Diffusion and anomalous diffusion of light in two-dimensional photonic crystals.
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 upsilon(E) can be as much as 10(8) times less than its free space value, while just outside the cluster upsilon(E) 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.
Asatryan
A A
AA
School of Mathematical Sciences, University of Technology, Sydney, New South Wales 2007, Australia.
Robinson
P A
PA
McPhedran
R C
RC
Botten
L C
LC
Martijn de Sterke
C
C
Langtry
T L
TL
Nicorovici
N A
NA