Coupling Analysis in the Plane-Wave Scattering from Coplanar Thin Circular Disks: A Guaranteed-Convergence Technique

This paper investigates the coupling effects between coplanar thin circular disks illuminated by a plane wave using a generalized Helmholtz-Galerkin approach. The disks are modeled as planar surfaces, and the problem is formulated as a system of integral equations in the vector Hankel transform domain, describing the spectral-domain representations of the curl-free and divergence-free components of the induced surface current densities. A Fredholm second-kind matrix equation is then derived through the Method of Analytical Preconditioning (MAP). The matrix coefficients are represented as proper integrals of bounded continuous functions by employing a specifically developed analytical technique in the complex plane. The study examines the influence of disk spacing and the number of disks on coupling behavior, and results are compared with those obtained from CST Microwave Studio to validate the accuracy and effectiveness of the proposed method.