Uniform surface-to-line integral reduction of physical optics for curved surfaces by Keller-type equivalent edge currents in MER: Behaviors of fields on reflection shadow boundary

Abstract

The Modified Edge Representation (MER) is a procedure for defining the equivalent edge currents (EECs) to be used in the surface-to-line integral reduction for computing the physical optics radiation integrals in diffraction analysis. The physical optics surface integration is transformed into the line integration of MER-EECs rigorously for the planar surfaces. It works with the remarkable accuracy even for the curved surface. In contrast to conventional EECs, those in MER are defined without ambiguity not only at the diffraction points but also at arbitrary ones along the periphery. One remarkable advantage is that the MER-EECs, after integrated along periphery, provide uniform fields across the geometrical shadow boundaries though the EECs in the integrand consist of nonuniform Keller-type diffraction coefficients. As the starting point of the applicability check of MER for the curved surfaces, this paper investigates the MER diffraction field behaviors on and near the reflection shadow boundary (RSB). First, the stabilities or the robustness of the numerical line integration are interpreted. Second, the dependence of the RSB field errors upon the curvature of the surfaces is investigated. They become smaller in higher frequency and are related with the aberration of the geometrical reflected ray; for the dipole wave illumination, the error is generally smaller and larger for the concave and convex surfaces, respectively. This surface shape dependence of MER errors in diffraction is quite analogous to those in predicting geometrical optics contributions, the latter of which is the complement of the former and was previously reported by the authors.