近年来，因为体现出诸多异常拓扑现象，外尔超材料一直备受关注。此前的研究表明外尔超材料的反射场具有偏振转换特性。然而，关于反射本征态的讨论却不够深入，原因在于入射电磁场与反射电磁场处于不同的态空间，给分析计算带来了诸多不便。文中从电场为极矢量、磁场为轴矢量的基本特性出发，通过引入镜像算符将入射态空间与反射态空间联系起来，最后对全反射界面的本征态进行了明确的定义。依据上述定义，笔者对外尔超材料的反射本征态进行了计算，结果显示：在入射电磁场为线性偏振的前提下，外尔超材料的反射本征态均为线性偏振态。反射本征态为线性偏振态，这一性质是由系统能量守恒与洛伦兹互易性共同保证的。经过进一步探讨发现，当动量空间的路径绕外尔点一圈时，本征态的电磁场方向旋转角度为90°。这也意味着如果电磁场要回到初始状态，动量空间的路径需绕外尔点4圈。这一现象的拓扑结构可以类比为四阶莫比乌斯环。此外，依据反射本征态为互相垂直的线性偏振态这一特性，笔者定义了旋转角度θ用以描述本征态朝向的变化规律。值得一提的是，这种计算方法不仅仅适用于外尔超材料，满足条件的全反射界面的反射本征态均可以依照上述定义与方法进行分析求解。

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.