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

The article considers a problem of electromagnetic TM wave propagation in a layer with arbitrary nonlinearity. The physical problem is reduced to the nonlinear boundary eigenvalue problem for nonlinear ordinary differential equations. The numerical method to find propagation constants is suggested and numerical results for Kerr nonlinearity and nonlinearity with saturation are shown.