This book is concerned with the geometrical theory of diffraction (GTD) and its applications to electromagnetic wave diffraction. Its main interest, apart from expounding the techniques of GTD, is to develop useful formulations that can be readily applied to solve practical engineering problems. The approach taken is to begin with the solutions to canonical problems, from which we develop the GTD method to treat more complicated structures. In this way, the laws of geometrical optics are derived from the canonical problem of plane wave reflection and refraction at an infinite planar dielectric interface.

Canonical problems for GTD is reported. The high-frequency behaviour of the half-plane and wedge solution is the starting point for a GTD edge diffraction formulation.The canonical problem for geometrical optics is that of reflection and refraction of a plane wave at an infinite plane interface between two differing homogeneous media.

We begin our study of edge diffraction with the simplest case, namely, plane wave diffraction at a half-plane. The exact solution to this problem was derived in elsewhere and we shall now proceed to discuss the solution in detail. When a plane wave is normally incident upon a half-plane (i.e. the incident wavefront is parallel to the edge) and has a field component in the z-direction, then the exact solution for the z-component at any field point (p, φ) can be written in the compact form.

To illustrate some of the applications of GTD, a few worked examples are given in this chapter. The first example involves evaluation of the geometrical optics field. This is followed by the 2D edge diffraction problem of radiation from a parallel-plate waveguide. A comparison is made between GTD, the aperture field method, and the exact solution. Higher-order diffraction effects are considered, which include the use of the slope diffraction term and coupling effects between edges.