Transforming nondepolarizing Mueller matrices into Jones matrices

TL;DR

This paper demonstrates how to derive the Jones matrix from a nondepolarizing Mueller matrix using a four-dimensional complex vector, revealing a direct mathematical relationship between these two representations.

Contribution

It introduces a method to extract the Jones matrix from a nondepolarizing Mueller matrix via an associated complex vector, enhancing understanding of polarization optics.

Findings

The complex vector is isomorphic to the Jones matrix.

The complex vector can be obtained from the Mueller matrix up to an overall phase.

Provides a mathematical link between Mueller and Jones formalisms.

Abstract

It is well known that there exists a four dimensional complex vector associated with a nondepolarizing Mueller matrix. In this note it is shown that this complex vector, which is isomorphic to the Jones matrix, can be obtained from the nondepolarizing Mueller matrix apart from an overall phase.