Computer Modeling of Electromagnetic Problems Using the Geometrical Theory of Diffraction1

Abstract

The geometrical theory of diffraction (GTD) is -a high frequency ray optical solution to electromagnetic problems. Using the ray optical approach the radiation from an arbitrary radiator can be described in terms of an astigmatic bundle of rays. By enforcing the conservation of energy, Fermat's principle, and using the velocity of light, one can write an expression for the field at S in terms of the field at 0. Using this concept, one can describe the reflected field from a general curved surface. These two solutions encompass traditional geometrical optics (GO). However, GO lacks generality in solving complex electromagnetic problems in that it does not take into account the diffractions which occur at edges, vertices, and various other discontinuities. Thus, Keller1,2,3 developed in the early 1950s the concept of GTD, which adds these significant diffraction terms to the GO solution. These additional diffraction mechanisms are briefly presented and applied to several practical problems in this paper.