Regime of coupled electromagnetic TE-TM wave propagation in a plane layer waveguide with kerr nonlinearity

Coupled electromagnetic TE-TM wave propagation in a nonlinear dielectric layer filled with lossless, nonmagnetic, and isotropic medium is considered. The layer is located between two half-spaces with constant permittivities. The permittivity in the layer is described by Kerr law. The problem is reduced to the nonlinear two-parameter eigenvalue problem. We look for coupled eigenvalues of the problem and reduce the question to the analysis of the corresponding system of two dispersion equations. It is shown that the new waveguide regime for coupled TE and TM wave exists in a layer with Kerr nonlinearity.