Size Dependence and Convergence of the Retrieval Parameters of Metamaterials

TL;DR

This paper investigates how the size of unit cells in fishnet metamaterials affects their effective electromagnetic parameters and examines the convergence behavior of these parameters as the number of unit cells increases.

Contribution

It provides a detailed analysis of size dependence and convergence of retrieval parameters specifically for fishnet metamaterials, highlighting differences from other structures.

Findings

Smaller unit cells lead to higher magnitude of effective parameters.

Convergence of parameters is slower in fishnet structures compared to split ring resonators.

Strong coupling between unit cells affects the convergence rate.

Abstract

We study the dependence of the retrieval parameters, such as the electric permittivity, the magnetic permeability and the index of refraction, $n$, on the size of the unit cell of a periodic metamaterial. The convergence of the retrieved parameters on the number of the unit cells is also examined. We have concentrated our studies on the so-called fishnet structure, which is the most promising design to obtain negative $n$ at optical wavelengths. We find that as the size of the unit cell decreases, the magnitude of the retrieved effective parameters increases. The convergence of the effective parameters of the fishnet as the number of the unit cells increases is demonstrated but found to be slower than for regular split ring resonators and wires structures. This is due to a much stronger coupling between the different unit cells in the fishnet structure.