Designing Perturbative Metamaterials from Discrete Models: From Veselago lenses to topological insulators

TL;DR

This paper introduces a systematic method for designing perturbative metamaterials by linking discrete models to physical structures, enabling the realization of phenomena like Veselago lenses and topological insulators across various domains.

Contribution

The authors propose a new class of perturbative metamaterials with weakly interacting units, facilitating systematic design from discrete models to physical metamaterials.

Findings

Designed 2D mechanical metamaterials for Veselago lenses

Realized zero-dispersion bands and topological insulators

Applicable to acoustic, thermal, and photonic metamaterials

Abstract

Discrete models provide concise descriptions of complex physical phenomena, such as negative refraction, topological insulators, and Anderson localization. While there are multiple tools to obtain discrete models that demonstrate particular phenomena, it remains a challenge to find metamaterial designs that replicate the behavior of desired nontrivial discrete models. Here we solve this problem by introducing a new class of metamaterial, which we term 'perturbative metamaterial', consisting of weakly interacting unit cells. The weak interaction allows us to associate each element of the discrete model (individual masses and springs) to individual geometric features of the metamaterial, thereby enabling a systematic design process. We demonstrate our approach by designing 2D mechanical metamaterials that realize Veselago lenses, zero-dispersion bands, and topological insulators. While our selected examples are within the mechanical domain, the same design principle can be applied to acoustic, thermal, and photonic metamaterials composed of weakly interacting unit cells.