Asymptotic analysis of edge-excited currents on a convex face of a perfectly conducting wedge under overlapping penumbra region conditions

The edge-excited surface currents on a convex face of a perfectly conducting curved wedge are investigated in the asymptotic high-frequency limit for the case where the penumbra regions of the edge and surface diffractions overlap. The edge of the wedge is assumed straight, and the incident electromagnetic wave locally plane and normal to the edge. Both polarizations are considered. The surface field induced by the edge diffraction is synthesized in the spirit of the spectral theory of diffraction (STD): the solution for the edge-diffracted field is interpreted as a spectrum of inhomogeneous plane waves, and the surface field excited by each spectral plane wave is obtained by analytical continuation of the Fock (1965) functions into complex space. The main purpose of this work is to prove the reciprocity of a solution deduced previously for the problem of line source radiation from the wedge in question. As a by-product, useful identities for an incomplete Airy function and an Airy-Fresnel integral are developed.