The problem of propagation of electromagnetic waves in a layer with arbitrary nonlinearity (I. TE are the waves)

Electromagnetic propagation problem of TE-waves in a layer with arbitrary nonlinearity is considered. It was shown that the boundary value problem for Maxwell equations is reduced to a nonlinear boundary eigenvalue problem for an ordinary nonlinear differential equation of the 2${}$ order. Dispersion equation for the eigenvalues of the problem (propagation's constants) is obtained.