  It has previously been shown that a dye-filled microcavity can produce a
Bose-Einstein condensate of photons. Thermalization of photons is possible via
repeated absorption and re-emission by the dye molecules. In this paper, we
theoretically explore the behavior of the polarization of light in this system.
We find that in contrast to the near complete thermalization between different
spatial modes of light, thermalization of polarization states is expected to
generally be incomplete. We show that the polarization degree changes
significantly from below to above threshold, and explain the dependence of
polarization on all relevant material parameters.
