Evolutionary approach for the problem of electromagnetic field propagation through nonlinear medium

Abstract

The problem of transient electromagnetic wave propagation in unbounded nonlinear medium is solved by means of Evolutionary Approach. It consists in the conversion of the initial three-dimensional nonstationary problem to one- dimensional one for the set of evolutionary equations with initial and boundary conditions by the modal expansion of the initial problem. The construction of the analytical solution of a nonlinear problem in time domain is proposed by the step-by-step method in approximation of weak nonlinearity and losses taking into account new sources of current inside the medium