Realization of multifunctional optical devices based on valley topological photonic crystals with triangular lattice

The emergence of valley Hall topological photonic crystals (VPCs) has driven advancements in the field of optical applications such as optical communication and optical computing. In this work, we propose valley photonic crystals with triangular lattice composed of silicon rods to achieve topological edge states (TESs) and topological corner states (TCSs), and investigate the influence of two different domain interfaces of bearded-shaped and zigzag-shaped between two VPCs with opposite valley Chern numbers on TESs and TCSs. TESs and TCSs obtained from different interfaces have different frequencies and the robustness of them to defects is demonstrated. A rhomboidal hybrid structure with various valley interfaces is designed to achieve the functions of frequency division, beam splitting and three-channel photonic router based on TESs. In addition, a rhomboidal hybrid VPC waveguide-cavity coupling system is proposed, which comprises a Y-shaped air waveguide and two triangular box-shaped cavities with different domain interfaces. Both 'AND gate' and 'OR gate' logic gate functionalities can be achieved in the same structure corresponding to different frequency ranges by the coupling of air waveguides and box-shaped cavities utilizing the strong localization of corner states. This work provides a new approach for integrated devices, particularly in the fields of integrated circuits and integrated photonic devices, based on triangular photonic crystals.