Homogenization of nonlocal wire metamaterial via a renormalization approach

TL;DR

This paper develops an analytical renormalization method to homogenize finite wire metamaterials with finite conductivity, accurately capturing their non-local electromagnetic response and revealing their potential for robust, low-reflection applications.

Contribution

It extends non-local homogenization techniques to finite, lossy wire media using a two-scale renormalization approach, validated by numerical simulations.

Findings

Analytical non-local permittivity derived for finite wire media.

High accuracy confirmed through 3D finite element simulations.

Finite wire media exhibit large absorption with low reflection.

Abstract

It is well known that defining a local refractive index for a metamaterial requires that the wavelength be large with respect to the scale of its microscopic structure (generally the period). However, the converse does not hold. There are simple structures, such as the infinite, perfectly conducting wire medium, which remain non-local for arbitrarily large wavelength-to-period ratios. In this work we extend these results to the more realistic and relevant case of finite wire media with finite conductivity. In the quasi-static regime the metamaterial is described by a non-local permittivity which is obtained analytically using a two-scale renormalization approach. Its accuracy is tested and confirmed numerically via full vector 3D finite element calculations. Moreover, finite wire media exhibit large absorption with small reflection, while their low fill factor allows considerable freedom to control other characteristics of the metamaterial such as its mechanical, thermal or chemical robustness.