Resonance and Double Negative Behavior in Metamaterials

TL;DR

This paper introduces a class of metamaterials with frequency-dependent double negative properties, providing a rigorous method to determine their effective behavior and the existence of propagating Bloch waves within sub-wavelength structures.

Contribution

It develops a novel rigorous approach to calculate frequency intervals for double negative and positive properties and links these to the spectral characteristics of the material phases.

Findings

Identification of frequency intervals with double negative behavior.

Explicit determination of Bloch mode dispersion relations.

Connection between spectral properties and wave propagation in metamaterials.

Abstract

A generic class of metamaterials is introduced and is shown to exhibit frequency dependent double negative effective properties. We develop a rigorous method for calculating the frequency intervals where either double negative or double positive effective properties appear and show how these intervals imply the existence of propagating Bloch waves inside sub-wavelength structures. The branches of the dispersion relation associated with Bloch modes are shown to be explicitly determined by the Dirichlet spectrum of the high dielectric phase and the generalized electrostatic spectra of the complement.