Radiative energy transfer in disordered photonic crystals

TL;DR

This paper develops a theoretical framework for understanding radiative transfer in disordered photonic crystals, revealing how wave scattering and symmetry influence diffusion properties and mean free paths.

Contribution

It introduces a general multiple scattering approach to describe radiative transfer in disordered photonic crystals, deriving diffusion equations and analyzing anisotropy effects.

Findings

Diffusion in disordered photonic crystals is described by incoherent superpositions of ideal modes.

In symmetric crystals, diffusion becomes isotropic and characterized by a single mean free path.

The diffusion process depends on the crystal symmetry and disorder strength.

Abstract

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.