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文章来源：FUTURE | 远见
近日，南京大学王漱明团队以「Chip-scale metaphotonic singularities: topological, dynamical, and practical aspects」¹为题在Chip上发表长篇综述论文，对光子奇点在各种物理学科下的表现形式进行了总结，围绕拓扑、动态及应用方向对已有研究成果和未来发展方向做出了展望。共同第一作者为李添悦和刘梦蛟，通讯作者为王漱明、蔡定平、祝世宁和王振林。香港城市大学王书波教授亦对本文有重要贡献。Chip是全球唯一聚焦芯片类研究的综合性国际期刊，是入选了国家高起点新刊计划的「三类高质量论文」期刊之一。
奇点指的是在特定点上，常规法则失效的情况，如黑洞中心或物质相变时，属性可能变得无法定义。这一概念源自数学领域，后广泛应用于物理学，特别是在光学物理中，奇点的存在使研究新奇现象成为可能，并推动了技术的应用发展。文章对各种光子奇点进行了综述，将它们分类为实空间、动量空间以及其他参数空间的奇点，如图1所示。包括偏振奇点、相位奇点、无极子奇点；BIC诱导的奇点、Dirac点和Weyl点以及异常点等，从拓扑特性、动态演化和应用潜力三个方面探讨了它们的研究价值。
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通常来说，对奇点周围的封闭路径进行积分，会得到一个体系的拓扑不变量，可用来描述奇点的拓扑特性。文章中在介绍每一种奇点的同时，对其拓扑特性及拓扑荷数的定义做出了介绍。接下来，作者们还介绍了在微纳光子学中如何构造奇点现象。对于远场奇点，涡旋光场所携带的轨道角动量及其衍生产物被广泛研究，如光学莫比乌斯带、斯格明子等，这要求对相位梯度超构表面进行特殊设计；如若获得动量空间中的奇点，则需设计周期性光学晶格，如Dirac超构表面等。
图2为起点的动态演化特征。有些奇点在传播过程或绝热变换中的拓扑特性是守恒的，也就是说，局部的属性有可能会改变，但全局仍然不变，如自旋-轨道转换过程中的角动量守恒2,3、BIC诱导的偏振奇点的分裂与合并4。
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图2 | 奇异点的动态演化。a，多维超构表面的各向异性超原子。由各向异性元原子组成的超表面（上图），显示了入射光在不同偏振状态下可能的出射偏振响应。J-板和两种TAM板（下图）。b，蜂窝光子晶体及其单元胞满足C₆对称支持量子自旋霍尔效应（上图），自旋动量锁定拓扑特征（下图）。c，谷-霍尔晶格及其相关的谷霍尔晶格。d，单金属散射体和多金属散射体的c线和v线奇异动力学。e，通过调整参数将偶发BIC合并为对称保护BIC，从而形成MBIC。f，FW-BIC与偶发BIC的合并。g，不同方向环绕奇异点的轨迹（上侧）和不同波导模式之间的不对称切换示意图，以及上述奇异点环绕（下侧）的投影。h，通过调整通道波导的核心宽度w₂和隧道势垒宽度分布g₂来动态环绕奇异点，从而实现宽带宽拓扑时间不对称的硅波导结构设计。i，全偏振器示意图，相反的操作产生互补的偏振本征态。j，能够同时发射两种不同模式的单横模环绕奇异点激光器的示意图，每种模式都来自不同的面。k，基于反PT对称体系中环绕奇异点的传统偏振器与手性偏振器的比较，对于后者，任意输入偏振态在正向（反向）传播时，输出偏振态将旋转到垂直（水平）方向。
在应用方面，文章从片上光学路由、激光和传感、光学微操控和光力学、集成成像和显示三个方面对光学奇点所衍生的应用做出介绍，展现了光学奇点在微纳光学中重要的物理思想和强大的应用潜力。图3所示为基于超构光子学奇点的光子拓扑器件，图4则为超构光子奇点赋能的光学微操控研究5。
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图3 | 超构光子奇点的片上应用。a，为由量子自旋霍尔效应引导的拓扑边缘态，上图为配置和能带结构，下图为归一化强度。b，基于谷霍尔效应的样品及其能带结构（上图），以及三种实验结果（下图）。c，假自旋-谷耦合的拓扑光子路由器，左图为配置及相应的Chern数，右图为实验结果。d，由混合拓扑器件驱动的多通道、多频段拓扑路由。e，芯片上的拓扑彩虹器件，其超胞和场分布从左到右显示。f，拓扑错位局域态的概念、样品和结果。g，拓扑缺陷状态及其在拓扑缺陷内的体-缺陷对应。h，基于自旋霍尔效应的狄拉克体态激光器。i，受质量项控制的拓扑腔，带有单元胞扰动。j，拓扑腔表面发射激光器及其表征结果。k，奇异点驱动的单模激光器，两个增益-损耗环具有PT对称性。l，BIC诱导的OAM微腔激光器，用于超快切换。m，偏振奇点介导的可调光子晶体激光器，能带结构（左图）和实验结果（右图）。n，基于PT对称微谐振器的纳米光子陀螺仪，其中绿色（蓝色）实线对应泵浦1（泵浦2）的角频率ωp1（ωp2），红色（黄色）实线表示SBL 1（SBL 2）。橙色波浪线代表角频率为Ω的声子。o，基于奇异点的IgG传感器，源于双层等离子体结构的平移对称性破缺。
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图4 | a，光学集成超构光镊-光扳手（左图），能够分别生成用于光学捕获的高斯光束和用于光学扳手的聚焦轨道角动量（OAM）光束。b，双层光子晶体中由BIC介导的光学力，当αtop=αbot时，可视为光镊，而当αtop≠αbot时，它变成光学扳手。c，当纳米粒子嵌入拓扑波导时，由不匹配模式引导的光学牵引力。d，由动量拓扑诱导的光学牵引力，通过散射动量和入射波矢在动量空间同向实现。e，基于近场旋转向量的光学斯格明子（左图），通过光力探针方法展示（右图）。f，光力系统中的非厄米效应，左侧是两束光与粒子的相互作用，中间是粒子在总强度中的正负动量涡旋，右侧是由此产生的异常点。g，奇异点引起的光波导分选。装置中的光力分布显示在左侧，由TE-TM模式形成的诱导奇异点在右侧。总的来说，本文全面系统地回顾了各种光子奇点及其独特属性和相应的物理机制。此外，还探讨了这些奇点的动态行为及其相互作用，如合并、分裂和守恒关系，揭示了如何操控和利用这些奇点实现多功能性。重要的是，本文详细介绍了基于各种光子奇点效应的超构器件，展示了光子奇点在实际应用中的巨大潜力，为实现复杂结构光开辟了新可能；不同类型奇点之间的耦合和协同效应正逐渐扩展到更广泛的时空领域，以及在光操控、集成成像系统和通信等领域显示出重大价值，显示了片上奇异光子学广泛应用的前景。
展望未来，作为一个充满活力且迅速发展的前沿领域，超构光子奇点无疑将在推动光子技术的创新和发展中发挥越来越重要的作用。首先，深入探索和揭示不同奇点之间的内在联系，并建立全面而连贯的理论，对于加深我们对奇点物理的理解至关重要。其次，精确控制各种奇点的动态行为将极大推动片级光子设备的发展，不仅推动光子学的小型化和集成化，还可能将光电子技术引向更高效和智能的方向。作者们对奇点光子学的前景持乐观态度，坚信这一充满活力和创新的领域将继续为光子技术带来革命性的变革和发展，为科学研究和工程应用带来更多成果。Chip-scale metaphotonic singularities: topological, dynamical, and practical aspects¹
Singularities refer to scenarios where conventional rules fail at certain points, such as the centers of black holes or during phase transitions of matter, where properties may become undefinable. Originally derived from mathematics, this concept has been extensively applied in physics, particularly in optical physics. The presence of singularities enables the exploration of novel phenomena and drives the development of technological applications. The article provides a comprehensive review of various photonic singularities, categorizing them into singularities in real space, momentum space, and other parameter spaces, as illustrated in Fig. 1. This includes polarization singularities, phase singularities, and monopole singularities; singularities induced by bound states in the continuum (BIC), Dirac points, Weyl points, and exceptional points. The research value of these singularities is discussed from three perspectives: topological properties, dynamic evolution, and potential applications.![]()
Fig. 1 | The classification of metaphotonic singularities organized into three types based on their physical domains.Typically, integrating along a closed path around a singularity yields a topological invariant of the system, which characterizes the topological properties of the singularity. In this article, each type of singularity is introduced alongside its topological characteristics and the definition of its topological charge. Subsequently, the authors also discuss the construction of singularity phenomena in micro-nanophotonics. For far-field singularities, the orbital angular momentum carried by vortex light fields and their derivatives, such as optical Möbius strips and skyrmions, are extensively studied. This requires the special design of phase-gradient metasurfaces; to achieve singularities in momentum space, periodic optical lattices must be designed, such as Dirac metasurfaces.Fig. 2 represents the dynamic evolution starting from these points. Some singularities maintain their topological characteristics during propagation or adiabatic transformations, meaning that while local properties may change, the overall characteristics remain invariant2,3, such as the conservation of angular momentum in spin-orbit conversion processes and the splitting and merging of polarization singularities induced by bound states in the continuum (BIC)4.
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Fig. 2 | Dynamical control over singularities. a, Anisotropic meta-atoms for multidimensional metasurfaces. The metasurfaces composed of anisotropic meta-atoms (upper panel), showing possible emergent polarization responses under different polarization states of incident light. Illustrations of J-plate and two types of TAM-plate (lower panel). b, Honeycomb PhC and its unit cell satisfies C₆ symmetry supporting QSHE (upper panel), spin-momentum locking topological feature (lower panel). c, Valley-Hall lattices and their associated VPCs. d, Singularity dynamics of one and multiple metallic scatterers with C-line and V-line. e, merging accidental BIC into symmetry-protected BICs by tuning parameters, resulting in the formation of MBIC. f, the merging of FW-BIC and accidental BIC. g, Trajectories encircling an EP with different directions (upper side) and schematic of an asymmetric switch between different waveguide modes with the projection of the above EP-encircling (lower side). h, the design of silicon waveguide structure generating broad bandwidth topological time-asymmetry, achieved by dynamically encircling an EP through adjusting the core width w₂(z) of the channel waveguide Ch2 and the tunnel-barrier width profile g₂(z). i, Schematic of an omni-polarizer, and opposite operations yield complementary polarized eigenstates. j, Illustration of a single transverse mode EP-encircling laser capable of simultaneously emitting two different modes, each from a different facet. k, the comparison between conventional polarizer and the chiral polarizer based on encircling an EP in an anti-![]()
-symmetric system, for the latter one, the output polarization state will be rotated to the vertical (horizontal) direction for arbitrary input polarization states in forward (backward) propagation.
In terms of applications, the article introduces the derived applications of optical singularities from three aspects: on-chip optical routing, lasers and sensing, optical micro-manipulation and optomechanics, integrated imaging, and display. This showcases the important physical concepts and strong application potential of optical singularities in micro-nano optics. Fig. 3 illustrates photonic topological devices based on metaphotonic singularities, while Fig. 4 presents research on optical micro-manipulation enabled by metaphotonic singularities5.![]()
Fig. 3 | Photonic topological devices based on metaphotonic singularities. a, topological edge states led by QSHE, where the upper is the configuration and band structure, the lower is the normalized intensity. b, QVHE-based PCS sample with its band structure (upper panel), and three cases of experiment results (lower panel). c, pseudospin-valley coupled topological photonic router, where the left is the configuration and the corresponding Chern number, and the right is the experiment results. d, multi-channel, multi-band topological routing driven by hybrid topological devices, from the top to bottom are PhC setup, QHE-guided wave, QVHE-guided wave. e, on-chip topological rainbow devices, whose supercell and field distribution are shown from left to right. f, the concept, sample and result of topological dislocation localized states. g, Topological disclination states and the bulk-disclination correspondence within topological defect. h, Dirac bulk state lasers based on QSHE. i, mass-term-controlled topological cavity with unit-cell perturbations. j, Topological-cavity surface-emitting lasers and their characterization result. k, EP-driven single-mode lasers coupled in two gain-loss rings with PT symmetry. l, BIC-induced OAM microcavity lasers for ultrafast switching. m, Polarization singularity-mediated tunable photonic crystalline lasers. Band structure (left panel) and experiment result (right panel). n, Nanophotonic gyroscope based on PT-symmetric microresonator, where the green (blue) solid line corresponds to pump 1 (pump 2) with an angular frequency of ωp1 (ωp2), while the red (yellow) solid line indicates SBL 1 (SBL 2). The orange wavy line represents acoustic phonons with an angular frequency of Ω phonon. o, EP-based sensor of IgG arising from breaking the translational symmetry of bilayer plasmonic structures.![]()
Fig. 4 | a, optical integrated meta-tweezer-spanner (left inset), which is in the possession of generating Gaussian beam for optical trapping and focused OAM beam for optical spanning, respectively. b, BIC-mediated optical forces in bilayer PCS, regarding as an optical tweezer when αtop=αbot, while αtop≠αbot, it becomes an optical spanner. c, optical pulling force led by modes unmatched when nanoparticle embedded in topological waveguide. d, momentum-topology-induced optical pulling forces, which accomplished by the scattered momentum and the incident wave vector are in the same direction in momentum space. e, optical skyrmion based on spin vectors in the near field (left panel) demonstrated by force-probe method (right panel). f, non-Hermitian effect in optical binding, On the left is the interaction of two beams of light with the particle, in the middle is the positive and negative momentum vorticity of the particle in the total intensity, and on the right is the resulting EP. g, Optical sorting with EP-caused waveguide. The optical force distribution in the device is illustrated at left side, and the induced EP is formed by TE-TM modes.
Overall, this review provides a comprehensive and systematic review of various optical singularities, their unique attributes, and corresponding physical mechanisms. Moreover, it explores the dynamic behaviors of these singularities and their interactions, such as merging, splitting, and conservation relations, revealing how to manipulate and utilize these singularities to achieve multifunctionality. Importantly, the article details the meta devices based on various optical singularity effects, demonstrating the immense potential of optical singularities in practical applications and opening new possibilities for complex structured light. The coupling and synergistic effects between different types of singularities are gradually expanding into broader spatiotemporal domains, and showing significant value in light manipulation, integrated imaging systems, and communication, illustrating the broad application prospects of on-chip singular photonics.Looking forward, as a vibrant and rapidly evolving frontier field, meta photonic singularities will undoubtedly play an increasingly important role in driving the innovation and development of photonic technologies. First, deeply exploring and revealing the intrinsic connections between different singularities, and establishing a comprehensive and coherent theory, is crucial for deepening our understanding of singularity physics. Second, precise control over the dynamic behavior of various singularities will greatly advance the development of chip-level photonic devices, not only pushing photonics towards miniaturization and integration but also potentially steering optoelectronic technologies towards more efficient and intelligent directions. The authors are optimistic about the prospects of singularity photonics, firmly believing that this dynamic and innovative field will continue to bring revolutionary changes and developments to photonic technologies, contributing more outcomes to scientific research and engineering applications.
1. Li, T. et al. Chip-scale metaphotonic singularities: topological, dynamical, and practical aspects. Chip 3, 100109 (2024).
2. Li, T. et al. Generation and conversion dynamics of dual Bessel beams with a photonic spin-dependent dielectric metasurface. Phys. Rev. Appl. 15, 014059 (2021).
3. Li, T. et al. Spin-selective tri-functional metasurfaces for deforming versatile non-diffractive beams along the optical trajectory. Laser Photonics Rev. 18, 2301372 (2024).
4. Kang, M. et al. Merging bound states in the continuum by harnessing higher-order topological charges. Light Sci. Appl. 11, 228 (2022).
5. Li, T. et al. Integrating the optical tweezers and spanner onto an individual single-layer metasurface. Photon. Res. 9, 1062-1068 (2021).
https://www.sciencedirect.com/science/article/pii/S2709472324000273王漱明，南京大学物理学院教授，博士生导师，兼任南智先进光电集成技术研究院院长。获得国家杰出青年科学基金资助和第四届江苏省青年光学科技奖。长期致力于微纳光子体系在线性、非线性与量子光学等方面的研究，及其在集成光学成像、光场调控、光力学和拓扑光子学等领域中的应用。在Science、Nature 子刊、Chip、Advanced Materials、Light: Science & Applications、Laser & Photonics Reviews等期刊上发表论文90余篇，总引用次数超3000次。相关研究成果荣获2018年和2020年「中国光学十大进展」。
Shuming Wang is a professor at Nanjing University and a doctoral supervisor. He has received funding from the National Science Fund for Distinguished Young Scholars and was awarded the Fourth Jiangsu Provincial Young Optics Science and Technology Award. Wang has dedicated his career to the research of micro-nano photonic systems in linear, nonlinear, and quantum optics, with applications in integrated optical imaging, light field manipulation, optomechanics, and topological photonics. He has published over 90 papers in prestigious journals, with more than 3,000 citations. His work was recognized among the 「Top Ten Advances in Chinese Optics」 in both 2018 and 2020.
蔡定平，Photonics Insights 创刊共主编，香港城市大学讲座教授。多年来致力于纳米光子学及光电物理领域前沿的实验与理论工作，发表学术论文360余篇、专著及会议论文70篇、技术报告及其它论文共39篇、国内外专利共45项。曾荣获国际光电工程学会（SPIE）墨子奖、爱思唯尔SCI高被引学者、中国光学十大进展奖等。曾参加国内外举行的重要国际会议340次做特邀报告，目前担任多种重要国际期刊的编辑委员或编辑，以及多种国际知名期刊的文章审稿人。
Din Ping Tsai, co-founding editor of Photonics Insights and Chair Professor at City University of Hong Kong, has devoted to pioneering experimental and theoretical work in nanophotonics and optoelectronics. He has authored over 360 academic papers, 70 monographs and conference papers, 39 technical reports and other papers, and holds 45 patents both domestically and internationally. Tsai has been honored with several prestigious awards, including the Mozi Award from the International Society for Optics and Photonics (SPIE), recognized as an Elsevier Highly Cited Researcher, and recipient of the Top Ten Advances in Chinese Optics award. He has been an invited speaker at 340 significant international conferences worldwide and currently serves as an editorial board member or editor for various prominent international journals, as well as a peer reviewer for numerous well-known journals.
祝世宁，南京大学教授、中国科学院院士。主要从事微结构功能材料和物理研究 , 研究兴趣包括：微结构对经典光、非经典光场调控基础理论，发展新的实验和表征技术，开拓微结构在材料和信息领域的实际应用。作为主要完成人曾获国家自然科学一等奖（2006），国家级教学成果奖二等奖（2018）。个人荣誉有:「求是」杰出青年学者（1998)、美国光学学会会士（2013）、美国物理学会会士（2017）及首届江苏省基础研究重大贡献奖（2019）等。
Shining Zhu, is a professor at Nanjing University and an academician of the Chinese Academy of Sciences, primarily focuses on the research of microstructure materials and physics, including the fundamental theories of controlling classical and non-classical light fields with microstructures, developing new experimental and characterization techniques, and advancing the practical applications of microstructures in the fields of materials and information. As a principal contributor, he has received the National Natural Science Award First Prize (2006) and the National Teaching Achievement Award Second Prize (2018). Personal honors include a Fellow of the Optical Society of America (2013), a Fellow of the American Physical Society (2017), and receiving the inaugural Major Contribution Award in Basic Research from Jiangsu Province (2019).
王振林，南京大学副校长，研究生院院长，物理学院教授，博士生导师，兼任江苏省光学学会理事长。国家杰出青年基金获得者，教育部长江学者特聘教授。曾获教育部自然科学一等奖，江苏省科学技术奖一等奖等。长期从事人工微结构光子材料的设计、制备与表征的研究。先后主持国家自然科学基金委重点项目、国家973计划课题和国家重大研究计划课题等，著有教材《现代电动力学》，发表SCI论文170余篇，授权专利10余项。
Zhenlin Wang, Vice President of Nanjing University, Dean of the Graduate School, Professor at the School of Physics, and doctoral supervisor, also serves as the Chairman of the Jiangsu Optical Society. He is a recipient of the National Science Fund for Distinguished Young Scholars and a specially appointed professor under the Ministry of Education's Yangtze River Scholars Program. He has been awarded the Ministry of Education's First-Class Award in Natural Sciences and the First-Class Jiangsu Province Science and Technology Award. His long-term research focuses on the design, fabrication, and characterization of artificial microstructured photonic materials. He has led key projects funded by the National Natural Science Foundation, the National 973 Plan, and other major national research initiatives. Wang has authored the textbook 「Modern Electrodynamics」, published over 170 SCI-indexed papers, and holds more than 10 patents.
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