Reinterpreting the magnetoelectric coupling of polarizability tensors of infinite cylinders using symmetry: a simple TM/TE view

TL;DR

This paper clarifies the magnetoelectric coupling in infinite cylinders by reformulating their polarizability tensors using symmetry, simplifying analysis into TM and TE modes, and resolving apparent contradictions with existing theorems.

Contribution

It introduces a symmetry-based reformulation of cylinder polarizability tensors, enabling straightforward interpretation of magnetoelectric coupling as TM/TE response contrast.

Findings

Reformulated polarizability tensors into diagonal form separating TM and TE responses.

Derived a transformation linking previous formulations to the new symmetric approach.

Provided geometric insights into the scaling and symmetry properties of magnetoelectric coupling.

Abstract

Recently, Strickland et al retrieved dynamic polarizabilities of infinitely long wires at oblique incidence, reporting non-zero magnetoelectric coupling, seemingly defying existing theorems which forbid this in centrosymmetric scatterers. We reconcile this finding with existing symmetry restrictions on microscopic polarizabilities using a property of line dipoles. This motivates a reformulation of cylinder polarizability, yielding diagonal tensors that decompose the response into TM and TE contributions, simplifying subsequent treatment by homogenization theories. A transformation is derived between Strickland et al.'s formulation and our reformulation, allowing magnetoelectric coupling to be identified as the contrast between TM and TE responses, and enabling simple geometric insights into all its scaling and symmetry properties.