Complex eigenvalues of natural TM ‐oscillations in an open resonator formed by two sinusoidally corrugated metallic strips

Abstract

The diffraction of an E-polarized plane wave from two finite sinusoidal gratings is investigated by a rigorous approach, based on the Method of Analytical Regularization. This allows us to analyse the problem in a wide frequency band without limitations on the depth of the sinusoidal corrugation, the wave size of the gratings, or their relative location. The homogeneous version of the equations obtained is used for accurate computation of the complex eigenvalues in an open resonator of Fabry-Perot type with sinusoidally corrugated strips. In the calculations, two types of structures were used: one is formed by parallel translation of the sinusoidally corrugated strips and the other is obtained by rotation of one of the strips in the first structure. For each relative location of the corrugated strips, the resonance excitation of the structure by an obliquely incident Epolarized plane wave is considered. Based on the calculation of the surface current density for different incidence angles, their specific values for optimal excitation of the complex modes are established.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

Guest Editorial: Method of analytical regularisation for new frontiers of applied electromagnetics

“…They can be analytically regularised via Abel's integral transform to yield coupled systems of linear algebraic equations with the Fredholm second‐kind operators, giving rise to fast‐converging algorithms that are successfully applied to the accurate analysis of isolated and coupled PEC open resonators in the papers ‘Scattering of an obliquely incident E‐polarised plane wave from ensembles of slotted cylindrical cavities: A rigorous approach’ and ‘Complex eigenvalues of natural TM‐oscillations in an open resonator formed by two sinusoidally corrugated metallic strips’ by Vinogradova et al. [12, 13].…”

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

“…Usually, it can be a suitable asymptotic part (e.g., the static part or the high-frequency part, etc.) or a canonical-shape part, which can be inverted by means of functional techniques such as Wiener-Hopf, Cauchy, Titchmarsh, Abel, Riemann-Hilbert Problem, and the separation of variables techniques [12][13][14][15][16][17][18][19][20]. Following this line of reasoning, the resulting integral equation is of the Fredholm second-kind; hence, the Fredholm theory [21], generalized by Steinberg for operators [22], can be applied.…”