Related papers: Parametrization of 3x3 unitary matrices based on p…
Mueller polarimetry is a powerful technique with broad applications in astronomy, remote sensing, advanced material analysis, and biomedical imaging. However, instrumental constraints frequently restrict the measurement to an incomplete…
With assumption that an optical element is described by a Mueller matrix of the Lorentzian type, a method to find a 3-dimensional complex vector parameter for a corresponding Mueller matrix from results of four specially chosen polarization…
The 3-dimensional coherence matrix is interpreted by emphasising its invariance with respect to spatial rotations. Under these transformations, it naturally decomposes into a real symmetric positive definite matrix, interpreted as the…
From an appropriate parameterization of the three-dimensional (3D) coherency matrix R, that characterizes the second-order, classical states of polarization, the coherency matrices are classified and interpreted in terms of incoherent…
The formalism is developed for a tree-dimensional ($3D$) nonlinear Stokes-Mueller polarimetry. The expressions are derived for the generalized $3D$ linear and nonlinear Stokes vectors, and the corresponding nonlinear Mueller matrix. The…
Despite the intrinsic coupling between electric and magnetic fields in random stationary light, their polarization properties are not mutually determined. A complete second-order description thus necessitates a joint electromagnetic…
Inspecting three-dimensional partially polarized light fields we show that there is no unambiguous correspondence between the three-dimensional field and coherence matrix (or light beam tensor). Therefore, it is needed to clarify the…
This paper presents a parametrization of a degenerate density matrix. The problem needs to be approached first with a diagonalized form (the spectral representation) to deal with degeneracy. Such a form is useful for this parametrization in…
The depolarization properties of a medium with associated Mueller matrix M are characterized through two complementary sets of parameters, namely the three indices of polarimetric purity (IPP), which are directly linked to the relative…
An analysis of the matrix models representing the polarimetric properties of light and material media is carried out by using the concept of the coherency matrix, which leads to the identification and definition of their corresponding…
An arbitrary Mueller matrix can be decomposed into a sum of up to four deterministic Mueller-Jones matrices, with strengths given by the eigenvalues of an associated Hermitian matrix. A geometrical representation of the eigenvalues in terms…
A measure of the degree of polarization for the three-dimensional polarization matrix (coherence matrix) of an electromagnetic field is proposed, based on Rayleigh scattering. The degree of polarization, due to dipole scattering of the…
We discuss our preliminary attempts to extend previous work on 2x2 Hermitian octonionic matrices with non-real eigenvalues to the 3x3 case.
Partially coherent electromagnetic sources with cylindrical symmetry and infinite extent radiating outwards are introduced. Their 3x3 cross-spectral density matrix is given through expansions of the field components in terms of basis…
The absolute values of the three degrees of mutual coherence between the analytic signals representing the components of the electric field of a given three-dimensional (3D) polarization state are relative quantities that depend on the…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
The geometric approach presented in this paper concerns the degree of polarization (DoP) of a random 3D statistical electromagnetic field. We use that a 3*3 coherency matrix can always be decomposed into an incoherent superposition of three…
Formulas describing all 2-element and 3-element factorizations of arbitrary element of the groups SU(2) and SO(3,R) are derived. Six 2-element factorizations, $ (U_{2}U_{3}U'_{2}), (U_{3}U_{2}U'_{3}), (U_{3}U_{1}U'_{3}), (U_{1}U_{3}U'_{1}),…
We previously showed that the real eigenvalues of 3x3 octonionic Hermitian matrices form two separate families, each containing 3 eigenvalues, and each leading to an orthonormal decomposition of the identity matrix, which would normally…
A method is presented for fast diagonalization of a 2x2 or 3x3 real symmetric matrix, that is determination of its eigenvalues and eigenvectors. The Euler angles of the eigenvectors are computed. A small computer algebra program is used to…