Subwavelength Su-Schrieffer-Heeger topological modes in acoustic waveguides.

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 because 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, generally, one has no precise control on the properties of the obtained topological modes, such as their frequency or localization length. In this work, a unique construction is proposed to couple acoustic resonators such that acoustic modes are mapped exactly to the eigenmodes of the Su-Schrieffer-Heeger (SSH) model. The relation between energy in the lattice model and the acoustic frequency is controlled by the characteristics of the resonators. In this way, SSH topological modes are obtained at any given frequency, for instance, in the subwavelength regime. The construction is also generalized to obtain well-controlled topological edge modes in alternative tunable configurations.