Second-order phononic and photonic topological insulators hosting topologically protected edge and corner states provide opportunities for the robust manipulation of elastic/acoustic and electromagnetic (EM) waves, respectively. Despite their potential, the development of second-order phoxonic topological insulators, which combine functionalities of second-order phononic and photonic topological insulators, remains largely unexplored. Herein, we design second-order phoxonic topological insulators (SPTI) with customized bandgaps. An inverse design approach is proposed to engineer phoxonic crystals (PCs) featuring customized odd-order phononic and photonic bandgaps simultaneously. Topological phase transition is induced by translating the primitive unit cell (UC) of the inverse-designed PC with half of the lattice constant horizontally and vertically. Thereafter, the SPTI is constructed by juxtaposing the primitive and translated UCs to form a corner between them. Multiple SPTIs, capable of manipulating both acoustic and EM waves, as well as those governing elastic and EM waves, are created. Our work paves the way for customized SPTIs with tailored bandgaps to support diverse phononic and photonic corner states. Meanwhile, the designed SPTIs also provide a platform to design the higher-order topological optomechanical devices.

中文翻译：

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定制带隙二阶辉声拓扑绝缘体的设计


具有拓扑保护的边缘和角态的二阶声子和光子拓扑绝缘体分别为弹性/声波和电磁（EM）波的鲁棒操纵提供了机会。尽管具有潜力，但结合了二阶声子和光子拓扑绝缘体功能的二阶声子拓扑绝缘体的开发在很大程度上仍未得到探索。在这里，我们设计了具有定制带隙的二阶磷光拓扑绝缘体（SPTI）。提出了一种逆向设计方法来同时设计具有定制的奇数阶声子和光子带隙的光子晶体（PC）。通过水平和垂直平移具有一半晶格常数的反设计 PC 的原始晶胞 (UC) 来诱导拓扑相变。此后，通过并置原始UC和翻译UC以在它们之间形成角来构建SPTI。创建了多个能够操纵声波和电磁波以及控制弹性波和电磁波的 SPTI。我们的工作为具有定制带隙的定制 SPTI 铺平了道路，以支持不同的声子和光子角态。同时，所设计的SPTI还为设计高阶拓扑光机器件提供了平台。