Wave Packets Propagation in the Subwavelength Regime Near the Dirac Point

Abstract

In Ammari et al. (SIAM J Math Anal 52:5441–5466, 2020), 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 packet, which are spectrally concentrated near such conical points. We prove that the wave packet dynamic is governed by a time-dependent effective Dirac system, which still depends, but in a simple way, on the subwavelength scale.