Luneberg-Kline analysis of scattering from a sinusoidal dielectric interface

Application of the Luneberg-Kline asymptotic series to the solution of electromagnetic boundary value problems is extended to problems involving dielectric media. The series is employed to obtain an approximate value for the field near a sinusoidal interface between dielectric media when a perpendicularly polarized plane wave is incident. The resulting formulas are used to evaluate quantitatively the accuracy of the geometrical optics solution of the problem for a range of parameter values. It is found that for the parameter values considered, the geometrical optics solution is an excellent approximation to the exact solution.