# Wave packet dynamics in slowly modulated photonic graphene

## TL;DR

This paper mathematically analyzes wave packet dynamics in photonic graphene with honeycomb structures, showing that wave packets near Dirac points evolve according to a Dirac equation with a varying mass, illuminating topological phenomena.

## Contribution

It provides a rigorous mathematical derivation of wave packet evolution in modulated photonic graphene, linking electromagnetic wave behavior to Dirac equations with variable mass.

## Key findings

- Wave packets near Dirac points follow a Dirac equation with varying mass.
- The analysis offers mathematical insights into topological phenomena in photonic graphene.
- Wave packet dynamics are governed by the spectral concentration at Dirac points.

## 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.