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摘要:以超表面为代表的二维人工超材料通过其亚波长单元增强光与物质的相互作用，进而操控光的振幅、相位、偏振、轨道角动量等物理量。目前，非平凡拓扑性质的二维人工超材料由于具有鲁棒的光单向传输等性质成为了光学领域的研究重点。拓扑相不仅成为了凝聚态物理领域一种描述物质的新的自由度，也成为描述人工超材料光学性质的一个新的参量。本文从拓扑光子学的起源出发，介绍了二维人工超材料的拓扑性质分类以及最新的拓扑光子学研究进展，并进行了总结与展望。Abstract:Two dimensional artificial metamaterials, represented by metasurfaces, could control the amplitude, phase, polarization and orbital angular momentum of light, through tailoring the interaction between light and matter. Nowadays, two dimensional artificial metamaterials with nontrivial topological properties have become research focus in optics due to their advantages in robust unidirectional transmission. The topological phase is not only a new degree of freedom to describe matter in the field of condensed matter physics, but also a new parameter to describe optical properties of artificial metamaterials. In this review, the origin of topological photonics and classification for topological properties of two dimensional metamaterials are introduced. The latest progress in topological photonics has also been presented. The summary and prospect of topological metamaterials are given at the end of the review.
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图 1(a) 利用旋磁材料制备的光学拓扑超材料示意图；（b）实验测试得到的体透射系数，光学拓扑超材料的能带图（标签为能带的陈数）[21]，实验测得的边界透射系数；（c）大陈数拓扑光子晶体的实验样品以及仿真结构；（d）实验和计算得到的能带结构[24]
Figure 1.(a) Structure diagram of optical topological metastructure fabricated by gyromagnetic material; (b) experimental bulk transmission and band structure of optical topological metastructure[21]; (c) topological photonics crystal sample and simulation scheme with large chern number; (d) band structure obtained by experiment and calculation[24]
图 2（a）单个单元的耦合环形波导示意图以及实验测试系统；（b）实验测试得到免疫缺陷的鲁棒的边界传输[28]；（c）拓扑 器结构SEM图；（d）拓扑 器和拓扑平凡 器在不同泵浦强度下的激发光谱[31]
Figure 2.(a) Scheme diagram and experimental setup for each ring coupling unit; (b) defect-imunne robust edge transmission by experimental mearsurement[28]; (c) SEM images of topological laser; (d) emission spectra of topological and trivial laser under different bump intensity[31]
图 3（a）拓扑光子晶体示意图[32]；（b）
$ {p}_{x}\left({p}_{y}\right) $ 和$ {d}_{xy}\left({d}_{{x}^{2}-{y}^{2}}\right) $ 构成的赝自旋态[32]；（c）光学拓扑结构能带图[32]；（d）Al2O3柱构成的光学拓扑结构、实验测试得到的7.41 GHz频率时场分布、在S1点和S2点的透射强度[34]Figure 3.(a) Schemetic diagram of topological photonic crystal[32]; (b) pseudo-spin states of
$ {p}_{x}\left({p}_{y}\right) $ and$ {d}_{xy}\left({d}_{{x}^{2}-{y}^{2}}\right) $ [32]; (c) band structure of topological optical structure[32]; (d) topological optical structure consisiting of Al2O3pillars, field distribution with frequency of 7.41 GHz in experimental, transmitted energy atS1andS2[34]
图 4（a）利用能谷自由度设计的光学拓扑结构[43]；（b）能谷依赖的光学拓扑结构的自旋分离行为[43]；（c）左右分别为介电常数为14和17时自旋向上的体态投影以及受拓扑保护的平边界态[43]
Figure 4.(a)Optical topological structure designed by energy valley freedom[43]; (b) spin separation behavior in valley dependent optical topological structure[43]; (c) flat edge dispersions in a photonic crystal with different permittivtities. Only the spin-up polarized projection bands (shaded blue region) and the spin-up edge states are illustrated[43]
图 5（a）利用硅基板设计的具有不同边界的能谷依赖光学拓扑结构[44]；（b）实验和仿真得到的对不同边界路径的透射[44]；（c）光子路由示意图[44]；（d）光子路由的拓扑光传输[44]
Figure 5.(a) Topological optical structure on the substrate of Si with different boundary[44]; (b) transmission spectra obtained by experiment and simulation[44]; (c) schemetic diagram of photon route[44]; (d) topological optical transimission of photon route[44]
图 6（a）利用介质层厚度构建参数空间示意图[66]；（b）在三维合成维度中的人工外尔点[66]；（c）光子晶体截断面上的反射相位分布[66]；（d）在外尔点频率处的反射相位，白色虚线为费米弧轨迹[66]
Figure 6.(a) Schematic diagram of parameter space constructed by dielectric thickness[66]; (b) artificial Weyl point in 3 synthetic dimensional topological structure[66]; (c) reflection phase on the truncated face of photonic crystal[66]; (d) reflection phase at Weyl point, Fermi arc is marked in white dashed line[66]
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