Diffraction of Electromagnetic Wave by Circular Disk and Circular Hole

TL;DR

This paper rigorously solves the electromagnetic diffraction problem involving a circular disk and hole using the Kobayashi potential method, providing analytical and numerical results validated against physical optics approximations.

Contribution

It introduces a novel application of the Kobayashi potential method to diffraction problems involving circular geometries, deriving matrix equations and series solutions for the problem.

Findings

Numerical results match well with physical optics method.

Series solutions are validated through Gaussian quadrature.

The method provides a rigorous analytical framework for diffraction analysis.

Abstract

The problem of diffraction of an electromagnetic plane wave by a perfectly conducting circular disk and its complementary problem, diffraction by a circular hole in an infinite conducting plate, are rigorously solved using the method of the Kobayashi potential. The mathematical formulation involved dual integral equation derived from the potential integral and boundary condition on the plane where a disk or hole is located. The weighting function in the potential integral are determined by applying the properties of the Weber-Schafheitlin's discontinuous integral and the solution are obtained in the form of a matrix equation. The matrix elements of the equations for the expansion coefficients are given by three kinds of infinite integral and the series solution for these infinite integral are derived. For the verification of these series solution, the numerical integral are derived and the results are computed numerically using the method of Gaussian quadrature for conformation. The numerical results are given for the far-field pattern diffraction by a perfectly conducting disk and the results are compared with those obtained from physical optics method (PO), which is fairly good.