Deterministic generation of multiple topological corner states based on an extremely expanded coupling condition

Abstract

Photonic higher-order topological insulators (HOTIs) based on kagome photonic crystals (PCs) possess rich physics of corner states for the unignorable long-range interactions. Theoretically, there should be multiple corner states, i.e., type I, antisymmetric type II, and symmetric type II corner states, in the kagome PCs. However, for the generation of some corner states, especially the symmetric type II corner states, it is necessary to obtain a large ratio of intercell coupling to intracell coupling, which makes the spacing between dielectric units very small and difficult to achieve experimentally. Here, we propose a scheme for the deterministic generation of multiple topological corner states based on an extremely expanded coupling condition. We construct an equilateral triangular cavity that consists of nontrivial unit cells in triangular PCs. All three topological corner states can exist robustly in the triangular cavity with large dielectric unit spacing. By establishing a tight-binding model for the nontrivial unit cell, we reveal that the extremely expanded coupling condition is the core physical mechanism for the deterministic generation of multiple corner states. The study provides a simple and deterministic method to generate multiple topological corner states, which has great potential in topological robust cavity, optical switches and lasers in integrated photonics on a silicon-on-insulator (SOI) or III-V active semiconductor platform.