Application of quantum graph theory to metamaterial design: Negative refraction of acoustic waveguide modes

We leverage quantum graph theory to quickly and accurately characterize 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 nonresonant 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. Published by the American Physical Society 2024