Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique

• Main Author: Mario Lucido
• Format: Article
• Language: English
• Published: MDPI AG 2021-09-01
• Series: Applied Sciences
• Subjects: resistive disk; generalized boundary conditions; Helmholtz decomposition; Galerkin method; Fredholm second-kind equation
• Online Access: https://www.mdpi.com/2076-3417/11/17/8173

In this paper, the scattering of a plane wave from a lossy Fabry–Perót resonator, realized with two equiaxial thin resistive disks with the same radius, is analyzed by means of the generalization of the Helmholtz–Galerkin regularizing technique recently developed by the author. The disks are modelled as 2-D planar surfaces described in terms of generalized boundary conditions. Taking advantage of the revolution symmetry, the problem is equivalently formulated as a set of independent systems of 1-D equations in the vector Hankel transform domain for the cylindrical harmonics of the effective surface current densities. The Helmholtz decomposition of the unknowns, combined with a suitable choice of the expansion functions in a Galerkin scheme, lead to a fast-converging Fredholm second-kind matrix operator equation. Moreover, an analytical technique specifically devised to efficiently evaluate the integrals of the coefficient matrix is adopted. As shown in the numerical results section, near-field and far-field parameters are accurately and efficiently reconstructed even at the resonance frequencies of the natural modes, which are searched for the peaks of the total scattering cross-section and the absorption cross-section. Moreover, the proposed method drastically outperforms the general-purpose commercial software CST Microwave Studio in terms of both CPU time and memory occupation.