Recent advancements in metasurfaces indicate that achieving high efficiency requires nonlocal designs where the coupling between constituent units is fully considered. However, most metasurfaces for elastic waves are still designed as local structures based on the Generalized Snell's Law (GSL), which ignore the coupling between sub-units, often results in low efficiency. In this paper, we extend a previously proposed method based on the Multi-port Structural Model (MPSM) for acoustic metasurfaces, to design nonlocal structures for flexural wave in thin elastic plate. Using this method, we can design anomalous reflector/refractor with large diffraction angle and planar focuser with large numerical aperture for flexural waves in thin elastic plates.
As shown in Fig. A1(a), we consider an infinite free thin elastic plate with elastic cylinder pairs assembled symmetrically on both surfaces. The design target is to optimize the height of the cylinder pairs, by which anomalous reflection or refraction for flexural wave in plate can be realized. We show that, by modelling the structure as a MPSM, configurations with the desired functionalities can be efficiently determined. Through three-dimensional finite element simulations, we demonstrate that the proposed anomalous reflectors and refractors can both achieve near-unity efficiencies, even for structures with a deflection angle as large as 80°. As illustration, the field distribution of the scattering wave in two example structures under normal incidence is shown in Fig. A1(b). For the figure, the structures are designed as the 60° anomalous refractor (left panel) and reflector (right panel) under normal incidence.
By the same method, we further design a planar focuser with functionality illustrated schematically in Fig. A2(a). We show that, by optimizing the heights of each cylinder pair, the normally incident flexural wave can be focused on the incident side or the transmitting side of the metasurface with arbitrary focal length. As illustration, we show in Fig. A2(b) the focusing effect of a reflection-type and a transmission-type focuser. The illustrated structures have lateral length of 20λ₀ and focal length of 2λ₀. We find the focusing efficiency of our nonlocal designs is significantly higher than that of their GSL-based counterparts, particularly for structures with numerical apertures approaching unity.
This work not only introduces an effective design method for nonlocal metasurfaces for flexural waves in thin elastic plates, but also provides two highly efficient nonlocal structures with promising applications in areas such as sensing, energy harvesting, and more.