2008/01/31 by Mikhail Erementchouk, M. V. Erementchouk, Lev Deych +6
Engineering · Physics and Astronomy · #Anisotropy #Computational physics #Condensed matter physics #Diffusion #Isotropy #Lattice (music) #Mean free path #Photonic Crystals and Applications #Photonic crystal #Physics #Quantum mechanics #Radiative transfer #Random lasers and scattering media #Scattering #Statistical physics #Thermal Radiation and Cooling Technologies #cond-mat.dis-nn
paper · pdf · doi:10.1088/0953-8984/21/17/175401
published as J. Phys.: Condens. Matter 21, 175401 (2009) · 27 pages, 4 figures
openalex publication_date 2009/03/24 · arxiv created 2009/10/16 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
The difficulty of description of the radiative transfer in disordered photonic crystals arises from the necessity to consider on an 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 an 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 can the effect of the disorder be characterized by a single mean free path depending on frequency.