Anisotropy in a wire medium resulting from the rectangularity of a unit cell

TL;DR

This paper investigates how the rectangular lattice geometry of a wire medium causes anisotropic dispersion properties near the plasma frequency, contradicting the isotropic predictions of effective medium theory.

Contribution

It provides the first detailed analysis of anisotropy caused by lattice rectangularity in wire media, supported by numerical simulations and an analytical dispersion relation.

Findings

Anisotropy reaches over 6% along wires and 75% across for thick wires.

Anisotropy depends on lattice rectangularity and vanishes for extremely thin wires.

An analytical dispersion relation near the $b0$-point is derived.

Abstract

The study is focused on the dispersion properties of a wire medium formed by a rectangular lattice of parallel wires at the frequencies close to its plasma frequency. While the effective medium theory predicts isotropic behaviour of transverse magnetic (TM) waves in the structure, numerical simulations reveal noticeable anisotropic properties. This anisotropy is dependent on the lattice rectangularity and reaches over 6% and over 75% along and across the wires respectively for thick wires with the radii about 20 times smaller than the smallest period. This conclusion is confirmed by line-of-current approximation theory. The revealed anisotropy effect is observed when the wavelength at the plasma frequency is comparable to the period of the structure. The effect vanishes in the case of extremely thin wires. A dispersion relation for TM waves in the vicinity of the $\Gamma$-point was obtained in a closed form. This provides an analytical description of the anisotropy effect.