Renormalization-group approach to the problem of light-beam self-focusing - art. no. 033809

A method of renormalization-group symmetries is applied fur analytical solu tion to the nonlinear Schrodinger equation which describes the electromagne tic beam self-focusing in a medium with a cubic nonlinearity. The boundary- value problem for the incident Gaussian light beam has been solved analytic ally in a cylindrical geometry although the method could be applied to othe r boundary conditions too. The solution describes a detailed structure of w ave self-focusing and its global characteristics such as the light power tr apped in the singularity, laser beam radius, and self-focusing length. A co mparison with the results of previous studies demonstrates advantages of th e renormalization-group symmetry method as a tool fur the nonlinear electro dynamics theory.