Propagation of light polarization in a birefringent medium: Exact analytic models

Driving the analogy between the coherent excitation of a two-state quantum system and the torque equation of motion, we present exact analytic solutions to different models for manipulation of polarization in birefringent medium. These models include the one-dimensional model, the Landau-Zener model, and the Demkov-Kunike model. We also give an example for robust, broadband manipulation of polarization by suitably tailoring the birefringence vector.