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 provide a numerical example that supports the validity of the homogenization method, and we then perform optimization calculations based on the waveguide settings of the acoustic metasurfaces. In addition, we discuss the mechanism of the obtained optimized structures.

在本文中，我们提出了一种基于水平集的拓扑优化方法，通过使用两尺度均质化方法进行声学超表面的单元设计。基于先前的工作，我们首先提出了一种可以与拓扑优化相结合的声学超表面均质化方法。在这种方法中，在宏观问题中出现了取决于超表面单位单元的非局部传输条件。接下来，我们在基于水平集的拓扑优化方法的框架内制定优化问题，其中目标函数表示为通过均质化获得的宏观响应，并将晶胞中的材料分布设置为设计变量。基于拓扑导数的概念进行敏感性分析。为了证实所提出方法的有效性，提供了二维数值例子。首先，我们提供了一个支持均质化方法有效性的数值例子，然后我们根据声学超表面的波导设置进行优化计算。此外，我们讨论了获得的优化结构的机制。