On the theory of TM- electromagnetic guided waves in a film with nonlinear permittivity

TM-electromagnetic guided waves propagating in a lossless nonmagnetic structure, consisting of a film with Kerr-type nonlinear permittivity, bounded by two semi-infinite media, are investigated. The problem is reduced to an exact differential equation leading to a first integral that relates the electric field components. Eliminating one field component by means of the first integral an exact analytical relation for the remaining field component is derived. Combination with the boundary conditions yields the exact analytical dispersion relation expressed in terms of elliptic integrals. Numerical results for the propagation constant are presented.