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Wave packets propagation in the subwavelength regime near the Dirac point

by H. Ammari and X. Fu and W. Jing

(Report number 2024-26)

Abstract
In [Ammari et al., SIAM J Math Anal., 52 (2020), pp. 5441-5466], the first author with collaborators proved the existence of Dirac dispersion cones at subwavelength scales in bubbly honeycomb phononic crystals. In this paper, we study the time-evolution of wave packets, which are spectrally concentrated near such conical points. We prove that the wave packets dynamics is governed by a time-dependent effective Dirac system, which still depends, but in a simple way, on the subwavelength scale.

Keywords: Dirac degeneracy, bubbly honeycomb phononic crystals, time-dependent Dirac equation, evolution of wave packets

@Techreport{AFJ24_1108,
  author = {H. Ammari and X. Fu and W. Jing},
  title = {Wave packets propagation in the subwavelength regime near the Dirac point},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2024-26},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2024/2024-26.pdf },
  year = {2024}
}

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