Design of second-order phoxonic topological insulators with customized bandgaps

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.