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

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.