Abstract
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 $n\approx 1.7$. 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.
Highlights
One interesting observation is that all the optical materials that we know of, with a positive index of refraction at visible wavelengths, universally have an index of order unity, n ∼ Oð1Þ
In large-scale numerics, we find that the maximum index does not indefinitely grow with density, and it saturates to a maximum value of n ≈ 1.7, when the typical distance between atoms becomes smaller than the length scale associated with the resonant cross section, i.e., d < λ0
We have shown that despite the large resonant scattering cross section of a single atom, a dense atomic medium does not exhibit an anomalously large optical response
Summary
Our RG theory is based upon the key intuition gained in the collective scattering of just two atoms to build up an understanding of the many-atom problem in a hierarchical manner. (6) and (7) (with the near-field interactions of renormalized atoms suitably removed; see Appendix B) to calculate the maximum real index (optimized over detunings) as a function of density η of the ensemble with renormalized resonance frequencies. After the system is mapped to an inhomogeneously broadened distribution, PðωeffÞ, where near-field interactions and the influence of single neighbors are seen to be strongly reduced, one can apply a smooth medium approximation. We stress that the emergence of a finite bound to the maximum index predicted by Eq (10) can be directly related to the invariance of the distribution Pðωeff=ηÞ and to the linear growth of broadening with density
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
