Polarized Light in Optics and Spectroscopy

David S. Kliger, James W. Lewis

• Publisher: Academic Press
• Year: 2012
• ISBN:
  9780080571041
• Topic: Ciencias físicas
• Subtopic: Óptica y luz

This comprehensive introduction to polarized light provides students and researchers with the background and the specialized knowledge needed to fully utilize polarized light. It provides a basic introduction to the interaction of light with matter for those unfamiliar with photochemistry and photophysics. An in-depth discussion of polarizing optics is also given. Different analytical techniques are introduced and compared and introductions to the use of polarized light in various forms of spectroscopy are provided.

• Starts at a basic level and develops tools for research problems
• Discusses practical devices for controlling polarized light
• Compares the Jones, Mueller, and Poincaré sphere methods of analysis

CHAPTER 1

The Nature of Light

1 Historical Background

Before getting into discussions of the polarization properties of light and how light interacts with matter, it is useful, and fun, to see how we came to our present understanding of these matters. We thus present here a very brief history of how theories about the nature of light evolved. We will see how it is particularly interesting, in view of the topic of this book, that polarization properties of light played a key role in leading us to our present understanding of the nature of light. The history presented here is necessarily very brief. It cannot do justice to the many natural philosophers and scientists who contributed over the centuries to our understanding of the nature of light. Nor can it give justice to the many subtle arguments involved in each theory of light. It is presented here, nonetheless, to place our discussions of light in a context so that the reader has some appreciation for the development of our present views of light. For more detailed arguments presented through the ages you might use references 1–4 cited at the end of the chapter.

The book of Genesis tells us that “In the beginning God said, ‘Let there be light’. And there was light.” It has only been in the relatively recent past, however, that we have come to our present understanding of what light is. When we ask, “what is the nature of light?” we are really asking for a description of light in terms of other phenomena with which we are familiar. The search for this type of understanding of the nature of light has been a long one. Early studies of optics came from the Greeks, who were not so much interested in the nature of light as in the mechanism of vision (still an active area of scientific investigation after 2500 years). A common view of the Greeks was that we see objects when light is emitted from the eye, bounces off of the objects, and returns to the eye. Light was believed to emerge from the eye as a thread. Studies of these effects led to the idea that light was made up of rays that travel in straight lines and that these rays all travel at the same speed. The studies of the Greeks did not reveal much about the nature of light, but they did introduce the concepts of geometrical optics.

During the middle ages the Western philosophical and scientific world underwent a major crisis, and progress in the study of light came from the Middle East. There people began to think of light as an external entity rather than an emanation from the eye. Looking at very bright objects was observed to be painful, yet it was difficult to explain why reflection of the emanations from the eye due to one object would cause this while reflections due to other objects would not.

In the 17th century, studies of light turned from questions about the mechanism of vision to questions about the nature of light itself. Over the course of the years four major concepts of light were popular. Light was known to travel in straight lines, so it was reasoned that its nature must be that of something that moves. Various people took this to be liquids, particles (sometimes referred to as corpuscles or projectiles), vibrations of an ethereal fluid, or waves.

The idea of light as a fluid came from the discovery of diffraction phenomena by Grimaldi in the mid-1600s. The diffraction patterns could not be explained by particle theories. Instead, they were reminiscent of wave patterns seen in liquids, analogous to diffraction patterns one sees when two pebbles are thrown into water. Even having suggested the idea of light as a fluid, however, Grimaldi realized that there were difficulties with this proposition. Fluid theories of light were advocated for some time, but arguments for them were usually based on theological rather than scientific arguments. The idea of light as a liquid was never well supported and was quickly replaced by other theories. Its biggest problem was that it could not explain how light could penetrate solid bodies and also travel in a vacuum. It did, however, introduce the idea of wave properties of light, a concept that was not really understood for two more centuries.

The corpuscular theory of light became widely accepted after about 1687 when Newton published his Principia. Newton argued against the wavelike nature of light because of the way shadows were formed. Water and sound waves propagated around the edges of an intervening obstacle, affecting points within the geometrical shadow of the obstacle. Light did not seem to behave this way. Newton thus argued that light is a material body that is susceptible to attractive and repulsive forces just as particles obey Newton’s second law of motion. Newton also could not reconcile wave theories of light with rectilinear motion of light. He was careful not to specify the nature of light, since he saw inconsistencies in both wave and particle theories, and he thus talked of “rays of light” rather than particles of light. Newton’s successors, however, took Newton’s views and expanded their interpretation to say that light was made up of particles. By the mid-1700s this corpuscular theory of light was well-entrenched, though some argued against it in favor of a vibration theory of light. In the corpuscular theory light was viewed as being made up of very light particles that travel at high speed (Roemer had measured the speed of light in 1676 by timing the eclipse of one of Jupiter’s moons). It was argued that light had properties similar to matter in that neither was subject to decay or transmutation. Refractive dispersion, which produced the prism’s rainbow, was explained by saying that violet-making rays consisted of small bodies and red-making rays consisted of larger, heavier bodies.

One argument considered to favor the corpuscular theory of light involved polarization effects. In 1669 Bartholinus discovered the effect of double refraction, which occurred when light passed through crystals of Icelandic spar (what we now call calcite). Later, in 1690, Huygens discovered the phenomenon of light polarization by passing light through two calcite crystals in series. Although Huygen’s work relied extensively on analyses of waves, this discovery of polarization was used by others to support a particle theory. In 1808 Malus passed partially reflected light through a calcite crystal and found that it was polarized. Newton had suggested that the effect of double refraction might indicate that particles of light were asymmetric. Malus took this idea and used it to explain both double-refraction and partial-reflection phenomena. He suggested that the particles could be considered to initially be randomly oriented. As the particles passed through a double-refracting crystal, they aligned and became ordered. In analogy to magnetic bodies, Malus suggested that the corpuscles had poles, and he thus called the oriented light polarized light.

The corpuscular theory of light was attacked in the mid-1700s by people like Euler and Young. They proposed instead a vibration theory of light. There were several arguments put forward to attack the corpuscular theory. Principally, these were that (1) the mass of the particles composing the light rays would have to be exceedingly small; (2) when two light beams intersected they do not affect each other; and (3) one did not observe “wastage” of light. By wastage it was meant, for example, that one can observe sharp images of stars. If rays of light from the stars were made up of particles, however, they should, over the large distances traveled, impinge on many other particles. This should smear out the image of the star and make stars appear fuzzy.

In the vibration theory, light is considered to be the manifestation of a vibratory motion of some invisible, omnipresent material referred to as the ether. The strongest defense of this theory came from Euler and Young. They suggested that distant objects can affect us by emitting particles or by propagating motions through intermediates (analogous to the propagation of sounds). They discounted the particle theory of light for the reasons already given and because they did not believe it was possible, as it would have to be if the particle theory were correct, that transparent solid objects had pores running in all directions.

In the vibration theory, different colors were said to be manifestations of vibrations of different frequencies through the ether. The theory more easily explained the phenomenon of partial reflection than the particle theory did, and gained strong support from the double-slit experiments of Young, which showed interference effects. Nevertheless, there were problems with the vibration theory. If there was an omnipresent ethereal fluid, its presence should affect motions of planets and comets. Also, if light were due to vibration of an ether, in analogy to sound or water waves, light should bend around solid objects. Neither of these phenomena were observed. In spite of this, the double-slit experiments of Young, which were carried out in the early 19th century, made the vibration theory of light very attractive.

Progress during the 19th century caused the role of mathematics in analyzing and interpreting physical phenomena to grow in importance. Thus, the principle of interference, which was used by Young to explain diffraction phenomena, was placed on a more mathematical footing by Fresnel. He interpreted these phenomena, however, in terms of a wave theory of light rather than a vibration theory. The difference between these two theories is that, in the vibration theory, light was seen as a longitudinal vibration of the ether just as sound waves are longitudinal vibrations in air. The wave theory initially considered light also to involve oscillations of an ether, but the motions were now taken to be transverse waves.

Either longitudinal vibrations or transverse waves could be used to explain diffraction phenomena. However, work on the polarization of light gave more credence to the wave theory. It was shown that when two polarizers were crossed no light emerged from them. Furthermore, an interesting thing happened when light passed through double-refracting substances. Two beams of unpolarized light could be combined to form interference patterns. However, combination of the ordinary and extraordinary beams emerging from double-refracting materials in the same way did not produce such patterns. These phenomena could easily be explained in terms of transverse waves but not longitudinal vibrations.

These successes of the wave theory led to increasing doubt about the corpuscular theory of light during the 19th century. Experiments performed in 1849 by Fizeau and in 1862 by Foucault, measuring the velocity of light in different media, essentially ended the support of the corpuscular theory. These experiments showed that the velocity of light was smaller in liquids than in air or in a vacuum, the opposite of what the corpuscular theory would predict.

The wave theory was commonly accepted after these experiments, but the concept of the nature of the wave changed. In 1873 Maxwell advanced the theory of light as electromagnetic waves, and experiments of Hertz, carried out in 1888, confirmed the predictions that electromagnetic waves produced from oscillating electric currents exhibited reflection, refraction, diffraction, interference, and polarization. The wave theory of light was on solid footing. This situation lasted, however, for only a brief time.

In the beginning of the 20th century a new view of the nature of light emerged. Einstein, Planck, and others realized that a number of phenomena, including the energy distribution of blackbody radiation, the Compton effect, and the photoelectric effect, could not be explained in terms of light as a continuous wave of electromagnetic energy. Instead, they showed that the explanation of these phenomena required that light be made of quantized packets of energy called photons. In a sense, then, a corpuscular view of light reemerged, though now light was seen not as particles in the sense of objects that followed Newton’s laws of motion, but rather as bundles of discrete amounts of energy.

The introduction of the concept of photons produced a dilemma for a theory of light. It appeared that to interpret some experiments one needed a wave theory of light, whereas to interpret other experiments a quantum, or “particle,” theory was needed. The solution to this dilemma came from DeBroglie. He pointed out that each of these experiments does not directly demonstrate a property of light per se but demonstrates how light interacts with the experimental apparatus. Thus, light exhibits both wave properties and particle properties, depending on what it interacts with. This view of the wave-particle duality of photons is the view of light most commonly held today. In fact, this dual nature of light was demonstrated in an elegant experiment [5].

The experiment, carried out by Philippe Grangier, Gérard Roger, and Alain Aspect of the Institute of Theoretical and Applied Optics in Orsay, France, was designed in a way that photons could be observed one at a time. This involved using a very low intensity light source and a detection system able to observe individual photons and avoid observation of bunches of photons. The single photons were then observed under two different experimental conditions. In the first, the light passed through a beam splitter, which deflected 50% of the photons onto a path oriented 90° to the original path. The remaining 50% of the photons were transmitted along the original path. Light detectors were then set up to detect photons traveling along each of these two paths. As you would expect from a particle model of light, the individual photons were detected at one or the other photon detectors, but coincidences, indicating that a single photon was “split in two,” were not seen.

In a second stage of the experiment, the photon detectors were removed and the photons traveling along the two paths were sent into two arms of a Mach-Zehnder interferometer. As the path lengths of the two beams were varied and the numbers of photons emerging from each path were counted, an interference pattern emerged. This indicated that in an apparatus designed to show wave interference phenomena, single ...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Preface
• Chapter 1: The Nature of Light
• Chapter 2: Polarization Properties of Light
• Chapter 3: Devices for Control of Polarized Light
• Chapter 4: Introduction to the Jones Calculus, Mueller Calculus, and Poincaré Sphere
• Chapter 5: The Jones Calculus, Mueller Calculus, and Poincaré Sphere Revisited
• Chapter 6: Spectroscopy with Polarized Light
• Chapter 7: Orientation and Photoselection Effects
• Chapter 8: Polarized Light in Condensed Phases
• Appendix A: Jones and Stokes Vectors of Various Forms of Polarized Light
• Appendix B
• Appendix C: Jones N-Matrices
• Index