Abstract: Mathematical analysis on electromagnetic waves in photonic graphene, a photonic topological material which has a honeycomb structure, is a current research focus. In this talk, we investigate the 2-D wave propagation derived from Maxwell’s equation. We will present the time evolution of wave packets spectrally concentrated at the Dirac point in a modulated honeycomb material weight, and rigorously prove that such wave packet dynamics is governed by the 2-D Dirac equation with a varying mass in a large but finite time. In our article, we derive our justification mainly by Floquet-Bloch theory, and decompose the integral domain into near and far parts from the Dirac point.

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