Non-Hermitian effective medium theory and complex Dirac-like cones

In this work, we propose a non-Hermitian effective medium theory to interpret the spawning rings of exceptional points out of the Dirac cones in the band structures of photonic crystals with loss/gain. Based on this theory, we predict and demonstrate two unique types of band dispersions of fully passive photonic crystals. In one type, the exceptional ring shrinks into a complex Dirac point associated with a complex Dirac-like cone. In the other type, a point of quadratic degeneracy is realized in the imaginary frequency spectrum. Our theory provides a unified picture for the exceptional points in effective media and gives rise to novel concepts like complex Dirac-like cones in non-Hermitian photonics.