Decomposition of a depolarizing Mueller matrix into its nondepolarizing components by using symmetry conditions

Abstract

A procedure for the parallel decomposition of a depolarizing Mueller matrix with an associated rank 2 covariance matrix into its two nondepolarizing components is presented. We show that, if one of the components agrees with certain symmetry conditions, the arbitrary decomposition becomes unique, and its calculation is straightforward. Solutions for six different symmetries, which are relevant for the physical interpretation of polarimetric measurements, are provided. With this procedure, a single polarimetric measurement is sufficient to fully disclose the complete polarimetric response of two different systems and evaluate their weights in the overall response. The decomposition method we propose is illustrated by obtaining the ellipsometric responses of a silicon wafer and a holographic grating from a single measurement in which the light spot illuminates sectors of both materials. In a second example, we use the decomposition to analyze an optical system in which a polarizing film is partially covered by another misaligned film.

Sixteen Pairs of 4-Component Spinors for SL(4,C) and Four Types of Transformations with a Conjugate Space Which Has No Counterpart in SL(2,C)

“…Here Z can be type A, B, C or D. 16 Now let us consider the inner product of two state vectors α, β|γ, δ = αγ + βδ 0 0 αγ + βδ (151)…”

“…First column corresponds to the eigenvalue +1 and the second column corresponds to the eigenvalue −1. 16 Let |χ (x) denote a state vector of any kind and let | χ(x) be its dotted contravariant version. These objects live in the state space and they all fit the pattern that given in Equation (149).…”

Complete Mueller matrix from a partial polarimetry experiment: the 12-element case

“…The former case commonly arises in finite spot size measurements in reflection configuration where the spot covers two optically different areas, e.g. an isotropic substrate and an anisotropic diffraction grating ruled in it [27][28][29][30][31]. The latter case is typical of optically thick slabs of transparent homogeneous material (e.g.…”

“…For instance, this is the case with an (anisotropic) diffraction grating whose lateral dimensions are smaller than the spot size, ruled in an (isotropic) substrate. There exist both algebraic [29,30] and numerical [31] robust practical procedures for recovering the two components M 1 and M bd given the experimental M.…”

“…Appendix C describes an algebraic procedure solving this problem. Once M is completed, it can be subsequently resolved into its two matrix components by the known methods [29][30][31].…”