Propagation of coupled electromagnetic TE and TM waves in a plane layer with Kerr nonlinearity

The researchers investigate coupled electromagnetic TE and TM wave propagation in a nonlinear plane layer. Nonlinearity inside the layer is described by Kerr law. It is shown that physical problem is reduced to a nonlinear twoparameter eigenvalue problem for a system of (nonlinear) ordinary differential equations. The authors prove the existence of coupled surface TE and TM waves and find the intervals of localization of paired eigenvalues.