Polarized Light and the Mueller Matrix Approach

José J. Gil, Razvigor Ossikovski

• Publisher: CRC Press
• Year: 2022
• ISBN:
  9781000568691
• Edition: 2
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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

Now thoroughly revised, Polarized Light and the Mueller Matrix Approach 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 with introducing the arbitrary decomposition and other useful parallel decompositions, and compare the powerful serial decompositions of depolarizing Mueller matrices. They also analyze the general formalism and specific algebraic quantities and notions related to the concept of differential Mueller matrix. Useful approaches that provide a geometric point of view on the polarization effects exhibited by different types of media are also comprehensively described. The book concludes with a new chapter devoted to the main procedures for filtering measured Mueller matrices.

Suitable for advanced graduates 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.

1Polarized Electromagnetic Waves

DOI: 10.1201/9780367815578-1

1.1 Introduction: Nature of Polarized Electromagnetic Waves

Due to the specific nature of electromagnetic waves, the electric field of the wave evolves in time at any given point r in space. The complete description of the electromagnetic wave at point r requires the knowledge of four field vectors, namely the electric field strength E, the electric displacement density (electric induction) D, the magnetic field strength H, and the magnetic flux density (magnetic induction) B.

In general, the microscopic forces exerted by the electric field of the wave on matter are much larger than the forces produced by the magnetic field, so the temporal evolution of the electric field is chosen as the representative of the property called polarization.

When, in particular, the electromagnetic wave propagates in an isotropic medium, the electric and magnetic strengths are tangent to the wavefront at the considered point r (Figure 1.1). Nevertheless, in the case of an anisotropic medium, it is D, and not E, what is tangent to the wavefront at each given point r. Thus, unlike the case of isotropic media, for anisotropic media the temporal evolution of D is usually taken as the representative of the polarization of the electromagnetic wave (Cloude 2009, p. 13), even though we shall use the symbol E without distinction in the mathematical formulation of polarization.

FIGURE 1.1When the electromagnetic wave propagates in an isotropic medium, both electric and magnetic strength vectors lie in a plane Π which is tangent to the wavefront at the considered point r.

In spite of the fact that we sometimes use the term light, in general and unles...

Table of contents

• Cover
• Half-Title Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Preface to the second edition
• Acknowledgements
• Authors
• 1 Polarized Electromagnetic Waves
• 2 Three-Dimensional States of Polarization
• 3 Nondepolarizing Media
• 4 Nondepolarizing Media: Retarders, Diattenuators and Serial Decompositions
• 5 The Concept of Mueller Matrix
• 6 Physical Quantities in a Mueller Matrix
• 7 Parallel Decompositions of Mueller Matrices
• 8 Serial Decompositions of Depolarizing Mueller Matrices
• 9 Differential Jones and Mueller Matrices
• 10 Geometric Representation of Mueller Matrices
• 11 Filtering of Measured Mueller Matrices
• References
• Index