Size Effects in Periodic Metamaterials

TL;DR

This paper investigates how the optical reflection and transmission of periodic electromagnetic metamaterials depend on their unit cell size relative to the wavelength, revealing limitations of homogenization models when the unit cell size is comparable to the wavelength.

Contribution

It provides a numerical analysis of reflection and transmission across various unit cell sizes, challenging the applicability of homogenization in certain regimes.

Findings

Reflection and transmission vary significantly with unit cell size.

Homogenization concept is not valid when unit cell size is comparable to wavelength.

Identifies specific regimes where metamaterial behavior deviates from homogenized models.

Abstract

The optical properties of periodic electromagnetic metamaterials are considered as functions of their relative unit cell size $d / \lambda$. The reflection $R$ and transmission $T$ coefficients are numerically calculated for some realistic metamaterials in a wide range of their relative unit cell size values that comprises different operating regimes of the metamaterials. Peculiarities in $R$ and $T$ behavior are discussed and the causes of those peculiarities are outlined. The obtained results support the opinion on inapplicability of the very homogenization concept to metamaterials whose unit cell size is comparable to the incident wavelength, in contrast to some previously published results.