Light propagation beyond the mean-field theory of standard optics

With ready access to massive computer clusters we may now study light propagation in a dense cold atomic gas by means of basically exact numerical simulations. We report on a direct comparison between traditional optics, that is, electrodynamics of a polarizable medium, and numerical simulations in an elementary problem of light propagating through a slab of matter. The standard optics fails already at quite low atom densities, and the failure becomes dramatic when the average interatomic separation is reduced to around $k^{-1}$, where $k$ is the wave number of resonant light. The difference between the two solutions originates from correlations between the atoms induced by light-mediated dipole-dipole interactions.