Abstract

We show numerically for continuous-wave beams and experimentally for femtosecond pulses propagating in air, that the collapse distance of intense laser beams in a bulk Kerr medium scales as 1/P1/2 for input powers P that are moderately above the critical power for self focusing, but that at higher powers the collapse distance scales as 1/P.

© 2005 Optical Society of America

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References

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  1. P. L. Kelley, "Self-Focusing of Optical Beams," Phys. Rev. Lett. 15, 1005 (1965).
    [CrossRef]
  2. Y. Shen, "Self-focusing: Experimental," Prog. Quant. Electron. 4, 1 (1975).
    [CrossRef]
  3. A. J. Campillo, S. L. Shapiro, and B. R. Suydam, "Relationship of self-focusing to aptial instability modes" Appl. Phys. Lett. 24, 178 (1974).
    [CrossRef]
  4. B. R. Suydam, "Self-focusing of very powerful laser beams II," IEEE J. Quantum Electron. 10, 837 (1974).
    [CrossRef]
  5. L. Wöste, C. Wedekind, and H. Wille, P. Rairoux, B. Stein, S. Nikolov, Chr. Werner, S. Niedermeier,H. Schillinger, R. Sauerbrey "Femtosecond Atmospheric Lamp," Laser Optoelektron 29, 51 (1997).
  6. S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, A. Mysyrowicz, "Breakup and Fusion of Self-Guided Femtosecond Light Pulses in Air," Phys. Rev. Lett. 86, 5470 (2001).
    [CrossRef] [PubMed]
  7. A. Couairon, "Light bullets from femtosecond filamentation," Eur. Phys. J. D. 27, 159 (2003).
    [CrossRef]
  8. 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, L. Wöste, "White-Light Filaments for Atmospheric Analysis," Science 301, 61 (2004)
    [CrossRef]
  9. V. I. Bespalov and V. I. Talanov, "Filamentary Structure of Light Beams in Nonlinear Media," JETP Lett. 3, 307 (1966).
  10. G. Fibich and B. Ilan, "Vectorial and random effects in self-focusing and in multiple filamentation," Physica D 157, 112 (2001).
    [CrossRef]
  11. K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-Similar Optical Wave Collapse: Observation of the Townes Profile," Phys. Rev. Lett. 90, 203902 (2003).
    [CrossRef] [PubMed]
  12. F. Merle and P. Raphael, "On universality of blow-up profile for L2 critical nonlinear Schrödinger equation," Invent. Math. 156, 565 (2004).
    [CrossRef]
  13. G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, "Control of Multiple Filamentaion in Air," Opt. Lett. 29, 1772 (2004).

Appl. Phys. Lett.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, "Relationship of self-focusing to aptial instability modes" Appl. Phys. Lett. 24, 178 (1974).
[CrossRef]

Eur. Phys. J. D.

A. Couairon, "Light bullets from femtosecond filamentation," Eur. Phys. J. D. 27, 159 (2003).
[CrossRef]

IEEE J. Quantum Electron.

B. R. Suydam, "Self-focusing of very powerful laser beams II," IEEE J. Quantum Electron. 10, 837 (1974).
[CrossRef]

Invent. Math.

F. Merle and P. Raphael, "On universality of blow-up profile for L2 critical nonlinear Schrödinger equation," Invent. Math. 156, 565 (2004).
[CrossRef]

JETP Lett.

V. I. Bespalov and V. I. Talanov, "Filamentary Structure of Light Beams in Nonlinear Media," JETP Lett. 3, 307 (1966).

Laser Optoelektron

L. Wöste, C. Wedekind, and H. Wille, P. Rairoux, B. Stein, S. Nikolov, Chr. Werner, S. Niedermeier,H. Schillinger, R. Sauerbrey "Femtosecond Atmospheric Lamp," Laser Optoelektron 29, 51 (1997).

Opt. Lett.

Phys. Rev. Lett.

K. D. Moll, A. L. Gaeta, and G. Fibich, "Self-Similar Optical Wave Collapse: Observation of the Townes Profile," Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, A. Mysyrowicz, "Breakup and Fusion of Self-Guided Femtosecond Light Pulses in Air," Phys. Rev. Lett. 86, 5470 (2001).
[CrossRef] [PubMed]

P. L. Kelley, "Self-Focusing of Optical Beams," Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Physica D

G. Fibich and B. Ilan, "Vectorial and random effects in self-focusing and in multiple filamentation," Physica D 157, 112 (2001).
[CrossRef]

Prog. Quant. Electron.

Y. Shen, "Self-focusing: Experimental," Prog. Quant. Electron. 4, 1 (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, L. Wöste, "White-Light Filaments for Atmospheric Analysis," Science 301, 61 (2004)
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

On-axis phase S(z) (dashes) and focusing level maxx,y|A(z,x,y)|/|A0(0,0)| (solid) of the solution of the NLS (1) with noiseless Gaussian input beam. Dotted line is z|A0(0,0)|2. (a) P = 10Pcr (b) P = 300Pcr

Fig. 2.
Fig. 2.

Same as Fig. 1 with 10% random noise.

Fig. 3.
Fig. 3.

On-axis phase at the onset on collapse, as a function of P/Pcr, for clean beams (dashed line) and for beams with 10% noise (sold line).

Fig. 4.
Fig. 4.

Collapse distance Lcol as a function of input beam power (simulations). (o) - no noise, (*) - 10% random noise. Solid lines are the best fitting power laws.

Fig. 5.
Fig. 5.

Spatial profile Gaussian beams with 10% random noise at various input powers as they begin to collapse (simulations).

Fig. 6.
Fig. 6.

The collapse distance Lcol as a function of input power P (experimental). Circles and stars represent data where a single amplifier and two amplifiers were used, respectively. Solid lines are the best-fitting power laws. Note the similarity to Fig. 4.

Fig. 7.
Fig. 7.

Spatial beam profile as it begins to collapse (experimental). Note the similarity to Fig. 5.

Equations (1)

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iA z x y z + Δ A + A 2 A = 0 , A 0 x y = A 0 x y

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