Polarized Light

Dennis H. Goldstein

• Publisher: CRC Press
• Year: 2017
• Print ISBN: 9781439830406
• eBook ISBN: 9781351833677
• Edition: 3
• Topic: Technology & Engineering
• Subtopic: Physics
• Index: Physics

Polarized light is a pervasive influence in our world—and scientists and engineers in a variety of fields require the tools to understand, measure, and apply it to their advantage. Offering an in-depth examination of the subject and a description of its applications, Polarized Light, Third Edition serves as a comprehensive self-study tool complete with an extensive mathematical analysis of the Mueller matrix and coverage of Maxwell's equations.

Links Historical Developments to Current Applications and Future Innovations

This book starts with a general description of light and continues with a complete exploration of polarized light, including how it is produced and its practical applications. The author incorporates basic topics, such as polarization by refraction and reflection, polarization elements, anisotropic materials, polarization formalisms (Mueller–Stokes and Jones) and associated mathematics, and polarimetry, or the science of polarization measurement.

New to the Third Edition:

• A new introductory chapter
• Chapters on: polarized light in nature, and form birefringence
• A review of the history of polarized light, and a chapter on the interference laws of Fresnel and Arago—both completely re-written
• A new appendix on conventions used in polarized light
• New graphics, and black-and-white photos and color plates

Divided into four parts, this book covers the fundamental concepts and theoretical framework of polarized light. Next, it thoroughly explores the science of polarimetry, followed by discussion of polarized light applications. The author concludes by discussing how our polarized light framework is applied to physics concepts, such as accelerating charges and quantum systems.

Building on the solid foundation of the first two editions, this book reorganizes and updates existing material on fundamentals, theory, polarimetry, and applications. It adds new chapters, graphics, and color photos, as well as a new appendix on conventions used in polarized light. As a result, the author has re-established this book's lofty status in the pantheon of literature on this important field.

Part I

Introduction to Polarized Light

1

Introduction

The story of polarized light is integral to the development of the science of optics, which itself plays a central role in the history of physics. The story surely begins when someone first saw the double images one sees when looking through a calcite crystal, a form of calcium carbonate (CaCO₃), as in Figure 1.1. As we pointed out in the historical review, the Vikings may have used these crystals for navigation by observation of the polarized sky patterns. In any event, they certainly knew about these crystals, which are also called Iceland spar, and they must have seemed magical. The histori-cal record begins in 1669 with Erasmus Bartholinus, the first modern scientist to describe the phe-nomenon. He was the first in a long line of eminent scientists who held these crystals in their hands and wondered about them. A means of explaining this double image provided impetus for the devel-opment of ideas about the nature of light, and as theories about the character of light developed, they had to explain and be compatible with the observations made when looking through calcite.

The wave theory of light of Huygens and the corpuscular theory of the light of Newton were the competing theories of these seventeenth century scientists, whose lives overlapped. Newton’s theory was dominant during the eighteenth century, but at the beginning of the nineteenth century, the inter-ference experiments of Young, and somewhat later the work on diffraction by Fresnel and Arago, gave the wave theory a legitimacy and attention it did not have before.

This early work eventually resulted in the principle of particle–wave duality, now one of the basic principles of physics, but this did not happen until after the work of Maxwell, who succeeded in set-ting forth a unified theory of electromagnetic radiation in rigorous mathematical form (1873), and the work of Michelson and Morley (1887), who showed that the medium then thought to exist and support propagation of light waves, the luminiferous aether, apparently did not exist.

We now know that electromagnetic radiation is a transverse wave; that is, an oscillation of elec-tric and magnetic fields in a direction perpendicular to the direction of propagation. What we refer to as light, in the broader sense electromagnetic radiation from ultraviolet to infrared, and in human visual experience from violet to red, the wavelength region from 400 to 700 nm, is a subset of the entire electromagnetic spectrum.

When we refer to the polarization of light, we refer to one of the basic properties of a light wave; that is, the polarization is defined to be the description of the vibration of the electric field. Linear polarization is then a vibration along one direction in three-dimensional space with the propagation along a second direction, as in Figure 1.2, where the curve traces the location of the tip of the elec-tric field vector as the light propagates through space. Linear polarization is one extreme of a con-tinuum of possible polarizations, called states, where circular polarization, illustrated in Figure 1.3, is the other extreme. In this case, the plot of the tip of the electric field vector results in a helix. Elliptical polarization is a general term that can be used to describe any state in the continuum from linear to circular.

As Clarke and Grainger point out [1], the term polarization is perhaps unfortunate, but it is now one that we are obliged to use as there is no convenient substitute. The term appears to come from Newton, who discussed the “sides” that light exhibited in double refraction, as in passing through calcite. Newton compares this to poles of magnets. Having a piece of iron magnetically polarized, or a molecule or electron that is polarized, has little to do with polarized light, so the term can be confusing.

The very essence of light, a spatially asymmetric electromagnetic wave, means that light is natu-rally polarized. Polarization, along with frequency of vibration, is a fundamental property. Where there is light, there is polarized light, and truly randomly polarized light is an elusive phenomenon.

FIGURE 1.1 (See color insert following page 394.) The double image seen through a calcite crystal. (Photo courtesy of D. H. Goldstein.)

FIGURE 1.2 Linear polarization.

And even if randomly polarized light is achieved, any interaction whatsoever, through the typically asymmetric processes of reflection, transmission, or scattering, will induce a polarization.

A few examples will serve to illustrate polarization by reflection and transmission (polarization by scattering is shown in Chapter 2). Figure 1.4a shows a black and white image of an automobile in a field. Figure 1.4b is an image of the automobile where the linear polarizations in the +45° direction and –45º direction (with respect to horizontal) are encoded in the colors blue and red, respectively, and light areas have little polarization in these directions. The final image, Figure 1.4c, has the amount of polarization at each point in the image encoded as a color. This is the degree of polarization, and is encoded so that dark areas are not polarized and red areas are very highly polarized. Light has been polarized through reflection from the smooth surfaces of the vehicle.

Figure 1.5 shows a sheet of mica in between crossed linear polarizers. An ideal linear polarizer will absorb light of one linear polarization and transmit light of the orthogonal polarization. In this case, light of one linear polarization is transmitted through the first polarizer and is blocked by the

FIGURE 1.3 Circular polarization.

FIGURE 1.4 (See color insert following page 394.) Images of an automobile in a field; (a) black and white photograph, (b) linear ±45° polarization encoded in pseudocolor, and (c) degree of polarization encoded in pseudocolor. (Photos courtesy of D. H. Goldstein.)

FIGURE 1.5 (See color insert following page 394.) Mica between crossed polarizers. (Photo courtesy of D. H. Goldstein.)

second polarizer in all black areas of the photo. Mica is a silicate mineral that has a different refrac-tive index in each of the three Cartesian directions. The phase of polarized light is retarded upon passing through the mica, the retardation being dependent upon the thickness and the frequency, and the polarization of light is thus changed. Mica naturally occurs in very thin sheets, and the dif-ferent colors observed in Figure 1.5 correspond to those colors that have been rotated into a polar-ization that will pass through the polarizer closest to the viewer because of the passage of the light through different thicknesses in the sheet.

In Figure 1.6 we have another type of crystalline material, camphor, as photographed under a polarized light microscope with crossed polarizers. Camphor is an organic molecule that has chiral-ity, or handedness, and it can rotate the direction of polarization. In this photograph, the different colors correspond once again to different thicknesses of the camphor and thus where different colors­ have been rotated by the amount necessary to pass through the polarizer closest to the viewer.

As a further example, Figure 1.7 shows a bottle of corn syrup as seen through (a) aligned polar-izers, (b) polarizers at 45° to one another, and (c) crossed polarizers. Corn syrup is also a chiral material, able to rotate the polarization. Again we see different colors corresponding to different degrees of rotation of the polarization direction.

FIGURE 1.6 (See color insert following page 394.) Camphor between crossed polarizers. (Photo courtesy of D. H. Goldstein.)

FIGURE 1.7 (See color insert following page 394.) Corn syrup (a) between parallel polarizers, (b) between polarizers at 45° to one another, and (c) between crossed polarizers. (Photos courtesy of D. H. Goldstein.)

FIGURE 1.8 (See color insert following page 394.) View from vehicle as seen (a) without polarized sun-glasses, and (b) with polarized sunglasses. (Photo courtesy of D. H. Goldstein.)

These are all entertaining and colorful examples of polarized light phenomena. Polarized light has to be considered in almost any optics application, and it has many important practical uses. In Part I of this book, we will explore the basic physics ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright
• Table of Contents
• Preface to the Third Edition
• Polarized Light: A History
• PART I Introduction to Polarized Light
• Chapter 1 Introduction
• Chapter 2 Polarization in the Natural Environment
• Chapter 3 Wave Equation in Classical Optics
• Chapter 4 The Polarization Ellipse
• Chapter 5 Stokes Polarization Parameters
• Chapter 6 Mueller Matrices for Polarizing Components
• Chapter 7 Fresnel Equations: Derivation and Mueller Matrix Formulation
• Chapter 8 Mathematics of the Mueller Matrix
• Chapter 9 Mueller Matrices for Dielectric Plates
• Chapter 10 The Jones Matrix Formalism
• Chapter 11 The Poincaré Sphere
• Chapter 12 Fresnel–Arago Interference Laws
• PART II Polarimetry
• Chapter 13 Introduction
• Chapter 14 Methods of Measuring Stokes Polarization Parameters
• Chapter 15 Measurement of the Characteristics of Polarizing Elements
• Chapter 16 Stokes Polarimetry
• Chapter 17 Mueller Matrix Polarimetry
• Chapter 18 Techniques in Imaging Polarimetry*
• Chapter 19 Channeled Polarimetry for Snapshot Measurements*
• PART III Applications
• Chapter 20 Introduction
• Chapter 21 Crystal Optics
• Chapter 22 Optics of Metals
• Chapter 23 Polarization Optical Elements
• Chapter 24 Ellipsometry
• Chapter 25 Form Birefringence and Meanderline Retarders
• PART IV Classical and Quantum Theory of Radiation by Accelerating Charges
• Chapter 26 Introduction to Classical and Quantum Theory of Radiation by Accelerating Charges
• Chapter 27 Maxwell’s Equations for Electromagnetic Fields
• Chapter 28 The Classical Radiation Field
• Chapter 29 Radiation Emitted by Accelerating Charges
• Chapter 30 Radiation of an Accelerating Charge in the Electromagnetic Field
• Chapter 31 The Classical Zeeman Effect
• Chapter 32 Further Applications of the Classical Radiation Theory
• Chapter 33 The Stokes Parameters and Mueller Matrices for Optical Activity and Faraday Rotation
• Chapter 34 Stokes Parameters for Quantum Systems
• Appendix A: Conventions in Polarized Light
• Appendix B: Jones and Stokes Vectors
• Appendix C: Jones and Mueller Matrices
• Appendix D: Relationships between the Jones and Mueller Matrix Elements
• Appendix E: Vector Representation of the Optical Field: Application to Optical Activity
• Bibliography
• Index