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Volume 33, Issue 2
Band Structure Calculations of Dispersive Photonic Crystals in 3D Using Holomorphic Operator Functions

Wenqiang Xiao, Bo Gong, Junshan Lin & Jiguang Sun

DOI: 10.4208/cicp.OA-2022-0233

Commun. Comput. Phys., 33 (2023), pp. 628-646.

Published online: 2023-03

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  • 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.

  • Keywords

Band structure, dispersive photonic crystal, Maxwell’s equations, nonlinear eigenvalue problem, edge element, holomorphic operator function.

  • AMS Subject Headings

35P30, 65N25, 65N30, 78M10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-33-628, author = {Xiao , WenqiangGong , BoLin , Junshan and Sun , Jiguang}, title = {Band Structure Calculations of Dispersive Photonic Crystals in 3D Using Holomorphic Operator Functions}, journal = {Communications in Computational Physics}, year = {2023}, volume = {33}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0233}, url = {http://global-sci.org/intro/article_detail/cicp/21502.html} }
TY - JOUR T1 - Band Structure Calculations of Dispersive Photonic Crystals in 3D Using Holomorphic Operator Functions AU - Xiao , Wenqiang AU - Gong , Bo AU - Lin , Junshan AU - Sun , Jiguang JO - Communications in Computational Physics VL - 2 SP - 628 EP - 646 PY - 2023 DA - 2023/03 SN - 33 DO - http://doi.org/10.4208/cicp.OA-2022-0233 UR - https://global-sci.org/intro/article_detail/cicp/21502.html KW - Band structure, dispersive photonic crystal, Maxwell’s equations, nonlinear eigenvalue problem, edge element, holomorphic operator function. AB -

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.

Xiao , WenqiangGong , BoLin , Junshan and Sun , Jiguang. (2023). Band Structure Calculations of Dispersive Photonic Crystals in 3D Using Holomorphic Operator Functions. Communications in Computational Physics. 33 (2). 628-646. doi:10.4208/cicp.OA-2022-0233
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