Frequency redistribution and step-size distribution of light scattered by atomic vapor: applications to L\'evy flight random walk

TL;DR

This paper models light propagation in atomic vapor as a Le9vy flight, analyzing how frequency redistribution and vapor size influence step-size distribution and random walk behavior.

Contribution

It calculates the frequency redistribution and step-size distribution for light in atomic vapor, revealing effects of vapor size and atomic structure on Le9vy flight characteristics.

Findings

Finite vapor size introduces a cutoff in the step-size distribution.

Multi-level atomic structure causes oscillations in the distribution slope.

The Le9vy parameter b5 depends on step size, affecting transport properties.

Abstract

The propagation of light that undergoes multiple-scattering by resonant atomic vapor can be described as a L\'evy flight. L\'evy flight is a random walk with heavy tailed step-size (r) distribution, decaying asymptotically as $P(r)\sim r^{-1-\alpha}$, with $\alpha<2$. The large steps, typical of L\'evy flights, have its origins in frequency redistribution of the light scattered by the vapor. We calculate the frequency redistribution function and the step-size distribution for light diffusion in atomic vapor. From the step-size distribution we extract a L\'evy parameter $\alpha$ that depends on the step's size. We investigate how the frequency redistribution function and step-size distribution are influenced by the finite size of the vapor and the many-level structure typical for alkali vapors. Finite size of the vapor introduces cutoff on the light scattered spectrum and thus in the size of steps. Multi-level structure introduces oscillations in $P(r)$ slope. Both effects might have an impact on measurables related to the L\'evy flight random walk.