The problem of propagation of electromagnetic waves in a layer with arbitrary nonlinearity (II. TM waves)

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