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By means of the Poincar\'e-sphere representation, new exact solutions for the evolution of the polarization in anisotropic crystals exhibiting a third-order nonlinearity and subjected to a dc electric field are found. This allows us to discover the existence of bifurcations of the nonlinear eigenpolarizations. A stability analysis of the eigenpolarizations shows how the intrinsic instabilities evolve in the interaction between self-induced and dc-field--induced birefringence.
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Gregori et al. (1986) studied this question.
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