GTD, UTD, UAT and STD: A Historical Revisit

Abstract

In his landmark paper dated February 1962, Prof. Keller introduced the notion of Keller's cone and 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 an 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 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 wave front. We also know that the diffracted field is of the order of k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1/2</sup> in comparison to the geometrical optics field which is of the order of k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> . In many antenna and scattering problems this added diffracted term enhances the accuracy of the total field immensely. Due to the boundary layer properties of the diffracted ray field, along the incident and shadow boundaries and also caustics the original form of Keller's construction fails. This shortcoming has been overcome through construction of the Uniform Theory of Diffraction (UTD by Kouyoujian and Pathak), Uniform Asymptotic Theory (UAT by Ahluwalia, Beorsma, Lewis, Lee and Deschamps) and the Spectral Theory of Diffraction (STD by Rahmat-Samii and Mittra). An overview and salient features of these theories are revisited in a novel and unified manner.