Analytical Regularization Approach to Plane Wave Diffraction From Circular Hole in Infinite Resistive Plane

In this article, the diffraction of a plane wave from a circular hole in an infinite resistive plane is addressed. In contrast to the holed perfectly electrically conducting (PEC) screens, neither the equivalence principle combined with the image theory nor the Babinet principle can be applied here, and the problem has to be solved directly. The method adopted in this article belongs to the family of methods of analytical preconditioning. The revolution symmetry allows us to reduce the problem to an infinite set of dual integral equations in the vector Hankel transform (VHT) domain for suitable unknowns vanishing outside the hole. Such equations are transformed into matrix equations by means of the Helmholtz-Galerkin discretization technique. The orthogonal eigenfunctions of the most singular part of the integral operator, reconstructing the behavior of the fields at the edge and around the center of the hole, are selected as expansion functions, thus leading to fast converging Fredholm second-kind matrix equations, whose elements can be expressed as quickly evaluable proper integrals. Numerical results show the near-field and far-field characteristics for various cases; the in-house software code is validated by means of comparisons with general-purpose commercial software.