Anisotropic multiple scattering in diffusive media

TL;DR

This paper investigates scalar wave multiple scattering in diffusive media using the radiative transfer equation, providing quantitative predictions for anisotropic scattering effects without relying on the diffusion approximation.

Contribution

It offers an exact analytical approach to anisotropic multiple scattering in diffusive media, including effects of internal reflections and regimes of high anisotropy.

Findings

Derived predictions for reflected and transmitted intensities in thick slabs

Analyzed the impact of anisotropy on scattering observables

Solved the Schwarzschild-Milne equation exactly in specific regimes

Abstract

The multiple scattering of scalar waves in diffusive media is investigated by means of the radiative transfer equation. This approach, which does not rely on the diffusion approximation, becomes asymptotically exact in the regime of most interest, where the scattering mean free path $\ell$ is much larger than the wavelength $\lambda_0$. Quantitative predictions are derived in that regime, concerning various observables pertaining to optically thick slabs, such as the mean angle-resolved reflected and transmitted intensities, and the width of the enhanced backscattering cone. Special emphasis is put on the dependence of these quantities on the anisotropy of the cross-section of the individual scatterers, and on the internal reflections due to the optical index mismatch at the boundaries of the sample. The large index mismatch regime is studied analytically, for arbitrary anisotropic scattering. The regime of very anisotropic scattering, where the transport mean free path $\ell^*$ is much larger than the scattering mean free path $\ell$, is then investigated in detail. The relevant Schwarzschild-Milne equation is solved exactly in the absence of internal reflections.