Ray analysis of conformal antenna arrays

The aperture design of conformal arrays is predicated on the knowledge of the element patterns and coupling coefficients in a mutually coupled environment. For equispaced identical slits on a perfectly conducting cylinder, a previous analysis has utilized the modal theory of periodic structures to simplify the calculations. Modal procedures are rather difficult to apply when the array surface has a more general, though rotationally symmetric and separable, shape; they become practically inapplicable when the surface is nonseparable. These difficulties may be overcome by recourse to the geometrical theory of diffraction and utilization of surface rays whose properties are determined from an appropriately defined local environment on the array surface. Depending on the problem under consideration, the local environment may involve either the unperforated array surface or a surface with periodic loading. It is shown how the surface ray technique can be applied to the analysis of mutual coupling in full ring arrays and finite arrays on a circular cylinder, and in nonperiodic or almost periodic arrays on surfaces of variable curvature. For finite arrays, a theoretical model leading to a representation of finiteness effects in terms of multiple scattering of surface rays of the periodic array structure between the edge discontinuities is confirmed by independently calculated numerical results. Although the demonstrations in this paper are confined to two-dimensional geometries, the procedure is applicable also to three-dimensional configurations.