Uniform Analytical Solution for Scattering by Circular PEC Apertures via Detour-Enhanced Extended BDW Theory

Abstract

We present a uniform analytical formulation for electromagnetic scattering by a circular aperture in an infinite perfectly electrically conducting plane. The formulation extends the boundary diffraction wave theory by incorporating both incident and reflected field contributions into a single analytical framework. A detour parameter combined with Fresnel uniformization is used to obtain a continuous edge-integral representation through the light–shadow transition. The resulting formulation reduces the aperture problem to a one-dimensional rim contribution and provides a compact analytical description of circular-aperture diffraction from a conducting screen over the considered angular range. Numerical evaluations based on the derived expressions illustrate the smooth behavior of the angular field, the symmetry associated with the conducting boundaries, and the edge-enhanced oscillatory features arising from the combined incident, reflected, and diffracted contributions. The main contribution of the study is a detour-enhanced uniform boundary diffraction wave formulation that provides a compact analytical representation of conductive circular-aperture diffraction and establishes a structured basis for future comparison with full-wave numerical and experimental benchmarks.