二维Stampfli-Triangle光子晶体的拓扑角态及其性能与机理研究

高阶拓扑绝缘体的拓扑角态为光学成像、光子局域及控制光波导传输等应用提供了新思路。然而，拓扑角态的频率、强度、位置及其机理尚待研究。其频率的改变可实现多频微腔局域态，其强度的增强可提高微腔的品质因数，其位置的改变可影响局域态的分布，即性能及其机理研究将对提高波导与微腔的耦合效率、增强微腔非线性光学效应及实现高灵敏传感器与高Q值及高功率激光器具有重要意义。本项目拟推导具有高对称度及丰富散射子排布方式的二维Stampfli-Triangle光子晶体的哈密顿量并解释其能带反转产生拓扑非平庸态的原因，研究拓扑角态及其频率与光子晶体能带结构及结构参数的定性关系，且构建非厄米系统研究其强度、位置与光子晶体材料及结构参数的定性及定量关系，并理论揭示及实验验证其机理。本项目的研究结果将为Stampfli型光子准晶实现拓扑角态及其性能分析与器件应用提供理论依据，且对丰富人工带隙材料的拓扑理论具有重要价值。

Topological corner states in higher-order topological insulators have provided new ideas for the applications including optical imaging, photonic localization and controlling optical waveguide transmission, etc. However, the frequency, intensity, position of topological corner states and their mechanisms have not yet been investigated. The variation of the frequency of the topological corner states can achieve the multi-frequency microcavity localized state, and the enhancement of the intensity of the topological corner states can increase the quality factor of the microcavity and the variation of the position of topological corner states can affect the distribution of localized state. That is, the investigation on the properties and their mechanisms will be of important significance to improve the coupling efficiency between the waveguide and the microcavity, enhance the nonlinear optical effect of microcavity and realize sensor with high sensitivity and laser with high-Q value and high power. In this project, the Hamiltonian of the two-dimensional Stampfli-Triangle photonic crystal (2D S-T PC) with high symmetry degree and rich scatterers arrangement style will be deduced, and the reason for band inversion to generate topological nontrivial state will be explained. The topological corner states and the qualitative relations between the frequencies of the topological corner states and the band structure and structural parameters of the PC will be investigated. Moreover, the qualitative and quantitative relations between the intensity and the position of topological corner states and the material and structural parameters of the PC will be investigated by constructing non-Hermitian system. The mechanisms of the above phenomena will be revealed theoretically and be verified experimentally. The investigation results of this project will provide theoretical basis for investigation on the realization of topological corner states and their property analysis and device application of Stampfli-type photonic quasi-crystal, and will have important value for enriching the topological theory of artificial bandgap materials.