Geodesic splitting on general paraboloid of revolution and its implications to the surface ray analysis

Abstract

The authors have observed geodesic splitting in the case of surface ray propagation over a general paraboloid of revolution (GPOR). Since even the primary geodesics are split in both clockwise and counterclockwise directions, this leads to a double of the ray paths to be considered in antenna characteristics computations. The authors provide an insight into the ray-splitting phenomenon for the simplest (i.e. lowest order) possible convex surface. It is noted that, in general, the ray tracing over a GPOR would require a bivariate search. The ray splitting in the case of the GPOR tends to further increase the computer time required for the determination of the surface ray geometric parameters. The authors have developed a geodesic constant method (GCM) involving an accurate simple univariate search which has brought the electromagnetic field computations within the ambit of tractability. >