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

T. M. Lawrie, T. A. Starkey, G. Tanner, D. B. Moore, P. Savage, G. J. Chaplain
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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.
量子图论在超材料设计中的应用:声波导模式的负折射
我们利用量子图理论快速准确地描述了由相互连接的管道网络组成的声学超材料。模型中加入了各向异性的键长,这些键长与空间卷曲声学结构相对应,表现出令人联想到双曲超材料的频散谱。我们构建了两个具有嵌入式图形结构的元表面,并在图形理论的激励下,推断和微调了它们的色散特性,以在它们的界面上设计声表面波的非共振负折射。图模型、全波模拟和实验之间的一致性增强了量子图理论作为超材料设计新范例的地位。
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