Topology optimization design and experimental validation of an acoustic metasurface for reflected wavefront modulation

Based on a level set-based topology optimization method, this study designs an acoustic metasurface capable of tailoring reflection wave arbitrarily. The present metasurface is composed of a periodic array of supercells and the supercell is constructed by eight inhomogeneous units possessing a full 2 pi reflection phase coverage with an interval of pi/4. In the optimization, each unit in the supercell is designed through the topology optimization method to achieve a specific reflection phase, i.e., reaching a target reflection coefficient corresponding to the desired reflection phase. During the optimization process, the boundary of the unit is updated via solving the level set function, while the normal velocity is derived from the sensitivity analysis. The optimal unit configurations have relatively smooth and distinct boundaries and sample structures. The reflection fields of the designed optimal metasurface under normal and oblique plane wave incidences are investigated numerically and experimentally, and a generally good agreement between them is achieved. Results reveal that a desired reflection wave manipulation is realized by the designed metasurface based on diffraction theory, demonstrating the effectiveness and efficiency of the present topology optimization design method. Furthermore, applications of these optimal units to acoustic flat focusing and acoustic self-bending beam generation are successfully demonstrated by numerical simulations. The presented design approach is quite promising for metasurface design and may be generally used in a variety of metamaterials with a prescribed set of properties.