Edge modes in active systems of subwavelength resonators

TL;DR

This paper investigates topologically protected edge states in active acoustic systems with gain and loss, demonstrating localized modes in non-Hermitian structures of subwavelength resonators and analyzing their topological properties.

Contribution

It introduces the study of topological edge modes in non-Hermitian acoustic systems with gain and loss, providing explicit calculations and topological analysis.

Findings

Localized edge modes appear in structures with gain/loss defects

Edge modes are linked to eigenmode winding, despite non-quantized invariants

Explicit frequency and decay length of edge modes are computed

Abstract

Wave scattering structures with amplification and dissipation can be modelled by non-Hermitian systems, opening new ways to control waves at small length scales. In this work, we study the phenomenon of topologically protected edge states in acoustic systems with gain and loss. We demonstrate that localized edge modes appear in a periodic structure of subwavelength resonators with a defect in the gain/loss distribution, and explicitly compute the corresponding frequency and decay length. Similarly to the Hermitian case, these edge modes can be attributed to the winding of the eigenmodes. In the non-Hermitian case, the topological invariants fail to be quantized, but can nevertheless predict the existence of localized edge modes.