Global aspects of polarization optics and coset space geometry

Abstract: We use group theoretic ideas and coset space methods to deal with problems in polarization optics of a global nature. These include the possibility of a globally smooth phase convention for electric fields for all points on the Poincar\'{e} sphere, and a similar possibility of real or complex bases of transverse electric vectors for all possible propagation directions. It is shown that these methods help in understanding some known results in an effective manner, and in answering new questions as well. We find that apart from the groups $SU(2)$ and $SO(3)$ which occur naturally in these problems, the group $SU(3)$ also plays an important role.