拓扑光子学研究进展

王洪飞; 解碧野; 詹鹏; 卢明辉; 陈延峰

doi:10.7498/aps.68.20191437

摘要

受凝聚态中拓扑相和拓扑相变概念的启发, 一种基于拓扑能带论的新的研究领域——拓扑光子学正在兴起, 它突破了传统基于实空间光场叠加原理和倒空间固体能带色散理论的光场调控思想, 提供了一种新颖的光场调控机制和丰富的输运和光操控性质. 例如, 背散射抑制且缺陷免疫的边界输运特性、自旋轨道依赖的选择传输特性、高维度的光场调控等. 本文将从拓扑光子体系的维度出发, 简要介绍不同维度中的拓扑模型、新奇物理现象以及相应的物理图像, 如SSH模型、光量子霍尔效应、光量子自旋霍尔效应、Floquet拓扑绝缘体、三维拓扑绝缘体等; 结合当前的研究热点, 对光子学领域的其他先进拓扑平台也进行了简要的讨论, 如高阶拓扑系统、非厄米拓扑系统、非线性拓扑系统等; 本文的最后, 对相关领域的发展现状、优势与挑战进行了相应的总结与展望.

关键词:

Abstract

Inspired by topological phases and phase transitions in condensed matter, a new research field based on topological band theory, topological photonics, has emerged. It breaks through the traditional idea of light regulation by optical superposition principle of real space and energy band theory of solids of reciprocal space, providing a novel mechanism of optical regulation and rich properties of transport and light manipulation. Such as transmission properties of against backscattering and rubout to defects and disorders, selective transports dependent on spin-orbit coupling, and high dimensional manipulation of light. This review paper classifies different topological photonic systems by dimensions, briefly introducing the topological model, the novel physical phenomena, and the corresponding physical picture, such as SSH models, photonic quantum Hall effects, photonic quantum spin Hall effects, photonic Floquet topological insulator, and photonic three-dimensional topological insulator; other advanced platforms such as higher-order, non-Hermitian, and nonlinear topological platforms are also involved; a summary and outlook about the current development, advantages, and challenges of this field are present in the end.

Keywords:

topological phases in condensed matter /
topological photonics /
higher-order topological insulators /
non-Hermitian photonic systems

作者及机构信息

1.
南京大学材料科学与工程系, 固体微结构物理国家重点实验室, 南京　210093

2.
南京大学物理学院, 南京　210093

3.
南京大学, 人工微结构协同创新中心, 南京　210093

4.
江苏省人工功能材料重点实验室, 南京　210093

通信作者: 卢明辉, luminghui@nju.edu.cn

基金项目: 国家重点研发计划(批准号: 2018YFA0306200, 2017YFA0303702)、国家自然科学基金(批准号: 11474158, 51732006, 11890700)和国家杰出青年科学基金(批准号: 11625418)资助的课题

Authors and contacts

1.
National Laboratory of Solid State Microstructures, Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China

2.
School of Physics, Nanjing University, Nanjing 210093, China

3.
Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

4.
Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing 210093, China

Corresponding author: Lu Ming-Hui, luminghui@nju.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant Nos. 2018YFA0306200, 2017YFA0303702), the National Natural Science Foundation of China (Grant Nos. 11474158, 51732006, 11890700), and the National Science Fund for Distinguished Young Scholars of China (Grant No.11625418)

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施引文献

图 1 SSH模型示意图, 每个元胞包含两个格点

Fig. 1. Schematic of the SSH model, there are two sites in each unit cell.

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图 2 (a) 微纳加工(SSH 模型)的SEM图; (b) 单个柱子的模式; (c) 不同能带中的态及存在的边界态; (d) 利用波导环形阵列实现SSH模型

Fig. 2. (a) SEM image of the coupled micropillars; (b) Modes of single micropillars; (c) Different modes of the micropillar array and edge states; (d) SSH microring array.

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图 3 (a) 旋磁光子晶体的示意图; (b) 向前向后的传输谱以及具有手性边界态的投影能带; (c) 大陈数光子晶体结构图; (d) 能带的带隙及其陈数

Fig. 3. (a) Schematic of the gyromagnetic photonic crystal; (b) forward and backward spectra, and projected band structures with chiral edge states; (c) the diagram of large Chern number photonic crystals; (d) the band gap map and their Chern number.

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图 4 (a) Poincaré球上的LCP和RCP, 以及由PE和PM材料构成的光子晶体; (b) 没有赝自旋耦合以及具有赝自旋耦合的能带以及后者的投影能带; (c) 通过调节金属柱子实现赝自旋的耦合

Fig. 4. (a) The polarization of LCP and RCP on the Poincaré sphere, and the photonic crystal consisting of PE and PM superlattices; (b) band structures without coupling between dseudospin states and with their coupling, and the projected band structures for the latter case; (c) photonic crystals consisting of metallic rods and collars at different positions, and their band strucutres.

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图 5 (a) 全介质光子晶体结构; (b) 收缩、高对称以及扩张晶格所对应的能带; (c) 赝自旋依赖的边界态的实验观测

Fig. 5. (a) Schematic of all-dielectric photonic crystals; (b) band structures of shrinking and expanding lattices; (c) visualization of pseudospin-dependent edge states.

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图 6 (a) 谐振腔耦合单元; (b) 周期排布形成的耦合阵列

Fig. 6. (a) Two coupled resonators in one unit cell; (b) a periodic array arranged by unit cells.

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图 7 (a) 光学谐振腔阵列的动态调制; (b) 激光直写波导系统的拓扑绝缘体构型; (c) 四种耦合组成的周期构型

Fig. 7. (a) The resonator lattice with dynamic modulation; (b) floquet topological insulators using the femtosecond laser writing method; (c) four different bonds with different coupling.

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图 8 (a) 能够产生Weyl点以及节线的双螺旋光子晶体; (b) 具有Weyl点的金属夹杂的光子晶体

Fig. 8. (a) Photonic crystals with two gyroid structures in one unit cell, and their band structures with Weyl points or nodal-line; (b) schematic of photonic crystals with the saddle-shaped metallic inclusion, and their Weyl points.

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图 9 (a) 三维全介质与双各向异性光子晶体; (b) 两种构型的光子晶体对应的能带; (c) 通过引入磁场破缺Dirac点的光子晶体构型

Fig. 9. (a) 3 D all-dielectric and bianisotropic metacrystals; (b) band structures corresponding to two structures in (a); (c) photonic crystals with opened Dirac points when magnetization is applied on rods.

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图 10 (a) 动量空间中的奇异点以及具有增益损耗的紧束缚模型; (b) 具有增益损耗的波导阵列; (c) 具有奇异环的光子晶体板结构

Fig. 10. (a) Exceptional points in momentum space, and the tight-binding model with gain and loss for α_i and β_i; (b) the waveguide array with gain and loss; (c) photonic crystal slabs with the ring of exceptional points.

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图 11 (a) 非线性SSH模型; (b) 与光强度相关的环绕数(贝利相位); (c) 将量子比特与它们的耦合器铺成二维格子的示意图; (d) 包含三个超导量子比特的超导回路

Fig. 11. (a) The nonlinear SSH model; (b) the winding number (Berry phase) changed by intensity; (c) schematic diagram of qubits and their couplers in 2 D lattice; (d) the superconducting circuit including three qubits.

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图 12 (a) 介质柱构成的二维SSH模型的光子晶体; (b) 收缩、高对称与扩张晶格构型的能带结构; (c) 由收缩区域包围扩张区域构成的整体结构, 解的序号与本征频率的关系; (d) 实验中放于一个角的源激发的拐角态

Fig. 12. (a) Photonic crystals of the 2D SSH model consisting of dielectric pillars; (b) band structures of shrinking, high symmetry and expending structures; (c) shrinking supercells contain expanding supercells, and the relationship between solution numbers and eigenfrequencies; (d) experimentally measured corner states when the source is placed at the corner.

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