Light Velocity around Exceptional Points of Non-Hermitian Photonic Crystals

We analyzed the energy velocity of electromagnetic eigenmodes for non-Hermitian photonic crystals with radiation loss. For C 4v and C 6v -symmetric photonic crystals, we have successfully derived an exact analytical expression of the energy velocity within the framework of the first-order k · p perturbation theory, focusing on the distorted Dirac cone and exceptional point created by the accidental degeneracy of two modes with particular symmetry combinations. We show that, while the group velocity diverges, the energy velocity does not have singularities, and rather it is vanishing at the exceptional point.