Multiple scattering of polarized light in disordered media exhibiting short-range structural correlations

We develop a model based on a multiple scattering theory to describe the diffusion of polarized light in disordered media exhibiting short-range structural correlations. Starting from exact expressions of the average field and the field spatial correlation function, we derive a radiative transfer equation for the polarization-resolved specific intensity that is valid for weak disorder and we solve it analytically in the diffusion limit. A decomposition of the specific intensity in terms of polarization eigenmodes reveals how structural correlations, represented via the standard anisotropic scattering parameter $g$, affect the diffusion of polarized light. More specifically, we find that propagation through each polarization eigenchannel is described by its own transport mean free path that depends on $g$ in a specific and nontrivial way.

Figure 1

Evolution of (a) the transport coefficient $1/{\ell }^{*\left(p\right)}$ and (b) the attenuation coefficient $1/{\ell }_{\text{eff}}^{\left(p\right)}$ of polarization eigenmodes with short-range structural correlations. The coefficients are given in units of $1/\ell$ and shown on a restricted range of $g$ since the model is expected to remain valid to first order near $g=0$. The scalar mode ($p=1$, cyan solid curve) has a transport coefficient scaling as $(1-g)$ and an attenuation coefficient equal to zero (not shown). The polarization modes $p=2\text{–}4$ (gray dashed curves) and $p=5\text{–}9$ (orange dot-dashed curves) exhibit different slopes, indicating that both their transport properties are affected differently by short-range structural correlations.

Figure 2

Evolution of the transport coefficient of the scalar mode, $1/{\ell }^{*\left(1\right)}$, in units of $1/\ell$, with the scattering anisotropy factor $g$. We compare the raw prediction obtained from the eigenmode decomposition, Eq. (35), before the development to order $g$ (solid cyan curve), with the expected $1-g$ scaling relation (black dashed curve). Our theoretical predictions are expected to be valid for short-range structural correlations, i.e., for $g$ close to zero.