Subwavelength Su-Schrieffer-Heeger topological modes in acoustic waveguides

TL;DR

This paper introduces a method to realize subwavelength topological acoustic modes in waveguides by precisely coupling resonators to emulate the Su-Schrieffer-Heeger model, enabling control over mode frequency and localization.

Contribution

The authors develop a novel resonator coupling technique that maps acoustic modes to the SSH model, allowing exact control of topological mode properties at any frequency.

Findings

Achieved topological modes at subwavelength frequencies.

Controlled the frequency and localization of edge modes.

Generalized the approach for tunable configurations.

Abstract

Topological systems furnish a powerful way of localizing wave energy at edges of a structured material. Usually this relies on Bragg scattering to obtain bandgaps with nontrivial topological structures. However, this limits their applicability to low frequencies since that would require very large structures. A standard approach to address the problem is to add resonating elements inside the material to open gaps in the subwavelength regime. Unfortunately, one usually has no precise control on the properties of the obtained topological modes, such as their frequency or localization length. In this work, we propose a new construction to couple acoustic resonators such that acoustic modes are mapped exactly to the eigenmodes of the Su-Schrieffer-Heeger model. The relation between energy in the lattice model and the acoustic frequency is controlled by the characteristics of the resonators. This allows us to obtain Su-Schrieffer-Heeger topological modes at any given frequency, for instance in the subwavelength regime. We also generalize the construction to obtain well-controlled topological edge modes in alternative tunable configurations.