Maximum refractive index of an atomic medium

Francesco Andreoli

ICFO - francesco.andreoli@icfo.eu

All optical materials with a positive refractive index have a value of index that is of order unity. Surprisingly, a deep understanding of this universal behavior seems to be lacking. Here, we theoretically and numerically investigate the optical properties of an ensemble of ideal atoms as a function of density, starting from the dilute gas limit, including the effects of multiple scattering and near-field interactions. We find that the maximum index reaches a limiting value n=1.7, at densities far below those where chemical processes become important. We propose an explanation based upon strong-disorder renormalization group theory, in which the near-field interaction combined with random atomic positions results in an inhomogeneous broadening of atomic resonance frequencies. This mechanism ensures that, regardless of the physical atomic density, light at any given frequency only interacts with at most a few near-resonant atoms per cubic wavelength, thus limiting the maximum index.