Hybird Coupling Of Two-dimensional Photonic Crystal Topological Edge States And Waveguide Modes

Photonic crystals are periodic artificial materials that are favored in optical communication applications due to their photon locality and photon band gap properties.Constructing photonic crystal waveguides by introducing defects can effectively control the transmission path of light waves,but the drawbacks of traditional photonic crystal waveguides are quite obvious-serious scattering in non-transmission directions and low transmission efficiency at corners.With the concept of topology introduced into photonics,the design of topological photonic crystals quietly emerged.Topological photonic crystals have unique one-way locking properties in controlling the transmission of light waves and are protected by topological boundary modes.They also have good robustness to defects on the transmission path,which enables them to maintain high efficiency even in situations with long paths and many defects,providing a good design idea for scientists in efficient control of light wave transmission methods.In order to achieve strong topological edge state locality,this paper first constructs a two-dimensional photonic crystal topological structure with a wide band gap by scaling,and introduces defects on its structural boundary to form a coexistence of defect states and topological edge states.The changes in photonic locality effects under the influence of defects are analyzed,and then a transmission channel with a waveguide-coupled cavity is further constructed.Combining the one-way transmission property,the potential optical transmission path is analyzed,providing a feasible approach for constructing topological photonic crystal waveguides and coupled cavity models with strong localization effects.Secondly,based on the Valley Hall Effect,this paper breaks the degeneracy of the photonic crystal at the K point by rotating the lattice,thereby obtaining a wider photonic band gap.The Berry curvature,topological invariant,and phase distribution at the K point of the rotated lattice are analyzed to demonstrate the different topological properties of the two lattices,which can lead to valley topological boundary states at their edges.Based on this,a nested loop model is constructed,which can achieve energy transfer between loops without the need for introducing defects.The main principle of this model is the theory of vanishing coupling between fields,and each loop has its own resonant frequency.With different frequency and position of the light source,the resonant modes of single or multiple loops can be selectively excited,enabling control of the transmission path.Finally,regarding the SSH model in the current topological photonic crystal models,most of the research focuses on obtaining corner states and their related applications,but it is difficult to establish the application of photonic crystal waveguides solely based on the characteristics of the topological SSH model.Therefore,this paper aims to construct topological photonic crystal waveguides,and deeply optimizes the topological SSH model to expand its actual working bandwidth of topological boundary states,and designs corresponding waveguide microcavities for verification.The results show that after introducing defects,the originally poor photon localization effect has been significantly improved,providing a method for solving the working bandwidth problem of topological photonic crystal waveguides.In summary,this paper provides a reliable design approach for obtaining the widest range and best transmission performance of topological edge states in various photonic crystal structures and combining them with the characteristics of waveguide modes.