High frequency diffraction, focus on ray methods

Summary form only given. In the first half of the last century there was relatively little work on high frequency diffraction. However all that changed in 1953 when Keller introduced the geometrical theory of diffraction (GTD) as an extension of geometrical optics to include diffracted rays. This was a very important development, because it made it possible to calculate the high frequency radiation from antennas and scatterers of a quite general shape and to understand the various radiation mechanisms involved. Also, the GTD motivated the asymptotic treatment of the numerous canonical problems to determine the fields diffracted from edges, vertices and smooth curved surfaces. Unfortunately the GTD diffracted fields failed at and near the shadow boundaries of the incident and reflected fields, so the uniform GTD (UTD) was developed to overcome this limitation. In the UTD the canonical problems are solved by uniform asymptotic methods, and the resulting diffracted field not only describes the field in the shadow region, it also compensates the discontinuities in the geometrical optics field at the shadow boundaries. In this paper the canonical problems which have been solved are reviewed and some of the work which remains to be done is described. In conclusion, the relationship of the UTD to other high frequency methods such as the physical theory of diffraction and the method of incremental edge diffraction is discussed.