An objective analysis is carried out of the matricial models representing the polarimetric properties of light and material media leading to the identification and definition of their corresponding physical quantities, using the concept of the coherency matrix. For light, cases of homogeneous and inhomogeneous wavefront are analyzed, and a model for 3D polarimetric purity is constructed. For linear passive material media, a general model is developed on the basis that any physically realizable linear transformation of Stokes vectors is equivalent to an ensemble average of passive, deterministic nondepolarizing transformations. Through this framework, the relevant physical quantities, including indices of polarimetric purity, are identified and decoupled. Some decompositions of the whole system into a set of well-defined components are considered, as well as techniques for isolating the unknown components by means of new procedures for subtracting coherency matrices. These results and methods constitute a powerful tool for analyzing and exploiting experimental and industrial polarimetry. Some particular application examples are indicated.

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Polarimetric characterization of light and media - Physical quantities involved in polarimetric phenomena

Publisher Summary This chapter discusses the polarimetric optical fibers and sensors. The chapter reviews the achievements and efforts in research related to the development of a new generation of polarimetric optical fibers and sensors at both fundamental and applied levels. The chapter provides an overview of the physical origin of the perturbations on the lowest-order mode propagation in highly birefringent (HB) polarization-maintaining fibers, together with their impact on applications in optical fiber sensors and systems. When birefringence is introduced into an isotropic fiber, the circular symmetry of the ideal fiber is broken, thus producing the anisotropic refractive index distribution into the core region. The asymmetry results from either intrinsic birefringence including a geometrical deformation of the core and stresses induced during the manufacturing process or from material anisotropy due to induced (extrinsic) elastic birefringence. The deformation effects in highly birefringent fibers include symmetrical deformation effects, hydrostatic pressure, axial strain, nonsymmetric deformation effect (twist), and twist under pressure/strain. A potential application of polarimetric optical fibers and sensors is to embed them directly inside various ceramic and composite materials, and to measure strain distribution in different structures using the concept of smart skins and structures.

I Polarimetric optical fibers and sensors

We describe the evolution of a paraxial electromagnetic wave characterizing by a non-uniform polarization distribution with singularities and propagating in a weakly anisotropic medium. Our approach is based on the Stokes vector evolution equation applied to a non-uniform initial polarization field. In the case of a homogeneous medium, this equation is integrated analytically. This yields a 3-dimensional distribution of the polarization parameters containing singularities, i.e. C-lines of circular polarization and L-surfaces of linear polarization. The general theory is applied to specific examples of the unfolding of a vectorial vortex in birefringent and dichroic media.

Singular polarimetry: Evolution of polarization singularities in electromagnetic waves propagating in a weakly anisotropic medium

The equation for evolution of the four-component Stokes vector in weakly anisotropic and smoothly inhomogeneous media is derived on the basis of a quasi-isotropic approximation of the geometrical optics method, which provides the consequent asymptotic solution of Maxwell's equations. Our equation generalizes previous results obtained for the normal propagation of electromagnetic waves in stratified media. It is valid for curvilinear rays with torsion and is capable of describing normal mode conversion in inhomogeneous media. Remarkably, evolution of the four-component Stokes vector is described by the Bargmann-Michel-Telegdi equation for relativistic spin precession, whereas the equation for the three-component Stokes vector resembles the Landau-Lifshitz equation describing spin precession in ferromagnetic systems. The general theory is applied for analysis of polarization evolution in a magnetized plasma. We also emphasize fundamental features of the non-Abelian polarization evolution in anisotropic inhomogeneous media and illustrate them by simple examples.

Stokes-vector evolution in a weakly anisotropic inhomogeneous medium.

In radio astronomy, the polarimetric properties of radiation are often modified during propagation and reception. Effects such as Faraday rotation, receiver cross talk, and differential amplification act to change the state of polarized radiation. A general description of such transformations is useful for the investigation of these effects and for the interpretation and calibration of polarimetric observations. Such a description is provided by the Lorentz group, which is intimately related to the transformation properties of polarized radiation. In this paper, the transformations that commonly arise in radio astronomy are analyzed in the context of this group. This analysis is then used to construct a model for the propagation and reception of radio waves. The implications of this model for radio astronomical polarimetry are discussed.

https://iopscience.iop.org/article/10.1086/308595/pdf

Radio Astronomical Polarimetry and the Lorentz Group

A unified formalism for polarization optics is presented. This formalism was developed to use the Stokes-Mueller matrix equation and the Lorentz group to provide a conceptual framework and a systematic method to model and understand complicated polarization phenomena in optical media (such as optical fibers, fiber systems, devices, and networks). Central to this approach is the utilization of operator and group theoretic techniques to exploit the analogy that exists between the dichroism and birefringence elements of the Mueller matrix of polarization optics and the boost and rotation generators, respectively, of the Lorentz transformations of special relativity. This formalism incorporates the other popular [i.e., the Jones, the coherency (or density), and the Mueller matrix] polarization approaches into a single unified formalism. To address polarization issues for complicated systems, we introduce several rudimentary deterministic Mueller matrices. First, the Mueller matrix for arbitrary birefringence and dichroism is given. Second, the Mueller matrix for arbitrary but uniform birefringence and dichroism is given. Third, the Mueller matrix for optical media with successive (series) birefringence and dichroism along the optical path are given. Fourth, the Mueller matrix for optical media with simultaneous (parallel) birefringences and dichroisms along the optical path are given. Finally, the formalism is applied to a comparison between polarimetric data [for a short (~ 1 m) optical fiber with low internal linear birefringence under the influence of a constant external twist rate] and a theoretical model. The agreement between measurement and theory are excellent.

Unified formalism for polarization optics with application to polarimetry on a twisted optical fiber

We give a derivation of the explicit form of the general Mueller matrix of polarization optics for the case of arbitrary and uniform birefringence and dichroism. We first point out that the general Mueller matrix is essentially a Lorentz transformation. Then a set of complex Lorentz generator and a complex polarization vector is introduced. The complex generators are related to the usual Lorentz generators of special relativity, while the complex vector is related to the Stokes representation of the birefringence and dichroism vectors. Next, the explicit form of the general Lorentz transformation, and subsequently the general Mueller matrix for arbitrary and uniform berefringence and dichroism is derived. The general form is used to derive new Mueller matrices for three special cases. The special cases are (1) the Mueller matrix for a material with finite dichroism and weak birefringence, (2) the Mueller material with both finite birefringence and dichroism that are equal in magnitude and perpendicular in direction. Then, we derive an algorithm to determine the material parameters from the general Mueller matrix elements. Finally, we apply the algorithm to theoretical and experimental Mueller matrices.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

General Lorentz transformation and its application to deriving and evaluating the Mueller matrices of polarization optics

Recently, the authors developed the deterministic aspects of a formalism for polarization optics. This formalism, called the unified polarization calculus, uses the Stokes-Mueller equation and the Lorentz group provide a conceptual framework and a systematic method to model and understand birefringence and dichroism in optical media. In this paper, we explore the stochastic aspects of the calculus.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Aakhut Em Bak

Papers

Unified formalism for polarization optics with application to polarimetry on a twisted optical fiber

General Lorentz transformation and its application to deriving and evaluating the Mueller matrices of polarization optics

Stochastic aspects of the unified polarization calculus