Spectroscopic ellipsometry data analysis : measured versus calculated quantities

Polarization of light and topological phases

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

A complete and minimum set of necessary and sufficient conditions for a real 4×4 matrix to be a physical Mueller matrix is obtained. An additional condition is presented to complete the set of known conditions, namely, the four conditions obtained from the nonnegativity of the eigenvalues of the Hermitian matrix H associated with a Mueller matrix M and the transmittance condition. Using the properties of H, a demonstration is also presented of Tr(MTM)=4m002 as being a necessary and sufficient condition for a physical Mueller matrix to be a pure Mueller matrix.

Characteristic properties of Mueller matrices

From the contents: Preface.- 1. Description of Polarized Light.- 2. Single Scattering.- 3. Plane-parallel Media.- 4. Orders of Scattering and Multiple-Scattering Matrices.- 5. The Adding-doubling Method.- A. Mueller Calculus.- B. Generalized Spherical Functions.- C. Expanding the Elements of F (T).- D. Size Distributions.- E. Proofs of Relationships for Multiple-Scattering Matrices.- F. Supermatrices and Extended Supermatrices.- Bibliography.- Index.

Transfer of Polarized Light in Planetary Atmospheres: Basic Concepts And Practical Methods

Development of simple tools to test physical realizability of measured or computed Mueller matrices is the subject of this paper. In particular, the overpolarization problem, i.e., the problem of ensuring that the output degree of polarization does not exceed unity is solved by finding an easily implementable necessary and sufficient condition. With G being the Lorentz metric, it states that a given matrix M is not overpolarizing if and only if the spectrum of GM T GM is real and an eigenvector associated with the largest eigenvalue is a physical Stokes vector. This result is used to characterize some M classes of special interest, and is used to test several examples from recent literature.

A Simple Necessary and Sufficient Condition on Physically Realizable Mueller Matrices

The issue of physical realizability constraints on depolarizing scattering or imaging systems is addressed. In particular, the overpolarization problem, i.e., the problem of ensuring that the output degree of polarization is always smaller than (or equal to) unity, is discussed in detail. A set of necessary conditions for the elements of a Mueller matrix is derived. These conditions can be used to test the accuracy of polarimetric measurements and computations. Several recent experimental examples from polarization optics and radar are discussed.

Constraints on Mueller matrices of polarization optics.

The purpose of this Communication is to derive a generalized trace condition for a Mueller–Jones polarization matrix that is based on the Brosseau–Barakat [ Opt. Commun.84, 127 ( 1991)] analysis of the effects of fluctuations in a linear scattering medium on a polarized wave field. The expression developed contains the previously known trace condition for a deterministic optical system as a special case.

Generalized trace condition on the Mueller–Jones polarization matrix

Transformation of a partially polarized light by a passive linear optical system must satisfy certain physical realizability constraints imposed on the elements of the Jones operator (matrix) characterizing the system. In this note we extend earlier work by Jones, Barakat, and Azzam and Bashara and derive a set of conditions on the elements of the Jones operator which depend explicitly on the input light degree of polarization. This is accomplished by a simple and novel approach based on the Cauchy-Schwartz—Bunyakowski inequality for coherency matrices.

On the Gain of a Passive Linear Depolarizing System

We address the issue of physical realizability constraints on depolarizing scattering or imaging systems. In particular, the overpolarization problem, that is the problem of ensuring that the output degree of polarization is always smaller than (or equal to) unity, is discussed in detail. We derive a set of necessary conditions on the elements of a Mueller matrix. These conditions can be used to test the accuracy of polarimetric measurements and computations. Numerical examples are given.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Clark R. Givens

Papers

A Simple Necessary and Sufficient Condition on Physically Realizable Mueller Matrices

Constraints on Mueller matrices of polarization optics.

Generalized trace condition on the Mueller–Jones polarization matrix

On the Gain of a Passive Linear Depolarizing System

Some necessary conditions on Mueller matrices