Numerical simulations and analysis of the diffraction problem on the nonlinear dielectric layer

On an example of the open nonlinear electrodynamic system-transverse nonhomogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on the nonlinear object and the results of the numerical analysis of the nonlinear problem are shown. The nonlinear diffraction problem reduced the solutions of the system of the nonhomogeneous nonlinear equations of the second kind. The first of algorithm based on the iterative scheme on the basis of Simpson´s quadrature is applicable to the solution of the nonlinear equations system. The following algorithms are based on the Newtonian method for the Simpson´s quadrature and the Newtonian algorithm for the Teilor-series of the diffraction field.