Multiple scattering theory in one dimensional space and time dependent disorder: Average field

We study theoretically the propagation of light in a one-dimensional spaceand time dependent disorder. The disorder is described by a fluctuatingpermittivity $\epsilon(x,t)$ exhibiting short-range correlations in space andtime, without cross correlation between them. Depending on the illuminationconditions, we show that the intensity of the average field decaysexponentially in space or in time, with characteristic length or time definingthe scattering mean-free path $\ell_s$ and the scattering mean-free time$\tau_s$. In the weak scattering regime, we provide explicit expressions for$\ell_s$ and $\tau_s$, that are checked against rigorous numerical simulations.