Impact of the inherent periodic structure on the effective medium description of left-handed and related meta-materials

TL;DR

This paper investigates how the inherent periodic structure of left-handed meta-materials affects their effective electromagnetic parameters, introducing a model to distinguish resonant behavior from periodicity effects, and analyzing numerical data to clarify resonance phenomena.

Contribution

It presents a periodic effective medium model that accounts for the influence of structural periodicity on electromagnetic response, improving understanding of resonance behaviors in meta-materials.

Findings

Periodic structure influences effective electromagnetic parameters.

The model distinguishes resonance effects from periodicity effects.

Periodic effects can be neglected for wavelengths larger than 30 periods.

Abstract

We study the frequency dependence of the effective electromagnetic parameters of left-handed and related meta-materials of the split ring resonator and wire type. We show that the reduced translational symmetry (periodic structure) inherent to these meta-materials influences their effective electromagnetic response. To anticipate this periodicity, we formulate a periodic effective medium model which enables us to distinguish the resonant behavior of electromagnetic parameters from effects of the periodicity of the structure. We use this model for the analysis of numerical data for the transmission and reflection of periodic arrays of split ring resonators, thin metallic wires, cut wires as well as the left-handed structures. The present method enables us to identify the origin of the previously observed resonance/anti-resonance coupling as well as the occurrence of negative imaginary parts in the effective permittivities and permeabilities of those materials. Our analysis shows that the periodicity of the structure can be neglected only for the wavelength of the electromagnetic wave larger than 30 space periods of the investigated structure.