GTD, UTD, UAT, and STD: A Historical Revisit and Personal Observations

In his landmark paper, dated February 1962, Prof. Joseph Keller detailed the notion of Keller´s cone. He stated, “Geometrical optics, the oldest and most widely used theory of light propagation, fails to account for certain optical phenomena called diffraction....” I had a personal encounter with Keller´s cone at a hotel in Florida! In the early morning on October 14, 2007, I witnessed Keller´s cone on the door of my hotel room, resulting from edge diffraction from a TV stand due to the sun´s rays coming through an opening of a window curtain. By now we know how to construct the local plane-wave behavior of the diffracted field along the diffracted rays, by invoking the fact that an edge forms one of the caustics of the diffracted wavefront. We also know that the diffracted field is of the order of k^-1/2, in comparison to the geometrical-optics field, which is of the order of k⁰. In many antenna and scattering problems, this added diffracted term immensely enhances the accuracy of the total field. Due to the boundary-layer properties of the diffracted ray field along the incident and reflected shadow boundaries and also caustics, the original form of Keller´s construction fails. These shadow-boundary shortcomings have been overcome through construction of the Uniform Theory of Diffraction (UTD, by Kouyoumjian and Pathak), the Uniform Asymptotic Theory (UAT, by Ahluwalia, Boersma, Lewis, Lee, and Deschamps), and the Spectral Theory of Diffraction (STD, by Rahmat-Samii, Ko, and Mittra). An overview and the salient features of these theories are revisited in a novel and unified manner, and a representative reflector-antenna example is highlighted.