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arXiv · 1903.04187

Wave packet dynamics in slowly modulated photonic graphene

Peng Xie·Yi Zhu
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Abstract

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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Peng Xie, Yi Zhu. 2019-03-11. Wave packet dynamics in slowly modulated photonic graphene. https://doi.org/10.1016/j.jde.2019.06.006

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