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Self-focusing distance of very high power laser pulses

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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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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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