Beyond leading order logarithmic scaling in the catastrophic self-focusing (collapse) of a laser beam in Kerr media

Abstract

We study the catastrophic stationary self-focusing (collapse) of laser beam in nonlinear Kerr media. The width of a self-similar solutions near collapse distance $z=z_c$ obeys $(z_c-z{)}^{1/2}$ scaling law with the well-known leading order modification of loglog type $\propto (\ln |\ln (z_c-z)|{)}^{-1/2}$. We show that the validity of the loglog modification requires double-exponentially large amplitudes of the solution $\sim {10^{10}}^{100}$, which is unrealistic to achieve in either physical experiments or numerical simulations. We derive a new equation for the adiabatically slow parameter which determines the system self-focusing across a large range of solution amplitudes. Based on this equation we develop a perturbation theory for scaling modifications beyond the leading loglog. We show that for the initial pulse with the optical power moderately above ($\lesssim 1.2$) the critical power of self-focusing, the new scaling agrees with numerical simulations beginning with amplitudes around only three times above of the initial pulse.

9 pages, 5 figures; extended text compare with previous version

References in corpus (3)

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• Non-Gaussian Statistics of Multiple Filamentation
• On Spectra of Linearized Operators for Keller-Segel Models of Chemotaxis

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