A two-Gaussian model for stabilized filament formation in nonlinear media

Abstract

We describe the effects of energy conservation on the growth of a Gaussian perturbation superimposed on a Gaussian profile laser beam. Using a simple two-step energy conservation criterion, we obtain a relationship between the self-focal distance zff for the smooth Gaussian profile laser beam and the distance Dt at which the growth in the Gaussian spike terminates. For a very intense laser beam, with appreciable amplitude of the perturbation, the growth of the perturbation is studied using a continuous energy-conservation criterion. The results explain the stabilization of intensity in the perturbation at a certain distance inside the medium. Our model explains formation of bright stabilized filaments and gives reasonable estimates for the distance of the first appearance of filaments.