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The polarization direction of an electromagnetic field changes and eventuallyreaches a steady state when propagating through a birefringent material withoff axis absorption or gain. The steady state orientation direction depends onthe magnitude of the absorption (gain) and the phase retardation rate. Thechange in the polarization direction is experimentally demonstrated in weaklydoped ($0.05\%$) 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 thepropagation. This means that the absorption coefficient, $\alpha$, inbirefringent materials generally varies with length. This is important for,e.g., laser crystal gain media, highly absorbing and narrow band spectralfilters and quantum memories.

Wave propagation in birefringent materials with off axis absorption or gain