Asymptotic Theory of Diffraction in Inhomogeneous Media

Abstract

Some boundary value problems are considered for the reduced wave equation in media having planar or cylindrical stratification. They are solved exactly and the solutions are expanded asymptotically for high frequencies by using the method of stationary phase in conjunction with the WKB method and the Watson transformation. The asymptotic expansions are compared with the corresponding diffracted fields found by using the geometrical theory described in the companion article “Geometrical theory of diffraction in inhomogeneous media.” In all cases the asymptotic expansions agree completely with the corresponding results derived by the geometrical theory, thus verifying this theory.