Strong spatial dispersion in wire media in the very large wavelength limit

TL;DR

This paper demonstrates that wire media exhibit significant spatial dispersion even at very large wavelengths, challenging the adequacy of local dielectric models and highlighting the importance of non-local effects in metamaterials.

Contribution

It reveals that local dielectric tensor models are insufficient for wire media at large wavelengths, emphasizing the need to consider non-local effects in metamaterial analysis.

Findings

Strong spatial dispersion persists at very large wavelengths

Local dielectric models lead to unphysical wave propagation results

Non-local constitutive relations are necessary for accurate modeling

Abstract

It is found that there exist composite media that exhibit strong spatial dispersion even in the very large wavelength limit. This follows from the study of lattices of ideally conducting parallel thin wires (wire media). In fact, our analysis reveals that the description of this medium by means of a local dispersive uniaxial dielectric tensor is not complete, leading to unphysical results for the propagation of electromagnetic waves at any frequencies. Since non--local constitutive relations have been usually considered in the past as a second order approximation, meaningful in the short wavelength limit, the aforementioned result presents a relevant theoretical interest. In addition, since such wire media have been recently used as a constituent of some discrete artificial media (or metamaterials), the reported results open the question of the relevance of the spatial dispersion in the characterization of these artificial media.