Topology in the Random Scattering of Light

Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness of light introduces topological aspects into the picture. The dynamics of electromagnetic waves follow the same differential equations as those of a spin-$1$ Weyl semimetal. In the presence of disorder, this equivalence leads to a range of phenomena explored in this paper. These include topological protection against localization when helicity hybridization is weak, the emergence of exotic phases in weakly scattering media, and anomalies in optical transparency in the presence of synthetic `magnetic fields'. We argue that some of these effects should be visible and investigated already in weakly disordered optical materials.