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

Abstract

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.

Keywords

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

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Acknowledgements

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.

RIGHTS & PERMISSIONS

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature