The pseudo-diffusive phenomenon in photonic crystals with Dirac cones

Abstract

Pseudo-diffusive phenomenon is an abnormal transmission phenomenon both in electric system and photonic system which hold conical dispersion relations in their band structures. The phenomenon is: near a Dirac point, the transmittance of the system is inversely proportional to the sample’s thickness as if the material was a disordered medium. It is known that in photonic system, Dirac cones can be classified into three different types, which are standard single Dirac cone, double Dirac cones and Dirac-like cone. Some of them can be found either at the center and the corners of the first Brillouin zone. So it raises the questions that: Do the types of the Dirac cones affect the pseudo-diffusive phenomenon? And further, is there any connection between the pseudo-diffusive phenomenon and the locations of the Dirac cones? Through theoretical investigation, we found that the locations of the Dirac cones play a critical role on the pseudo-diffusive phenomenon. If the Dirac cone is located in the center of the Brillouin zone, the pseudo-diffusive phenomenon doesn't exist at the Dirac frequency. Besides, the shapes of the Dirac cones also affect the pseudo-diffusive phenomenon. The non-conical dispersion band of the Dirac-like cone makes the transmission quite different from linear decrease with the increase of the thickness.