  Recent experiments have shown rotation of the plane of polarization of light
reflected from the surface of some superconductors. This indicates that time
reversal and certain mirror symmetries are broken in the ordered phase. The
photon energy exceeds the electronic bandwidth, so that completely filled or
completely empty bands must play a role. We show that in strong-coupling theory
a Coulomb interaction may produce an order parameter in the unoccupied band
that explains the observations. The theory puts tight constraints on the form
of the order parameter in different bands. We propose that the experiments have
detected, for the first time, the existence of a superconducting order
parameter in a band far from the Fermi energy.
