  Light scattering in dense media is a fundamental problem of many-body
physics, which is also relevant for the development of optical devices. In this
work we investigate experimentally light propagation in a dense sample of
randomly positioned resonant scatterers confined in a layer of sub-wavelength
thickness. We locally illuminate the atomic cloud and monitor
spatially-resolved fluorescence away from the excitation region. We show that
light spreading is well described by a diffusion process, involving many
scattering events in the dense regime. For light detuned from resonance we find
evidence that the atomic layer behaves as a graded-index planar waveguide.
These features are reproduced by a simple geometrical model and numerical
simulations of coupled dipoles.
