Polarization elements: a group-theoretical study

Abstract

The classification of polarization elements, the polarization affecting optical devices that have a Jones-matrix representation according to the type of eigenvectors they possess, is given a new visit through the group-theoretical connection of polarization elements. The diattenuators and retarders are recognized as the elements corresponding to boosts and rotations, respectively. The structure of homogeneous elements other than diattenuators and retarders are identified by giving the quaternion corresponding to these elements. The set of degenerate polarization elements is identified with the so-called null elements of the Lorentz group. Singular polarization elements are examined in their more illustrative Mueller-matrix representation, and, finally the eigenstructure of a special class of singular Mueller matrices is studied.

Advanced Jones calculus for the classification of periodic metamaterials

“…This is only the case for linear, circular and a special class of elliptical polarization. In all other cases the eigenstates are non-orthogonal [33][34][35]. Note that systems with orthogonal eigenstates are sometimes termed homogeneous systems whereas systems with non-orthogonal states are termed inhomogeneous ones [36].…”

Polarimetric characterization of light and media

“…and the corresponding Stokes vector is given by (158) The polarization state of the complete emerging beam is obtained through the incoherent superposition of the beams emerging from the different elements, resulting in the following Stokes vector…”

“…The properties of nonsingular Jones and Mueller-Jones matrices can be studied by means of their representation in the SL(2C) group or in the proper orthochronous Lorentz group respectively [157][158][159][160]. In the case of diattenuators, this requires a normalization that violates the passivity condition.…”

Two-vector representation of a nondepolarizing Mueller matrix

“…The notions of normality [20,21] (or homogeneity [22]) and degeneracy of nondepolarizing systems, developed in previous works under the scope of Jones algebra [22,23] are particularly useful for the analysis and understanding of the geometric representation of a pure Mueller matrix J M by means of its constitutive vectors D, P and R . M J is said to be normal (or homogeneous) when it satisfies the commutation property…”