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 vE can be as much as 10⁸ times less than its free space value,
while just outside the cluster vE 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.
