Research On The Tarnsmission Characteristics Of Topological Boundary States Based On Two-Dimensional Phttonic Crystals

In recent years,researchers have been inspired by topological electronics,and have a strong interest in topological photonics.By introducing the concept of topology,topological photonic crystals,as artificial microstructures,have emerged.Due to its unidirectional boundary transmission,defect immunity,and no backscattering characteristics,this structure has enormous application prospects in fields such as optical communication and quantum computing.This article designs three two-dimensional topological photonic crystal structures based on lattice symmetry.A systematic study was conducted on its band structure,topological phase transition mechanism,and topological boundary state characteristics through the k·p perturbation theory and finite element method.Finally,based on the pseudo spin properties of electromagnetic waves,the application of topological boundary states and valley topological boundary states in optical devices was achieved.The main research contents and innovations are as follows:（1）A fully dielectric photonic crystal structure is proposed based on the C₆ symmetry of the lattice.The double degenerate Dirac cone and topological phase transition are realized by simply rotating the isosceles triangle dielectric cylinder.Two structures with different topological properties were concatenated and simulated to verify the unidirectionality and robustness of boundary state spin locking.The current transmission efficiency of topological waveguides can reach over 97%.In addition,adjusting the transmission path of electromagnetic waves by changing the pseudo spin state can achieve functions such as "Ohm" shaped,"U" shaped,"straight" shaped,and "Z" shaped electromagnetic wave transmission and topological optical resonators.（2）A topological optical structure composed of high degree of freedom photonic crystals was proposed,which achieved multiple topological transitions by changing the relative dielectric constants of the inner and outer ring dielectric columns,compressing and stretching the dielectric columns,and changing the size of the dielectric columns.Based on the COMSOL Multiphysics finite element simulation software,the energy bands under different structural parameters were calculated,and the laws under three topological phase transition mechanisms were analyzed and summarized.Splicing photonic crystals with different topological phases to construct topological waveguides,verifying the properties of topological boundary states through numerical simulation,and calculating the transmission efficiency of the waveguides under each mechanism.Finally,a line defect is introduced into the waveguide,and the transmission efficiency of the waveguide can reach 98.8%.It is applied in the design of the beam splitter to achieve tunable topological boundary states,which also proves that the line defect has a mixed defect mode with topological protection.（3）A valley topology photonic crystal structure was designed to achieve unequal energy valleys in the optical momentum space by controlling the height of triangles in the honeycomb lattice.The boundary states in the structure are achieved by constructing Bearded type and Zigzag type domain walls,which are composed of two types of topological valley photonic crystals with the same bandwidth but different chiral states.Analyzing the band structure of transverse electromagnetic modes at high symmetry points under different asymmetric parameters,it was found that the band width increases with the enhancement of the degree of asymmetry in the structure.Three different defects were constructed in the waveguide to verify the robustness of the current system in the valley topology boundary state in the terahertz frequency domain.Based on this characteristic,a valley topology beam splitter has been designed,which has strong anti-interference ability,so electromagnetic waves have extremely strong stability when transmitted in the waveguide.The numerical analysis results indicate that the variation trend of transmission rate in the two output terminals is almost consistent,which means that electromagnetic waves can achieve equal power beam splitting within the operating frequency range.