Theory of light diffusion in disordered media with linear absorption or gain

TL;DR

This paper develops a microscopic transport theory for light in strongly scattering disordered media with absorption or gain, deriving key transport parameters and highlighting frequency-dependent effects due to resonant scattering and gain or loss.

Contribution

It introduces a fully vectorial kinetic equation approach with an exact Ward identity to account for absorption and gain effects in light diffusion within disordered media.

Findings

Transport quantities are strongly frequency-dependent due to resonant scattering.

Absorption and gain modify transport parameters through additional terms in the Ward identity.

The theory provides a foundation for understanding random lasing in 3D disordered systems.

Abstract

We present a detailed, microscopic transport theory for light in strongly scattering disordered systems whose constituent materials exhibit linear absorption or gain. Starting from Maxwell's equations, we derive general expressions for transport quantities such as energy transport velocity, transport mean free path, diffusion coefficient, and absorption/gain length. The approach is based on a fully vectorial treatment of the generalized kinetic equation and utilizes an exact Ward identity (WI). While for loss- and gainless media the WI reflects local energy conservation, the effects of absorption or coherent gain are implemented exactly by novel, additional terms in the WI. As a result of resonant (Mie) scattering from the individual scatterers, all transport quantities acquire strong, frequency-dependent renormalizations, which are, in addition, characteristically modified by absorption or gain. We illustrate the influence of various experimentally accessible parameters on these quanitities for dilute systems. The transport theory presented here may set the stage for a theory of Random Lasing in three-dimensional disordered media.