Radiative Transfer Theory and Diffusion of Light in Nematic Liquid Crystals

TL;DR

This paper develops a diffusion model for light in nematic liquid crystals based on radiative transfer theory, linking diffusion constants to director fluctuation dynamics and showing how temporal correlations reveal fast director mode dynamics.

Contribution

It introduces a diffusion equation approach for multiple scattered light in nematic liquid crystals, connecting diffusion constants to the dynamic structure factor of director fluctuations.

Findings

Diffusion constants are related to the dynamic structure factor.

Temporal correlations probe fast director mode dynamics.

Absorption terms account for decaying correlations.

Abstract

In nematic liquid crystals light is strongly scattered from director fluctuations. We are interested in the limit where the incoming light wave is scattered many times. Then, the light transport can be described by a diffusion equation for the energy density of light with diffusion constants $D_{\|}$ and $D_{\perp}$, respectively, parallel and perpendicular to the director. We start from a radiative transfer theory, connect the diffusion constants to the dynamic structure factor of director fluctuations, and shortly discuss our results. Temporal correlations of the diffusing light probe the dynamics of director modes on much shorter time scales than single light scattering experiments. To account for the decaying temporal correlations, one has to add an absorption term to the diffusion equation, which we also link to the dynamic structure factor.