Wave-Freezing and other Phenomena in Temporal Metasurfaces driven by Nonlocal Interactions

Space-time metamaterials, or materials with properties changing in space and time, have gained a wide-spread interest due to their exotic properties. In this Letter, we propose a novel temporal metasurface of phononic crystals in one and two-dimensions, that combines the use of nonlocal interactions in phononic crystals to customize dispersion relations, and the use of temporal interfaces to transition from a local material to a nonlocal material and vice-versa, to achieve the interesting phenomenon of \textit{wave-freezing}, where the entire propagating wave is stopped without diffusing or spreading. The phononic crystals are modeled using spring-mass systems and we use finite difference calculations to present our numerical results. We also demonstrate other effects observed in such temporal metasurfaces, such as time-reversed waves, and anomalous temporal refraction.