Band engineering method to create Dirac cones of accidental degeneracy in general photonic crystals without symmetry

Abstract

Symmetry usually plays a key role in the formation of the Dirac cone in the band structure of triangular or hexagonal systems. In this work, we demonstrate a systematic method to create Dirac cones of accidental degeneracy in general photonic crystals without symmetry. With this method, a band gap can be closed gradually through a series of modification to the unit structure based on the eigenfields of the band edges, and consequently a Dirac point is formed with Dirac conical dispersions in its vicinity. The validity of this approach is demonstrated by three examples. We further show that the Dirac cones of accidental degeneracy have the same properties as the symmetry-induced Dirac cones, such as finite group velocity and pseudo-diffusive transmission. Our finding opens a route for the engineering of accidental degeneracy in general photonic crystals beyond the scope of high-symmetry ones.