Anisotropic multiple scattering in diffuse media

Abstract

The multiple scattering of scalar waves in diffusive media is investigated by means of the radiative transfer equation. This approach amounts to a resummation of the ladder diagrams of the Born series; it does not rely on the diffusion approximation. Quantitative predictions are obtained, concerning various observables pertaining to optically thick slabs, such as the mean angle-resolved reflected and transmitted intensities, and the shape 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 regime of very anisotropic scattering, where the transport mean free path $\ell^*$ is much larger than the scattering mean free path $\ell$, is studied in full detail. For the first time the relevant Schwarzschild-Milne equation is solved exactly in the absence of internal reflections, and asymptotically in the regime of a large index mismatch. An unexpected outcome concerns the angular width of the enhanced backscattering cone, which is predicted to scale as $Δθ\simλ/\sqrt{\ell\ell^*}$, in contrast with the generally accepted $λ/\ell^*$ law, derived within the diffusion approximation.