梦想照进现实：拓扑光子学推动集成光子器件的发展 近五十年来，大规模集成电路和光通信技术的持续突破催生了信息产业革命。然而随着晶体管尺寸逼近物理极限、铜电互连逼近带宽和功耗瓶颈，摩尔定律正逐渐失效。伴随着云计算、人工智能、5G/6G、数据中心等新兴技术的蓬勃发展，数据需求呈现爆炸式增长，需求和性能间的矛盾日益突出。如何延续摩尔定律已成为信息领域的核心问题。为此，将光子技术与微电子技术结合，实现 “以光代电，光电融合”，是提升计算架构并发规模、灵活度，降低功耗，使更多晶体管协同工作进而释放极致性能的重要发展方向。稳健性是集成光子器件的共性难题。当数量巨大的光子器件构成高度集成的片上光子系统，即“光子芯片”时，器件的稳健性决定了光子芯片整体的可靠性和制造成本。近年来，研究者们发现，稳健性与拓扑学这一基础理论紧密相连。将光子学与拓扑理论结合，催生了“拓扑光子学”这一光学新兴分支，或将为发展稳健的集成光子器件、推动大规模光电混合集成技术走向实用开辟新思路。拓扑学研究连续变化下的不变性质，用拓扑不变量描述。当某一物理效应仅依赖于拓扑不变量时，该效应受拓扑保护，因此具有扰动下的稳健性。2016年诺贝尔物理学奖被授予了“物质拓扑相变和拓扑相”工作，其揭示了拓扑机理在微观奇异世界中的关键作用，在拓宽基础研究视野的同时，为新材料、新器件和新应用指出了方向。拓扑光子学领域正在发生激动人心的进展。北京大学彭超副教授受邀在Photonics Research 2020年Topological Photonics and Beyond专题发表综述文章（Xuefan Yin, Chao Peng. Manipulating light radiation from a topological perspective[J]. Photonics Research, 2020, 8(11): 11000B25），并被选为该虚拟专题封面文章，从拓扑光子学发展背景、非厄米光子体系拓扑性质、以及拓扑光子辐射调控三个方面介绍了拓扑光子学与集成光子器件领域的最新进展。1. 拓扑光子学发展背景拓扑学原本是数学的一个分支。然而在研究量子霍尔效应研究时，人们惊奇地发现拓扑在物理上的重要意义： 分立的霍尔电导是一类拓扑不变量——TKNN不变量（即陈数）的体现。受此启发，研究者们在凝聚态物理体系中构造了各式各样的拓扑绝缘体，其共同特征是：体态波函数的几何性质可以用某一类拓扑不变量描述，而边界态和体态波函数则被 “体-边对应关系”约束。2008年，研究者证明，拓扑相是波动系统的普遍特征。之后，拓扑观点被用于描述各类物理波动系统，光子体系就是典型例子之一。作为量子体系的电磁对应物，光子体系具有易于调控的优点，从而成为研究和验证普遍拓扑规律的理想平台，拓扑光子学也应运而生。然而，与凝聚态体系相比，光子体系也具有自己独特的特征。特别是光子体系不可避免地存在损耗，这会导致光子的耗散和逃逸现象，因此大部分实际光子体系本质上是非厄米的，无法由经典的厄米拓扑理论来描述。2、非厄米光子体系中的拓扑性质由于光子耗散现象的存在，面向厄米体系定义的拓扑不变量、体边对应关系等在非厄米光子体系中“失效”，因此研究者们着力发展新的理论来诠释非厄米拓扑性质。此外，一些研究者专注于一种重要的能量交换形式，即光学辐射。他们提出，存在辐射泄漏的体系中存在一些特殊能态，如连续区束缚态（BIC）、奇异点（EP）等，其远场辐射具有特殊的几何性质，可以由一类新的拓扑不变量——拓扑荷来描述（如图1）。拓扑荷为光子器件辐射调控提供了一个全新的视角：人们可以通过观测远场辐射的几何性质，实现体系内拓扑性质的观测;也可以通过改变光学态辐射场的拓扑性质，实现光辐射的灵活调控。图1 (a)光子晶体辐射示意图 (b)动量空间远场辐射偏振示意图 (c)拓扑荷示意图3、拓扑光子辐射调控研究进展数值优化一直是光子器件设计的主要方法，但多参数扫描最优设计往往存在计算代价巨大，且容易陷入局部极值陷阱的缺点。 然而，拓扑视角关注连续变化下的全局观点，为器件优化提供了新范式，同时催生了许多新现象和新器件。研究人员提出，连续区束缚态对应辐射场的拓扑荷，因此可通过操纵拓扑荷在动量空间中的演化，来调控辐射通道的关闭和开启，实现灵活的辐射调控。在第一个实例中，研究人员通过合并多个拓扑荷，改变了布里渊区中心附近能态品质因子随波矢变化的渐进关系，从而可抑制工艺误差导致的随机散射。在第二个实例中，研究人员通过破缺光子晶体对称性，在器件一侧表面分裂再合并拓扑荷，进而关闭一侧辐射通道，由此构造了无需镜面的单侧辐射态（如图2）。图2 (a)动量空间中拓扑荷合并示意图 (b)拓扑荷合并后，附近谐振态品质因子依赖关系的变化 (c)单面拓扑荷的构造示意图 (d),(e)单向辐射导模共振态模场及品质因子示意图除了操控辐射通道的开启与关闭，辐射本身性质如波前的偏振和偏振等，也可以通过拓扑荷来进行调控。例如，研究人员通过调制光子晶体增益分布，实现了拓扑荷的湮灭与恢复，成功构造了集成的片上涡旋光激光器，可支持涡旋光束与线偏振光束间的可控快速切换，切换速度达到1~1.5 ps量级（如图3）。图3 (a)微激光器出射光波前与增益分布的关系 (b)通过调制增益分布，实现了涡旋出射光与线偏光的动态切换4. 总结和展望拓扑光子学是一个充满生命力的年轻领域，各种拓扑新机理、新效应的发现，揭示了拓扑规律背后深刻的内涵。将拓扑观点引入光子集成领域中，将进一步推动光子器件稳健性的提升、新调控维度的开辟以及光子芯片的成熟应用。 Topological photonics and on-chip photonic integration Photonics integration is a burgeoning field from both academic and industrial points of view because of its great potentials in aggregating photonic technology with high-performance integrated circuits that may revolutionarily change the architecture of computing. However, many photonics integration platforms suffer from huge challenges in robustness, which make device fabrication, assembling and packaging not compatible with massive production and large-scale integration. To this end, topological concepts are applied and successfully clarified many extraordinary phenomena and further promoted the performance of many devices, as a result, spawn a new branch of modern optics – topological photonics.Topology deals with conserved quantities that do not change when the system is continuously deformed. Topological ideas are applied in designing and optimizing a series of optoelectronic system. As a specific example of radiation manipulation, researchers studied the non-Hermitian photonic systems from the viewpoint of topology, and found out that several special energy states can be depicted by a class of topological invariants – topological charges. Further, researchers investigated the physics behind it, and proposed topological methodology to manipulate radiation characteristics that give rise to many novel optoelectronic applications, such as photonic crystal microcavity with ultra-high Q factors, guided resonances with unidirectional radiation, and vortex beam generator with ultra-fast switching time. These progresses show that, topology is not only mathematical convenience, but also reality in physics and will boost the applications of photonics integration in many aspects.The invited review article published in Photonics Research, Vol. 8, No. 11, 2020 (Xuefan Yin, Chao Peng. Manipulating light radiation from a topological perspective[J]. Photonics Research, 2020, 8(11): 11000B25)，which was chosen as On the Cover of Topological Photonics and Beyond , provides a comprehensive overview on the milestones as well as the latest progresses in the field of photonic devices based on topological concepts, particularly for radiation manipulation.1. Background of topological photonicsAs a branch of mathematics, topology engages in physics during the discovery of integer quantum Hall effect (IQHE). In this case, quantized Hall conductance was found to be the consequence of a class of topological invariant—TKNN invariant. IQHE as well as the topological invariants boosted the emergence of topological insulators in condensed matter. In these systems, the geometric properties of bulk wave functions can be described by a certain type of topological invariant, while the relationship between edge states and bulk bands is constrained by so-called bulk-boundary-correspondence accordingly.In 2008, researchers proved that topological phases of matter are ubiquitous in a wide range of wave systems. After, topological ideas were expanded to various wave systems, in particular, the photonic system. As a classical counterpart of quantum systems, photonic systems enjoy the benefits of flexibility and diversity, thus become an ideal platform for explore topological ideas and principle. Therefore, topological photonics was born.However, compared to electron in condensed matter, there are some unique characteristics of photon. Most importantly, photons are non-conserved particles with finite lifetime in most realistic photonic devices, subjecting to a variety of non-equilibrium processes. It indicates that most photonic systems are non-Hermitian in nature. As a result, conventional topological theory that is developed for Hermitian system needs to be revisited.2. Topology in non-Hermitian photonic systemsSince photons escaping is inevitable in realistic devices, non-Hermitian photonic systems and the topology in them has been hot spotted. The researchers are devoted in finding new topological invariants and the bulk-boundary correspondence to depict non-Hermitian systems. On the other hand, the radiation had been paid particular attention since it is a major source for photonic devices exchanging energy with the surroundings. Some unique photonic states have been discovered, such as bound states in continuum (BICs), exceptional points (EPs) and etc., which connect to the topology of radiation field and being described by topological charges. Such concept reveals new perspectives of investigating non-Hermitian photonic systems: we can observe the geometric characteristics of radiation field to probe and explore the intrinsic topological phases underlying, or manipulate the radiation for practical usage through tuning the topological charges.Fig. 1 (a) Schematic of radiation from photonic crystal slab. (b) Polarization vortex in momentum space. (c) Schematic of topological charges3. Research progresses in radiation manipulation from topological conceptsFor a long time, numerical optimization is a well-established method in photonic device design, however, it usually suffers from the huge computation cost and the risk of falling into local optima. Topological optimization provides a new and complementary method since it offers a global picture for optimization. For instance, because the BICs correspond to integer topological charges in radiation field that imply zero radiation, it is reasonable to manipulate the evolution of topological charges in momentum space to flexibly close and open radiation channels as will, and achieve desired radiation behaviors.In the first example, researchers merge multiple topological charges towards Brillouin zone center, thus modify the scaling rule of quality factors that make the resonances nearby robust to random scatterings. In the second example, researchers break the symmetries of photonic crystal, which splits and restores the topological charge at a single side of the device, eventually construct a class of unidirectional radiative resonance without mirror on the other side.Fig. 2 (a) Topological charges evolution for merging BICs. (b) Scaling rules of quality factors for isolated BICs and merging BICs. (c) Topological charges evolution for Unidirectional Guided Resonances (UGRs). (d) Profile of electric field component of UGR. (e) Experimental and simulated results of downward quality factors around UGR.In addition to open and close radiation channels, other merits of light wave fronts, such as polarization and phase can also be tailored from topological charges. For example, researchers annihilate and restore the topological charge by modulating the gain profile, and successfully demonstrate an on-chip vortex micro-laser that support ultra-fast switching between vortex beam and linearly polarized beam dynamically, in a switching time as short as 1~1.5ps.Fig.3 (a) Dynamic control of output beam based on manipulating the optical gain profile. (b) Top: Transition from a donut beam to a linearly-polarized beam. Bottom: Transition from a donut beam to two-lobe beam and back within picosecond-scale transition time.4. Summary and outlookAs a young and burgeoning field of photonic research, topological photonics is experiencing exciting progress and breakthroughs, and leading to new devices and application in photonics. Topology is not just abstract mathematical theory but reality in physics. We are expecting the findings from topological concepts could broaden the horizon of science, and boost many applications in photonic integration, quantum computing and others.