Wave packet dynamics in slowly modulated photonic graphene

Peng Xie Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China Yi Zhu Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China

Analysis of PDEs mathscidoc:2204.03001

2019.3
Mathematical analysis on electromagnetic waves in photonic graphene, a photonic topological material which has a honeycomb structure, is one of the most important current research topics. By modulating the honeycomb structure, numerous topological phenomena have been observed recently. The electromagnetic waves in such a media are generally described by the 2-dimensional wave equation. It has been shown that the corresponding elliptic operator with a honeycomb material weight has Dirac points in its dispersion surfaces. In this paper, we study the time evolution of the wave packets spectrally concentrated at such Dirac points in a modulated honeycomb material weight. We prove that such wave packet dynamics is governed by the Dirac equation with a varying mass in a large but finite time. Our analysis provides mathematical insights to those topological phenomena in photonic graphene.
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@inproceedings{peng2019wave,
  title={Wave packet dynamics in slowly modulated photonic graphene},
  author={Peng Xie, and Yi Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220421120427045369090},
  year={2019},
}
Peng Xie, and Yi Zhu. Wave packet dynamics in slowly modulated photonic graphene. 2019. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220421120427045369090.
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