Numerical simulation of the diffraction problem on a Kerr-type nonlinear layer

The diffraction of a plane wave of small intensity by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The diffraction problem is reduced to a boundary value problem for a semi linear second-order ordinary differential equation with a cubic nonlinearity on the excitation frequency of the nonlinear structure. Within the framework of weak solutions, existence and uniqueness are proved. A numerical solution technique by the finite element method is proposed and investigated.