Some Constraints of the Concept of Effective Material Parameters in Metamaterials

We review some important properties of common characterization techniques for left-handed metamaterials. Such metamaterials are typically described by effective material values as functions of frequency. A double negative metamaterial, with effective permittivity and effective permeability below zero, is able to feature left-handed waves and some other non-standard electromagnetic effects. However, the concept of an equivalent homogeneous material has several important limitations in terms of accuracy, and sometimes even in terms of passivity and causality. In order to avoid such problems, we propose to characterize metamaterials by the more general approach of a dispersion analysis of periodic structures. We concentrate on 3D metamaterial concepts such as the well-known split ring resonator (SRR) and similar structures, which can be analyzed by full-wave simulation techniques.