# Quaternion algebra for Stokes-Mueller formalism

## TL;DR

This paper introduces a quaternion-based reformulation of the Stokes-Mueller formalism, providing a more suitable mathematical framework for describing optical systems and their polarization states.

## Contribution

It presents a novel quaternion approach to the Stokes-Mueller formalism, unifying different representations and extending to depolarization phenomena.

## Key findings

- Quaternion states are isomorphic to vector and matrix states.
- Quaternion approach simplifies the description of nondepolarizing systems.
- Reformulation includes depolarization phenomena using quaternion states.

## Abstract

It is shown that the Stokes-Mueller formalism can be reformulated in terms of quaternions, and the quaternion approach is more suitable for the formalism of Mueller-Jones states that we have recently described. In terms of quaternions it can be shown that the vector and matrix states and the Jones matrix associated to nondepolarizing optical systems are different representations isomorphic to the same quaternion state, and this quaternion state turns out to be the rotator of the Stokes quaternion. It is also shown that the coherent linear combination of nondepolarizing optical media states and depolarization phenomena can be reformulated in terms of quaternion states.