  The polarization direction of an electromagnetic field changes and eventually
reaches a steady state when propagating through a birefringent material with
off axis absorption or gain. The steady state orientation direction depends on
the magnitude of the absorption (gain) and the phase retardation rate. The
change in the polarization direction is experimentally demonstrated in weakly
doped ($0.05\%$) Pr$^{3+}$:Y$_2$SiO$_5$ crystals, where the light polarization,
if initially aligned along the most strongly absorbing principal axis,
gradually switch to a much less absorbing polarization state during the
propagation. This means that the absorption coefficient, $\alpha$, in
birefringent materials generally varies with length. This is important for,
e.g., laser crystal gain media, highly absorbing and narrow band spectral
filters and quantum memories.
