Two types of corner states in two-dimensional photonic topological insulators

Higher-order topological insulators, which go beyond the conventional bulk-boundary correspondence, have become a hot research topic in recent years. In this paper, we propose a two dimensional second-order topological photonic crystal based on a C4 symmetric lattice. By tuning the distance between the dielectric cylinders, the topological phase transition of the structure is realized, one edge state and two types of corner states (one topological and one trivial corner state) are found. Our findings provide an evolution of bulk–corner–edge–corner–bulk in a hierarchy of dimensions, which enriches the study of corner states in photonic systems. Besides, we distinguish two corner states by discussing robustness and mode area, and we verify the topological corner state can be embedded in the bulk states, forming a bound state in continuum by simulation.