Two types of corner states in two dimensional photonic crystals with finite sizes

Abstract

Using two-dimensional (2D) square lattice photonic crystals (PCs) with different topological properties, we design different combined structures to construct two types of topological corner states (CSs), named as Type I and Type II CSs. Then by tuning sizes of inner PCs in the combined structures, we systematically investigate size effects on the two types of CSs. Numerical results demonstrate as the structures decrease to their critical sizes, due to the interactions of opposite interfaces and the couplings of corners, size changes of inner PCs in the combined structures have significant effects on the frequencies, degeneracies and mode field distributions of the two types of CSs. Moreover, Type I CSs peform better topological stability than Type II CSs during the size changes of structures. We also monitor mode field localizations of the two types of CSs and reveal that their localizations are only related to the types of the CSs, and have no relations to sizes and overall symmetries of the combined structures. Our research enriches the study of higher order topological CSs and paves the way for design and manufacture of optical micro-nano devices with photonic topological CSs.