Self-focusing Distance of Very High Power Laser Pulses

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/P;1/2 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.

Atmospheric propagation of gradient-shaped and spinning femtosecond light pulses

“…The dependence z fil ∼ P cr /P in was recently confirmed in Ref. [45] for perturbed Gaussian beams conveying enough power (>100P cr ). The procedure followed so far enables us to generalize this property to arbitrary optical shapes, since all information drawn about modulational instability primarily depends on the level of the initial intensity.…”

“…These theoretical arguments give us an estimation of the number of filaments N = P in /P fil pα/2.65 for an input beam with power ratio p ≡ P in /P cr . The maximal growth rate Im(µ) max defines the longitudinal distance of filamentation, z fil ∼ Im(µ) −1 max scaling as ∼ 1/ p [44,45], along which smallscale filaments grow exponentially.…”

32 TW atmospheric white-light laser

“…For the ultrahigh powers ͑P ӷ 100P cr ͒, as is the case in our experiment, multifilamentation occurs through modulational instability that breaks up the beam into periodic cells over very short propagation distances z fil Ϸ 2P cr / ͑ 0 I 0 ͒Ϸ1 -3 m for an incident intensity I 0 ϳ 4- comb beam structure, the cells of light being separated by "bridges." [13][14][15] These structures appear as dark straight lines on the beam profile recorded on a photosensitive paper after only 11 m propagation ͑Fig. 1͒.…”

Light propagation in media with a highly nonlinear response: An analytical study

“…In Ref. [22] this effect was studied numerically and experimentally and assumed to be one of the possible mechanisms for multiply filamentation. From our analytical solutions we see, that for the Kerr nonlinearity, considered in this section, dependence of the self-focusing position on the initial beam intensity scales as z sf ∼ 1/ √ I 0 for each peaks.…”