A general formulation of the additive composition and decomposition of Mueller matrices is presented, which is expressed in adequate terms for properly performing the "polarimetric subtraction," from a given depolarizing Mueller matrix M, of the Mueller matrix of a given nondepolarizing component that is incoherently embedded in the whole system represented by M. A general and comprehensive procedure for the polarimetric subtraction of depolarizing Mueller matrices is also developed.
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.
The algebraic methods for serial and parallel decompositions of Mueller matrices are combined in order to obtain a general framework for a suitable analysis of polarimetric measurements based on equivalent systems constituted by simple components. A general procedure for the parallel decomposition of a Mueller matrix into a convex sum of pure elements is presented and applied to the two canonical forms of depolarizing Mueller matrices [Ossikovski, J. Opt. Soc. Am. A 27, 123 (2010).], leading to the serial-parallel decomposition of any Mueller matrix. The resultant model is consistent with the mathematical structure and the reciprocity properties of Mueller matrices.
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