Double Negative Dispersion Relations from Coated Plasmonic Rods

TL;DR

This paper develops a theoretical framework for a metamaterial made of coated plasmonic rods, deriving explicit power series for its dispersion relation and validating predictions through numerical simulations.

Contribution

It introduces explicit power series expansions for the dispersion relation of a coated rod-based metamaterial, linking lattice scale to wave behavior.

Findings

Power series accurately predict dispersive behavior

Leading order term matches numerical simulations

Metamaterial exhibits double negative properties

Abstract

A metamaterial with frequency dependent double negative effective properties is constructed from a sub-wavelength periodic array of coated rods. Explicit power series are developed for the dispersion relation and associated Bloch wave solutions. The expansion parameter is the ratio of the length scale of the periodic lattice to the wavelength. Direct numerical simulations for finite size period cells show that the leading order term in the power series for the dispersion relation is a good predictor of the dispersive behavior of the metamaterial.