Nonlinear control of topological corner and edge states in a loop resonator

The modulation and transformation of topological states play a crucial role in controlling light transport in optical communication system. Herein, we construct a Su-Schrieffer-Heeger (SSH) lattice beyond the linear optical regime. The SSH model has resulted in the topological edge states (TESs) and the topological corner states (TCSs). It is demonstrated that the second-harmonic generation (SHG) and third-harmonic generation (THG) can occur in a topological edge loop based on the frequency matching in all-dielectric photonic crystals. Different from previous studies in which the excitation of TESs and TCSs is achieved through the selection of frequencies, in this paper the excitation of TESs and TCSs has been achieved through the harmonic generations with different orders. More importantly, there is a transformation from the trapping of optical signal on the TCS to the releasing of optical signal on the TES. The mode transformation between TESs and TCSs has important applications in optical flow control, optical signal storing and releasing.