Band Structure Calculations of Dispersive Photonic Crystals in 3D Using Holomorphic Operator Functions
Year: 2023
Author: Wenqiang Xiao, Bo Gong, Junshan Lin, Jiguang Sun
Communications in Computational Physics, Vol. 33 (2023), Iss. 2 : pp. 628–646
Abstract
We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D. The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator function. The Nédélec edge elements are employed to discretize the operators, where the divergence free condition for the electric field is realized by a mixed form using a Lagrange multiplier. The convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions with the regular approximation of the edge elements. The spectral indicator method is then applied to compute the discrete eigenvalues. Numerical examples are presented demonstrating the effectiveness of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0233
Communications in Computational Physics, Vol. 33 (2023), Iss. 2 : pp. 628–646
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Band structure dispersive photonic crystal Maxwell’s equations nonlinear eigenvalue problem edge element holomorphic operator function.