A Metamaterial Homogenization Approach with Application to the Characterization of Microstructured Composites with Negative Parameters

TL;DR

This paper introduces a new homogenization method for non-magnetic periodic metamaterials that accurately captures complex effects like dispersion and coupling, applicable even in lossy or band-gap conditions.

Contribution

A systematic, eigenvalue-free homogenization approach for arbitrary metamaterials that accounts for frequency dispersion, magneto-electric coupling, and spatial dispersion.

Findings

Successfully homogenized split ring resonator metamaterials.

Method handles frequency band-gaps and lossy materials.

Reduces complex integral-differential systems to standard integral equations.

Abstract

In this work, we develop a new systematic and self-consistent approach to homogenize arbitrary non-magnetic periodic metamaterials. The proposed method does not rely on the solution of an eigenvalue problem and can fully characterize the effects of frequency dispersion, magneto-electric coupling, and spatial dispersion, even in frequency band-gaps or when the materials are lossy. We formulate a homogenization problem to characterize a generic microstructured artificial material, and demonstrate that it is equivalent to an integral-differential system. We prove that this complex system can be reduced to a standard integral equation and solved using standard methods. To illustrate the application of the proposed method, we homogenize several important metamaterial configurations involving split ring resonators and metallic wires.