  The photon self-energy from chirally imbalanced quark matter is evaluated at
finite temperature and density using the real time formulation of thermal field
theory. The analytic structure is explored in detail exposing the cut structure
which corresponds to a variety of physical scattering and decay processes in
the medium and their thresholds. The mass of the quarks in the chiral symmetry
broken phase are obtained from the gap equation of the Nambu--Jona-Lasinio
model. It is found that, in presence of finite chiral chemical potential, the
chiral condensate tends to get stronger at low temperature while the opposite
is observed at high values of temperature. A continuous spectrum is obtained
for the electromagnetic spectral function and this is purely a finite chiral
chemical potential effect.
