We investigate the optical response of strongly disordered quantum Hall
states in two-dimensional Dirac materials and find qualitatively different
effects in the radiation properties of the bulk versus the edge. We show that
the far-field radiation from the edge is characterized by large multipole
moments (> 50) due to the efficient transfer of angular momentum from the
electrons into the scattered light. The maximum multipole transition moment is
a direct measure of the coherence length of the edge states. Accessing these
multipole transitions would provide new tools for optical spectroscopy and
control of quantum Hall edge states. On the other hand, the far-field radiation
from the bulk appears as random dipole emission with spectral properties that
vary with the local disorder potential. We determine the conditions under which
this bulk radiation can be used to image the disorder landscape. Such optical
measurements can probe sub-micron length scales over large areas and provide
complementary information to scanning probe techniques. Spatially resolving
this bulk radiation would serve as a novel probe of the percolation transition
near half-filling.Comment: v2: 8 pages, 4 figure
