A Poynting vector approach to creeping-wave analysis of the sphere

A ray path geometry is derived using the Poynting vector to calculate the surface fields due to creeping waves in both the
E
- and
H
-planes of the sphere. The geodesics (great circles) are determined by assuming that at each point on the shadow boundary the initial direction of the ray is specified by the direction of real power flow calculated from the exact Poynting vector. The resulting ray geometry allows calculation of the creeping-wave surface field in both the
E
- and
H
-planes.