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Guo M, Norrman A, Friberg AT, Gil JJ, Setälä T. Three-dimensional polarization effects in optical tunneling. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2023; 40:1831-1840. [PMID: 37855538 DOI: 10.1364/josaa.499914] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 08/28/2023] [Indexed: 10/20/2023]
Abstract
We consider the three-dimensional (3D) polarimetric properties of an evanescent optical field excited in the gap of a double-prism system by a random plane wave. The analysis covers the case of frustrated total internal reflection (FTIR), i.e., optical tunneling, and relies on the characteristic decomposition of the 3×3 polarization matrix. We find in particular that, for any incident partially polarized plane wave, the evanescent field inside the gap is necessarily in a nonregular, genuine 3D polarization state. We also show that the 3D polarimetric properties of the field at the second boundary are sensitive to the changes of the gap width and that the relevant effects occur for the smaller widths when the angle of incidence of the plane wave becomes larger. The results of this work uncover new aspects of the polarimetric structure of genuine 3D evanescent fields and may find applications in near-field optics and surface nanophotonics.
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2
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Bhattacharya A, Dey S, Frery AC, Gil JJ. Dual views of the generalized degree of purity. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2022; 39:2339-2342. [PMID: 36520757 DOI: 10.1364/josaa.476423] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Accepted: 11/01/2022] [Indexed: 06/17/2023]
Abstract
Several approaches and descriptors have been proposed to characterize the purity of coherency or density matrices describing physical states, including the polarimetric purity of 2D and 3D partially polarized waves. This work introduces two interpretations of the degree of purity: one derived from statistics and another from algebra. In the first one, the degree purity is expressed in terms of the mean and standard deviation of the eigenvalue spectrum of the density or coherency matrix of the corresponding state. The second one expresses the purity in terms of two specific measures obtained by decomposing the coherency matrix as a sum of traceless symmetric, antisymmetric, and scalar matrices. We believe these two approaches offer better insights into the purity measure. Furthermore, interesting relations with existing quantities in polarization optics also are described.
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3
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Guo M, Norrman A, Friberg AT, Setälä T. Probing coherence Stokes parameters of three-component light with nanoscatterers. OPTICS LETTERS 2022; 47:2566-2569. [PMID: 35561402 DOI: 10.1364/ol.457963] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Accepted: 04/19/2022] [Indexed: 06/15/2023]
Abstract
We establish a method to determine the spectral coherence Stokes parameters of a random three-component optical field via scattering by two dipolar nanoparticles. We show that measuring the intensity and polarization-state fringes of the scattered far field in three directions allows us to construct all nine coherence Stokes parameters at the dipoles. The method extends current nanoprobe techniques to detection of the spatial coherence of random light with arbitrary three-dimensional polarization structure.
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Abstract
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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Sheppard CJR, Bendandi A, Le Gratiet A, Diaspro A. Purity of 3D polarization. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2022; 39:6-16. [PMID: 35200971 DOI: 10.1364/josaa.444326] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Accepted: 10/29/2021] [Indexed: 06/14/2023]
Abstract
Measures of purity for 3D partially polarized fields, and in particular, the separation into circularly and linearly polarized contributions, are reexamined, and a new degree of total linear polarization introduced. Explicit expressions for the characteristic decomposition in terms of coherency matrix elements are presented, including the special case of an intrinsic coherency matrix. Parameterization of the coherency matrix in terms of ellipticity, and the directions of the ellipse normal and major axis are investigated. Phase consistency is discussed. A comprehensive collection of results regarding intrinsic polarization properties is presented.
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6
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Goldberg AZ, Sánchez-Soto LL, Ferretti H. Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology. PHYSICAL REVIEW LETTERS 2021; 127:110501. [PMID: 34558938 DOI: 10.1103/physrevlett.127.110501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2021] [Revised: 06/30/2021] [Accepted: 07/29/2021] [Indexed: 06/13/2023]
Abstract
The quantum Cramér-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a scalar form with a properly chosen weight matrix. Multiparameter estimation thus elicits trade-offs in the precision with which each parameter can be estimated. We show that, if the information is encoded in a unitary transformation, we can naturally choose the weight matrix as the metric tensor linked to the geometry of the underlying algebra su(n), with applications in numerous fields. This ensures an intrinsic bound that is independent of the choice of parametrization.
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Affiliation(s)
- Aaron Z Goldberg
- National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada
| | - Luis L Sánchez-Soto
- Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain
- Max-Planck-Institute für die Physik des Lichts, 91058 Erlangen, Germany
| | - Hugo Ferretti
- Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada
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7
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Geometric Interpretation and General Classification of Three-Dimensional Polarization States through the Intrinsic Stokes Parameters. PHOTONICS 2021. [DOI: 10.3390/photonics8080315] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
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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8
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Depolarization of Light in Optical Fibers: Effects of Diffraction and Spin-Orbit Interaction. FIBERS 2021. [DOI: 10.3390/fib9060034] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Polarization is measured very often to study the interaction of light and matter, so the description of the polarization of light beams is of both practical and fundamental interest. This review discusses the polarization properties of structured light in multimode graded-index optical fibers, with an emphasis on the recent advances in the area of spin-orbit interactions. The basic physical principles and properties of twisted light propagating in a graded index fiber are described: rotation of the polarization plane, Laguerre–Gauss vector beams with polarization-orbital angular momentum entanglement, splitting of degenerate modes due to spin-orbit interaction, depolarization of light beams, Berry phase and 2D and 3D degrees of polarizations, etc. Special attention is paid to analytical methods for solving the Maxwell equations of a three-component field using perturbation analysis and quantum mechanical approaches. Vector and tensor polarization degrees for the description of strongly focused light beams and their geometrical interpretation are also discussed.
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Sheppard CJR, Bendandi A, Le Gratiet A, Diaspro A. Eigenvectors of polarization coherency matrices. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2020; 37:1143-1154. [PMID: 32609675 DOI: 10.1364/josaa.391902] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
Calculation of the eigenvectors of two- and three-dimensional coherency matrices, and the four-dimensional coherency matrix associated with a Mueller matrix, is considered, especially for algebraic cases, in the light of recently published algorithms. The preferred approach is based on a combination of an evaluation of the characteristic polynomial and an adjugate matrix. The diagonal terms of the coherency matrix are given in terms of the characteristic polynomial of reduced matrices as functions of the eigenvalues of the coherency matrix. The analogous polynomial form for the off-diagonal elements of the coherency matrix is also presented. Simple expressions are given for the pure component in the characteristic decomposition.
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10
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Sources of Asymmetry and the Concept of Nonregularity of n-Dimensional Density Matrices. Symmetry (Basel) 2020. [DOI: 10.3390/sym12061002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
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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11
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Reiche D, Busch K, Intravaia F. Nonadditive Enhancement of Nonequilibrium Atom-Surface Interactions. PHYSICAL REVIEW LETTERS 2020; 124:193603. [PMID: 32469548 DOI: 10.1103/physrevlett.124.193603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2019] [Accepted: 04/06/2020] [Indexed: 06/11/2023]
Abstract
The motion-induced drag force acting on a particle moving parallel to an arrangement of N objects is analyzed. Particular focus is placed on the nonequilibrium statistics of the interaction and on the interplay between the system's geometry and the different dissipative processes occurring in realistic setups. We show that the drag force can exhibit a markedly nonadditive enhancement with respect to the corresponding additive approximation. The specific case of a planar cavity-a relevant configuration for many experiments-is calculated, showing an enhancement of about one order of magnitude. This and similar configurations are of significant potential interest for future measurements that aim to detect the drag force.
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Affiliation(s)
- D Reiche
- Humboldt-Universität zu Berlin, Institut für Physik, AG Theoretische Optik & Photonik, 12489 Berlin, Germany
- Max-Born-Institut, 12489 Berlin, Germany
| | - K Busch
- Humboldt-Universität zu Berlin, Institut für Physik, AG Theoretische Optik & Photonik, 12489 Berlin, Germany
- Max-Born-Institut, 12489 Berlin, Germany
| | - F Intravaia
- Humboldt-Universität zu Berlin, Institut für Physik, AG Theoretische Optik & Photonik, 12489 Berlin, Germany
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12
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Bliokh KY, Alonso MA, Dennis MR. Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:122401. [PMID: 31514179 DOI: 10.1088/1361-6633/ab4415] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Geometric phases are a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases have been thoroughly studied in two-component fields, such as two-level quantum systems or paraxial optical waves. However, their description for fields with three or more components, such as generic nonparaxial optical fields routinely used in modern nano-optics, constitutes a nontrivial problem. Here we describe geometric, dynamical, and total phases calculated along a closed spatial contour in a multi-component complex field, with particular emphasis on 2D (paraxial) and 3D (nonparaxial) optical fields. We present several equivalent approaches: (i) an algebraic formalism, universal for any multi-component field; (ii) a dynamical approach using the Coriolis coupling between the spin angular momentum and reference-frame rotations; and (iii) a geometric representation, which unifies the Pancharatnam-Berry phase for the 2D polarization on the Poincaré sphere and the Majorana-sphere representation for the 3D polarized fields. Most importantly, we reveal close connections between geometric phases, angular-momentum properties of the field, and topological properties of polarization singularities in 2D and 3D fields, such as C-points and polarization Möbius strips.
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Affiliation(s)
- Konstantin Y Bliokh
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan. Nonlinear Physics Centre, RSPE, The Australian National University, Canberra, ACT 0200, Australia
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13
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Intravaia F, Oelschläger M, Reiche D, Dalvit DAR, Busch K. Quantum Rolling Friction. PHYSICAL REVIEW LETTERS 2019; 123:120401. [PMID: 31633977 DOI: 10.1103/physrevlett.123.120401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Indexed: 06/10/2023]
Abstract
An atom moving in a vacuum at constant velocity and parallel to a surface experiences a frictional force induced by the dissipative interaction with the quantum fluctuations of the electromagnetic field. We show that the combination of nonequilibrium dynamics, the anomalous Doppler effect, and spin-momentum locking of light mediates an intriguing interplay between the atom's translational and rotational motion. In turn, this deeply affects the drag force in a way that is reminiscent of classical rolling friction. Our fully non-Markovian and nonequilibrium description reveals counterintuitive features characterizing the atom's velocity-dependent rotational dynamics. These results prompt interesting directions for tuning the interaction and for investigating nonequilibrium dynamics as well as the properties of confined light.
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Affiliation(s)
- F Intravaia
- Humboldt-Universität zu Berlin, Institut für Physik, AG Theoretische Optik & Photonik, 12489 Berlin, Germany
| | | | - D Reiche
- Max-Born-Institut, 12489 Berlin, Germany
| | - D A R Dalvit
- Theoretical Division, MS B213, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - K Busch
- Humboldt-Universität zu Berlin, Institut für Physik, AG Theoretische Optik & Photonik, 12489 Berlin, Germany
- Max-Born-Institut, 12489 Berlin, Germany
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14
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Gil JJ, Norrman A, Friberg AT, Setälä T. Intensity and spin anisotropy of three-dimensional polarization states. OPTICS LETTERS 2019; 44:3578-3581. [PMID: 31305576 DOI: 10.1364/ol.44.003578] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2019] [Accepted: 06/16/2019] [Indexed: 06/10/2023]
Abstract
Anisotropy is a natural feature of polarization states, and only fully random three-dimensional (3D) states exhibit complete isotropy. In general, differences between the strengths of the electric field components along the three orthogonal directions give rise to intensity anisotropy. Moreover, polarization states involve an average spin whose inherent vectorial nature constitutes a source of spin anisotropy. In this work, appropriate descriptors are identified to characterize quantitatively the levels of intensity anisotropy and spin anisotropy of a general 3D polarization state, leading to a novel interpretation for the degree of polarimetric purity as a measure describing the overall polarimetric anisotropy of a 3D optical field. The mathematical representation, as well as the physical features of completely intensity-isotropic 3D polarization states with a maximum spin anisotropy, are also examined. The results provide new insights into the polarimetric field structure of random 3D electromagnetic light states.
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15
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Gil JJ, Norrman A, Friberg AT, Setälä T. Nonregularity of three-dimensional polarization states. OPTICS LETTERS 2018; 43:4611-4614. [PMID: 30272696 DOI: 10.1364/ol.43.004611] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2018] [Accepted: 08/23/2018] [Indexed: 06/08/2023]
Abstract
Regular states of polarization are defined as those that can be decomposed into a pure state (fully polarized), a two-dimensional (2D) unpolarized state (a state whose polarization ellipse evolves fully randomly in a fixed plane), and a three-dimensional (3D) unpolarized state (a state whose polarization ellipse evolves fully randomly in the 3D space) [Phys. Rev. A95, 053856 (2017)PLRAAN1050-294710.1103/PhysRevA.95.053856]. For nonregular states, the middle component can be considered as an equiprobable mixture of two pure states, whose polarization ellipses lie in different planes. In this work, we identify a perfect nonregular state and introduce the degree of nonregularity as a measure of the proximity of a nonregular state to regularity. We also analyze and interpret the notion of polarization-state regularity in terms of polarimetric parameters. Our results bring new insights into the polarimetric structure of 3D light fields.
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16
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Gil JJ. Components of purity of a three-dimensional polarization state. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2016; 33:40-43. [PMID: 26831583 DOI: 10.1364/josaa.33.000040] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The degree of polarimetric purity of a three-dimensional (3D) polarization state is a measure of the closeness to a pure state and can be expressed as a weighted quadratic average of two indices of polarimetric purity, invariant with respect to unitary transformations and defined in terms of the relative weights of certain incoherent components of the state. An alternative view of the polarimetric purity is formulated in terms of three contributions, namely, the degree of directionality, the degree of linear polarization, and the degree of circular polarization. While the indices of polarimetric purity give complete information on the structure of randomness but are insensitive to other attributes of the state of polarization, the three components of purity are invariant under orthogonal transformations (rotations in the real space) and provide a meaningful framework for the representation of 3D polarization states in terms of quantities that are intrinsic for each given state.
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17
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Sheppard CJR. Partial polarization in three dimensions. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2011; 28:2655-2659. [PMID: 22193279 DOI: 10.1364/josaa.28.002655] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Various different parameters have been introduced to describe the degree of polarization of a partially polarized electromagnetic field in three dimensions. Of these, parameters based on the eigenvalues of the coherency matrix are invariant under a unitary transformation. Here, explicit expressions are presented for the eigenvalues, thus providing a geometrical interpretation of the behavior. These expressions are applied to the Huynen decomposition and allow interrelations between different parameters to be developed.
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Affiliation(s)
- Colin J R Sheppard
- Optical Bioimaging Laboratory, Division of Bioengineering, National University of Singapore, Singapore.
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18
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Klimov AB, Björk G, Söderholm J, Madsen LS, Lassen M, Andersen UL, Heersink J, Dong R, Marquardt C, Leuchs G, Sánchez-Soto LL. Assessing the polarization of a quantum field from stokes fluctuations. PHYSICAL REVIEW LETTERS 2010; 105:153602. [PMID: 21230901 DOI: 10.1103/physrevlett.105.153602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2010] [Revised: 09/07/2010] [Indexed: 05/30/2023]
Abstract
We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincaré sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.
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Affiliation(s)
- A B Klimov
- Departamento de Física, Universidad de Guadalajara, 44420 Guadalajara, Jalisco, Mexico
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19
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Hannay J. Radiative transfer: exact Rayleigh scattering series and a formula for daylight. Proc Math Phys Eng Sci 2007. [DOI: 10.1098/rspa.2007.0125] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Daylight, or sky light, is sunlight Rayleigh scattered by the atmosphere onto the ground. This random scattering propagation through clear air is governed by ‘radiative transfer’. Beyond the single-scattering approximation, the famous virtuoso analysis of Chandrasekhar formulated the problem and offered exact, but rather involved, and ultimately numerical, algorithms for its solution. However, there is no real difficulty in writing down directly the exact Rayleigh scattering series in integrals. Its practical utility is limited to fairly small thicknesses
T
of atmosphere (compared with the mean free path), but the Earth has just such. Here even the next order beyond single scattering (error order
T
2
) supplies a formula for the brightness and partial polarization of daylight across the sky, which captures the essential topology of the polarization pattern, and also remains uniformly valid in the small thickness limit, for all elevations of the Sun and viewing angles. The status of the mathematical polarization direction pattern invented by Berry, Dennis and Lee as the simplest fit to the required topology is clarified.
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Affiliation(s)
- J.H Hannay
- H. H. Wills Physics Laboratory, University of BristolTyndall Avenue, Bristol BS8 1TL, UK
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Dennis MR. A three-dimensional degree of polarization based on Rayleigh scattering. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2007; 24:2065-9. [PMID: 17728831 DOI: 10.1364/josaa.24.002065] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
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 at a point is defined as an average, over all scattering directions, of an imagined dipole scattering of the three-dimensional state of polarization. This gives a well-defined purity measure, which, unlike other proposed measures of the three-dimensional degree of polarization, is not a unitary invariant of the matrix. This is demonstrated and discussed for several examples, including a partially polarized transverse beam.
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Affiliation(s)
- Mark R Dennis
- School of Mathematics, University of Southampton, UK.
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21
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Luis A. Degree of coherence for vectorial electromagnetic fields as the distance between correlation matrices. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2007; 24:1063-8. [PMID: 17361292 DOI: 10.1364/josaa.24.001063] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
We assess the degree of coherence of vectorial electromagnetic fields in the space-frequency domain as the distance between the cross-spectral density matrix and the identity matrix representing completely incoherent light. This definition is compared with previous approaches. It is shown that this distance provides an upper bound for the degree of coherence and visibility for any pair of scalar waves obtained by linear combinations of the original fields. This same approach emerges when applying a previous definition of global coherence to a Young interferometer.
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Affiliation(s)
- Alfredo Luis
- Departamento de Optica, Facultad de Ciencias Físicas, Universidad Complutense, 28040 Madrid, Spain.
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