Surface Electromagnetic TM Waves along the Boundary between Two Nonlinear Anisotropic Dielectrics

It is shown that the Maxwell's equations for surface electromagnetic TM waves, propagating along the plane boundary between two nonlinear dielectrics with arbitrary diagonal tensor of dielectric permittivity, depending on | (E) over right arrow |(2), can be integrated in quadratures. For the TM plane wave the magnetic intensity has only the transverse component, but the electric intensity has both transverse and longitudinal ones. This fact permits one to find the first integral of the Maxwell's equations and eliminate the magnetic intensity. The resulting equations for the electric intensity can be simplified and integrated, if one uses the transverse permittivity as the independent variable. Finally, we consider the Kerr dielectrics, with the permittivity being a quadratic function of the electric intensity. In this case the quadratures can be reduced to the elliptical integrals.