Diffusion and anomalous diffusion of light in two-dimensional photonic crystals

Abstract

The transport properties of electromagnetic waves in disordered, finite, two-dimensional photonic crystals composed of circular cylinders are considered. Transport parameters such as the transport and scattering mean free paths and the transport velocity are calculated, for the case where the electromagnetic radiation has its electric field along the cylinder axes. The range of the parameters in which the diffusion process can take place is specified. It is shown that the transport velocity [Formula presented] can be as much as [Formula presented] times less than its free space value, while just outside the cluster [Formula presented] can be 0.3c. The effects of weak and strong disorders on the transport velocity are investigated. Different regimes of the wave transport—ordered propagation, diffusion, and anomalous diffusion—are demonstrated, and it is inferred that Anderson localization is incipient in the latter regime. Exact numerical calculations from the Helmholtz equation are shown to be in good agreement with the diffusion approximation. Show more