Bloch theory-based gradient recovery method for computing topological edge modes in photonic graphene

Hailong Guo School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia Xu Yang Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA Yi Zhu Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, China, 100084

Numerical Analysis and Scientific Computing mathscidoc:2204.25001

2018.12
Photonic graphene, a photonic crystal with honeycomb structures, has been intensively studied in both theoretical and applied fields. Similar to graphene which admits Dirac Fermions and topological edge states, photonic graphene supports novel and subtle propagating modes (edge modes) of electromagnetic waves. These modes have wide applications in many optical systems. In this paper, we propose a novel gradient recovery method based on Bloch theory for the computation of topological edge modes in the honeycomb structure. Compared to standard finite element methods, this method provides higher order accuracy with the help of gradient recovery technique. This high order accuracy is highly desired for constructing the propagating electromagnetic modes in applications. We analyze the accuracy and prove the superconvergence of this method. Numerical examples are presented to show the efficiency by computing the edge mode for the P-symmetry and C-symmetry breaking cases in honeycomb structures.
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@inproceedings{hailong2018bloch,
  title={Bloch theory-based gradient recovery method for computing topological edge modes in photonic graphene},
  author={Hailong Guo, Xu Yang, and Yi Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220421115426029915088},
  year={2018},
}
Hailong Guo, Xu Yang, and Yi Zhu. Bloch theory-based gradient recovery method for computing topological edge modes in photonic graphene. 2018. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220421115426029915088.
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