光的传播通常是互易的，传统的互易性光学器件面临光学衍射极限等问题，限制了其性能的进一步提升。非互易性光学器件能够实现光的单向可控传输，非互易拓扑光子态具有抗背向散射、免疫障碍物和缺陷等多种优异的物理性质，因而在光集成电路、非线性光学等多个领域具有潜在的应用价值。本文聚焦并回顾了非互易拓扑光子学的应用价值和研究进展，分别介绍了通过旋磁材料光子晶体、基于磁表面等离子激元、利用光学非线性效应和基于时间调制等不同的途径和手段实现非互易光子拓扑态的理论依据和研究进展，比较各自特点，并对其未来发展趋势和面临的关键问题进行了分析和展望。

拓扑光子学是光学领域一个重要的新兴研究方向，它的奇异光学响应特性颠覆了人们对光传播的理解，为人工操控光的传播提供了一种全新方法。Floquet拓扑光子绝缘体是拓扑光子学的一个重要分支，它利用周期性的驱动来探索物质的相变过程，发现了很多违反直觉的新奇物理现象。本文综述了近十年来Floquet拓扑光子绝缘体的主要研究进展。根据实现方式将其分为基于时间调制、基于空间调制、基于耦合谐振调制的三个大类进行详细论述。对于每一类Floquet拓扑光子绝缘体，从基础理论和物理实现平台两个方面论述了Floquet拓扑光子绝缘体的独特光学特性和奇异物理现象，并讨论了其潜在的应用前景。最后，总结了该领域当前面临的主要挑战，并对Floquet拓扑光子绝缘体的未来研究方向进行了展望。

Photonic and acoustic topological insulators exhibiting one-way transportation that is robust against defects and impurities are typically realized in coupled arrays of two-dimensional ring resonators. These systems have produced a series of applications, including optical isolators, delay lines, and lasers. However, the structures are complicated because an additional coupler ring between neighboring rings is needed to construct photonic pseudospin. A photonic anomalous Floquet topological insulator is proposed and experimentally demonstrated in the microwave regime. This improved design takes advantage of the efficient and backward coupling of negative-index media. The results contribute to the understanding of topological structures in metamaterials and point toward a unique direction for constructing useful topological photonic devices.

Originally a pure mathematical concept, topology has been vigorously developed in various physical systems in recent years, and underlies many interesting phenomena such as the quantum Hall effect and quantum spin Hall effect. Its widespread influence in physics led the award of the 2016 Nobel Prize in Physics to this field. Topological photonics further expands the research field of topology to classical wave systems and holds promise for novel devices and applications, e.g., topological quantum computation and topological lasers. Here, we review recent developments in topological photonics but focus mainly on their realizations based on metamaterials. Through artificially designed resonant units, metamaterials provide vast degrees of freedom for realizing various topological states, e.g., the Weyl point, nodal line, Dirac point, topological insulator, and even the Yang monopole and Weyl surface in higher-dimensional synthetic spaces, wherein each specific topological nontrivial state endows novel metamaterial responses that originate from the feature of some high-energy physics.

It is experimentally verified that nonreciprocal photonic systems with continuous translation symmetry may have an ill-defined topology. The topological classification of such systems is only feasible when the material response is regularized with a spatial-frequency cutoff. We experimentally demonstrate that adjoining a small air layer to the relevant material interface may effectively imitate an idealized spatial cutoff that suppresses the nonreciprocal response for short wavelengths and regularizes the topology. Furthermore, it is experimentally verified that nonreciprocal systems with an ill-defined topology may be used to abruptly halt the energy flow in a unidirectional waveguide due to the violation of the bulk-edge correspondence. In particular, we report the formation of an energy sink that absorbs the incoming electromagnetic waves with a large field enhancement at the singularity.

We present a discovery of an unusual unidirectionally rotating windmill scattering of electromagnetic waves by a magnetized gyromagnetic cylinder via an analytical theory for rigorous solution to fields and charges and an understanding of the underlying mathematical and physical mechanisms. Mathematically, the generation of nonzero off-diagonal components can break the symmetry of forward and backward scattering coefficients, producing unidirectional windmill scattering. Physically, this windmill scattering originates from the nonreciprocal unidirectional rotation of polarized magnetic charges on the surface of a magnetized gyromagnetic cylinder, which drives the scattering field to radiate outward in the radial direction and unidirectionally emit in the tangential direction. Interestingly, the unidirectional electromagnetic windmill scattering is insensitive to the excitation direction. Moreover, we also discuss the size dependence of unidirectional windmill scattering by calculating the scattering spectra of the gyromagnetic cylinder. These results are helpful for exploring and understanding novel interactions between electromagnetic waves and gyromagnetic materials or structures and offer deep insights for comprehending topological photonic states in gyromagnetic systems from the aspect of fundamental classical electrodynamics and electromagnetics.