Propagation of TM wave in a layer with Kerr law nonlinearity

Propagation of TM electromagnetic waves through a nonlinear homogeneous nonmagnetic isotropic dielectric layer is considered. The layer is located between two homogeneous isotropic half-spaces with constant permittivities. The permittivity in the layer obeys the Kerr law. The dispersion equation for the propagation constants of the waves in the layer is presented. Presented results allow to study nonlinear material and nonlinear metamaterial.