  We consider the propagation of polarized light in the medium with Maxwell
fish eye refraction index profile. We show that polarization violates the
additional symmetries of medium, so that ray trajectories no longer remain
closed. Then we suggest a modified, polarization-dependent Maxwell fish eye
refraction index which restores all symmetries of initial profile and yields
closed trajectories of polarized light. Explicit expressions for the
polarization dependent integrals of motion and the solutions of corresponding
ray trajectories are presented.
