Acoustic graphene network loaded with Helmholtz resonators: a first-principle modeling, Dirac cones, edge and interface waves

Abstract

In this work, we study the propagation of sound waves in a honeycomb waveguide network loaded with Helmholtz resonators (HRs). By using a plane wave approximation in each waveguide we obtain a first-principle modeling of the network, which is an exact mapping to the graphene tight-binding Hamiltonian. We show that additional Dirac points appear in the band diagram when HRs are introduced at the network nodes. It allows to break the inversion (sub-lattice) symmetry by tuning the resonators, leading to the appearence of edge modes that reflect the configuration of the zigzag boundaries. Besides, the dimerization of the resonators also permits the formation of interface modes located in the band gap, and these modes are found to be robust against symmetry preserving defects. Our results and the proposed networks reveal the additional degree of freedom bestowed by the local resonance in tuning the properties of not only acoustical graphene-like structures but also of more complex systems.

Subwavelength Su-Schrieffer-Heeger topological modes in acoustic waveguides

“…The correspondance between waveguides of alternating cross sections was already established and studied in [13], and also used to obtain two dimensional generalizations [16][17][18][19]. In such a setup, properties of the SSH model are directly realized in acoustics.…”

Robustness of topological corner modes against disorder and application to acoustic networks

“…For this we consider a network of narrow air channels of equal length L but varying cross-sections. The typical transverse length ⊥ of the channels is assumed much smaller that its length L ( ⊥ L) so that inside each channel the propagation is monomodal [37][38][39]. In [30] it was shown that using cross-sections alternating between two values w and w , the system is described by an effective Hamiltonian that coincide with the 2D SSH model with hopping coefficients…”

Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to the Su-Schrieffer-Heeger model

“…In this paper, we report on an acoustic SSH lattice model based on a different approach. The idea relies on considering acoustic waveguides made of segments of alternating cross sections but more importantly, equal lengths [19][20][21][22][23][24]. Starting from the 2D wave equation, for slender waveguide segments, we use a continuous monomode 1D approximation.…”