Non-local design method of metasurface by the grating diffraction theory enabling efficient wave control

Currently, the metasurface design of flexural wave is primarily based on the generalized Snell's law (GSL). However, due to GSL only considering phase gradient, high-order parasitic diffraction leads to poor performance of larger angle anomalous refraction. In this paper, to suppress parasitic diffraction, a collaborative optimal method is proposed for metasurface design. Firstly, the diffraction formula considering both phase gradient and periodicity of grating structures is derived based on the grating diffraction theory (GDT). Then, the reconfigurable metasurface constructed of ‘screw-nut’ substructures are designed in conjunction with the genetic algorithm (GA). For the vertical incident flexural wave, the anomalous refractions of medium angle 51° and large angle 77° for 6.4 kHz, as well as 90° for 6.066 kHz are considered. Finally, oblique incidence is considered, in which the improvements of collaborative optimization design methods to 1 and −1 orders anomalous refractions are analyzed separately. The results are compared with the local ones obtained by GSL. It indicates that the proposed non-local design method opens a new perspective for parasitic diffraction suppression and efficient flexural wave manipulation.