First-principle calculation of Chern number in gyrotropic photonic crystals

Ran Zhao, Guo Da Xie, Menglin L.N. Chen, Zhihao Lan, Zhixiang Huang, Wei E.I. Sha

Research output: Journal article publicationJournal articleAcademic researchpeer-review

46 Citations (Scopus)


As an important figure of merit for characterizing the quantized collective behaviors of the wavefunction, Chern number is the topological invariant of quantum Hall insulators. Chern number also identifies the topological properties of the photonic topological insulators (PTIs), thus it is of crucial importance in PTI design. In this paper, we develop a first principle computatioal method for the Chern number of 2D gyrotropic photonic crystals (PCs), starting from the Maxwell’s equations. Firstly, we solve the Hermitian generalized eigenvalue equation reformulated from the Maxwell’s equations by using the full-wave finite-difference frequency-domain (FDFD) method. Then the Chern number is obtained by calculating the integral of Berry curvature over the first Brillouin zone. Numerical examples of both transverse-electric (TE) and transverse-magnetic (TM) modes are demonstrated, where convergent Chern numbers can be obtained using rather coarse grids, thus validating the efficiency and accuracy of the proposed method.

Original languageEnglish
Pages (from-to)4638-4649
Number of pages12
JournalOptics Express
Issue number4
Publication statusPublished - 17 Feb 2020
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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