Edge modes in subwavelength resonators in one dimension

TL;DR

This paper develops a mathematical framework for one-dimensional chains of subwavelength resonators, analyzing both Hermitian and non-Hermitian systems, and identifies conditions for localized edge modes and their topological properties.

Contribution

It introduces a finite-dimensional eigenvalue approach to predict resonances and modes, and characterizes edge modes and Zak phases in both Hermitian and non-Hermitian cases.

Findings

Quantized Zak phase in Hermitian systems

Existence of localized edge modes from defects

Complete characterization of edge modes in non-Hermitian systems

Abstract

We present the mathematical theory of one-dimensional infinitely periodic chains of subwavelength resonators. We analyse both Hermitian and non-Hermitian systems. Subwavelength resonances and associated modes can be accurately predicted by a finite dimensional eigenvalue problem involving a capacitance matrix. We are able to compute the Hermitian and non-Hermitian Zak phases, showing that the former is quantised and the latter is not. Furthermore, we show the existence of localised edge modes arising from defects in the periodicity in both the Hermitian and non-Hermitian cases. In the non-Hermitian case, we provide a complete characterisation of the edge modes.