Solution of the nonlinear eigenvalue boundary-value problem for tm electromagnetic waves propagating in a Kerr-nonlinear layer by means of the cauchy problem method

The problem of propagation of TM electromagnetic waves in Kerr-nonlinear layer is considered. The problem is reduced to the solution of a nonlinear eigenvalue boundary-value problem for a system of two ordinary differential equations. A numerical method is proposed for solving the considered eigenvalue boundary-value problem. It is shown that the proposed method makes it possible to investigate more complicated types of nonlinearity. Numerical results are reported. The method is compared to another known technique and to the linear case.