Variational approach to nonparaxial self-focusing of high power laser beams in nonlinear media

摘要

We apply the variational approach to solve the nonparaxial nonlinear Schrodinger equation to disclose the nonparaxial propagation properties of a Gaussian beam. A system of differential equations for the evolution of the parameters of Gaussian beam is obtained. The obtained analytical results clearly show the nonparaxial propagation process of periodic focusing-defocusing. This process is significantly influenced by the initial power and chirp of the beam. A positive chirp retards the first self-focus, while a negative chirp brings forward the first self-focus. Both positive and negative chirps increase the subsequent focusing-defocusing cycles