This paper proposes a level set-based topology optimization method for acoustic metasurfaces consisting of multiple types of unit cells. As a type of acoustic metasurface, we focus on a two-layered metasurface, where each layer contains various types of unit cell designs. To handle this metasurface, we first propose a two-scale homogenization method based on previous studies targeting metasurfaces composed of a single type of unit cell structure. As a result of homogenization, each layer of the array of unit cells is replaced with an interface with a nonlocal transmission condition. Next, an optimization problem is formulated. We set an objective function to achieve negative refraction, and macroscopic responses obtained by the homogenization method are used to define the objective function. The material distributions in each unit cell of the metasurface are set as the design variables. Based on these settings, we perform a sensitivity analysis based on the concept of the topological derivative. A level set-based topology optimization method is introduced to solve the optimization problem, and two-dimensional numerical examples are provided to demonstrate the validity of the proposed method. An optimal design of a two-layered acoustic metasurface that induces negative refraction is proposed, and a discussion of its mechanism is provided.

本文提出了一种基于水平集的拓扑优化方法，用于由多种类型的单位单元组成的声学超表面。作为一种声学超表面，我们专注于两层超表面，其中每一层都包含各种类型的单元设计。为了处理这种超表面，我们首先提出了一种基于先前针对由单一类型的晶胞结构组成的超表面的研究的两尺度均质化方法。作为均质化的结果，单位单元阵列的每一层都被具有非局部传输条件的界面所替代。接下来，制定优化问题。我们设置了一个目标函数来实现负折射，并使用均质化方法获得的宏观响应来定义目标函数。超表面的每个晶胞中的材料分布被设置为设计变量。基于这些设置，我们基于拓扑导数的概念进行敏感性分析。引入基于水平集的拓扑优化方法求解优化问题，并通过二维数值算例验证了该方法的有效性。提出了一种引起负折射的两层声学超表面的优化设计，并讨论了其机制。并提供了二维数值例子来证明所提出方法的有效性。提出了一种引起负折射的两层声学超表面的优化设计，并讨论了其机制。并提供了二维数值例子来证明所提出方法的有效性。提出了一种引起负折射的两层声学超表面的优化设计，并讨论了其机制。