Asymptotic analysis of mutual coupling in concave circular cylindrical arrays. I. Far-zone

This work addresses the basis for the periodic structure ray method (PSRM) for evaluating coupling coefficients in large arrays on concave surfaces. A canonical model of a concave array is analyzed. It consists of an equispaced stacked-ring array of open-ended rectangular waveguides in a perfectly conducting concave circular cylindrical ground surface. It is shown that in such an array the coupling coefficients may be evaluated as a superposition of a small number of periodic structure ray contributions. A typical such contribution consists of a number of factors, each indicative of a specific physical event that takes place during the ray travel from the transmitting to the receiving element. The ray expressions are presented in an invariant form, independent of element type, lattice, and shape of the array surface. This form admits a straightforward GTD generalization of the periodic structure ray formalism to arrays on concave surfaces with variable curvature