Resonant and anti-resonant frequency dependence of the effective parameters of metamaterials

TL;DR

This study numerically investigates the resonant and anti-resonant behaviors of effective parameters in metamaterials, revealing how finite unit cell size influences negative refractive index properties.

Contribution

It demonstrates the frequency-dependent resonant and anti-resonant behaviors of effective parameters in metamaterials and explains the role of finite unit cell size in these phenomena.

Findings

Resonant behavior of magnetic permeability correlates with anti-resonant permittivity.

Opposite signs in imaginary parts of permittivity and permeability.

Anti-resonant behavior arises from finite unit cell size.

Abstract

We present a numerical study of the electromagnetic response of the metamaterial elements that are usedto construct materials with negative refractive index. For an array of split ring resonators (SRR) we find that the resonant behavior of the effective magnetic permeability is accompanied by an anti-resonant behavior of the effective permittivity. In addition, the imaginary parts of the effective permittivity and permeability are opposite in sign. We also observe an identical resonant versus anti-resonant frequency dependence of the effective materials parameters for a periodic array of thin metallic wires with cuts placed periodically along the length of the wire, with roles of the permittivity and permeability reversed from the SRR case. We show in a simple manner that the finite unit cell size is responsible for the anti-resonant behavior.