Optical transmission through a dipolar layer

Abstract: The interaction between light and matter is fundamental to developments in quantum optics and information. Over recent years enormous progress has been made in controlling the interface between light and single emitters including ions, atoms, molecules, quantum dots and ensembles. For many systems, inter-particle interactions are typically negligible. However, if the emitters are separated by less than the emission wavelength, resonant dipole--dipole interactions modify the radiative decay rate and induce a splitting or shift of the resonance. Here we map out the transition between individual dipoles and a strongly interacting ensemble by increasing the density of atoms confined in a layer with thickness much less than the emission wavelength. We find two surprising results: whereas for a non-interacting ensemble the opacity increases linearly with atomic density, for an interacting ensemble the opacity saturates, i.e., a thin dipolar layer never becomes opaque regardless of how many scatterers are added. Secondly, the relative phase of the dipoles produces an abrupt change in the optical transmission around the thickness \lambda/4.