The Parabolic Equation Method and the Fresnel Approximation in the Application to Weinstein’s Problems

Abstract

The problem of diffraction of a high-frequency plane wave by a grating composed of absorbing screens is studied. Difficulties of a correct mathematical formulation are discussed. It is shown how this problem is connected with the classical Weinstein’s problem of reflection by an open end of a planar waveguide. All results are proved by two different approaches, namely, by the parabolic equation approach and by the method of Fresnel integrals. The equivalence of these approaches allows one to use the Fresnel integrals for rigorous arguments, while the integral equation method can be used to get a clear physical understanding of the results.