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We investigate the optical response of strongly disordered quantum Hallstates in two-dimensional Dirac materials and find qualitatively differenteffects in the radiation properties of the bulk versus the edge. We show thatthe far-field radiation from the edge is characterized by large multipolemoments (> 50) due to the efficient transfer of angular momentum from theelectrons into the scattered light. The maximum multipole transition moment isa direct measure of the coherence length of the edge states. Accessing thesemultipole transitions would provide new tools for optical spectroscopy andcontrol of quantum Hall edge states. On the other hand, the far-field radiationfrom the bulk appears as random dipole emission with spectral properties thatvary with the local disorder potential. We determine the conditions under whichthis bulk radiation can be used to image the disorder landscape. Such opticalmeasurements can probe sub-micron length scales over large areas and providecomplementary information to scanning probe techniques. Spatially resolvingthis bulk radiation would serve as a novel probe of the percolation transitionnear half-filling.

High-Order Multipole Radiation from Quantum Hall States in Dirac Materials