Reflection and transmission of a plane TE-wave at a lossless nonlinear dielectric film

A general analytical solution of the Helmholtz equation describing the scattering of a plane, monochromatic, TE-polarized wave with a film exhibiting a local Kerr-like nonlinearity is presented. The film is situated between two semi-infinite media. All media are assumed to be non-absorbing, non-magnetic isotropic and homogeneous. The results derived contain conditions for unbounded field intensities expressed in terms of the imaginary half-period of Weierstrass’ elliptic function ℘. The reflectivity R is calculated as a function of the film thickness and the transmitted intensity. The critical values of R are determined. The results are a generalization of the linear optics results.