Wave packet dynamics in slowly modulated photonic graphene
arXiv:1903.04187 · doi:10.1016/j.jde.2019.06.006
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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Cited by in corpus (7)
- Functional analytic methods for discrete approximations of subwavelength resonator systems
- Unfitted Nitsche's method for computing band structures in phononic crystals with impurities
- Linear and nonlinear electromagnetic waves in modulated honeycomb media
- Dirac equation in curved spacetime: the role of local Fermi velocity
- So (2, 1) algebra, local Fermi velocity, and position-dependent mass Dirac equation
- Wave packets in the fractional nonlinear Schrödinger equation with a honeycomb potential
- Unfitted Nitsche's method for computing wave modes in topological materials