论文标题
陀螺光子晶体中Chern数量的第一原则计算
First-principle calculation of Chern number in gyrotropic photonic crystals
论文作者
论文摘要
作为表征波功能的量化集体行为的重要值，Chern数是量子厅绝缘子的拓扑不变。 Chern数字还标识了光子拓扑绝缘子（PTI）的拓扑特性，因此在PTI设计中至关重要。在本文中，我们从麦克斯韦方程开始，为2D陀螺光子晶体（PC）的Chern数量开发了第一个原理计算方法。首先，我们通过使用全波有限差异频域（FDFD）方法来解决从麦克斯韦方程重新重新重新构建的Hermitian广义特征值方程。然后，通过计算第一个Brillouin区域上浆果曲率的整体来获得Chern数。展示了横向电动（TE）和横向磁性（TM）模式的数值示例，其中可以使用相当粗的网格获得收敛的Chern数字，从而验证了所提出方法的效率和准确性。
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.
