Rays and modes on concave surfaces

The objective of the research program has been to gain an understanding of the electromagnetic propagation and diffraction properties of concave surfaces having radii of curvature large compared to the wavelength, with application to ground wave propagation, large reflector antennas, and mutually coupled conformal antenna arrays. This basic objective has been accomplished. When the program was initiated, there was only incomplete and non-conclusive information available on how the radiation, diffraction and guiding of fields is affected by a nearby large-radius concave surface. It was recognized that neither a geometrical optics nor a whispering gallery mode representation is satisfactory for description of the field, and that a mixture of rays and modes, or a more complicated formulation involving a canonical integral analogous to the Fock integral for convex surfaces, may be the most effective. However, the foundations for these conjectures were lacking; accurate criteria for the appropriate combination of rays and modes were not at hand, nor were comprehensive numerical comparisons to assess the utility and quality of various field representations. Missing also were tractable results for the case when the observation point approaches the source or when the radius of curvature of a circular contour tends to infinity (infinite plane limit). This work has succeeded in establishing a sound analytical basis for any of the above-mentioned field formulations.