A simple and versatile analytical approach for planar metamaterials

TL;DR

This paper introduces an analytical model for calculating the effective material parameters of planar metamaterials with arbitrary unit cells, enabling systematic design and prediction of their optical properties.

Contribution

The paper presents a versatile analytical approach that models the coupling of resonant electric dipoles in arbitrary wire-based metaatoms to determine the metamaterial's effective tensor.

Findings

Model accurately predicts optical activity in modified split ring resonators.

Enables systematic design of metamaterials with desired properties.

Provides a building block approach for various metaatoms.

Abstract

We present an analytical model which permits the calculation of effective material parameters for planar metamaterials consisting of arbitrary unit cells (metaatoms) formed by a set of straight wire sections of potentially different shape. The model takes advantage of resonant electric dipole oscillations in the wires and their mutual coupling. The pertinent form of the metaatom determines the actual coupling features. This procedure represents a kind of building block model for quite different metaatoms. Based on the parameters describing the individual dipole oscillations and their mutual coupling the entire effective metamaterial tensor can be determined. By knowing these parameters for a certain metaatom it can be systematically modified to create the desired features. Performing such modifications effective material properties as well as the far field intensities remain predictable. As an example the model is applied to reveal the occurrence of optical activity if the split ring resonator metaatom is modified to L- or S-shaped metaatoms.