# Topologically protected edge modes in one-dimensional chains of subwavelength resonators

## TL;DR

This paper develops a design for subwavelength resonator chains that supports topologically protected edge modes, enabling robust wave localization at deep subwavelength scales despite imperfections.

## Contribution

It introduces a topological framework for designing stable, subwavelength waveguiding structures using high-contrast resonator chains.

## Key findings

- Topologically protected edge modes are demonstrated in finite resonator chains.
- Wave localization is robust against random imperfections.
- Design principles for stable subwavelength waveguides are established.

## Abstract

The goal of this paper is to advance the development of wave-guiding subwavelength crystals by developing designs whose properties are stable with respect to imperfections in their construction. In particular, we make use of a locally resonant subwavelength structure, composed of a chain of high-contrast resonators, to trap waves at deep subwavelength scales. We first study an infinite chain of subwavelength resonator dimers and define topological quantities that capture the structure's wave transmission properties. Using this for guidance, we design a finite crystal that is shown to have wave localization properties, at subwavelength scales, that are robust with respect to random imperfections.