Multiple Scattering Formulation of Two Dimensional Acoustic and Electromagnetic Metamaterials

TL;DR

This paper develops a multiple scattering framework for two-dimensional acoustic and electromagnetic metamaterials, enabling the design of materials with tunable, negative, and anisotropic effective parameters for advanced wave control.

Contribution

It introduces a novel multiple scattering formulation that models both acoustic and electromagnetic metamaterials, including complex scatterers and their frequency-dependent effective parameters.

Findings

Effective acoustic parameters can be positive or negative.

Surface fields on scatterers influence anomalous medium behavior.

Electromagnetic resonances enable negative permittivity and permeability.

Abstract

This work presents a multiple scattering formulation of two dimensional acoustic metamaterials. It is shown that in the low frequency limit multiple scattering allows us to define frequency-dependent effective acoustic parameters for arrays of both ordered and disordered cylinders. This formulation can lead to both positive and negative acoustic parameters, where the acoustic parameters are the scalar bulk modulus and the tensorial mass density and, therefore, anisotropic wave propagation is allowed with both positive or negative refraction index. It is also shown that the surface fields on the scatterer are the main responsible of the anomalous behavior of the effective medium, therefore complex scatterers can be used to engineer the frequency response of the effective medium, and some examples of application to different scatterers are given. Finally, the theory is extended to electromagnetic wave propagation, where Mie resonances are found to be the responsible of the metamaterial behavior. As an application, it is shown that it is possible to obtain metamaterials with negative permeability and permittivity tensors by arrays of all-dielectric cylinders and that anisotropic cylinders can tune the frequency response of these resonances.