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

Gil, José J.

doi:10.3390/photonics8080315

Cited by 8 publications

(6 citation statements)

References 44 publications

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“…However, this approach is not so useful for the 4D case, as we need to consider a hyperspherical surface in a 4D space with coordinates and the square roots of the eigenvalues. We have mentioned before that an analogy with the case of 3D polarization can lead to interesting results for the 4D case [38,100], and we anticipate future results [104,105].…”

Section: Discussionmentioning

confidence: 63%

Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging

et al. 2022

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Depolarization has been found to be a useful contrast mechanism in biological and medical imaging. The Mueller matrix can be used to describe polarization effects of a depolarizing material. An historical review of relevant polarization algebra, measures of depolarization, and purity spaces is presented, and the connections with the eigenvalues of the coherency matrix are discussed. The advantages of a barycentric eigenvalue space are outlined. A new parameter, the diattenuation-corrected purity, is introduced. We propose the use of a combination of the eigenvalues of coherency matrices associated with both a Mueller matrix and its canonical Mueller matrix to specify the depolarization condition. The relationships between the optical and polarimetric radar formalisms are reviewed. We show that use of a beam splitter in a reflectance polarization imaging system gives a Mueller matrix similar to the Sinclair–Mueller matrix for exact backscattering. The effect of the reflectance is canceled by the action of the beam splitter, so that the remaining features represent polarization effects in addition to the reflection process. For exact backscattering, the Mueller matrix is at most Rank 3, so only three independent complex-valued measurements are obtained, and there is insufficient information to extract polarization properties in the general case. However, if some prior information is known, a reconstruction of the sample properties is possible. Some experimental Mueller matrices are considered as examples.

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Section: Discussionmentioning

confidence: 63%

Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging

et al. 2022

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“…Although the electromagnetic field in the far zone is transverse, many problems of near-field optics, data storage, optical microscopy, and focusing and scattering need to be analyzed, taking into account the longitudinal component of the field E z . For strongly focused beams, the Stokes 2 × 2 formalism should be extended to 3 × 3 coherency matrices [74][75][76][77][78][79]. In [67,72,73], the evolution of three-dimensional electromagnetic fields in a graded-index medium was studied.…”

Section: Discussionmentioning

confidence: 99%

Depolarization of Vector Light Beams on Propagation in Free Space

Petrov¹

2022

Photonics

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Nonparaxial propagation of the vector vortex light beams in free space was investigated theoretically. Propagation-induced polarization changes in vector light beams with different spatial intensity distributions were analyzed. It is shown that the hybrid vector Bessel modes with polarization-OAM (orbital angular momentum) entanglement are the exact solutions of the vector Helmholtz equation. Decomposition of arbitrary vector beams in the initial plane z = 0 into these polarization-invariant beams with phase and polarization singularities was used to analyze the evolution of the polarization of light within the framework of the 2 × 2 coherency matrix formalism. It is shown that the 2D degree of polarization decreases with distance if the incident vector beam is not the modal solution. The close relationship of the degree of polarization with the quantum-mechanical purity parameter is emphasized.

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“…Note that |t| = λ1 − λ2 and |τ τ τ| + |t| = λ1 + λ2 − 2 λ3 coincide, respectively, with the degree of linear polarization and the degree of directionality defined by Gil [111][112][113][114], both of which are smaller than or equal to unity. An inequality for s follows from that in relation (30), and can be written as…”

Section: Inequalities For the Three Vectorsmentioning

confidence: 98%

“…However, note that this is precisely the local spin density vector of the field shown in Fig. 12 [111][112][113][114] has referred to as the the degree of linear polarization and the degree of directionality, respectively.…”

Section: Definition Of the Parametersmentioning

confidence: 99%

Geometric descriptions for the polarization of nonparaxial light: a tutorial

Alonso

2023

Adv. Opt. Photon.

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This tutorial provides an overview of the local description of polarization for nonparaxial light, for which all Cartesian components of the electric field are significant. The polarization of light at each point is characterized by a three-component complex vector in the case of full polarization and by a 3 × 3 polarization matrix for partial polarization. Standard concepts for paraxial polarization such as the degree of polarization, the Stokes parameters, and the Poincaré sphere then have generalizations for nonparaxial light that are not unique and/or not trivial. This work aims to clarify some of these discrepancies, present some new concepts, and provide a framework that highlights the similarities and differences with the description for the paraxial regimes. Particular emphasis is placed on geometric interpretations.

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

Cited by 8 publications

References 44 publications

Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging

Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging

Depolarization of Vector Light Beams on Propagation in Free Space

Geometric descriptions for the polarization of nonparaxial light: a tutorial

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