  Rotation of polarization of light on transmission and reflection at materials
with time-reversal breaking (Faraday and Kerr effects, respectively) have been
studied for over a hundred years. We add to such phenomena by studying optical
properties of magneto-chiral states which are loop currents with topological
Hall effect. These break time-reversal and are chiral but the product of
chirality and time-reversal is preserved. Qualitatively new features arise in
reflection and transmission through such a state. This state is shown to be
induced in underdoped cuprates given the observed magneto-electric loop-current
order in cuprates and certain other specified condition. These results explain
the observation of Kerr effects with unusual properties in the underdoped
cuprates and help further confirm the nature of the symmetry breaking in
underdoped cuprates.
