Propagation Over a Constant Impedance Plane: Arbitrary Primary Sources and Impedance, Analysis of Cut in Active Case, Exact Series, and Complete Asymptotics

We analyze and detail here a compact solution for the electromagnetic field scattered by an arbitrary constant impedance plane, considering exact potentials for primary current sources composed of dipoles with arbitrary orientations. The special function involved in our expressions is rewritten with nonsingular integral expression valid for any complex arguments that exhibits a correct cut in active case. We describe efficient exact series for arbitrary cases and complete asymptotics, which are both expressed in terms of error functions.