Metamaterials: $\textit{supra}$-classical dynamic homogenization

TL;DR

This paper introduces new mathematical formulas for predicting the frequency-dependent effective parameters of 2D metamaterials at higher frequencies, enabling advanced wave control beyond traditional low-frequency limits.

Contribution

It provides the first general solution for dynamic effective constants in metamaterials at higher frequencies, expanding the design possibilities for wave manipulation.

Findings

Derived novel expressions for effective parameters at high frequencies

Validated formulas with examples involving sound, elastic, and electromagnetic waves

Opened new avenues for metamaterial design beyond low-frequency regimes

Abstract

Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material parameters that can be electronic, magnetic, acoustic, or elastic, and must adequately represent the wave interaction behaviour in the composite within desired frequency ranges. In some cases -- for example, the low frequency regime -- there exist various efficient ways by which effective material parameters for wave propagation in metamaterials may be found. However, the general problem of predicting frequency-dependent dynamic effective constants has remained unsolved. Here, we obtain novel mathematical expressions for the effective parameters of two-dimensional metamaterial systems valid at higher frequencies and wavelengths than previously possible. By way of an example, random configurations of cylindrical scatterers are considered, in various physical contexts: sound waves in a compressible fluid, anti-plane elastic waves, and electromagnetic waves. Our results point towards a paradigm shift in our understanding of these effective properties, and metamaterial designs with functionalities beyond the low-frequency regime are now open for innovation.