Singular Mueller matrices

TL;DR

This paper systematically investigates the formal reasons behind the singularity of Mueller matrices, providing a classification and geometric interpretation that aids experimental analysis of polarization media.

Contribution

It offers a comprehensive analysis and classification of singular Mueller matrices using serial decompositions and characteristic ellipsoids, enhancing understanding of their properties.

Findings

Identifies conditions leading to singular Mueller matrices

Provides a geometric classification framework

Enhances interpretation of polarization media behavior

Abstract

Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance, or because its associated canonical depolarizer has the property of fully randomizing, the circular component (at least) of the states of polarization of light incident on it. The formal reasons for which the Mueller matrix M of a given medium is singular are systematically investigated, analyzed and interpreted in the framework of the serial decompositions and the characteristic ellipsoids of M. The analysis allows for a general classification and geometric representation of singular Mueller matrices, of potential usefulness to experimentalists dealing with such media.