Electromagnetic Symmetric Hybrid Wave Propagation Problem in a Medium with Arbitrary Nonlinear Saturation

The paper treats a problem of propagation of electromagnetic symmetric hybrid wave in a plane non-homogeneous nonlinear dielectric waveguide. The physical problem is reduced to a nonlinear transmission eigenvalue problem for Maxwell's equations with appropriate boundary and transmission conditions. The eigenvalue problem is, in fact, a two-parameter problem, where the spectral parameter depends on another parameter, which is chosen in accordance with special conditions. Uniqueness of solution to the two-parameter eigenvalue problem is proved, numerical method is proposed and numerical results are presented.