maximum densities and minimum sizes of atom-light interfaces needed to realize high-fidelity quantum technologies. Finally, while we focus here on the linear optical response of a dense atomic medium, we believe that the validity of RG is quite general, and can constitute a versatile new tool for the generally challenging problem of multiple scattering in near-resonant disordered media [@Chomaz2012AbsorptionAnalysis; @Lagendijk1996ResonantLight; @Skipetrov2014AbsenceScatterers; @Schilder2017HomogenizationScatterers; @Javanainen2016LightOptics; @Fayard2015IntensityPatterns; @Guerin2017LightEffects; @Corman2017TransmissionAtoms; @Zhu2016LightMedia; @Jennewein2018CoherentTheory; @Cottier2019MicroscopicLight], including in the nonlinear and quantum regimes [@Binninger2019NonlinearCloud].

This paper is structured as follows. First, we briefly review the theoretical formulation of the multiple scattering problem of atoms or other point-like dipoles, and the standard atomic physics model of refractive index, when atomic granularity and multiple scattering are ignored. We then formulate our large-scale numerical simulations, describing a few implementation details that allow index to be efficiently calculated, and show that the index eventually saturates with increasing density to a maximum value of $n\approx 1.7$. We then introduce our RG theory, which highlights the importance of granularity and nearby atomic pairs on the macroscopic optical response, before concluding with an expanded discussion of future interesting directions to investigate.

![**Simulated physical system.** a) A cylindrical ensemble of randomly distributed atoms (green points) 