Resonance Scattering by a Circular Dielectric Cylinder

Abstract

A unified approach is developed for the analysis of singularities of the scattered field and vanishing of scattering harmonics. Rigorous proofs are presented of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder. The method employs a mathematically correct approach of the spectral theory of open structures involving generalized conditions at infinity when complex resonance frequencies may be considered. The result is obtained by verifying the existence of complex singularities of the series solution coefficients considered as functions of the problem parameters. The recently developed theory of generalized cylindrical polynomials (GCPs) is used that enables one to reduce determination of singularities (resonances) to finding zeros (real or complex) of a particular subfamily of GCPs.

On a Method of Investigating Nonlinear Dispersion Relations of Electromagnetics in the Complex Domain

“…Remarkably, Φ(κ, ζ ) is a ratio of two second-order GCPs (because one can call that partial derivatives of GCPs are GCPs as well), which makes it possible to show that the existence of the sought implicit functions κ = κ(ζ ) (i.e. the existence of the corresponding resonance frequencies) follow form the fact (verified explicitly [2]) that ∂ g n ∂ κ (w * ) = 0.…”

“…For a circular dielectric rod of radius a the parameter sets [2] at which g n (κ, ζ ) = 0, n = 0, 1, 2, . .…”

Outline, Achievements and Recent Trends: Spectral Theory of Open Structures. Dedicated to the 100 Anniversary of Victor P. Shestopalov

“…The main idea of the analysis is as follows: if one of the series solution coefficients considered as a function of all three problem parameters is singular then the whole solution is singular. The present approach leading to the rigorous proofs employs the technique set forth for the determination of complex waves in metal-dielectric waveguides [13,14].…”

TE-Polarized Electromagnetic Wave Diffraction by a Circular Slotted Cylinder

“…Note that in some particular cases, it is possible to obtain exact solutions by means of PDM. For example, in [16][17][18], the exact solution is constructed and the resonance modes are studied on this basis for the problem of the TE-polarized electromagnetic wave scattering on a cylindrical dielectric resonator with a circular cross section.…”