Abstract
By means of the Poincaré-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-fieldinduced birefringence.