Electromagnetic Fields Near a Concave Perfectly Conducting Cylindrical Surface

Although no shadowing or diffraction effects occur, the surface fields excited by a high frequency source located on a perfectly conducting concave cylindrical boundary cannot be analyzed by geometrical optics since the caustics for rays, which have experienced many reflections, accumulate. In a previous study, alternative field representations in terms of whispering gallery (VVG) modes, canonical integrals, and hybrid ray-mode combinations have been explored to compensate for the failure of geometrical optics. As the source and/or observation points move off the boundary, the number of relevant multiply reflected rays decreases, and the caustics eventually become separated sufficiently to be treated as isolated. Ray optics is then expected to apply provided that uniform corrections near caustics and their endpoints are included. This conjecture is confirmed in the present investigation, which tracks the field continuously from the “boundary layer” near the concave surface, where ray optics is invalid, to off-surface points where it applies, by generalizing the alternative field representations used previously. A rich variety of hybrid ray-mode combinations exists for off-surface source and observation points. Especially intriguing is the possibility of choosing a hybrid mix that completely avoids the need for the caustic (and endpointj correction functions in a purely ray-optical formulation. The utility, accuracy, and range of validity of the various field representations is assessed by numerical comparison with a reference solution in terms of WG modes plus a continuous spectrum.