The theoretical analysis of ultra-fast laser propagation in disordered matter is enormously complicated by the need to account for a 3D enviroment (Anderson localization and related phenomena are indeed a trivial issue in reduced dimensionality), material dispersion, multiple-scattering processes, polidispersivity and many other phenomena.

Ab initio computation based on Finite Difference Time Domain codes is probably the most extensive approach to the problem.

In a recent article, Silvia Gentilini, Andrea Fratalocchi, and Claudio Conti have reported the first 3D simulations of 100fs laser pulses in a disordered medium by the MD-FDTD approach.

We reported a quantitave calculation of the light diffusion constant (in agreement with experiments from the literature) and also of the dynamics of the diffusion constant.

The figure below shows on the left panel (a) the edge of the trasmitted pulse in log scale (the gray area in the inset is the input pulse, the black line the trasmitted pulse); while on panel (b) the diffusivity constant versus the material filling factor (the inset is the dynamical diffusivity for two different particle diameters)