Second-order topological phases in <i>C</i> _4<i>v</i>-symmetric photonic crystals beyond the two-dimensional Su-Schrieffer–Heeger model

Abstract Second-order photonic topological insulators (SPTIs) with topologically protected corner states provide a unique platform for realizing the robust manipulation of light in lower dimensions. Previous SPTIs proposed in C 4 v -symmetric lattices are mainly based on the two-dimensional (2D) Su-Schrieffer–Heeger (SSH) model consisting of an even number of sites in the unit cell. Moreover, second-order topological phases within high-order band gaps are rarely explored. Here, we propose a new principle of SPTIs beyond the 2D SSH model, which is realized in C 4v -symmetric lattices consisting of an odd number of sites in the unit cell. The midgap-gap-ratios of these odd-order band gaps, from the first-order to the nineteenth-order with step of two-order, are maximized by the method of topology optimization. Second-order topological phases are successfully created within these sizeable band gaps and highly localized corner states are observed. Our work offers a new route for exploring high-order topological states in photonics and other classical systems.