Cloaking: analytical theory for benchmark structures

Abstract

Proceeding from the scattered field expansion in cylindrical harmonics, we define partial invisibility or partial cloaking as suppression of finitely many lowest-order field harmonics. We show that for benchmark structures (a dielectric rod and a perfectly conducting cylinder of circular cross section covered by a concentric dielectric layer), such multiple suppression can be achieved. For this purpose, we prove the solvability and explicitly determine the solution of the corresponding equation system which provide vanishing of the lowest-order field expansion coefficients and the resulting simultaneous suppression of up to five lowest-order scattered harmonics. We investigate the character and qualitative properties of partial invisibility and partial cloaking by analyzing the scattered field patterns.

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.…”

Resonance Scattering by a Circular Dielectric Cylinder

“…This work is a continuation of the study (Shestopalov, 2020) and is aimed at obtaining rigorous proofs of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder, a DR. In doing so we proceed from a mathematically correct approach of the spectral theory of open structures (Shestopalov and Shestopalov, 1996) involving generalized conditions at infinity (Reichardt, 1960) that enables one to handle complex resonance frequencies.…”

“…This work is a continuation of the study (Shestopalov (2020)) and is aimed at obtaining rigorous proofs of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder, a DR.…”