A route to all frequency homogenization of periodic structures

TL;DR

This paper develops a new approach for defining effective parameters in periodic structures that ensures causality and passivity, overcoming divergence issues at band gap edges, and extends to 3D and dispersive cases.

Contribution

It introduces an alternative set of effective parameters based on propagation index and surface impedance that are valid across all frequencies and satisfy physical principles.

Findings

First-order expansion reveals magnetoelectric coupling in dielectric multilayers.

Second-order expansion shows artificial magnetism with low contrast.

Proposed parameters are analytic and consistent with causality and passivity.

Abstract

We start from a one-dimensional periodic multilayered stack in order to define a frequency power expansion of effective permittivity, permeability and bianisotropic parameters. It is shown from the first order that a simple dielectric multilayer can display a magnetoelectric coupling effect and, from the second order, that artificial magnetism can be obtained with arbitrary low contrast. However, this frequency power expansion is found to diverge at the first band gap edge. Thus, an alternative set of effective parameters, made of the propagation index and the surface impedance, is proposed. It is established that these effective parameters, as functions of the complex frequency, possess all the analytic properties required by the causality principle and passivity. Finally, we provide arguments to extend these results to the three-dimensional and frequency-dispersive case.