stagira, "Characterization of a high-energy self-phase-stabilized near-infrared parametric source," J. Opt. Soc. Am. B 25,112-117 (2008).
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Cerullo, G.

D. Brida, G. Cirmi, C. Manzoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, "Sub-two-cycle light pulses at 1.6 m from an optical parametric amplifier," Opt. Lett. 33,741-743 (2008).
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C. Vozzi, C. Manzoni, F. Calegari, E. Benedetti, G. Sansone, G. Cerullo, M. Nisoli, S. De Silvestri, and S. Stagira, "Characterization of a high-energy self-phase-stabilized near-infrared parametric source," J. Opt. Soc. Am. B 25,112-117 (2008).
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Chakraborty, H. S.

A. Couairon and H. S. Chakraborty and M. B. Gaarde, "From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases," Phys. Rev. A 77,053814 (2008).
[CrossRef]

Champeaux, S.

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, "(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments," Phys. Rev. E 77,036406 (2008).
[CrossRef]

S. Champeaux and L. Bergé, "Long-range multifilamentation of femtosecond laser pulses versus air pressure," Opt. Lett. 31,1301-1303 (2006).
[CrossRef] [PubMed]

S. Champeaux and L. Bergé, "Femtosecond pulse compression in pressure-gas cells filled with argon," Phys. Rev. E 68,066603 (2003).
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Chang, Z.

B. Shan and Z. Chang, "Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field," Phys. Rev. A 65,011804(R) (2001).
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Chin, S. L.

O. G. Kosareva, N. A. Panov, D. S. Uryupina, M. V. Kurilova, A. V. Mazhorova, A. B. Savel’ev, R. V. Volkov, V. P. Kandidov, and S. L. Chin, "Optimization of a femtosecond pulse self-compression region along a filament in air," Appl. Phys. B 91,35-43 (2008).
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J. Bernhardt, W. Liu, S. L. Chin, and R. Sauerbrey, "Pressure independence of intensity clamping during filamentation: theory and experiment," Appl. Phys. B 91,45-48 (2008).
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W. Liu and S. L. Chin, "Direct measurement of the critical power of femtosecond Ti:sapphire laser pulse in air," Opt. Express 13,5750-5755 (2005).
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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]

N. Ak¨ozbek, M. Scalora, C. M. Bowden, and S. L. Chin, "White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air," Opt. Commun. 191,353-362 (2001).
[CrossRef]

A. Talebpour, J. Yang, and S. L. Chin, "Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse," Opt. Commun. 163,29-32 (1999).
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C. P. Hauri, R. B. Lopez-Martens, C. I. Blaga, K. D. Schultz, J. Cryan, R. Chirla, P. Colosimo, G. Doumy, A. M. March, C. Roedig, E. Sistrunk, J. Tate, J. Wheeler, L. F. DiMauro, and E. P. Power, "Intense self-compressed, self-phase-stabilized few-cycle pulses at 2m from an optical filament," Opt. Lett. 32,868-870 (2007).
[CrossRef] [PubMed]

K. D. Schultz, C. I. Blaga, R. Chirla, P. Colosimo, J. Cryan, A. M. March, C. Roedig, E. Sistrunk, J. tate, J. Wheeler, P. Agostini, and L. F. DiMauro, "Strong field physics with long wavelength lasers," J. Mod. Opt. 54,1075-1085 (2007).
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Cirmi, G.

Colosimo, P.

C. P. Hauri, R. B. Lopez-Martens, C. I. Blaga, K. D. Schultz, J. Cryan, R. Chirla, P. Colosimo, G. Doumy, A. M. March, C. Roedig, E. Sistrunk, J. Tate, J. Wheeler, L. F. DiMauro, and E. P. Power, "Intense self-compressed, self-phase-stabilized few-cycle pulses at 2m from an optical filament," Opt. Lett. 32,868-870 (2007).
[CrossRef] [PubMed]

K. D. Schultz, C. I. Blaga, R. Chirla, P. Colosimo, J. Cryan, A. M. March, C. Roedig, E. Sistrunk, J. tate, J. Wheeler, P. Agostini, and L. F. DiMauro, "Strong field physics with long wavelength lasers," J. Mod. Opt. 54,1075-1085 (2007).
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R. Wiehle, B. Witzel, H. Helm, and E. Cormier, "Dynamics of strong-field above-threshold ionization of argon: Comparison between experiment and theory," Phys. Rev. A 67,063405 (2003).
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E. Cormier, P.-A. Hervieux, R. Wiehle, B. Witzel, and H. Helm, "ATI of complex systems: Ar and C60," Eur. Phys. J. D. 26,83-90 (2003).
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D. Faccio, A. Lotti, M. Kolesik, J. V. Moloney, S. Tzortzakis, A. Couairon, and P. Di Trapani, "Spontaneous emergence of pulses with constant carrier-envelope phase in femtosecond filamentation," Opt. Express 16,11103-11114 (2008).
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A. Couairon and H. S. Chakraborty and M. B. Gaarde, "From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases," Phys. Rev. A 77,053814 (2008).
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A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 44,47-189 (2007).
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A. Za¨ır, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, "Spatio-temporal characterization of few-cycle pulses obtained by filamentation," Opt. Express 15,5394-5405 (2007).
[CrossRef] [PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79,673-677 (2004).
[CrossRef]

Cryan, J.

K. D. Schultz, C. I. Blaga, R. Chirla, P. Colosimo, J. Cryan, A. M. March, C. Roedig, E. Sistrunk, J. tate, J. Wheeler, P. Agostini, and L. F. DiMauro, "Strong field physics with long wavelength lasers," J. Mod. Opt. 54,1075-1085 (2007).
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C. P. Hauri, R. B. Lopez-Martens, C. I. Blaga, K. D. Schultz, J. Cryan, R. Chirla, P. Colosimo, G. Doumy, A. M. March, C. Roedig, E. Sistrunk, J. Tate, J. Wheeler, L. F. DiMauro, and E. P. Power, "Intense self-compressed, self-phase-stabilized few-cycle pulses at 2m from an optical filament," Opt. Lett. 32,868-870 (2007).
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A. Dalgarno and A. E. Kingston, "The refractive indices and Verdet constants of the inert gases," Proc. Royal Soc. London A 259,424-429 (1960).
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C. Vozzi, C. Manzoni, F. Calegari, E. Benedetti, G. Sansone, G. Cerullo, M. Nisoli, S. De Silvestri, and S. Stagira, "Characterization of a high-energy self-phase-stabilized near-infrared parametric source," J. Opt. Soc. Am. B 25,112-117 (2008).
[CrossRef]

D. Brida, G. Cirmi, C. Manzoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, "Sub-two-cycle light pulses at 1.6 m from an optical parametric amplifier," Opt. Lett. 33,741-743 (2008).
[CrossRef] [PubMed]

G. Sansone, E. Benedetti, F. Galegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314,443-446 (2008).
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M. Nisoli, S. de Silvestri, O. Svelto, R. Szip¨oecs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, "Compression of high-energy laser pulses below 5 fs," Opt. Lett. 22,522-524 (1997).
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Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. JETP 64,1191-1194 (1986).

Di Trapani, P.

DiMauro, L. F.

K. D. Schultz, C. I. Blaga, R. Chirla, P. Colosimo, J. Cryan, A. M. March, C. Roedig, E. Sistrunk, J. tate, J. Wheeler, P. Agostini, and L. F. DiMauro, "Strong field physics with long wavelength lasers," J. Mod. Opt. 54,1075-1085 (2007).
[CrossRef]

J. Tate, T. Auguste, H. G. Muller, P. Sali`eres, P. Agostini, and L. F. DiMauro, "Scaling of wave-packet dynamics in an intense midinfrared field," Phys. Rev. Lett. 98,013901 (2007).
[CrossRef] [PubMed]

C. P. Hauri, R. B. Lopez-Martens, C. I. Blaga, K. D. Schultz, J. Cryan, R. Chirla, P. Colosimo, G. Doumy, A. M. March, C. Roedig, E. Sistrunk, J. Tate, J. Wheeler, L. F. DiMauro, and E. P. Power, "Intense self-compressed, self-phase-stabilized few-cycle pulses at 2m from an optical filament," Opt. Lett. 32,868-870 (2007).
[CrossRef] [PubMed]

B. Sheehy, J. D. D. Martin, L. F. DiMauro, P. Agostini, K. J. Schafer, M. B. Gaarde, and K. C. Kulander, "High harmonic generation at long wavelengths," Phys. Rev. Lett. 83,5270-5273 (1999).
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Doumy, G.

Du, D.

Faccio, D.

Ferencz, K.

Flammini, R.

G. Sansone, E. Benedetti, F. Galegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314,443-446 (2008).
[CrossRef]

Franco, M.

Fuji, T.

Fuss, W.

N. Ak¨ozbek, S. A. Trushin, A. Baltuška,W. Fuss, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, "Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses," New J. Phys. 8,177 (2006).
[CrossRef]

Gaarde, M. B.

A. Couairon and H. S. Chakraborty and M. B. Gaarde, "From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases," Phys. Rev. A 77,053814 (2008).
[CrossRef]

B. Sheehy, J. D. D. Martin, L. F. DiMauro, P. Agostini, K. J. Schafer, M. B. Gaarde, and K. C. Kulander, "High harmonic generation at long wavelengths," Phys. Rev. Lett. 83,5270-5273 (1999).
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Gaeta, A. L.

Galegari, F.

G. Sansone, E. Benedetti, F. Galegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314,443-446 (2008).
[CrossRef]

Gallmann, L.

Gordon, D.

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, "(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments," Phys. Rev. E 77,036406 (2008).
[CrossRef]

Goulielmakis, E.

E. Goulielmakis, S. Koehler, B. Reiter, M. Schultze, A. J. Verheof, E. E. Serebryannikov, A. M. Zheltikov, and F. Krausz, "Ultrabroadband, coherent light source based on self-channeling of few-cycle pulses in helium," Opt. Lett. 33,1407-1409 (2008).
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N. Ak¨ozbek, S. A. Trushin, A. Baltuška,W. Fuss, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloemer, "Extending the supercontinuum spectrum down to 200 nm with few-cycle pulses," New J. Phys. 8,177 (2006).
[CrossRef]

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Hauri, C. P.

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J. Tate, T. Auguste, H. G. Muller, P. Sali`eres, P. Agostini, and L. F. DiMauro, "Scaling of wave-packet dynamics in an intense midinfrared field," Phys. Rev. Lett. 98,013901 (2007).
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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).
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K. D. Schultz, C. I. Blaga, R. Chirla, P. Colosimo, J. Cryan, A. M. March, C. Roedig, E. Sistrunk, J. tate, J. Wheeler, P. Agostini, and L. F. DiMauro, "Strong field physics with long wavelength lasers," J. Mod. Opt. 54,1075-1085 (2007).
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C. P. Hauri, R. B. Lopez-Martens, C. I. Blaga, K. D. Schultz, J. Cryan, R. Chirla, P. Colosimo, G. Doumy, A. M. March, C. Roedig, E. Sistrunk, J. Tate, J. Wheeler, L. F. DiMauro, and E. P. Power, "Intense self-compressed, self-phase-stabilized few-cycle pulses at 2m from an optical filament," Opt. Lett. 32,868-870 (2007).
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S. Skupin and L. Bergé, "Supercontinuum generation of ulrashort pulses in air at different central wavelengths," Opt. Commun. 280,173-182 (2007).
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S. Skupin, G. Stibenz, and L. Bergé, F. Lederer, T. Sokollik, M. Schnürer, N. Zhavoronkov, and G. Steinmeyer, "Self-compression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74,056604 (2006).
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S. Skupin, G. Stibenz, and L. Bergé, F. Lederer, T. Sokollik, M. Schnürer, N. Zhavoronkov, and G. Steinmeyer, "Self-compression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74,056604 (2006).
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G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, "Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament," Opt. Lett. 31,274-276 (2006).
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S. Skupin, G. Stibenz, and L. Bergé, F. Lederer, T. Sokollik, M. Schnürer, N. Zhavoronkov, and G. Steinmeyer, "Self-compression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74,056604 (2006).
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G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, "Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament," Opt. Lett. 31,274-276 (2006).
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S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, "(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments," Phys. Rev. E 77,036406 (2008).
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Yang, J.

A. Talebpour, J. Yang, and S. L. Chin, "Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse," Opt. Commun. 163,29-32 (1999).
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S. Skupin, G. Stibenz, and L. Bergé, F. Lederer, T. Sokollik, M. Schnürer, N. Zhavoronkov, and G. Steinmeyer, "Self-compression by femtosecond pulse filamentation: Experiments versus numerical simulations," Phys. Rev. E 74,056604 (2006).
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S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, "(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments," Phys. Rev. E 77,036406 (2008).
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Sov. Phys. JETP (2)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. JETP 64,1191-1194 (1986).

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Figures (8)

Fig. 1.
Fig. 1.

Ionization rates plotted from the PPT formula Eq. (4) with ion charge Z=1 and angular momentum equal to 1 for atom gases and 0 for air [30] at central wavelengths (a) 800 nm and (b) 2 µm. The blue curves refer to ionization in argon; the red curves correspond to xenon, and the green curves show the ionization rate in air for O2 molecules.

Fig. 2.
Fig. 2.

Peak intensities at 800 nm (a) in Ar for p=1 bar (solid curve), p=0.5 bar (dashed curve) and p=2 bar (dash-dotted curve); (b) in Xe at 2 bar (dotted curve), 1 bar (dash-dotted curve), 0.5 bar (dashed curve), and in air at 1 bar pressure (solid curve). Power ratios are specified in the text. (c) Peak electron densities in the zoomed filamentation range 0.3≤z≤0.55 m for Ar at 1 bar (solid curve) and in Xe at 0.5 bar (dashed curve), 1 bar (dash-dotted curve) and 2 bar (dotted curve). (d) Filament waist for Ar at 1 bar (blue solid curve), Xe at 0.5 bar (dashed curve), 1 bar (dash-dotted curve) and 2 bar (dotted curve) in the same range. The green solid curve shows wfil for air at p=1 bar.

Fig. 3.
Fig. 3.

Temporal evolution of 800 nm Gaussian pulses in the (t,z) plane for (a) argon and (b) air at 1 bar pressure, and for xenon at (c) 1 bar pressure and (d) 0.5 bar pressure.

Fig. 4.
Fig. 4.

(a) On-axis temporal profiles and (b) on-axis spectra (left axis) with spectral phases (right axis) for argon at 1 bar pressure, z=0.9 m (solid curve, FWHM=6.5 fs) and xenon at 0.5 bar pressure, z=0.6 m (dashed curve, FWHM=7 fs). The dashed-dotted line in Fig. 4(a) illustrates the latter case when the self-steepening operators are artificially suppressed (T=T -1=1). The dotted curve of Fig. 4(b) refers to the spectrum in argon at z=0.

Fig. 5.
Fig. 5.

Peak intensities at 2 µm (a) in Ar for p=1 bar (dash-dotted curve), p=0.5 bar (dashed curve) with P in=1P cr, and for p=1 bar with P in=1.2P cr (solid curve); (b) in Xe at 1 bar (dash-dotted curve) and 0.5 bar (dashed curve) for P in=1.3P cr, and in air at 1 bar (solid curve) and 2 bar (dotted curve) for P in=2.2P cr. (c) Peak electron densities in Ar and air at different pressures with the same plotstyles as in Figs. 5(a)–5(b). (d) Filament waists for the previous cases. The red dash-dotted curve shows the filament waist in Xe at 1 bar.

Fig. 6.
Fig. 6.

Temporal evolution of 2 µm Gaussian pulses in the (t,z) plane for (a) Xe at p=0.5 bar and P in=1.3P cr; (b) air at p=1 bar and P in=2.2P cr; (c) Ar at 1 bar pressure and P in=1.2P cr, and (d) Ar at 0.5 bar pressure and P in=1P cr.

Fig. 7.
Fig. 7.

(a) On-axis temporal profiles for argon at 1 bar pressure, z=0.6 m with (solid curve, FWHM=6.5 fs) and without pulse steepening (dash-dotted curve, FWHM=7.5 fs), and at 0.5 bar pressure, z=0.8 m (dashed curve, FWHM=5.5 fs). (b) On-axis spectra (left axis) with spectral phases (right axis) in 1 bar argon and in the xenon case (dashed curves) shown in Fig. 6(a). The dotted curve represents the spectrum in argon at z=0.

Fig. 8.
Fig. 8.

On-axis spectra of Gaussian pulses at distance of maximal compression (a) at 800 nm in 1 bar pressure Ar (blue solid curve), 0.5 bar Xe (red dashed curve) and in 1 bar air (green solid curve); (b) at 2 µm in 1 bar Ar with (blue solid curve) and without (blue dash-dotted curve) steepening terms [Fig. 7(a)], and in 0.5 bar Xe (red dashed curve).

Tables (1)

Tables Icon

Table 1. Physical parameters for Ar, Xe and air at 800 nm and 2 µm for the pressure p=1 bar. ρ nt is equal to 2.7×1019 cm-3 for the noble gases, and to 5.4×1018 cm-3 for the 20% dioxygen molecules of air. The critical plasma density takes the value ρ cr≃1.11×1021/λ 2 0[µm]. The last line contains estimations of I max computed from Eq. (7).

Equations (11)

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z U = i 2 k 0 T 1 2 U + i D U + i ω 0 c n 2 T × [ ( 1 x K ) U 2 + x K t h ( t t ) U ( t ) 2 dt ] U
i k 0 2 n 0 2 ρ c T 1 ρ U σ 2 ρ U ( ρ nt ρ ) U i W ( I ) 2 I U ,
h ( t ) = τ 1 2 + τ 2 2 τ 1 τ 2 2 e t τ 2 sin ( t τ 1 ) ,
t ρ = W ( I ) ( ρ nt ρ ) + σ U i ρ I ,
W ( E p ) = 4 2 π C n * , l * 2 ( 2 E 0 E p 1 + γ 2 ) 2 n * 3 2 m f ( l , m ) m ! e 2 ν [ sinh 1 ( γ ) γ 1 + γ 2 1 + 2 γ 2 ]
× U i γ 2 1 + γ 2 κ ν 0 + e α ( κ ν ) Φ m ( β ( κ ν ) ) ,
C n * , l * 2 = 2 2 n * n * Γ ( n * + l * + 1 ) Γ ( n * l * ) , f ( l , m ) = ( 2 l + 1 ) ( l + m ) ! 2 m m ! ( l m ) !
U ( r , z = 0 , t ) = 2 P in π w 0 2 e r 2 w 0 2 t 2 t p 2 ,
I fil ρ fil 2 ρ c n 0 n ̅ 2 , ρ fil Δ T ρ nt W ( I fil ) , W fil 2 π ( 2 k 0 2 n ̅ 2 I fil n 0 ) 1 2 ,
n ̅ 2 = n 2 ( 1 x K ) + n 2 x K max t t h ( t t ) e 2 t 2 t p 2 dt
Δ ω k 0 Δ z t ( n ̅ 2 I ρ 2 n 0 ρ c ) ,

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