Recent development of metasurfaces indicates 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 ignores the coupling between sub-units, thus often resulting in low efficiency. In order to design nonlocal structures for flexural wave in thin elastic plate, a previously proposed method based on the multi-port structural model (MPSM) for acoustic metasurfaces is extended in this work. Using this method, anomalous reflector and anomalous refractor, each with a large diffraction angle and planar focuser with large numerical aperture for flexural waves in thin elastic plates, are designed.

As the first example, an anomalous reflector or anomalous refractor for flexural wave on an infinite free thin elastic plate with elastic cylinder pairs assembled symmetrically on both surfaces is considered. The design target is to optimize the heights of the cylinder pairs, by which anomalous reflection or refraction for flexural wave in plate can be realized. It is shown that by modelling the structure as an MPSM, configurations with the desired functionalities can be efficiently determined. The three dimensional finite element simulations show that even for structures with a deflection angle as large as 80°, the proposed anomalous reflectors and refractors can achieve near-unity efficiency.

By the same method, a planar focuser is further designed. It is shown 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. It is found that the focusing efficiency of our nonlocal designs is significantly higher than that of their GSL-based counterparts, particularly for the structures with numerical apertures approaching unity.

This work not only presents an effective design method for nonlocal metasurfaces of flexural waves in thin elastic plates, but also provides two efficient nonlocal structures with broad application prospects in sensing, energy harvesting, and other fields.