Super-exponential extinction of radiation in a negatively correlated random medium

It was shown in recent work that spatial correlations among obstacles of a random, absorbing medium can lead to slower-than-exponential (sub-exponential) extinction of radiation with propagation distance. Exponential decay, described by the Beer-Lambert law, arises in a special case when the medium contains no correlations. A third possibility, examined here, is that of negative correlations which can lead to faster-than-exponential (super-exponential) extinction. Using a Monte Carlo approach, we confirm that sub-exponential decay occurs when the volume-averaged pair correlation function is greater than zero at the scale of interest and that the Beer-Lambert law is recovered when correlations vanish. We also find that when the volume-averaged pair correlation function is negative, super-exponential extinction with propagation distance occurs. These results are of special interest to the problem of radiative transfer in cloudy atmospheres, where the pair correlation function previously has been shown to be negative and positive at different scales.