Variational approach to nonlinear self-focusing of Gaussian laser beams

Abstract

The problem of nonlinear self-focusing of Gaussian laser beams is reformulated in terms of a variational principle. By means of approximating Gaussian functions, expressions are obtained for the equilibrium radii and nonlinear frequency shifts of stationary self-trapped laser beams. The nonsteady propagation is given an illuminating form in terms of a potential function description. The analysis confirms the recent results obtained by moment theory as opposed to those based on paraxial ray approximations.