Structure of polarimetric purity of three-dimensional polarization states

Abstract

It has recently been demonstrated that a general three-dimensional (3D) polarization state cannot be considered an incoherent superposition of (1) a pure state, (2) a two-dimensional unpolarized state, and (3) a 3D unpolarized state [J. J. Gil, Phys. Rev. A 90, 043858 (2014)]. This fact is intimately linked to the existence of 3D polarization states with fluctuating directions of propagation, but whose associated polarization matrices R satisfy rank R = 2. In this work, such peculiar states are analyzed and characterized, leading to a meaningful general classification and interpretation of 3D polarization states. Within this theoretical framework, the interrelations among the more significant polarization descriptors presented in the literature, as well as their respective physical interpretations, are studied and illustrated with examples, providing a better understanding of the structure of polarimetric purity of any kind of polarization state.

Polarimetric purity and the concept of degree of polarization

“…The main aim of this paper is to analyze and compare the above-mentioned approaches in the light of certain recent results dealing with the existence of regular and nonregular polarization states [10]. In particular, we consider the contributions of their linear and circular degrees of polarization to polarimetric purity.…”

“…In fact, polarization states can be classified into two types depending on whetherR m is a real matrix (regular states) or not (nonregular states) [10]. In the case of regular statesR m always represents a 2D unpolarized state.…”

“…In the case of nonregular states,R m corresponds to an equiprobable mixture of two mutually orthogonal states whose polarization ellipses lie in different planes, and thereforeR m does not represent a 2D unpolarized state, and exhibits nonzero contribution to P c and P l [10]. An example of a nonregular state (see Fig.…”

“…To complete the necessary framework for our analysis, let us further recall that, among the different possible representations of R as compositions of mutually incoherent states, a privileged view of the structure of polarimetric purity of R is given by its characteristic (or trivial) decomposition [2,10,18],…”

“…where the degree of elliptical purity P e ≡ P 2 l + P 2 c [10] summarizes all the contributions to polarimetric purity derived from the degrees of linear and circular purity (that is, all the contributions except for the purity due to the degree of directionality P d ).…”