  The difficulty of description of the radiative transfer in disordered
photonic crystals arises from the necessity to consider on the equal footing
the wave scattering by periodic modulations of the dielectric function and by
its random inhomogeneities. We resolve this difficulty by approaching this
problem from the standpoint of the general multiple scattering theory in media
with arbitrary regular profile of the dielectric function. We use the general
asymptotic solution of the Bethe-Salpeter equation in order to show that for a
sufficiently weak disorder the diffusion limit in disordered photonic crystals
is presented by incoherent superpositions of the modes of the ideal structure
with weights inversely proportional to the respective group velocities. The
radiative transfer and the diffusion equations are derived as a relaxation of
long-scale deviations from this limiting distribution. In particular, it is
shown that in general the diffusion is anisotropic unless the crystal has
sufficiently rich symmetry, say, the square lattice in 2D or the cubic lattice
in 3D. In this case, the diffusion is isotropic and only in this case the
effect of the disorder can be characterized by the single mean-free-path
depending on frequency.

Disordered Systems and Neural Networks