Effective medium theory of left-handed materials

TL;DR

This paper develops an effective medium theory for left-handed metamaterials, analyzing their transmission and reflection to determine effective parameters, and introduces a criterion to identify left- or right-handed transmission peaks.

Contribution

It provides analytical expressions for effective parameters of various metamaterial structures and a new criterion to distinguish left- from right-handed transmission peaks.

Findings

SRRs exhibit a strong electric response similar to cut-wires

Analytical models explain transmission characteristics of LHMs

A criterion to identify left- or right-handed peaks is proposed

Abstract

We analyze the transmission and reflection data obtained through transfer matrix calculations on metamaterials of finite lengths, to determine their effective permittivity and permeability. Our study concerns metamaterial structures composed of periodic arrangements of wires, cut-wires, split ring resonators (SRRs), closed-SRRs, and both wires and SRRs. We find that the SRRs have a strong electric response, equivalent to that of cut-wires, which dominates the behavior of left-handed materials (LHM). Analytical expressions for the effective parameters of the different structures are given, which can be used to explain the transmission characteristics of LHMs. Of particular relevance is the criterion introduced by our studies to identify if an experimental transmission peak is left- or right-handed.