Retarding parallel components of a Mueller matrix

TL;DR

This paper establishes mathematical conditions for identifying retarding components in Mueller matrices, enhancing the analysis of depolarizing samples in polarimetry across various scientific fields.

Contribution

It provides new criteria for detecting retarding incoherent components in Mueller matrices based on the rank of the coherency matrix and other properties.

Findings

Retarding components can be identified when the coherency matrix rank is 3 or 4.

Identification is possible at rank 2 only if diattenuation equals polarizance.

Results facilitate advanced polarimetric analysis in optics and remote sensing.

Abstract

Mueller matrix polarimetry constitutes a nondestructive powerful tool for the analysis of material samples that is used today in an enormous variety of applications. Depolarizing samples exhibit, in general, a complicated physical behavior that requires appropriate mathematical formulation through models involving decomposition theorems in terms of simpler components. In this work, the general conditions for identifying retarding incoherent components of a given Mueller matrix M are obtained. It is found that when the coherency matrix C associated with M has rank C = 3,4 it is always possible to identify one or two retarding incoherent components respectively, while in the case where rank C =2, such retarding component only can be achieved if and only if the diattenuation and the polarizance of M are equal. Since the Mueller matrices associated with retarders have a simple structure, the results obtained open new perspectives for the exploitation of polarimetric techniques in optics, remote sensing and other areas.