Ray analysis of two-dimensional radomes

Geometric-optical ray tracing is used to construct the fields transmitted from a line source through a two-dimensional curved dielectric layer of variable thickness. The tracing accounts for multiple reflections on the concave side, where the source is located, and for reflections between the layer boundaries. In addition, internally trapped rays, excited by evanescent tunneling, are included when source and observer are close to the layer boundaries but are displaced laterally along it. The multiple reflected contributions for weakly tapered configurations can be summed by applying Poisson summation to the ray series. These yield trapped and leaky local mdoes guided along the layer and a 'collective' ray field that incorporates a plane layer transmission coefficient, with curvature and slope corrections, instead of the conventional coefficients for individual boundaries. Detailed calculations are carried out for the special cases of a circularly curved layer of constant thickness and a tapered layer with nonparallel plane boundaries. For the former, the various ray-optically derived solutions agree fully with those obtained from a rigorous analysis; for the nonseparable configuration, however, no rigorous solution is available.