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Wave propagation in birefringent materials with off axis absorption or gain

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, $α$, 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.