Backward wave region and negative material parameters of a structure formed by lattices of wires and split-ring resonators

TL;DR

This paper analyzes a lattice structure of wires and split-ring resonators, deriving a dispersion relation and showing the existence of a backward wave region with negative permittivity and permeability, clarifying previous experimental interpretations.

Contribution

It provides a new dispersion equation for the structure and demonstrates that earlier formulas for effective parameters were incorrect, explaining past experimental results.

Findings

Backward wave region with negative parameters identified

Previous analytical formulas found to be inaccurate

Experimental results explained by negative material parameters

Abstract

A structure formed by combined lattices of infinitely long wires and split-ring resonators is studied. A dispersion equation is derived and then used to calculate the effective permittivity and permeability in the frequency band where the lattice can be homogenized. The backward wave region in which both the effective permittivity and permeability are negative is analyzed. Some open and controversial questions are discussed. It is shown that previous experimental results confirming the existence of backward waves in such a structure can be in deed explained in terms of negative material parameters. However, these parameters are not quasi-static and thus the known analytical formulas for the effective material parameters of this structure, which have been widely used and discussed in the literature, were not correct, and it was the reason of some objections to the authors of that experiment.