Propagation Characteristics And Applications Of Unidirectional Edge States Of Topological Photonic Crystals

The topological insulator realized by the quantum Hall effect opened a new chapter in the field of condensed matter physics.In particular,the topologically protected photonic crystal system has become the focus of research by many researchers due to its higher degree of freedom and unique properties of immunity to defects.This paper mainly studies the light-based quantum spin Hall effect,which constructs pseudo-spin states by adjusting the symmetry of the crystal lattice to realize the unidirectional transmission of electromagnetic waves in photonic crystals.An elliptical dielectric cylinder is used to construct a sandwich photonic crystal capable of spin coupling.The structure still maintains a stable unidirectional transmission under the air line defect.Using the anisotropy of liquid crystal materials,a large-bandwidth,adjustable-frequency optical waveguide device was designed.The main research contents are as follows:(1)A photonic crystal unidirectional transmission structure is designed based on the graphene-likeC₆ honeycomb structure.The pseudo-spin state is constructed by adjusting the ratio of graphene-likeC₆ lattice unit cells,and the topological boundary state in the TM mode is realized under the premise that the symmetry of the time reversal is not broken.The double degenerate Dirac cone at point(38)in the first Brillouin zone was opened,and phenomena such as mode inversion and topological phase transition appeared.The dispersion band gap of the model is calculated,and the topologically protected unidirectional spiral boundary state is obtained.Through the excitation of the harmonic source with orbital angular momentum,the one-way transmission of optical flow along the trivial-nontrivial interface is realized.It is verified that in the case of point defects and corners,the topological boundary state of the structure still maintains strong robustness.(2)Two types of air-line defect photonic crystal structures are constructed by using elliptical dielectric cylinders:the"trivial-nontrivial"type and the"trivial-nontrivial-trivial"type of sandwich photonic crystal defect structures.By removing a certain column of photonic crystal structures in the nontrivial sequence,three types of photonic crystal line defect structures were produced.Use the excitation of the resonance source to explore the transfer characteristics of the boundary state of the defect structure.It is verified that under the condition of breaking the symmetry ofC₆,the"trivial-nontrivial"air defect structure has a greater impact on the light transmission process,and cannot perfectly support the unidirectional light transmission in the structure.The"trivial-non-trivial-trivial"type of sandwich photonic crystal defect structure due to the similar properties of the two boundary states,the same spin direction,mutual coupling,and strong robustness,guarantees the light-in-air line defect structure It maintains stable unidirectional transmission characteristics,and its defect mode not only satisfies the"spin-mixing"defect of generating the topological boundary state,but also guarantees the"zig-zag"boundary that supports the forward movement of the spiral boundary state.(3)In order to dynamically control the transmission characteristics of the topological photonic crystal under high-speed operation,realize the free switching of the structural frequency band,and solve the problem of the narrow working bandwidth of the sandwich photonic crystal.It is proposed to use E7 liquid crystal as the background material of the interlayer photonic crystal to realize the dynamic conversion of the working frequency band of the photonic crystal.The simulation found that under different background refractive indexes,the optical flow is constrained to transmit in a single line in a non-banal area.The Poynting vector of the structure is calculated and the normalized vector of the spatial field and the transmission efficiency are measured.It is verified that in the case of disorder and defect,the unidirectional spiral boundary state has strong stability protected by the topology.Finally,it is proposed to inject liquid crystal material into the non-banal area to increase the working frequency band of the structure.