Abstract

We theoretically investigate the transverse-mode dependence of femtosecond filamentation in Ar gas. Three different transverse modes, Bessel, Gaussian, and Laguerre modes, are considered for incident laser pulses. By solving the extended nonlinear Schrödinger equation coupled with the electron density equation, we find that the lengths of the filament and the plasma channel induced by the Bessel incident beam is much longer than the other transverse modes with the same peak intensity, pulse duration, and beam diameter. Moreover we find that the temporal profile of the pulse with the Bessel incident mode is nearly undistorted during the propagation. Since the pulse energy that the Bessel beam can carry is more than one order of magnitude larger than the other modes for the same peak intensity, pulse duration, and beam diameter, the Bessel beam can be a very powerful tool in ultrafast nonlinear optics involving propagation in a Kerr medium.

© 2009 Optical Society of America

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    [CrossRef]
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  4. J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. -P. Wolf, Y. -B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, "Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-1399 (2000).
    [CrossRef]
  5. A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Self-compression of ultrashort laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
    [CrossRef]
  6. 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, 1944-1946 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
  8. J. Durnin, J. J. MiceliJr, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
    [CrossRef] [PubMed]
  9. J. Durnin, "Exact solutions for nondiffracting beams. I. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1987).
    [CrossRef]
  10. P. Polesana, M. Franco, A. Couairon, D. Faccio and P. Di Trapani, "Filamentation in Kerr media from pulsed Bessel beams," Phys. Rev. A 77, 043814 (2008).
    [CrossRef]
  11. E. Gaižauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, "Discrete damage traces from filamentation of Gauss-Bessel pulses," Opt. Lett. 31, 80-82 (2006).
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  16. K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
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    [CrossRef] [PubMed]
  19. S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, "Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon," Opt. Commun. 282, 129-134 (2009).
  20. G.A. Turnbull, D.A. Robertson, G.M. Smith, L. Allen, and M.J. Padgett, "The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate," Opt. Commun. 127,183-188 (1996).
    [CrossRef]
  21. M. W. Beijersbergen, R. P.C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112,321-327 (1994).
    [CrossRef]
  22. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, "Laser beams with phase singularities," Opt. Quantum Electron. 24,S951-S962 (1992).
    [CrossRef]
  23. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45,1231-1237 (1998).
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    [CrossRef]
  26. L.V. Keldysh, "Ionization in the field of a strong electromagnetic wave," Sov. Phys. JETP 20, 1307-1314 (1965).
  27. A.M. Perelemov, V. S. Popov, and M. V. Terent’ev, "Ionization of atoms in an alternating electric field," Sov. Phys. JETP 23, 924-933 (1966).
  28. 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).
  29. A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441,47 - 189 (2007)
    [CrossRef]
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    [CrossRef] [PubMed]
  31. J. Kasparian, R. Sauerbrey, and S. L. Chin, "The critical laser intensity of self-guided light filaments in air," Appl. Phys. B 71, 877-879 (2000).
  32. A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, "Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas," Appl. Phys. B 73, 287-290 (2001).
  33. 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]
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    [CrossRef] [PubMed]
  37. F. Vidal and T.W. Johnston, "Electromagnetic beam breakup: multiple filaments, single beam equilibria, and radiation," Phys. Rev. Lett. 77, 1282-1285 (1996).
    [CrossRef] [PubMed]
  38. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, "Self-channeling of high-peak-power femtosecond laser pulses in air," Opt. Lett. 20, 73-75 (1995).
    [CrossRef] [PubMed]

2009

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, "Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon," Opt. Commun. 282, 129-134 (2009).

2008

2007

2006

E. Gaižauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, "Discrete damage traces from filamentation of Gauss-Bessel pulses," Opt. Lett. 31, 80-82 (2006).
[CrossRef] [PubMed]

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Self-compression of ultrashort laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

2005

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, "Length of plasma filaments created in air by a multiterawatt femtosecond laser," Opt. Commun. 247, 171-180 (2005).
[CrossRef]

2004

A. Dubietis, E. Gaižauskas, G. Tamošauskas and P. Di. Trapani, "Light filaments without self-channeling," Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef] [PubMed]

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

2002

2001

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, "Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas," Appl. Phys. B 73, 287-290 (2001).

2000

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

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
[CrossRef]

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. -P. Wolf, Y. -B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, "Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-1399 (2000).
[CrossRef]

S. Chávez-Cerda and G. H. C. New, "Evolution of focused Hankel waves and Bessel beams," Opt. Commun. 181, 369-377 (2000).
[CrossRef]

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]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45,1231-1237 (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

K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
[CrossRef]

1996

F. Vidal and T.W. Johnston, "Electromagnetic beam breakup: multiple filaments, single beam equilibria, and radiation," Phys. Rev. Lett. 77, 1282-1285 (1996).
[CrossRef] [PubMed]

B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, "Focusing properties of Bessel beams," Opt. Commun. 131, 223-228 (1996).
[CrossRef]

G.A. Turnbull, D.A. Robertson, G.M. Smith, L. Allen, and M.J. Padgett, "The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate," Opt. Commun. 127,183-188 (1996).
[CrossRef]

1995

1994

M. W. Beijersbergen, R. P.C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112,321-327 (1994).
[CrossRef]

1992

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, "Laser beams with phase singularities," Opt. Quantum Electron. 24,S951-S962 (1992).
[CrossRef]

1991

1988

1987

J. Durnin, J. J. MiceliJr, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

J. Durnin, "Exact solutions for nondiffracting beams. I. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1987).
[CrossRef]

1986

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).

1966

A.M. Perelemov, V. S. Popov, and M. V. Terent’ev, "Ionization of atoms in an alternating electric field," Sov. Phys. JETP 23, 924-933 (1966).

1965

L.V. Keldysh, "Ionization in the field of a strong electromagnetic wave," Sov. Phys. JETP 20, 1307-1314 (1965).

Aközbek, N.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, "Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas," Appl. Phys. B 73, 287-290 (2001).

Akturk, S.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, "Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon," Opt. Commun. 282, 129-134 (2009).

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45,1231-1237 (1998).
[CrossRef]

G.A. Turnbull, D.A. Robertson, G.M. Smith, L. Allen, and M.J. Padgett, "The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate," Opt. Commun. 127,183-188 (1996).
[CrossRef]

Ammosov, M. V.

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).

André, Y. -B.

André, Y.-B.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, "Length of plasma filaments created in air by a multiterawatt femtosecond laser," Opt. Commun. 247, 171-180 (2005).
[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, 1944-1946 (2002).
[CrossRef]

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45,1231-1237 (1998).
[CrossRef]

Beaudin, G.

Becker, A.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, "Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas," Appl. Phys. B 73, 287-290 (2001).

Beijersbergen, M. W.

M. W. Beijersbergen, R. P.C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112,321-327 (1994).
[CrossRef]

Bergé, L.

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

Biegert, J.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Self-compression of ultrashort laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

Bourayou, R.

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

Bowden, C. M.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, "Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas," Appl. Phys. B 73, 287-290 (2001).

Braun, A.

Chávez-Cerda, S.

S. Chávez-Cerda and G. H. C. New, "Evolution of focused Hankel waves and Bessel beams," Opt. Commun. 181, 369-377 (2000).
[CrossRef]

Chin, S. L.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, "Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas," Appl. Phys. B 73, 287-290 (2001).

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

Coerwinkel, R. P.C.

M. W. Beijersbergen, R. P.C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112,321-327 (1994).
[CrossRef]

Couairon, A.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, "Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon," Opt. Commun. 282, 129-134 (2009).

P. Polesana, M. Franco, A. Couairon, D. Faccio and P. Di Trapani, "Filamentation in Kerr media from pulsed Bessel beams," Phys. Rev. A 77, 043814 (2008).
[CrossRef]

A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441,47 - 189 (2007)
[CrossRef]

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Self-compression of ultrashort laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, "Length of plasma filaments created in air by a multiterawatt femtosecond laser," Opt. Commun. 247, 171-180 (2005).
[CrossRef]

D’Amico, C.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, "Length of plasma filaments created in air by a multiterawatt femtosecond laser," Opt. Commun. 247, 171-180 (2005).
[CrossRef]

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).

Dholakia, K.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45,1231-1237 (1998).
[CrossRef]

Di Trapani, P.

Du, D.

Dubietis, A.

Durnin, J.

Eberly, J. H.

J. Durnin, J. J. Miceli, Jr, and J. H. Eberly, "Comparison of Bessel and Gaussian beams," Opt. Lett. 13, 79-80 (1988).
[CrossRef] [PubMed]

J. Durnin, J. J. MiceliJr, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Encrenaz, P.

Faccio, D.

P. Polesana, M. Franco, A. Couairon, D. Faccio and P. Di Trapani, "Filamentation in Kerr media from pulsed Bessel beams," Phys. Rev. A 77, 043814 (2008).
[CrossRef]

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. D. Trapani, and J. Moloney, "Generation of extended plasma channels in air using femtosecond Bessel beams," Opt. Express 16, 15733-15740 (2008).
[CrossRef] [PubMed]

Franco, M.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, "Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon," Opt. Commun. 282, 129-134 (2009).

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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, 1944-1946 (2002).
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J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. -P. Wolf, Y. -B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, "Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-1399 (2000).
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Gaižauskas, E.

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Hauri, C. P.

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N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, "Laser beams with phase singularities," Opt. Quantum Electron. 24,S951-S962 (1992).
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A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Self-compression of ultrashort laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
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B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, "Focusing properties of Bessel beams," Opt. Commun. 131, 223-228 (1996).
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Johnston, T.W.

F. Vidal and T.W. Johnston, "Electromagnetic beam breakup: multiple filaments, single beam equilibria, and radiation," Phys. Rev. Lett. 77, 1282-1285 (1996).
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K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
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L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, "Multiple filamentation of terawatt laser pulses in air," Phys. Rev. Lett. 92, 225002 (2004).
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A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Self-compression of ultrashort laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
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Kolesik, M.

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B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, "Focusing properties of Bessel beams," Opt. Commun. 131, 223-228 (1996).
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Kornelis, W.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Self-compression of ultrashort laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
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M. W. Beijersbergen, R. P.C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112,321-327 (1994).
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L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, "Multiple filamentation of terawatt laser pulses in air," Phys. Rev. Lett. 92, 225002 (2004).
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Lopez-Martens, R.B.

Lü, B.

B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, "Focusing properties of Bessel beams," Opt. Commun. 131, 223-228 (1996).
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McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, "Laser beams with phase singularities," Opt. Quantum Electron. 24,S951-S962 (1992).
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Méchain, G.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, "Length of plasma filaments created in air by a multiterawatt femtosecond laser," Opt. Commun. 247, 171-180 (2005).
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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, 1944-1946 (2002).
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Méjean, G.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, "Multiple filamentation of terawatt laser pulses in air," Phys. Rev. Lett. 92, 225002 (2004).
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M. Mlejnek, E. M. Wright, and J. V. Moloney, "Dynamic spatial replenishment of femtosecond pulses propagating in air," Opt. Lett. 23, 382-384 (1998).
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Moloney, J. V.

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)
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M. Mlejnek, E. M. Wright, and J. V. Moloney, "Dynamic spatial replenishment of femtosecond pulses propagating in air," Opt. Lett. 23, 382-384 (1998).
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Mondelain, D.

Mourou, G.

Munier, J.-M.

Mysyrowicz, A.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, "Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon," Opt. Commun. 282, 129-134 (2009).

A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441,47 - 189 (2007)
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A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Self-compression of ultrashort laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
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G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, "Length of plasma filaments created in air by a multiterawatt femtosecond laser," Opt. Commun. 247, 171-180 (2005).
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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, 1944-1946 (2002).
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J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. -P. Wolf, Y. -B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, "Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-1399 (2000).
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Neirdeimer, S.

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
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Oral, E.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, "Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas," Appl. Phys. B 73, 287-290 (2001).

Overfelt, P. L.

Padgett, M. J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "The production of multiringed Laguerre-Gaussian modes by computer-generated holograms," J. Mod. Opt. 45,1231-1237 (1998).
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Padgett, M.J.

G.A. Turnbull, D.A. Robertson, G.M. Smith, L. Allen, and M.J. Padgett, "The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate," Opt. Commun. 127,183-188 (1996).
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Patalano, G.

Perelemov, A.M.

A.M. Perelemov, V. S. Popov, and M. V. Terent’ev, "Ionization of atoms in an alternating electric field," Sov. Phys. JETP 23, 924-933 (1966).

Piskarskas, A.

Polesana, P.

Polynkin, P.

Popov, V. S.

A.M. Perelemov, V. S. Popov, and M. V. Terent’ev, "Ionization of atoms in an alternating electric field," Sov. Phys. JETP 23, 924-933 (1966).

Prade, B.

Rairoux, P.

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
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Roberts, A.

Robertson, D.A.

G.A. Turnbull, D.A. Robertson, G.M. Smith, L. Allen, and M.J. Padgett, "The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate," Opt. Commun. 127,183-188 (1996).
[CrossRef]

Rodriguez, M.

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

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. -P. Wolf, Y. -B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, "Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-1399 (2000).
[CrossRef]

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
[CrossRef]

Ronneberger, F.

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
[CrossRef]

Rubinsztein-Dunlop, H.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, "Laser beams with phase singularities," Opt. Quantum Electron. 24,S951-S962 (1992).
[CrossRef]

Salmon, E.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, "Length of plasma filaments created in air by a multiterawatt femtosecond laser," Opt. Commun. 247, 171-180 (2005).
[CrossRef]

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

Sasaki, H.

K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
[CrossRef]

Sauerbrey, R.

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, "Length of plasma filaments created in air by a multiterawatt femtosecond laser," Opt. Commun. 247, 171-180 (2005).
[CrossRef]

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

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

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
[CrossRef]

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. -P. Wolf, Y. -B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, "Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-1399 (2000).
[CrossRef]

Schillinger, H.

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
[CrossRef]

Shinozaki, K.

K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
[CrossRef]

Skupin, S.

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

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, "Laser beams with phase singularities," Opt. Quantum Electron. 24,S951-S962 (1992).
[CrossRef]

Smith, G.M.

G.A. Turnbull, D.A. Robertson, G.M. Smith, L. Allen, and M.J. Padgett, "The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate," Opt. Commun. 127,183-188 (1996).
[CrossRef]

Squier, J.

Stabinis, A.

Stein, B.

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
[CrossRef]

Tamošauskas, G.

A. Dubietis, E. Gaižauskas, G. Tamošauskas and P. Di. Trapani, "Light filaments without self-channeling," Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef] [PubMed]

Terent’ev, M. V.

A.M. Perelemov, V. S. Popov, and M. V. Terent’ev, "Ionization of atoms in an alternating electric field," Sov. Phys. JETP 23, 924-933 (1966).

Trapani, P. D.

Trapani, P. Di.

A. Dubietis, E. Gaižauskas, G. Tamošauskas and P. Di. Trapani, "Light filaments without self-channeling," Phys. Rev. Lett. 92, 253903 (2004).
[CrossRef] [PubMed]

Turnbull, G.A.

G.A. Turnbull, D.A. Robertson, G.M. Smith, L. Allen, and M.J. Padgett, "The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate," Opt. Commun. 127,183-188 (1996).
[CrossRef]

Tzortzakis, S.

Valiulis, G.

Vanagas, E.

Vidal, F.

F. Vidal and T.W. Johnston, "Electromagnetic beam breakup: multiple filaments, single beam equilibria, and radiation," Phys. Rev. Lett. 77, 1282-1285 (1996).
[CrossRef] [PubMed]

Vijayalakshmi, K.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, "Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas," Appl. Phys. B 73, 287-290 (2001).

Vuong, L. T.

Waite, D.

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
[CrossRef]

Wedekind, C.

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
[CrossRef]

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, "Laser beams with phase singularities," Opt. Quantum Electron. 24,S951-S962 (1992).
[CrossRef]

Wille, H.

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
[CrossRef]

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. -P. Wolf, Y. -B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, "Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-1399 (2000).
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Woerdman, J. P.

M. W. Beijersbergen, R. P.C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112,321-327 (1994).
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Wolf, J. P.

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

Wolf, J. -P.

Wöste, L.

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

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. -P. Wolf, Y. -B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, "Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-1399 (2000).
[CrossRef]

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
[CrossRef]

Wright, E. M.

Wright, E.M.

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J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J. -P. Wolf, Y. -B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, "Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-1399 (2000).
[CrossRef]

Zhai, Q.

B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, "Focusing properties of Bessel beams," Opt. Commun. 131, 223-228 (1996).
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Zhang, B.

B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, "Focusing properties of Bessel beams," Opt. Commun. 131, 223-228 (1996).
[CrossRef]

Zhou, B.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, "Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon," Opt. Commun. 282, 129-134 (2009).

Ziener, C.

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
[CrossRef]

Appl. Phys. B

P. Rairoux, H. Schillinger, S. Neirdeimer, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, "Remote sensing of the atmosphere using ultrashort laser pulses," Appl. Phys. B 71, 573-580 (2000).
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A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, "Self-compression of ultrashort laser pulses down to one optical cycle by filamentation," J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

J. Opt. Soc. Am. A

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B. Lü, W. Huang, B. Zhang, F. Kong, and Q. Zhai, "Focusing properties of Bessel beams," Opt. Commun. 131, 223-228 (1996).
[CrossRef]

S. Chávez-Cerda and G. H. C. New, "Evolution of focused Hankel waves and Bessel beams," Opt. Commun. 181, 369-377 (2000).
[CrossRef]

G. Méchain, C. D’Amico, Y.-B. André, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, "Length of plasma filaments created in air by a multiterawatt femtosecond laser," Opt. Commun. 247, 171-180 (2005).
[CrossRef]

K. Shinozaki, C. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
[CrossRef]

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, "Generation of long plasma channels in air by focusing ultrashort laser pulses with an axicon," Opt. Commun. 282, 129-134 (2009).

G.A. Turnbull, D.A. Robertson, G.M. Smith, L. Allen, and M.J. Padgett, "The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate," Opt. Commun. 127,183-188 (1996).
[CrossRef]

M. W. Beijersbergen, R. P.C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112,321-327 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

E. Gaižauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, "Discrete damage traces from filamentation of Gauss-Bessel pulses," Opt. Lett. 31, 80-82 (2006).
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[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, 1944-1946 (2002).
[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).
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A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, "Self-channeling of high-peak-power femtosecond laser pulses in air," Opt. Lett. 20, 73-75 (1995).
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A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, "Self-channeling of high-peak-power femtosecond laser pulses in air," Opt. Lett. 20, 73-75 (1995).
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Figures (12)

Fig. 1.
Fig. 1.

Spatial intensity distribution of the (a) Bessel, (b) Gaussian, and (c) Laguerre beams for the same beam diameter defined by the full width at the half maximum as shown by red arrows on the right panels.

Fig. 2.
Fig. 2.

Ionization probabilities of Ar calculated by the three different formulas, PPT model (solid), multiphoton ionization model (dashed), and ADK model (dotted), as a function of laser intensity. The duration and the central wavelength of the pulse are assumed to be 30 fs (FWHM) with a Gaussian temporal profile and 800 nm, respectively.

Fig. 3.
Fig. 3.

Variation of the beam diameters in vacuum for the Bessel (solid), Gaussian (dashed), and Laguerre (dotted) incident beams for the pulse with a 30 fs duration, which is nothing but the diffraction.

Fig. 4.
Fig. 4.

Variation of the beam diameter as a function of propagation distance in the Ar gas for the (a) Bessel, (b) Gaussian, and (c) Laguerre incident beams.

Fig. 5.
Fig. 5.

Color-coded plot of the time-integrated propagating pulse as a function of propagation distance and beam radius for the (a) Bessel, (b) Gaussian, and (c) Laguerre incident beams.

Fig. 6.
Fig. 6.

Maximum intensity of the pulse as a function of propagation distance for the Bessel (solid), Gaussian (dashed), and Laguerre (dotted) incident beams.

Fig. 7.
Fig. 7.

Temporal profile of the pulse integrated over the beam radius (a) at z=0 (note that this is exactly the same for the Bessel, Gaussian, and Laguerre incident beams), (b) at z=25 cm for the Bessel, (c) at z=25 cm for the Gaussian, (d) at z=25 cm for the Laguerre, and (e) at z=50 cm for the Bessel incident beams.

Fig. 8.
Fig. 8.

Color-coded plot of the temporal profiles integrated over the beam radius as a function of propagation distance, for the (a) Bessel, (b) Gaussian, and (c) Laguerre incident beams.

Fig. 9.
Fig. 9.

Temporal profiles of the pulse on axis (r=0) for the Bessel incident beam at different distances, (a) z=25 and (b) z=50 cm.

Fig. 10.
Fig. 10.

Ionization probability at r=0 as a function of propagation distance for the (a) Bessel, (b) Gaussian, and (c) Laguerre incident beams.

Fig. 11.
Fig. 11.

Color-coded plot of the ionization probability as a function of propagation distance and beam radius for the (a) Bessel, (b) Gaussian, and (c) Laguerre incident beams.

Fig. 12.
Fig. 12.

Variation of the beam diameter as a function of propagation distance in the Ar gas for the incident beams with (a) 150 µm, 3.2×1013 W/cm2, (b) 200 µm, 3.2×1013 W/cm2, (e) 100 µm, 2.0×1013 W/cm2, and (f) 100 µm, 4.0×1013 W/cm2. Ionization probability at r=0 corresponding to (a), (b), (e), and (f) are shown in (c), (d), (g), and (h), respectively.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

εb rt0 =ε0J0(αr)exp(t2t02)
εb rt0 =ε0exp(r2w02t2t02)
εl rt0 =ε0(12(βr)2)exp((βr)2t2/t02)
ε z =i (2εr2+εrr) 2 k0 n0 i k" (2εt2)2
+i k0 n2 ε2 εi k0 ρ ε 2 n0 ρc σ ρ ε 2 Ui W (I) (ρnt)ε2I
ρ t =W (I) (ρntρ)+σ ρ ε2 Ui
γ = ω0 2mUi e E
W ω0E =ωa.u. 6π Cn*,l* 2 f ( l , m ) (Ui2UH)
×Amω0γ (2E0E1+γ2)2n*m32 exp (2E0g(γ)3E)
W (E)=ωa.u. 6π Cn*,l* 2 (Ui2UH) (2E0E)2n*32 exp (2E03E)
W ω0I =σK IK

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