Superdimensional Metamaterial Resonators

TL;DR

This paper introduces a novel design approach for metamaterial resonators that behave as if they have higher dimensions, enabling advanced control over wave concentration and resonance for applications like antennas and focusing.

Contribution

It presents a new method based on eigenvalue asymptotics for designing superdimensional metamaterials applicable to any wave modeled by the Helmholtz equation.

Findings

Resonators exhibit superdimensional behavior with higher eigenvalue density.

Planar resonators can act as 3D or higher-dimensional media.

Potential for broadband applications in antennas and wave focusing.

Abstract

We propose a fundamentally new method for the design of metamaterial arrays, valid for any waves modeled by the Helmholtz equation, including scalar optics and acoustics. The design and analysis of these devices is based on eigenvalue and eigenfunction asymptotics of solutions to Schr\"odinger wave equations with harmonic and degenerate potentials. These resonators behave superdimensionally, with a higher local density of eigenvalues and greater concentration of waves than expected from the physical dimension, e.g., planar resonators function as 3- or higher-dimensional media, and bulk material as effectively of dimension 4 or higher. Applications include antennas with a high density of resonant frequencies and giant focussing, and are potentially broadband.