Polarized Light and the Mueller Matrix Approach  book cover
1st Edition

Polarized Light and the Mueller Matrix Approach

ISBN 9781482251555
Published May 18, 2016 by CRC Press
405 Pages 16 Color & 105 B/W Illustrations

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Book Description

An Up-to-Date Compendium on the Physics and Mathematics of Polarization Phenomena

Polarized Light and the Mueller Matrix Approach thoroughly and cohesively integrates basic concepts of polarization phenomena from the dual viewpoints of the states of polarization of electromagnetic waves and the transformations of these states by the action of material media. Through selected examples, it also illustrates actual and potential applications in materials science, biology, and optics technology.

The book begins with the basic concepts related to two- and three-dimensional polarization states. It next describes the nondepolarizing linear transformations of the states of polarization through the Jones and Mueller–Jones approaches. The authors then discuss the forms and properties of the Jones and Mueller matrices associated with different types of nondepolarizing media, address the foundations of the Mueller matrix, and delve more deeply into the analysis of the physical parameters associated with Mueller matrices.

The authors proceed to interpret arbitrary decomposition and other interesting parallel decompositions as well as compare the powerful serial decompositions of depolarizing Mueller matrix M. They also analyze the general formalism and specific algebraic quantities and notions related to the concept of differential Mueller matrix. The book concludes with useful approaches that provide a geometric point of view on the polarization effects exhibited by different types of media.

Suitable for novices and more seasoned professionals, this book covers the main aspects of polarized radiation and polarization effects of material media. It expertly combines physical and mathematical concepts with important approaches for representing media through equivalent systems composed of simple components.

Table of Contents

Polarized electromagnetic waves
Introduction: Nature of polarized electromagnetic waves
Polarization ellipse
Analytic signal representation and the Jones vector
Coherency matrix and Stokes vector
2D space–time and space–frequency representations of coherence and polarization
Poincaré sphere
Polarimetric interpretation of the Pauli matrices
Intrinsic coherency matrix
Polarimetric purity
Composition and decomposition of 2D states of polarization
Classification of 2D states of polarization
Invariant quantities of a 2D polarization state
Quantum description of 2D states of polarization

Three-dimensional states of polarization
3D Jones vector
3D Coherency matrix
3D Stokes parameters
Composition and decomposition of 3D states of polarization
3D space–time and space–frequency representations of coherence and polarization
Intrinsic 3D Coherency matrix
Intrinsic 3D Stokes parameters
3D polarimetric purity
Interpretation of the coherency matrix for 3D polarization states
Invariant quantities of a 3D polarization state
Quantum formulation for 3D polarization states

Nondepolarizing media
Basic polarimetric interaction: Jones calculus
Pure Mueller matrices
Singular states of Polarization
Normality and degeneracy of Jones and Mueller matrices

Nondepolarizing media: Retarders, diattenuators, and serial decompositions
Other mathematical representations of the polarimetric properties of nondepolarizing systems
Polar decomposition of a nondepolarizing system
General serial decomposition of a nondepolarizing system
Dual linear retarder transformation of a nondepolarizing system
Constitutive vectors of a nondepolarizing Mueller matrix
Invariant polarimetric quantities of a nondepolarizing Mueller matrix
Particular forms of nondepolarizing Mueller matrices

The concept of Mueller matrix
The concept of Mueller matrix
Covariance and coherency matrices associated with a Mueller matrix
Changes of reference frame and rotated Mueller matrices
Characterization of Mueller matrices: Covariance criterion
Normal form of a Mueller matrix
Reciprocity properties of Mueller matrices
Passivity constraints for Mueller matrices
Vectorial partitioned expression of a Mueller matrix
Spectral and characteristic decompositions of a Mueller matrix
Polarimetric purity of a Mueller matrix

Physical quantities in a Mueller matrix
Components of purity of a Mueller matrix
Indices of polarimetric purity
Invariant quantities of a Mueller matrix
Purity space
Anisotropy coefficients of a Mueller matrix
From a nondepolarizing to a depolarizing Mueller matrix

Parallel decompositions of Mueller matrices
Additive composition of Mueller matrices
Arbitrary decomposition of a Mueller matrix
On the rank of the covariance matrix of a parallel composition
Characteristic decomposition of a Mueller matrix
Polarimetric subtraction of Mueller matrices
Passivity constraints
Optimum filtering of measured Mueller matrices

Serial decompositions of depolarizing Mueller matrices
Generalized polar decomposition
Symmetric decomposition
Passivity constraints in serial decompositions of depolarizing Mueller matrices
Invariant-equivalent Mueller matrices
Arrow decomposition of a Mueller matrix
Singular Mueller matrices
Serial-parallel decompositions

Differential Jones and Mueller matrices
Differential Jones matrices and elementary polarization properties
Differential Mueller matrices
Differential decomposition of Mueller matrices
Differential Mueller matrix of a homogeneous depolarizing medium

Geometric representation of Mueller matrices
P-image and I-image of a Mueller matrix
Representative ellipsoids of a Mueller matrix
Ellipsoids associated with some special Mueller matrices
Characteristic ellipsoids of a depolarizing Mueller matrix
Intrinsic ellipsoids of a Mueller matrix
Topological properties of the characteristic ellipsoids
Five-vector representation
Geometric view of depolarization, diattenuation and polarizance
Geometric representation of nondepolarizing Mueller matrices
Experimental examples



A summary appears at the end of each chapter.

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José Jorge Gil is a professor at the University of Zaragoza, where he leads R&D projects in physics and e-learning technologies and methodologies. He has developed an original dual-rotating-retarder absolute Mueller polarimeter, introduced new concepts such as the depolarization index, and developed wireless systems for interactive meetings, which earned the Tecnova award from the Spanish Industry Ministry. Dr. Gil has also been a recipient of the G.G. Stokes Award from the International Society for Optics and Photonics (SPIE) in recognition of his "groundbreaking collection of rigorous mathematical descriptions of polarization that are used widely to interpret experimental data." He received his PhD in physics from the University of Zaragoza.

Razvigor Ossikovski is an associate professor at the Ecole Polytechnique, where he is the leader of the fundamental polarimetry and Raman spectroscopy activities in the Laboratory of Physics of Interfaces and Thin Films. His current research interests are the theory of polarimetry (Mueller matrix algebra) and experimental tip-enhanced Raman spectroscopy. He received his PhD in physics (materials science) from the Ecole Polytechnique.


"The best-ever treatise on the main concepts of both polarization states of light and Mueller matrices of media, illustrated with numerous figures, tables, and experimental examples. The comprehensiveness, clarity, and rigor make it essential for anyone interested in this field."
—Tiberiu Tudor, Professor, Faculty of Physics, University of Bucharest

"Gil and Ossikovski have gathered together in one source a wealth of information on the intricacies of the interpretation of representations of polarized light. Current research on the mathematics of polarized light is thoughtfully presented. This is an essential reference for the serious student or researcher in the field."
—Dr. Dennis Goldstein, Polaris Sensor Technologies, Inc.