Renormalization-group approach to the problem of light-beam self-focusing

A method of renormalization-group symmetries is applied for analytical solution to the nonlinear Schrödinger equation which describes the electromagnetic beam self-focusing in a medium with a cubic nonlinearity. The boundary-value problem for the incident Gaussian light beam has been solved analytically in a cylindrical geometry although the method could be applied to other boundary conditions too. The solution describes a detailed structure of wave self-focusing and its global characteristics such as the light power trapped in the singularity, laser beam radius, and self-focusing length. A comparison with the results of previous studies demonstrates advantages of the renormalization-group symmetry method as a tool for the nonlinear electrodynamics theory.