# Homogenization of an ensemble of interacting resonant scatterers

## TL;DR

This paper investigates the limits of optical homogenization in dense atomic ensembles, revealing that collective interactions prevent homogenization near resonance unless spatial correlations or non-radiative losses are introduced.

## Contribution

It demonstrates that the standard density criterion for homogenization is insufficient near resonance and highlights the role of collective modes and correlations in achieving homogenization.

## Key findings

- Homogenization criteria are not fulfilled near resonance despite high density.
- Light-induced dipole-dipole interactions lead to collective scattering modes.
- Spatial correlations or non-radiative losses enable homogenization in dense atomic ensembles.

## Abstract

We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density $\rho$. The ensemble is dense enough for the usual condition for homogenization, viz. $\rho\lambda^3 \gg 1$, to be reached. Introducing the coherent and incoherent scattered powers, we define two criteria to define the homogenization regime. We find that when the excitation field is tuned in a broad frequency range around the resonance, none of the criteria for homogenization is fulfilled, meaning that the condition $\rho\lambda^3\gg 1$ is not sufficient to characterize the homogenized regime around the atomic resonance. We interpret these results as a consequence of the light-induced dipole-dipole interactions between the atoms, which implies a description of scattering in terms of collective modes rather than as a sequence of individual scattering events. Finally, we show that, although homogenization can never be reached for a dense ensemble of randomly positioned laser-cooled atoms around resonance, it becomes possible if one introduces spatial correlations in the positions of the atoms or non-radiative losses, such as would be the case for organic molecules or quantum dots coupled to a phonon bath.