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The propagation of light in a resonant atomic vapor can \textit{a priori} bethought of as a multiple scattering process, in which each scattering eventredistributes both the direction and the frequency of the photons.Particularly, the frequency redistribution may result in L\'evy flights ofphotons, directly affecting the transport properties of light in a resonantatomic vapor and turning this propagation into a superdifusion process. Here,we report on a Monte-Carlo simulation developed to study the evolution of thespectrum of the light in a resonant thermal vapor. We observe the gradualchange of the spectrum and its convergence towards a regime of CompleteFrequency Redistribution as the number of scattering events increases. We alsoanalyse the probability density function of the step length of photons betweenemissions and reabsorptions in the vapor, which governs the statistics of thelight diffusion. We observe two different regime in the light transport:superdiffusive when the vapor is excited near the line center and normaldiffusion for excitation far from the line center. The regime of CompleteFrequency Redistribution is not reached for excitation far from resonance evenafter many absorption/reemission cycles due to correlations between emitted andabsorbed frequencies.

Redistribution of light frequency by multiple scattering in a resonant atomic vapor