Diffraction by a concave perfectly conducting circular cylinder

Abstract

The determination of surface currents induced by a magnetic line source on a perfectly conducting concave cylindrical surface is dealt with in this paper. A "perfect" planar absorber is postulated along the cylinder diameter. The condition that the field be bounded at the origin requires the spectral representation of the characteristic Green's function to possess, in addition to a discrete spectrum comprising a finite number of whispering gallery (WG) modes, also a continuous spectrum. In the asymptotic high frequency limit the latter yields an "intrinsic" diffraction effect that together with the WG mode series correctly reproduces the singularity of the source. The connection between ray optics and the modal series is established by means of a representation comprising modes and rays. This composite representation provides insight into possible generalizations of the results to arbitrary concave cylinders with slowly varying radii of curvature. For circular cylinders with large <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ka</tex> , numerical results are presented for the magnitude of the surface magnetic field distribution.