Topological edge and corner states of valley photonic crystals with zipper-like boundary conditions

Abstract The properties and applications of topological edge states (TESs) and topological corner states (TCSs) have attracted extensive attention from researchers. In this paper, we present a stable valley photonic crystal (VPC) unit cell with C 3v symmetric quasi-ring-shaped dielectric columns and realize its topological phase transition by breaking mirror symmetry. Based on this unit cell structure, TESs and TCSs are realized in the article. We obtain a new type of wave transmission mode based on photonic crystal zipper-like boundaries and apply it to a beam splitter assembled from rectangular PCs. The constructed beam splitter structure is compact and possesses frequency separation functions. In addition, we construct a box-shaped triangular PC structures with zipper-like boundaries and discover TCSs phenomena in the corners, comparing its corner states with those formed by other boundaries. Based on this, we explore the regularities of the electric field patterns of TESs and TCSs, explain the connection between the characteristic frequencies and locality of TCSs, which helps better control photons and ensure low power consumption of the system.