Hyper-ballistic transport of waves

In this month's Nature Physics there is a paper entitled "Hyper-transport of light and stochastic acceleration by evolving disorder" by Levi, et al. The work is an experimental and numerical study of the propagation of light in a disordered medium that has been carefully constructed to serve as a model for the transport of a 2D quantum wavepacket in a spatio-temporal random potential, i.e. a potential energy landscape that changes randomly in space and time. The authors demonstrate that a beam's spot-size and angular spectrum spreads faster as it propagates through this particular medium than it would if the beam propagated in free space or in a random distribution of parallel waveguides (the Anderson localized regime).

The crux of their demonstration is provided by the comparison of their measured transport regime to the two aforementioned regimes: ballistic and localized transport. Ballistic transport is characterized by a beam spot size that grows with propagation distance and a constant angular spectrum with many longitudinal plane wave components. Localized transport is characterized by a beam spot size that does not grow in size with propagation and takes place in a disordered medium with refractive index fluctuations that possess an angular spectrum of plane waves with all the same longitudinal components. These characteristics are illustrated in Figure 2 of the article.

In contrast, hyper-transport is defined by a spot size that grows faster with propagation than in the ballistic case and by an angular spectrum of the beam (not of the disorder!) that widens with propagation as well (see Figure 3C).

The authors do not provide a comparison with the case of diffusive propagation of the waves. I think that this may be because diffusive transport (increasing spot size and constant but uniform angular spectrum over all propagation directions) is a limiting case of the transport regime that they studied. In other words, they looked at the transient process of the waves becoming diffusive, but not the limiting case. I think that similar work has already been done in the area of beam propagation through atmospheric turbulence, though I can't provide any references.

To be fair, the authors do state that:

"Strictly within the domain of optics, the results described below are intuitive. However, this direct analogy to transport in quantum systems makes our findings relevant for very many wave systems containing disorder."

I would have liked to have seen a comparison to or discussion about the diffusive regime since it would reveal that any multiply scattering medium displays this hyper-transport for short propagation distances.

Finally, I like their technique for controlling the disorder's correlation distance in the z-direction. This seems to be a very good tool for studying transport in disordered systems.