Theoretical and numerical analysis of current-driven electromagnetic homogenization and the problem of effective medium parameters for finite samples

TL;DR

This paper critically examines the current-driven homogenization theory for metamaterials, demonstrating that it fails to accurately predict reflection and transmission in finite samples beyond the zero-cell limit, highlighting limitations in existing effective medium models.

Contribution

The paper provides an analytical comparison showing the inconsistency of current-driven homogenization with exact results for finite samples, emphasizing the need for boundary-aware models.

Findings

Current-driven homogenization is inconsistent with exact reflection and transmission data.

Infinite periodic theories do not accurately model finite sample electromagnetic behavior.

Boundary effects are crucial for correct effective medium parameter determination.

Abstract

Reflection and refraction of electromagnetic waves by artificial periodic composites (metamaterials) can be accurately modeled by an effective medium theory only if the boundary of the medium is explicitly taken into account and the two effective parameters of the medium -- the index of refraction and the impedance -- are correctly determined. Theories that consider infinite periodic composites do not satisfy the above condition. As a result, they cannot model reflection and transmission by finite samples with the desired accuracy and are not useful for design of metamaterial-based devices. As an instructive case in point, we consider the "current-driven" homogenization theory, which has recently gained popularity. We apply this theory to the case of one-dimensional periodic medium wherein both exact and homogenization results can be obtained analytically in closed form. We show that, beyond the well-understood zero-cell limit, the current-driven homogenization result is inconsistent with the exact reflection and transmission characteristics of the slab.