Wave packets propagation in the subwavelength regime near the Dirac point

TL;DR

This paper investigates how wave packets behave near Dirac points in bubbly phononic crystals, showing their dynamics are governed by an effective Dirac system at subwavelength scales.

Contribution

It demonstrates that wave packet evolution near Dirac points can be described by a simplified, time-dependent Dirac equation, extending previous spectral analysis results.

Findings

Wave packets near Dirac points follow a Dirac-type evolution.

The effective Dirac system depends on the subwavelength scale in a simple manner.

The results connect spectral properties with wave dynamics in phononic crystals.

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 that 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.