Numerical method for solving a nonlinear boundary value eigenvalue problem for electromagnetic TE waves propagating in a layer with arbitrary nonlinearity

The article considers a problem of electromagnetic TE-waves propagation in a layer with arbitrary nonlinearity. The physical problem is reduced to the nonlinear boundary eigenvalue problem for nonlinear ordinary differential equations. The author suggests a numerical method to find propagation constants and demonstrates numerical results for Kerr nonlinearity and nonlinearity with saturation.