# Global aspects of polarization optics and coset space geometry

## TL;DR

This paper applies group theory and coset space techniques to address global issues in polarization optics, revealing new insights and the importance of groups like SU(3) alongside SU(2) and SO(3).

## Contribution

It introduces a global geometric framework for polarization optics using coset space methods, highlighting the role of SU(3) in addition to traditional groups.

## Key findings

- Global smooth phase conventions are possible on the Poincaré sphere.
- Real or complex bases for electric vectors can be globally defined.
- SU(3) group plays a significant role in polarization optics.

## 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.