Surface ray analysis of mutually coupled arrays on variable curvature cylindrical surfaces

Two previously developed ray methods for conformal arrays on surfaces with variable curvature are further systematized and applied to arrays of equispaced identical slits on perfectly conducting parabolic cylindrical surfaces. The two methods differ in their definition of the canonical problems that are fundamental to the scattering process. In the first method, multiple scattering on the smooth cylinder surface accounts for interaction between isolated elements, while in the second, surface rays are defined on a local periodically loaded surface. The first method is valid under quite general conditions and yields reliable numerical results for mutual-coupling coefficients and radiation patterns. The second provides a simple explanation of a variety of coupling and radiation phenomena when the array possesses aspects of periodicity, and it is preferable for numerical calculation of mutual coupling in large arrays. These features are illustrated in detail on a particular example. The results obtained confirm the utility of the ray analysis in furnishing solutions for coupling coefficients and element patterns in conformal arrays, and they also demonstrate the fundamental insight gained by the local periodic-structure approach.