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Universal numerical calculation method for the Berry curvature and Chern numbers of typical topological photonic crystals


Chern number is one of the most important criteria by which the existence of a topological photonic state among various photonic crystals can be judged; however, few reports have presented a universal numerical calculation method to directly calculate the Chern numbers of different topological photonic crystals and have denoted the influence of different structural parameters. Herein, we demonstrate a direct and universal method based on the finite element method to calculate the Chern number of the typical topological photonic crystals by dividing the Brillouin zone into small zones, establishing new properties to obtain the discrete Chern number, and simultaneously drawing the Berry curvature of the first Brillouin zone. We also explore the manner in which the topological properties are influenced by the different structure types, air duty ratios, and rotating operations of the unit cells; meanwhile, we obtain large Chern numbers from–2 to 4. Furthermore, we can tune the topological phase change via different rotation operations of triangular dielectric pillars. This study provides a highly efficient and simple method for calculating the Chern numbers and plays a major role in the prediction of novel topological photonic states.

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This paper was supported by the National Natural Science Foundation of China (Grant Nos. 11604378, 91850117, and 11654003), Beijing Institute of Technology Research Fund Program for Young Scholars, and Double First Class University Plan. We would like to thank Prof. Xiangdong Zhang, Dr. Lu He, Dr. Yujing Wang, and Dr. Changyin Ji from the Beijing Institute of Technology for the useful discussion.

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Correspondence to Cuicui Lu.

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Mr. Chenyang Wang is an undergraduate student majoring in Applied Physics at the Beijing Institute of Technology, China. His research interests include nanophotonics and topological photonic crystals. He successfully applied for one national invention patent as the co-inventor. Furthermore, he received the excellent poster award during the 2019 CPS Fall Meeting as well as a National Scholarship.

Dr. Hongyu Zhang received her bachelor’s degree from the Hebei Normal University in 2018. She is currently a graduate student at the Beijing Institute of Technology and studies the interaction between light and matter in nanostructures, including the metal nanoparticles and photonic crystal cavities. She successfully applied for two national invention patents as the second inventor and received a National Scholarship during her first year in graduate school. Currently, she is focused on researching topological photonics and hybrid cavity systems.

Mr. Hongyi Yuan is currently an undergraduate in the Physics Department at the Beijing Institute of Technology. His research is focused on the design, calculation and simulation of nanophotonic devices. He is currently focused on general designing using algorithms. He successfully applied for two national invention patents as the co-inventor.

Mr. Jinrui Zhong is an undergraduate student at the Beijing Institute of Technology. He has been awarded a scholarship every semester and received an A–in the astrophysics course during the summer school program at the University of California, Berkeley. His major research interests include the theory of topological fields, Weyl semimetal, chiral anomaly, and axion electric dynamics in condensed matter physics. As a big fan of Richard Feynman, he is independently pursuing Ph.D. while conducting quantum transport experiments.

Prof. Cuicui Lu received her Ph.D. degree from the Peking University in 2015 and is currently an associate research scientist at the Beijing Institute of Technology. Her research interests include nanophotonic devices based on algorithm, topological photonics, photonic crystal cavity and applications, and plasmonics. She has published 30 papers in several journals, including Light: Science & Applications, Optica, Nano Letters, Laser & Photonics Reviews, and Advanced Optical Materials. She has led six scientific research projects, including three projects of National Natural Science Foundations of China, two projects of the Beijing Institute of Technology, and one independent innovation project of the Qian Xuesen Space Technology Laboratory. She received the SPIE Optics and Photonics Education Scholarship and World Quantitative and Science Scholarship in 2014. Email:

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Wang, C., Zhang, H., Yuan, H. et al. Universal numerical calculation method for the Berry curvature and Chern numbers of typical topological photonic crystals. Front. Optoelectron. 13, 73–88 (2020).

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  • Chern number
  • topological photonic crystal
  • finite element method
  • symmetry