A Fock-function representation of the fields induced on an impedance or coated cylindrical surface by a Z-directed point source

Summary form only given. For the two-dimensional problem of computing the surface fields due to a line source on the surface of an impedance or thinly-coated circular cylinder, a solution in terms of the canonical Fock integral v(/spl zeta/,q) is known to be available. With the aid of certain approximations, corresponding solutions in three dimensions for circular-cylinder problems involving z-directed electric and magnetic point sources can be derived. Such solutions are associated with geometrical theory of diffraction (GTD) ray paths in the usual manner. A feature of the three-dimensional case is the coupling that occurs between fields that are transverse electric (TE) and transverse magnetic (TM) with respect to the cylinder axis. Because of this feature, TE- and TM-polarized fields must each be computed by summing contributions associated with a pair of Fock functions, designated as v(/spl zeta/,q/sub h/) and v(/spl zeta/,q/sub s/). The parameters q/sub h/ and q/sub s/ depend upon the path direction. When the propagation is purely azimuthal, the coupling between TE and TM modes disappears, while q/sub h/ and q/sub s/ reduce to values appropriate, respectively, to representing TE and TM fields in the two dimensional problem. Well-known formulations for the surface fields due to sources located on perfectly-conducting surfaces which are convex and smoothly varying employ Fock functions and rely heavily for their justification on circular-cylinder canonical-problem solutions. The possibility of a parallel construction for impedance and thinly-coated surfaces is addressed by considering the dependence of q/sub h/ and q/sub s/, and the surface-ray torsion.