Why are optical refractive indices so small?
An international team of scientists reports in Physical Review X on a new theory that can explain why the refractive index of a disordered atomic medium only reaches a maximum value of 1.7.
The Iconic Album Cover: A Symbol and a Misunderstanding
Pink Floyd intended their Dark Side of the Moon cover, voted the greatest classic rock album of all time, to portray the prism and dispersion of light into a rainbow as metaphorical symbolism and a representation of their light show. However, they were unaware that many would later use this image to illustrate the concept of refractive index and how light changes speed and direction upon encountering a different medium.
Conceptual Accuracy and Educational Impact
Although conceptually the drawing was not accurate, it conveyed the message that light changes its speed when it moves into another medium and that the different speeds of different colors cause white light to disperse into its different components. This change in speed is related to the refractive index, a unitless number that represents the ratio of the speed of light in a vacuum and the speed of light in a medium.In general, all materials with positive refractive indices have values close to 1 for visible light. Whether this is just a coincidence or reflects some deeper physics has never been explained.
Now, in a recent study published in Physical Review X and highlighted by the editors, ICFO researchers Francesco Andreoli and ICREA Prof. at ICFO Darrick Chang, in collaboration with researchers from Princeton University, University of Chicago, and Institut d’Optique, have investigated and explained why the refractive index of a dilute atomic gas can only reach a maximum value of 1.7, regardless of how high the density of atoms becomes.
Challenging Conventional Theories
This result contradicts conventional textbook theories, which predict that more material leads to a larger optical response and refractive index. The challenge in understanding this problem lies in the multiple scattering of light—all the complex paths light can take within a medium—and the resulting interference. This causes each atom to experience a local intensity of light that differs greatly from the intensity we send in, and varies depending on the surrounding atoms’ geometry. Instead of dealing with the complex microscopic details of this granularity, textbooks often make assumptions that effectively smooth out the granularity and its effects on light.
In contrast to traditional methods, the teams leverage a theory called the strong-disorder renormalization group (RG), allowing them to capture granularity and multiple scattering effects in a simplified manner. Furthermore, this theory reveals that near-field interactions disproportionately affect the optical response of any given atom due to its single nearest neighbor, thus explaining why typical smoothing theories fall short. Specifically, the physical effect of these near-field interactions is the production of an inhomogeneous broadening of atomic resonance frequencies, with the amount of broadening increasing with density. Consequently, regardless of the physical density of atoms, incoming light of any frequency will only encounter approximately 1 near-resonant atom per cubic wavelength to scatter off efficiently. As a result, the refractive index is limited to a maximum value of 1.7.
More broadly, this study suggests that researchers could utilize the RG theory as a new versatile tool for understanding the complex problem of multiple scattering of light in near-resonant disordered media, particularly in the nonlinear and quantum regimes. Additionally, it highlights the potential of attempting to understand the limits of the refractive index of real materials by starting from the individual atoms that comprise them.
More information
Original article
F. Andreoli, M. Gullans, A. A. High, A. Browaeys, and D. Chang. 2021. Maximum Refractive Index of an Atomic Medium. Phys. Rev. X, 11, 011026.
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