Abstract Dirac point, the cornerstone of topological insulators, has been attracting ever-increasing attention due to its extraordinary properties. In this paper, a bottom-up topology optimization approach is established to systematically design the acoustic Dirac cones with customized double, triple and quadruple degeneracies at different wavelength scales. Using the proposed methodology, novel square-symmetric, chiral and orthogonal-symmetric sonic crystals (SCs) are constructed in a square lattice with tailored Dirac cones. The proposed design approach offers a unified framework to tailor SCs with exotic functionalities which are being widely researched in acoustic metamaterial community. As illustrative examples, zero-index acoustic cloaking and Talbot effect near the Dirac points of the optimized SCs are demonstrated numerically. Moreover, a novel acoustic pseudo-spin topological insulator is obtained, which entails a robust zigzag wave propagation and broadband, unidirectional, and topologically protected transport with a record-breaking relative bandwidth of 30.51%. The proposed design methodology shows promise and opens new horizons for customizing topological acoustics and conceiving high-efficiency wave devices.

中文翻译：

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通过拓扑优化定制方格中的声学狄拉克锥和拓扑绝缘体

摘要 狄拉克点是拓扑绝缘体的基石，因其非凡的特性而受到越来越多的关注。在本文中，建立了一种自底向上的拓扑优化方法，以系统地设计具有不同波长尺度下定制的双、三和四重简并的声学狄拉克锥。使用所提出的方法，新颖的方形对称、手性和正交对称声波晶体 (SC) 在具有定制狄拉克锥体的方形晶格中构建。所提出的设计方法提供了一个统一的框架来定制具有奇异功能的 SC，这些功能在声学超材料社区中得到了广泛的研究。作为说明性示例，在优化的 SC 的狄拉克点附近的零指数声学隐身和 Talbot 效应进行了数值演示。而且，获得了一种新的声学伪自旋拓扑绝缘体，它需要强大的锯齿波传播和宽带、单向和拓扑保护的传输，相对带宽达到创纪录的 30.51%。所提出的设计方法显示出前景，并为定制拓扑声学和构思高效波器件开辟了新的视野。