Geometrical Theory of Diffraction in Inhomogeneous Media

TLDR

The geometrical theory of diffraction is a framework for analyzing wave propagation in complex media. The study applies the theory to determine diffracted fields in inhomogeneous media. For smooth convex bodies, the theory extends Fermat’s principle to produce diffracted rays, and energy considerations yield diffraction coefficients and decay exponents expressed in terms of local medium and body properties. Exact solutions of the boundary value problems were obtained and their high‑frequency asymptotic expansions matched those from the geometric theory, confirming its validity.

Abstract

The geometrical theory of diffraction is described. It is used to determine the diffracted fields in inhomogeneous media. Cases in which such media contain smooth convex bodies are treated. The theory employs an extension of Fermat's principle which yields diffracted rays. By energy considerations the field associated with each ray is calculated. This calculation requires the introduction of diffraction coefficients and decay exponents. General formulas for these quantities are given in terms of local properties of the medium and of the body. In the companion article “Asymptotic theory of diffraction in inhomogeneous media” these problems are considered as boundary value problems. They are solved exactly and the solutions are expanded asymptotically for high frequencies. In all cases the asymptotic expansions agree completely with the corresponding results derived by the geometric theory, thus verifying this theory.