Floquet光子体系中含时拓扑模的研究

Topological photonics is a rapidly-emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. However the traditional photonics edge mode in the topological insulators is passive mode, recent research shows that the introduction of periodic-driving Floquet photonics topological insulators can realize active control, and periodically driven approach can achieve large number of Chern number corresponding to more topologic modes. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realise exotic topological models and to probe and exploit topological effects in new ways. Periodically-driven topological phases have attracted considerable attentions in condensed matters, but experimental demonstration of such driven quantum systems with engineered topological phases remains a great challenge. In this proposal, a photonic Floquet simulator (PFS) was designed and systematically investigated to study engineered topological phases in a periodically-driven Su-Schrieffer-Heeger model. The PFS was composed of an ultra-thin coupled microwave waveguide array with periodically-bending profiles, and was thoroughly tested the quantum transition from the adiabatic limit (slow-driving) to the high-frequency limit (fast-driving), and then, extend to design the integrated photonics devices. The results of the project will provides strong theoretical support for the new photonic diode, anti-electromagnetic signal crosstalk and Chern number measuring devices.

拓扑光子学为类比满足拓扑绝缘体中非平庸能带色散关系而设计格点模型和材料排布以获得人为地控制光场的传播，为光场调控提供了新颖途径。它是基于静态拓扑绝缘体展开的被动调控研究，研究表明引入周期性驱动的Floquet光子拓扑绝缘体可实现驱动型非平庸的主动调控，该方法可实现丰富特征的准能带以得到更多的拓扑模式。本项目拟引入周期性驱动调制开展受时间驱动拓扑模式的研究，对SSH拓扑模型施加周期调制的改进，研究包含驱动频率和规范特征的Floquet拓扑量子体系，采用周期性弯曲伪表面等离激元的Floquet波导阵列开展反常拓扑π模的实验研究。本项目将解决不同驱动频率的准能带分析和拓扑不变量的计算、反常拓扑π模的激发、反常拓扑相的驱动频率及Floquet规范的关联、有限尺寸效应下拓扑相的非绝热消去工程应用四个关键科学问题。项目结果将为新型光子二极管、抗电磁信号串扰器和陈数测量器等集成器件提供有力的理论支持。

受凝聚态领域蓬勃发展的拓扑绝缘体的启发，光子拓扑态是过去十年来人工微结构光场调控领域的研究焦点之一。光在微纳尺寸集成波导上传输时不可避免地遇到大角度弯曲、加工精度限制所造成的缺陷和无序等将被强烈散射，引发严重的散射损耗问题，从而影响到光子传输的整体性能。项目在弯曲波导阵列中探索模式局域传播的机理，首先构建Floquet哈密顿量用于描述周期性弯曲波导阵列，其次在理论上求解Floquet哈密顿量的准能带关系，最后基于Floquet拓扑绝缘体理论发展多种新型集成光子学器件。已发表学术论文11篇、EI会议论文4篇和授权发明专利1项，重要研究成果包括Nature Communications、Physical Review Letters、Physical Review B、Science Bulletin和Nanophotonics。以亥姆霍兹方程求解该光子体系的能谱，首次发现非傍轴导致该边缘态的电磁场在传播过程中被散射至体态模而不能在另一边界上复现边缘态。研究成果发表在Nat. Commun. 13, 249 (2022)，首次揭示非傍轴对能谱施加挤压和拉伸的作用，以非傍轴为微波频段波导阵列的拓扑物理研究赋能使其具有独特性；以含时薛定谔方程完美地描述周期性弯曲的波导阵列结构，调节驱动频率从绝热增加至高频，在驱动周期与禁带宽度比值ω/Δ处于区间[1/3,1]将出现一类特殊的受驱动周期依赖的局域Floquet π模，研究成果发表在Phys. Rev. Lett. 122, 173901 (2019)；研究在拓扑光子体系中非傍轴、拓扑输运、朗道-齐纳跃迁三者之间的相互作用，申请人采取理论解析和数值计算相结合的方法，在微波波段设计出非傍轴拓扑波导阵列。实验结果表明，非傍轴效应导致缩小的带隙，边界态激发实现朗道-齐纳跃迁过程，研究成果发表在 Phys. Rev. B 106, 174301 (2022)；申请人在实验上选择“C”字形和矩形超构表面用于补偿色散引起的相位偏差，同时选择与传输相位机制无关的几何相位来匹配初始频率的相位分布，最终在太赫兹频段实现了0.3THz至0.8THz的连续宽带消色差透镜和消色差艾里光束，成果分别发表在Sci. Bull. 64, 1525–1531(2019)和Nanophotonics 10, 1123–1131 (2021)。