Gaussian-to-Lévy statistical crossover in a random amplifying medium: Monte Carlo simulation

Abstract

We report Monte Carlo simulations of photons diffusing through a random amplifying medium and study the statistics of emitted intensity fluctuations. We observe a crossover from the Gaussian to the Lévy statistics corresponding to divergence of the variance of intensity fluctuations, as we go to large gain and strong scattering, consistent with our earlier analytical and experimental works. In the limit of very high gain, our simulations suggest a “Lévy microscope effect”, where the emitted mean intensity is expected to diverge, and the sum of intensities is dominated by the typical largest event.