Periodic structure ray method for analysis of coupling coefficients in large concave arrays. I. Theory

A description is given of the periodic structure ray method (PSRM), an efficient variant of the geometric theory of diffraction (GTD) for the determination of coupling (scattering) coefficients in large arrays on concave surfaces with slowly varying curvature and/or periodicity. The method is particularly suitable for applications involving low-side-lobe lens arrays and feed-through radomes. In such arrays the coefficients of coupling between array elements can be evaluated as a superposition of a small number of contributions from the periodic structure. A typical contribution consists of a number of constituents, each expressing a specific physical process occurring during the ray's travel from the transmitting to the receiving element. The periodic structure ray formalism applies equally well to two- and three-dimensional array geometries and to a broad class of radiating elements. The final results are presented in an application-oriented form