Coupled electromagnetic TE-TE waves propagation. Numerical approach to determine coupled propagation constants

In this paper the problem of electromagnetic TE and TE wave propagation is considered. The waves propagate along the surface of a plane dielectric layer. The permittivity in the layer is described by the Kerr law with an additional inhomogeneous term. These two TE waves form a new polarization - coupled TE-TE wave - that exists only in nonlinear media. The TE waves we call pseudopolarizations (pseudo-TE polarization). Each pseudopolarization propagates at its own frequency ω₁ and ω₂, respectively, and has its own propagation constant (PC) γ₁ and γ₂, respectively. Rigorous statement of the problem and numerical results are given.