On the problem of nonlinear coupled electromagnetic transverse-electric–transverse magnetic wave propagation

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Coupled electromagnetic TE and TM wave propagation in a nonlinear plane layer is considered. Nonlinearity inside the layer is described by Kerr law. Physical problem is reduced to a nonlinear two-parameter eigenvalue problem for a system of (nonlinear) ordinary differential equations. It is proved that TE and TM waves that form (nonlinear) coupled TE-TM wave can propagate at different frequencies ωE and ωM, respectively. These frequencies can be chosen independently. Existence of coupled surface TE and TM waves is proved. Intervals of localization of coupled eigenvalues are found.