Applications of Chebyshev polynomials and Toeplitz theory to topological metamaterials

TL;DR

This paper surveys how Chebyshev polynomials and Toeplitz theory are applied to analyze topological metamaterials, covering both Hermitian and non-Hermitian systems of subwavelength resonators.

Contribution

It introduces a mathematical framework that explains unique properties of topological metamaterials using Chebyshev polynomials and Toeplitz theory.

Findings

Mathematical framework for topological properties

Analysis of Hermitian and non-Hermitian systems

Explanation of spectacular metamaterial properties

Abstract

We survey the use of Chebyshev polynomials and Toeplitz theory for studying topological metamaterials. We consider both Hermitian and non-Hermitian systems of subwavelength resonators and provide a mathematical framework to explain some spectacular properties of metamaterials.