Topology optimization of acoustic metasurfaces by using a two-scale homogenization method

In this paper, we propose a level set-based topology optimization method for the unit-cell design of acoustic metasurfaces by using a two-scale homogenization method. Based on previous works, we first propose a homogenization method for acoustic metasurfaces that can be combined with topology optimization. In this method, a nonlocal transmission condition depending on the unit cell of the metasurface appears in a macroscale problem. Next, we formulate an optimization problem within the framework of a level set-based topology optimization method, wherein an objective functional is expressed as the macroscopic responses obtained through the homogenization, and material distributions in the unit cell are set as design variables. A sensitivity analysis is conducted based on the concept of the topological derivative. To confirm the validity of the proposed method, two-dimensional numerical examples are provided. First, we numerically demonstrate the validity of the homogenization method, and then perform optimization calculations based on the waveguide settings of the acoustic metasurfaces. In addition, we discuss the mechanism of the obtained optimized structures.