Application of Quantum Graph Theory to Metamaterial Design: Negative Refraction of Acoustic Waveguide Modes

TL;DR

This paper introduces a quantum graph theory-based approach for designing acoustic metamaterials, enabling precise control of wave dispersion and negative refraction phenomena, validated through simulations and experiments.

Contribution

It presents a novel application of quantum graph theory to model and engineer acoustic metamaterials with tailored dispersive properties for negative refraction.

Findings

Quantum graph models accurately predict dispersion spectra.

Engineered metasurfaces demonstrate non-resonant negative refraction.

Model predictions agree with full wave simulations and experiments.

Abstract

We leverage quantum graph theory to quickly and accurately characterise acoustic metamaterials comprising networks of interconnected pipes. Anisotropic bond lengths are incorporated in the model that correspond to space-coiled acoustic structures to exhibit dispersion spectra reminiscent of hyperbolic metamaterials. We construct two metasurfaces with embedded graph structure and, motivated by the graph theory, infer and fine-tune their dispersive properties to engineer non-resonant negative refraction of acoustic surface waves at their interface. Agreement between the graph model, full wave simulations, and experiments bolsters quantum graph theory as a new paradigm for metamaterial design.