High-efficiency wavefront manipulation in thin plates using elastic metasurfaces beyond the generalized Snell's law

Elastic metasurfaces have shown immense potential in exotic wavefront manipulations based on the generalized Snell's law (GSL), stimulating applications in various engineering fields such as vibration and noise reduction, structural health monitoring and signal processing. One recognized bottleneck is that the GSL can lead to limited efficiencies of metasurfaces at steep deflection angles, which thereby arouses intense efforts in realizing perfect efficiencies, however, mainly in acoustics and electromagnetics. In this paper, we propose a paradigm to design high-efficiency elastic metasurfaces beyond the GSL efficiency limit, for the refraction manipulations of flexural waves in thin plates. We first find that the theoretical efficiency limits of anomalous refractions of flexural waves approach to zero at large deflection angles, but are higher than those of acoustic and electromagnetic waves due to the inherent evanescent mode contributing to a better impedance matching. A genetic algorithm-based inverse method is then proposed to design metasurfaces with almost perfect efficiencies (>95%), by engineering the nonlocal coupling between neighboring unit cells, which works well for the coarse assembly of only two unit cells in one period. Furthermore, by introducing bianisotropy, we demonstrate advanced high-efficiency functions such as the asymmetric transmission and spatial filtering. This work may offer insights towards the design of high-efficiency and structurally simplified wave-based devices.