Sets of orthogonal three-dimensional polarization states and their physical interpretation

Gil, José J.; José, Ignacio San; Norrman, Andreas; Friberg, Ari T.; Setälä, Tero

doi:10.1103/physreva.100.033824

Cited by 8 publications

(7 citation statements)

References 30 publications

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“…The general framework introduced provides invariant descriptors for n-dimensional density matrices that, in turn, have been proven to be fruitful for the study of three-dimensional states of polarization [4,6,7,13,23,24,27,28,30,[36][37][38][40][41][42][43][44][45][46][47][48] and of the polarimetric properties of material media [4,5,8,13,[23][24][25][32][33][34][35][49][50][51], which supports a well-founded expectation for its useful application to n-dimensional density matrices representing quantum or classical systems.…”

Section: Discussionmentioning

confidence: 80%

“…For a given pure state u k its chirality vanishes when χ = 0, while from an overall point of view, ρ carries non-vanishing chirality as long as at least one of the eigenstates u k has nonzero spin (i.e., χ k 0, or, equivalently P c (u k ) 0). The features of the ellipticity angles and the associated spin vectors of generic sets (u 1 , u 2 , u 3 ) of orthonormal states for 3D polarization density matrices have been studied in [40].…”

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confidence: 99%

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Sources of Asymmetry and the Concept of Nonregularity of n-Dimensional Density Matrices

Gil

2020

Symmetry

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The information contained in an n-dimensional (nD) density matrix ρ is parametrized and interpreted in terms of its asymmetry properties through the introduction of a family of components of purity that are invariant with respect to arbitrary rotations of the nD Cartesian reference frame and that are composed of two categories of meaningful parameters of different physical nature: the indices of population asymmetry and the intrinsic coherences. It is found that the components of purity coincide, up to respective simple coefficients, with the intrinsic Stokes parameters, which are also introduced in this work, and that determine two complementary sources of purity, namely the population asymmetry and the correlation asymmetry, whose weighted square average equals the overall degree of purity of ρ. A discriminating decomposition of ρ as a convex sum of three density matrices, viz. the pure, the fully random (maximally mixed) and the discriminating component, is introduced, which allows for the definition of the degree of nonregularity of ρ as the distance from ρ to a density matrix of a system composed of a pure component and a set of 2D, 3D,… and nD maximally mixed components. The chiral properties of a state ρ are analyzed and characterized from its intimate link to the degree of correlation asymmetry. The results presented constitute a generalization to nD systems of those established and exploited for polarization density matrices in a series of previous works.

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Section: Discussionmentioning

confidence: 80%

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confidence: 99%

Sources of Asymmetry and the Concept of Nonregularity of n-Dimensional Density Matrices

Gil

2020

Symmetry

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“…In this work, the geometric representation introduced by Dennis [33] for general three-dimensional (3D) polarization states is studied and interpreted in terms of the intrinsic Stokes parameters [21] and other meaningful descriptors that are invariant under rotations of the reference frame [17][18][19][20][21][22][33][34][35][36][37][38][39][40][41][42][43][44][45]. The classification introduced in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…The classification introduced in Refs. [20,46] is improved and completed in the light of the recent approaches on nonregularity [39,42,45,47,48], polarimetric dimension [41], spin of a polarization state [43,47,49] and interpretation of sets of orthogonal 3D polarization states [44].…”

Section: Introductionmentioning

confidence: 99%

Geometric Interpretation and General Classification of Three-Dimensional Polarization States through the Intrinsic Stokes Parameters

Gil

2021

Photonics

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In contrast with what happens for two-dimensional polarization states, defined as those whose electric field fluctuates in a fixed plane, which can readily be represented by means of the Poincaré sphere, the complete description of general three-dimensional polarization states involves nine measurable parameters, called the generalized Stokes parameters, so that the generalized Poincaré object takes the complicated form of an eight-dimensional quadric hypersurface. In this work, the geometric representation of general polarization states, described by means of a simple polarization object constituted by the combination of an ellipsoid and a vector, is interpreted in terms of the intrinsic Stokes parameters, which allows for a complete and systematic classification of polarization states in terms of meaningful rotationally invariant descriptors.

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“…In this case,λ 3 0, and therefore only the first two eigenvectorŝ u 1 ,û 2 appear in the spectral decomposition (1), with corresponding weightsλ 1 2∕3,λ 2 1∕3. By means of the method described in [26], the respective ellipticity angles are found to be χ 1 π∕4, χ 2 0, showing thatû 1 represents a circularly polarized state, whileû 2 represents a linearly polarized state. Moreover, the electric field associated withû 2 vibrates along the direction normal to the polarization-circle plane ofû 1 .…”

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Intensity and spin anisotropy of three-dimensional polarization states

et al. 2019

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Sets of orthogonal three-dimensional polarization states and their physical interpretation

Cited by 8 publications

References 30 publications

Sources of Asymmetry and the Concept of Nonregularity of n-Dimensional Density Matrices

Sources of Asymmetry and the Concept of Nonregularity of n-Dimensional Density Matrices

Geometric Interpretation and General Classification of Three-Dimensional Polarization States through the Intrinsic Stokes Parameters

Intensity and spin anisotropy of three-dimensional polarization states

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