Invariant quantities of a Mueller matrix under rotation and retarder transformations

TL;DR

This paper investigates the invariant polarimetric quantities of Mueller matrices under rotation and retarder transformations, offering new parameterizations that reveal fundamental physical insights into polarization states.

Contribution

It introduces a comprehensive analysis of invariants of Mueller matrices under specific transformations, providing novel parameterizations linked to physical properties.

Findings

Identification of invariant quantities under rotation and retarder transformations

Parameterizations of Mueller matrices based on invariant physical quantities

Enhanced understanding of polarization state representations

Abstract

Mueller matrices are defined with respect to appropriate Cartesian reference frames for the representation of the states of polarization of the input and output electromagnetic waves. The polarimetric quantities that are invariant under rotations of the said reference frames about the respective directions of propagation (rotation transformations) provide particularly interesting physical information. Moreover, certain properties are also invariant with respect to the action of birefringent devices located at both sides of the medium under consideration (retarder transformations). The polarimetric properties that remain invariant under rotation and retarder transformations are analyzed and interpreted, providing significant parameterizations of Mueller matrices in terms of meaningful physical quantities.