Polarizability of radially anisotropic elliptic inclusion

Abstract

This article discusses a two-dimensional electrostatic scattering problem where an elliptic inclusion is suspended in a homogeneous background and impinged by an electric field which is uniform and static. The novelty of the discussion stems from the inclusion's material parameters. The material of the inclusion is assumed to be axially anisotropic, so that the axis of anisotropy aligns itself with the radial unit vector of the elliptic coordinate system. Similar varieties of anisotropy have been formerly referred to as radial anisotropy, and the same term is employed herein. The radially anisotropic elliptic inclusions are studied with an analytic method. The validation is likewise analytic. The validation method compares the new results with the results for radially anisotropic circles and homogeneous two-dimensional needles. The elliptic inclusion is found to facilitate both cloaking and field concentration. V C 2016 AIP Publishing LLC. [http://dx.

Implementing radial anisotropy with self-similar structures

“…For the punctured inclusion, the respective n is given by Eq. (21). However, the indexing, in the present context, starts from the outmost layer and not from a core, as was the case with the punctured inclusion.…”

“…Another flavor of radial anisotropy is the cylindrical anisotropy. Infinitely long cylinders with cylindrical anisotropy have been studied [19][20][21].…”

Polarizability of dielectric prolate half ellipse

“…Fig. 3 presents the normalized polarizability component α s of half ellipse and normalized polarizability component of a homogeneous ellipse with x-directed external excitation computed analytically using results of [11] and then substituting ε t = ε n = ε r as a function of relative permittivity ε r computed with matrix size N = 100. Similarly Fig.…”

“…It is defined as the ratio of the dipole moment and the magnitude of the incident field. Several articles have been published that study the polarizabilities of many different geometries like spheres [4], [5], circular cylinders or 2D disk [6], [7], hemisphere [8], half-disk [9] and anisotropic elliptic inclusions [11] as well. However, polarizability of dielectric half ellipse, which is also the topic of present study has not been considered yet.…”

“…However, polarizability of dielectric half ellipse, which is also the topic of present study has not been considered yet. Due to their manageable mathematics, elliptic coordinates/geometries have been analyzed widely in different areas of electromagnetics [11], [12], [13], [14], [15], [16].…”