Computing non-Euclidean wave dynamics with programmable photonic resonant circuits

Hyperbolic lattices, tessellations on a plane endowed with uniform negative Gaussian curvature, have garnered considerable interest in wave physics for their extended flat‐band spectra, distinct topological phases, and unconventional localization phenomena. However, their structure growing exponentially dense towards the boundary raised severe scalability issue for large scale implementation. In this talk, we demonstrate emulation of hyperbolic lattices with one dimensional array of coupled resonators to resolve scalability issue.