Diffusion of light in semitransparent media

TL;DR

This paper investigates light diffusion in nearly transparent media, showing that even at low optical thickness, transmitted light exhibits diffusive behavior over time, with boundary conditions significantly affecting transport properties.

Contribution

It demonstrates that diffusive transport occurs in thin, semi-transparent media and highlights the influence of boundary conditions on effective diffusion parameters.

Findings

Linear increase of mean square width with time at low optical thickness

Boundary conditions alter the effective diffusion coefficient

Diffusive behavior persists despite minimal scattering

Abstract

Light diffusion is usually associated with thick, opaque media. Indeed, multiple scattering is necessary for the onset of the diffusive regime and such condition is generally not met in almost transparent media. Nonetheless, at long enough times, transport in an infinite thin slab is still determined by a multiple scattering process whose complete characterization is lacking. In this paper we show that, after a short transient, the mean square width of the transmitted intensity still exhibits a simple linear increase with time as predicted by diffusion theory, even at optical thickness as low as one. Interestingly, such linear growth is predicted not to depend neither on the slab thickness nor on its refractive index contrast, yet the accuracy of this simple approximation in the ballistic-to-diffusive regime hasn't been investigated so far. By means of Monte Carlo simulations, we find clear evidence that boundary conditions play an active role in redefining the very asymptotic value of the diffusion coefficient by directly modifying the statistical distributions underlying light transport in such media. In this respect, we demonstrate the need to distinguish between a set of intrinsic and effective transport parameters, whose relation and interplay with boundary conditions remains to be fully understood.