02150nas a2200169 4500008004100000245004900041210004900090260001400139490000700153520166900160100002401829700002101853700002401874700002201898700002301920856003701943 2021 eng d00aMaximum Refractive Index of an Atomic Medium0 aMaximum Refractive Index of an Atomic Medium c2/18/20210 v113 a
It is interesting to observe that all optical materials with a positive refractive index have a value of index that is of order unity. Surprisingly, though, a deep understanding of the mechanisms that lead to this universal behavior seems to be lacking. Moreover, this observation is difficult to reconcile with the fact that a single, isolated atom is known to have a giant optical response, as characterized by a resonant scattering cross section that far exceeds its physical size. Here, we theoretically and numerically investigate the evolution of 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. Interestingly, despite the giant response of an isolated atom, we find that the maximum index does not indefinitely grow with increasing density, but rather reaches a limiting value n≈1.7. 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 attainable. Our work is a promising first step to understand the limits of refractive index from a bottom-up, atomic physics perspective, and also introduces renormalization group as a powerful tool to understand the generally complex problem of multiple scattering of light overall.
1 aAndreoli, Francesco1 aGullans, Michael1 aHigh, Alexander, A.1 aBrowaeys, Antoine1 aChang, Darrick, E. uhttps://arxiv.org/abs/2006.01680