Artificial magnetism and magnetoelectric coupling from dielectric layers

TL;DR

This paper develops a high-order homogenization method using transfer matrices to analyze periodic multilayered stacks, revealing artificial magnetism and magnetoelectric coupling effects in photonic crystals, with validation through numerical comparisons.

Contribution

It introduces a high-order homogenization algorithm for multilayer stacks that captures magnetoelectric and magnetic effects, extending previous low-order models.

Findings

Effective parameters match numerical results in low frequency range.

Magnetoelectric coupling vanishes in symmetric two-layer stacks.

Artificial magnetism persists in symmetric structures.

Abstract

We investigate a high-order homogenization (HOH) algorithm for periodic multilayered stacks. The mathematical tool of choice is a transfer matrix method. Expressions for effective permeability, permittivity and magnetoelectric coupling are explored by frequency power expansions. On the physical side, this high-order homogenization uncovers a magnetoelectric coupling effect (odd order approximation) and artificial magnetism (even order approximation) in moderate contrast photonic crystals. Comparing the effective parameters' expressions of a stack with three layers against that of a stack with two layers, we note that the magnetoelectric coupling effect vanishes while the artificial magnetism can still be achieved in a center symmetric periodic structure. Furthermore, we numerically check the effective parameters through the dispersion law and transmission curves of a stack with two dielectric layers against that of an effective bianisotropic medium: they present a good agreement in the low frequency (acoustic) band until the first stop band, where the analyticity of the logarithm function of transfer matrix ($\log\{T\}$) breaks down.