A Review: Topological Photonic States in Artificial Microstructures
Schematic diagram of two-dimensional topological optical waveguide.
Topology is an important branch of mathematics formed in the 19th century. It studies the invariant properties of geometric figures or space under continuous deformation. The idea of topological physics originated from the exciting discovery of the integer quantum Hall effect (IQHE) in condensed-state physics. Klitzing found that the two-dimensional (2D) electron gas in a strong perpendicular magnetic field has a quantized Hall conductance. The quantization originates from the non-trivial topology of the energy band structure, which is characterized by the Chern number according to the theoretical work of Thouless, Kohmoto, Nightingale, and den Nijs (TKNN). Haldane and Raghu creatively introduced the concept of topology to photonic crystals for the first time, as they proposed a photonics analogue of the quantum Hall effect in photonic crystals. Edge states appear at the domain wall between materials that have different Chern numbers and go through the topological bandgap in momentum space according to the bulk-edge correspondence.
Photonic systems as bosonic systems, have unique advantages to the electric systems. The entire spectrum of topological materials can be exploited because the Fermi levels are substituted with frequency in photonic systems, which means the equi-frequency contour of bulk and surface states in topological semimetals can be tuned by the frequency. The easier fabrication also allows the delicate design of the interface, edge, and corner, which greatly facilitates the study of topological states and their application in on-chip integration systems.
The research group led by Prof. Shuqi Chen from Nankai University introduce the topological photonic states in artificial microstructures in a review published in Chinese Optical Letters, Volume 19, No. 5, 2021 (Hui Liu, et al., Topological Photonic States in Artificial Microstructures). They introduce two types of topological gapped phases in photonics system caused by integer quantum Hall effect and quantum spin Hall effect, and topological gapless phases, including Weyl points, 3D Dirac points, and nodal structure in 3D photonic semimetals. At last, they introduce the recent progress in higher-order phases that rise beyond the conventional bulk–boundary correspondence. By presenting the theories and properties of the three topological phases in photonics system, they reviewed the development of topological photonics, and showed the recent hotspots of topological photonics research.
Topological-protected modes are immune to defects and backscattering, showing ideal transport property that achieve lossless transmission of light. Topological-protected wave manipulation may lead to radical changes in integrated optical devices, which indicates a bright future for real applications in topological photonics. The most straightforward applications exploit the topologically protected unidirectional edge states as robust optical delay lines or isolators. The topological phenomenon can be used in the development of lasers, amplifiers, and light sources to improve their performance. The robust transport of photons also boosts the development of photonic topological quantum information processing and quantum computing. Although the practical application of topological photonic devices is still a challenge, such as the limitation of manufacturing process and the properties of optical materials, the excellent properties of topological photons will ensure their future application potential.
综述：人工微结构中的拓扑光子态
拓扑形变示意图（图片来自网络）
南开大学陈树琪教授课题组在Chinese Optics Letters 2021年第19卷第5期(Hui Liu, et al., Topological Photonic States in Artificial Microstructures)发表的综述介绍了人工微结构中的拓扑光子态, 梳理了光子整数量子霍尔效应、光子量子自旋霍尔效应、拓扑半金属和高阶拓扑光子晶体的领域发展和最新前沿。
背景介绍
拓扑学是十九世纪数学领域形成的的一个重要分支，主要研究几何图形或空间在连续形变下的不变性质，它进入物理学领域后，最早被用来描述物质中电子的运动规律。凝聚态物理中整数量子霍尔效应的惊人发现赋予了拓扑学全新的物理意义，由此拓扑物理学作为一个新兴的领域得到了人们的广泛关注。
二维拓扑光波导示意图
拓扑光子态的产生和发展
1980年，Klitzing发现在强垂直磁场中的二维电子气体具有量子化的霍尔电导，后来Thouless等意识到量子化的霍尔电导来源于能带的非平庸拓扑性质，其拓扑不变量以第一陈数来表征。意识到拓扑的概念广泛存在于波动系统后，Haldane和Raghu首次创造性地将拓扑的概念引入光子晶体。他们利用磁光材料打破时间反演对称性，在二维光子晶体中构造出了陈数非零的拓扑绝缘体，得到了拓扑保护的边界态。
随着拓扑物理研究的深入，电子系统由于能带结构复杂难以得到干净的带隙，材料缺陷和杂质难以控制和拓扑描述所需的单电子近似失效等问题，研究人员逐渐将目光投往其他经典系统中。光学系统作为经典的玻色子系统，具有能带相对干净、样品设计简单和样品制作精度较高等优势，逐渐成为拓扑物理研究的重要平台，由此催生了光学领域许多新的研究方向。更低的制造难度使界面、边缘和角的精细设计成为可能，极大地促进了拓扑态的研究及其在片上集成系统中的应用。
南开大学陈树琪教授课题组综述了光学系统的两种拓扑有能隙相、整数量子霍尔效应和量子自旋霍尔效应，以及拓扑无能隙相，包括三维光子半金属、外尔点、三维狄拉克点和节点结构。还介绍了突破传统的体边界对应原则的高阶拓扑相近年来的研究进展。通过介绍光子系统中三种拓扑相的构造方法、理论和性质，梳理了拓扑光子学的发展脉络，并展示了目前拓扑光子学研究的前沿热点。
三维光子拓扑绝缘体示意图
前沿展望
拓扑保护波是一种前所未有的理想传输特性，它不受缺陷和背散射的影响，能够实现光的无损传输。拓扑保护的光波也许能给集成光学器件带来彻底的变革，在拓扑光子学中具有广阔的应用前景。最直接的应用是利用拓扑保护的单向边缘状态作为鲁棒的光学延迟线或隔离器。这种拓扑现象可以用于开发激光器、放大器和光源，以提高它们的性能。光子的鲁棒传输也促进了光子拓扑量子信息处理和量子计算的发展。尽管拓扑光子学的应用仍面临很大的挑战，比如制造工艺有限和光学材料特性的限制等，但是拓扑光子的优异性质将确保其在未来的应用潜力。