TM-waves guided by a nonlinear film with complex permittivity

The propagation of TM-waves in a planar waveguide with a nonlinear film surrounded by semi-infinite linear media is studied. The film is assumed to be nonmagnetic, anisotropic and it is defined by complex permittivity with a Lipschitz continuous nonlinearity. In the film Maxwell's equations are reduced to a system of two Volterra integral equations. By the Banach fixed point theorem it is shown that the unique solution exists as a uniform limit of iterations. The dispersion relation is presented and some numerical examples are given.