Abstract

We report a simple experiment to directly determine the critical power for self-focusing in air by measuring the focal shift of the focused femtosecond Ti:sapphire laser pulses. The measured critical power is 10 GW for the 42 fs laser pulse; it gradually decreases to 5 GW for (chirped) pulse duration longer than 200 fs.

© 2005 Optical Society of America

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  1. P. Rairoux, H. Schillinger, S. Niedermeier, 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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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  36. A. Talebpour, M. Abdel-Fattah, and S. L. Chin, "Focusing limits of intense ultrafast laser pulses in a high pressure gas: road to new spectroscopic source," Opt. Commun. 183, 479-484 (2000).
    [CrossRef]
  37. A. Talebpour, M. Abdel-Fattah, A. D. Bandrauk, and S. L. Chin, "Spectroscopy of the gases interacting with intense femtosecond laser pulses," Laser Physics 11, 68-76 (2001).
  38. W. Liu, S. L. Chin, O. G. Kosareva, I. S. Golubtsov, and V. P. Kandidov, "Multiple refocusing of a femtosecond laser pulse in a dispersive liquid (methanol)," Opt. Commun. 225, 193-209 (2003).
    [CrossRef]
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  40. V. I. Talanov, "Focusing of light in cubic media," JETP Lett. 11, 199 (1970).
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    [CrossRef]
  42. F. Théberge, N. Aközbek, W. Liu, J.-F. Gravel, and S. L. Chin, "Third harmonic beam profile generated in atmospheric air using femtosecond laser pulses," Opt. Commun. 245, 399-405 (2005).
    [CrossRef]
  43. J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, "Determination of the time dependence of n2 in air," Opt. Commun. 135, 310-314 (1997).
    [CrossRef]
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Advances in Multiphoton Proc. and Spectr

S. L. Chin, "From Multiphoton to Tunnel Ionization," in Advances in Multiphoton Processes and Spectroscopy, S. H. Lin, A. A. Villaeys and Y. Fujimura, eds. (World Scientific, Singapore, 2004).

Anal. Chem.

J.-F. Gravel, Q. Luo, D. Boudreau, X. P. Tang, and S. L. Chin, "Sensing of Halocarbons Using Femtosecond Laser-Induced Fluorescence," Anal. Chem. 76, 4799 4805 (2004).
[CrossRef] [PubMed]

Appl. Phys. B

H. Schillinger and R. Sauerbrey, "Electrical conductivity of long plasma channels in air generated by self-guided femtosecond laser pulses," Appl. Phys. B 68, 753-756 (1999).
[CrossRef]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Aközbek, G. Roy, and S. L. Chin, "Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules," Appl. Phys. B 77, 697-702 (2003).
[CrossRef]

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

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).
[CrossRef]

P. Rairoux, H. Schillinger, S. Niedermeier, 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]

F. Théberge, W. Liu, Q. Luo, and S. L. Chin, "Extension of ultrabroadband continuum generated in air up to 230 nm using ultrashort and intense laser pulse," Appl. Phys. B 80, 221-225 (2005).
[CrossRef]

N. Aközbek, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, "Continuum generation of the third-harmonic pulse generated by an intense femtosecond IR laser pulse in air," Appl. Phys. B 77, 177-183 (2003).
[CrossRef]

W. Liu, J.-F. Gravel, F. Théberge, A. Becker, and S. L. Chin, "Background reservoir: its crucial role for long distance propagation of femtosecond laser pulses in air," Appl. Phys. B 80, 857-860 (2005).
[CrossRef]

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, "Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media (or supercontinuum generation)," Appl. Phys. B 77, 149-165 (2003).
[CrossRef]

IEEE J. of Quant. Electron.

M. Mlejnek, E. M. Wright, and J. V. Moloney, "Moving-focus versus self waveguiding model for long-distance propagation of femtosecond pulses in air," IEEE J. of Quant. Electron. 35, 1771-1776 (1999).
[CrossRef]

X. M. Zhao, J.-C. Diels, C. Y. Wang, and J. M. Elizondo, "Femtosecond ultraviolet laser pulse induced lightning discharges in gases," IEEE J. of Quant. Electron. 31, 599 612 (1995).
[CrossRef]

J. Exp. Theor. Phys.

D. V. Vlasov, R. A. Garaev, V. V. Korobkin, and R. V. Serov, "Measurement of nonlinear polarizability in air," J. Exp. Theor. Phys., 49, 1033-1036 (1979).

J. Nonlinear Opt. Phys. Mater.

S. L. Chin, A. Brodeur, S. Petit, O. G. Kosareva, and V. P. Kandidov, "Filamentation and supercontinuum generation during the propagation of powerful ultrashort laser pulses in optical media (white light laser)," J. Nonlinear Opt. Phys. Mater., 8, 121-146 (1999).
[CrossRef]

J. Opt. Soc. Am. B

JETP Lett.

V. I. Talanov, "Focusing of light in cubic media," JETP Lett. 11, 199 (1970).

Jpn. J. Appl. Phys.

S. L. Chin, S. Petit, F. Borne, and K. Miyazaki, "The white light supercontinuum is indeed an ultrafast white light laser," Jpn. J. Appl. Phys. 38, L126-L128 (1999).
[CrossRef]

S. L. Chin and K. Miyazaki, "A comment on lightning control using a femtosecond laser," Jpn. J. Appl. Phys. 38, 2011-2012 (1999).
[CrossRef]

Laser Physics

A. Talebpour, M. Abdel-Fattah, A. D. Bandrauk, and S. L. Chin, "Spectroscopy of the gases interacting with intense femtosecond laser pulses," Laser Physics 11, 68-76 (2001).

Opt. Commun.

W. Liu, S. L. Chin, O. G. Kosareva, I. S. Golubtsov, and V. P. Kandidov, "Multiple refocusing of a femtosecond laser pulse in a dispersive liquid (methanol)," Opt. Commun. 225, 193-209 (2003).
[CrossRef]

F. Théberge, N. Aközbek, W. Liu, J.-F. Gravel, and S. L. Chin, "Third harmonic beam profile generated in atmospheric air using femtosecond laser pulses," Opt. Commun. 245, 399-405 (2005).
[CrossRef]

J.-F. Ripoche, G. Grillon, B. Prade, M. Franco, E. Nibbering, R. Lange, and A. Mysyrowicz, "Determination of the time dependence of n2 in air," Opt. Commun. 135, 310-314 (1997).
[CrossRef]

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, "Intensity clamping of a femtosecond laser pulse in condensed matter," Opt. Commun. 202, 189-197 (2002).
[CrossRef]

A. Talebpour, M. Abdel-Fattah, and S. L. Chin, "Focusing limits of intense ultrafast laser pulses in a high pressure gas: road to new spectroscopic source," Opt. Commun. 183, 479-484 (2000).
[CrossRef]

N. Aközbek, 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]

Opt. Express

Opt. Lett.

M. Rodriguez, R. Sauerbrey, H. Wille, L. Wste, T. Fuji, Y.-B. Andr, A. Mysyrowicz, L. Klingbeil, K. Rethmeier, W. Kalkner, J. Kasparian, E. Salmon, J. Yu, and J.-P. Wolf, "Triggering and Guiding High Voltage Discharge by Ohmic Connection through Ionized Filaments Created by Femtosecond Laser Pulses," Opt. Lett. 27, 772-774 (2002).
[CrossRef]

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J.-P. Wolf, Y.-B. Andre, 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]

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. Yu, D. Mondelain, G. Ange, R. Volk, S. Niedermeier, J. P. Wolf, J. Kasparian, and R. Sauerbrey, "Backward supercontinuum emission from a filament generated by ultrashort laser pulses in air," Opt. Lett. 26, 533-535 (2001).
[CrossRef]

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]

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, "Conical emission from self-guided femtosecond pulses in air," Opt. Lett. 21, 62-64 (1996).
[CrossRef] [PubMed]

A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, "Moving focus in the propagation of powerful ultrashort laser pulses in air," Opt. Lett. 22, 304-306 (1997).
[CrossRef] [PubMed]

Phys. Rev. A

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003-3009 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett.

G. L. McAllister, J. H. Marburger, and L. G. DeShazer, Phys. Rev. Lett. 21, 1648 1649 (1968).
[CrossRef]

A. L. Gaeta, "Catastrophic Collapse of Ultrashort Pulses," Phys. Rev. Lett. 84, 3582-3585 (2000).
[CrossRef] [PubMed]

Physics of Plasma

H. Pépin, D. Comtois, F. Vidal, C. Y. Chien, A. Desparois, T. W. Johnston, J. C. Kieffer, B. L. Fontaine, F. Martin, F. A. M. Rizk, C. Potvin, P. Couture, H. P. Mercure, A. Bondiou-Clergerie, P. Lalande, and I. Gallimberti, "Triggering and guiding high voltage large-scale leader discharges with sub-joule ultrashort laser pulses," Physics of Plasma 8, 2532-2539 (2001).
[CrossRef]

Prog. Quantum Electron.

J. H. Marburger, "Self-focusing: theory," Prog. Quantum Electron., 4, 35-110 (1975).
[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. Wöste, "White Light filaments for atmospheric analysis," Science 301, 61-64 (2003).
[CrossRef] [PubMed]

Other

R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992).

Y. R. Shen, The principles of nonlinear optics (Wiley, New York, 1984).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup. The inset is a typical picture recorded by the ICCD.

Fig. 2.
Fig. 2.

On axis nitrogen fluorescence distribution for three different energy levels: (a) 0.29 mJ; (b) 0.71 mJ; (c) 2.22 mJ. The black lines: experimental results; the red lines: Gaussian fitting.

Fig. 3.
Fig. 3.

Fluorescence signal peak position as function of the pulse energy. Solid squares: experimental results; red lines: straight lines used to determine the critical power.

Fig. 4.
Fig. 4.

The critical power changes in terms of the pulse duration. Black solid squares: positively chirped pulse; red solid circle: negatively chirped pulse.

Equations (4)

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

P cr = 3.77 λ 2 8 π n 2 n 0
f = f z sf f + z sf .
z sf = 0.367 ka 2 { [ ( P P cr ) 1 2 0.852 ] 2 0.0219 } 1 2
P cr = 0.42 mJ 42 fs = 10 GW .

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