Electromagnetic wave propagation in a plane dielectric layer under critical conditions

An exact solution to the problem of a plane wave propagation in a plane-stratified dielectric layer of arbitrary thickness is studied. An approach based on self-consistent finite differences is suggested, replacing the layer by a stack of homogeneous sublayers of variable thickness matched to the local behavior of the permittivity profile. For the region around zero permittivity, it is predicted that small perturbations of the physical parameters of the problem cause qualitative and quantitative changes in the solution. The conditions for the excitation of a surface wave are formulated. Computed data for the wave are presented.