Metamaterial acoustics on the Poincaré disk

Abstract

[EN] Historically, the Poincare disk model has taken a pioneering role in the development of non-Euclidean geometry. But still today, this model is critical as a playground for simulations and new theories. In this paper, we discuss how to implement and simulate acoustic wave phenomena on the Poincare disk with the help of so-called metamaterials. After formally developing a theory based on the acoustic potential for the curved spacetime of the Poincare model, we also provide practical instructions on how to manufacture the appropriate metadevice in a laboratory environment. Finally, as an example, analytical results for the nontrivial radial contributions in concentric wave propagation are derived, and the corresponding numerical predictions are presented.