Since the writing of the first edition the subject of Optics, as studied in universities, has grown greatly both in popularity and scope, and both we and the publishers thought that the time had arrived for a new edition of Optical Physics.

In preparing the new edition we have made substantial changes in several directions. First, we have attempted to correct all the mistakes and misconceptions that have been pointed out to us during the nine years the book has been in use. Secondly, we have made one important change in the subject matter: we have absorbed the chapter on Quantum Optics into the rest of the book. During the years, there have appeared many books devoted to laser physics, and it now seems impracticable for a book on physical optics to cover the subject at all satisfactorily in one chapter. However, since some knowledge of the principles of the laser is necessary for the understanding of physical optics today, particularly when coherence is being discussed, we have covered what we feel to be the necessary minimum as parts of Chapters 7 and 8.

In addition to the above changes in the subject matter, we have increased the number of exercises offered to the reader, organized them according to chapter, and provided solutions. We have also included a few suggestions, based on our experience, for student projects illustrating the material in the book.

We are, of course, most grateful to all those who have pointed out to us errors and room for improvement.

Electromagnetism and the wave equation

This chapter will discuss the electromagnetic wave as a specific and most important example of the general treatment of wave propagation presented in Chapter 2. We shall start at the point where the elementary features of classical electricity and magnetism have been summarized in the form of Maxwell's equations, and the reader's familiarity of the steps leading to this formulation will be assumed (see, for example Grant and Phillips, 1975; Jackson, 1975). It is well-known that Maxwell's formulation included for the first time the displacement current δD/δt, the time-derivative of the ficticious displacement field D = ε0E + P, which is a combination of the applied electric field E and the electric polarization density P. This field will turn out to be of prime importance when we come to extend the treatment in this chapter to wave propagation in anisotropic media in Chapter 6.

The development presented in this chapter emphasizes the properties of simple harmonic waves in isotropic linear media, and the way in which waves behave when they meet the boundaries between media. An isotropic medium is one in which all directions in space are equivalent, and there is no difference between right-handed and left-handed rotation. An example would be a monatomic liquid; in contrast, crystals are generally anisotropic. A linear medium is one in which the polarization produced by an applied electric or magnetic field is proportional to that field.

Introduction

Optics is the study of wave propagation and its quantum implications. Traditionally, it has centred around visible light waves, but in the modern era the concepts which have developed over the years have been found increasingly useful when applied to many other types of wave, both within and without the electromagnetic spectrum. Wave propagation in a medium is described mathematically in terms of a wave equation; this is a differential equation relating the dynamics and statics of small displacements of the medium, and whose solution may be a propagating disturbance. This chapter will be concerned with such equations and their solutions.

The term ‘displacements of the medium’ is not, of course, restricted to mechanical displacement but can be taken to include any field quantity (continuous function of r and t) which can be used to measure a departure from equilibrium, and the equilibrium state itself may be nothing more than the vacuum.

Although it is convenient, from an elementary point of view, to study wave equations arising from the mechanical relationships between displacement and velocity, we quickly learn that almost any relationships between derivatives of a field in space and time can replace them. Then the distinction, which is clear in the mechanical sense, between ‘static’ and ‘dynamic’ properties may become blurred. For example, in the electromagnetic wave, the variables are electric and magnetic fields.

Electromagnetic waves in restricted systems

This chapter will deal with two examples of electromagnetic wave propagation in systems where the scalar-wave approximation is inadequate, essentially because of the small dimensions of the constituent parts. The first is the optical waveguide, already familiar in everyday life as the optical fibre, which has caused a revolution in the communications industry. The second example is the dielectric multilayer system which, in its simplest form (the quarter-wave anti-reflexion coating) has been with us for more than a century, and can today be used to make optical filters of any degree of complexity that are common elements in the laboratory.

Optical waveguides

Transmission of light along a rod of transparent material by means of repeated total internal reflexion at its walls must have been observed countless times before it was put to practical use. In this section we shall describe the geometrical and physical optical approaches to this phenomenon, and derive some of the basic results for planar and cylindrical guides, the latter of which is a model for the optical fibre. Optical fibres have many uses, two of which will be described briefly at the end of the section; the first is for transmitting images, either faithfully or in coded form, without the use of lenses; the second is for optical communication.

Geometrical theory of wave guiding

The principle of the optical fibre can be illustrated by a two-dimensional model (corresponding really to a wide strip rather than a fibre) shown in Fig. 10.1.

Introduction

If this book were to follow historical order, the present chapter should have preceded the previous one, since lenses and mirrors were known and studied long before wave theory was understood. However, once we have grasped the elements of wave theory, it is much easier to appreciate the strengths and limitations of geometrical optics, so logically it is really more appropriate to put this chapter here. Essentially, geometrical optics, which considers light waves as rays which propagate along straight lines in uniform media and are related by Snell's law (§§2.7.2, 5.4.2) at interfaces, has a similar relationship to wave optics as classical mechanics does to quantum mechanics. For geometrical optics to be strictly true, it is important that the sizes of the elements we are dealing with be large compared with the wavelength λ. This means that we can neglect diffraction, which otherwise prevents the exact simultaneous specification of the positions and directions of rays on which geometrical optics is based. From the practical point of view, geometrical optics answers most questions about optical instruments extremely well and in a much simpler way than wave theory could do; it fails only in that it can not define the limits of performance such as resolving power, and does not work well for very small devices such as optical fibres. These will be dealt with by wave theory in Chapters 10 and 12.

The plan of the chapter is first to treat the classical ray theory of thin lens systems in the paraxial approximation.

Occurrence of diffraction

As we saw in Chapter 1, the wave theory of light was not at first generally accepted because light did not appear to have any obviously wave-like properties; for example, it did not bend round obstacles as water waves are clearly seen to do. The reason why this difficulty no longer prevents our acceptance of the wave theory is that we are now aware of the relative scales of the two sorts of waves: water waves are coarse and we can see that they only bend round obstacles that have dimensions of the same order of magnitude as the wavelength; larger objects merely stop the waves in the sense that the waves bending round the edge produce negligible effects. But the wavelength of light is about 5 × 10-7 (0.5 μm) and an object of about a hundred waves in size – sufficient to stop a light wave – is still very small by ordinary standards. Nevertheless some bending of the light waves round the edges of obstacles does occur and can be observed over a range of conditions. For particles of the order of a few wavelengths in size, no special apparatus is needed; for example, the water droplets that condense on a car window are surprisingly uniform in size and show beautiful halos round the street lights as the car passes by. For objects that are much larger, special apparatus is needed. The effects are called diffraction phenomena.

Classical dispersion theory

Many aspects of the interaction between radiation and matter can be described quite accurately by a classical theory in which the medium is represented by model atoms consisting of positive and negative parts bound by an attraction which depends linearly on their separation. Although quantum theory is necessary to calculate from first principles the magnitude of the parameters involved, in this chapter we shall show that many optical effects can be interpreted physically in terms of this model by the use of classical mechanics. In §13.5 we shall relax the restriction of linearity. Some of the quantum mechanical foundations will be discussed briefly in Chapter 14, but most are outside the scope of this book (see Yariv, 1989; Loudon, 1983).

The term dispersion means the dependence of dielectric response (dielectric constant and refractive index) on frequency of the wave field. This will be the topic of the present section. Afterwards we shall see some of the applications of dielectric response to spatial effects.

The classical atom

Our classical picture of an atom consists of a massive positive nucleus surrounded by a light spherically-symmetrical cloud of electrons with an equal negative charge. We imagine the two as bound together by springs as in Fig. 13.1, so that in equilibrium the centres of mass and charge of the core and electron charge coincide. As a result the static atom has zero dipole moment.

There are two sorts of textbooks. On the one hand, there are works of reference to which students can turn for the clarification of some obscure point or for the intimate details of some important experiment. On the other hand, there are explanatory books which deal mainly with principles and which help in the understanding of the first type.

We have tried to produce a textbook of the second sort. It deals essentially with the principles of optics, but wherever possible we have emphasized the relevance of these principles to other branches of physics – hence the rather unusual title. We have omitted descriptions of many of the classical experiments in optics – such as Foucault's determination of the velocity of light – because they are now dealt with excellently in most school textbooks. In addition, we have tried not to duplicate approaches, and since we think that the graphical approach to Fraunhofer interference and diffraction problems is entirely covered by the complex-wave approach, we have not introduced the former.

For these reasons, it will be seen that the book will not serve as an introductory textbook, but we hope that it will be useful to university students at all levels. The earlier chapters are reasonably elementary, and it is hoped that by the time those chapters which involve a knowledge of vector calculus and complex-number theory are reached, the student will have acquired the necessary mathematics.

Introduction

As we saw in Chapter 5, electromagnetic waves in isotropic materials are transverse, their electric and magnetic field vectors E and H being normal to the direction of propagation k. The direction of E or rather, as we shall see later, the electric displacement field D, is called the polarization direction, and for any given direction of propagation there are two independent such vectors, which can be in any two mutually orthogonal directions normal to k. When the medium through which the wave travels is anisotropic, which means that its properties depend on orientation, the above statements meet with some restrictions. We shall see that the result of anisotropy in general is that the fields D and B remain transverse to k under all conditions, but E and H, no longer having to be parallel to D and B, are not necessarily transverse. Moreover, the two independent polarizations that propagate must now be chosen specifically with relation to the axes of the anisotropy. A further direct consequence of E and H no longer being necessarily transverse, is that the Poynting vector Π = E × H may not be parallel to the wave-vector k.

In this chapter, we shall first discuss the various types of polarized radiation that can propagate. We shall then go on to extend the theory of electromagnetic waves as described in Chapter 5 to take into account anisotropic media.

Importance of history

Why should a textbook on physics begin with history? Why not start with what is known now and refrain from all the distractions of out-of-date material? These questions would be justifiable if physics were a complete and finished subject; only the final state would then matter and the process of arrival at this state would be irrelevant. But physics is not such a subject, and optics in particular is very much alive and constantly changing. It is important for the student to understand the past as a guide to the future. To study only the present is equivalent to trying to draw a graph with only one point.

It can also be interesting and sometimes sobering to learn how some of the greatest ideas came about. By studying the past we can sometimes gain some insight – however slight – into the minds and methods of the great physicists. No textbook can, of course, reconstruct completely the workings of these minds, but even to glimpse some of the difficulties that they overcame is worthwhile. What seemed great problems to them may seem trivial to us merely because we now have generations of experience to guide us; or, more likely, we have hidden them by cloaking them with words. For example, to the end of his life Newton found the idea of ‘action at a distance’ repugnant in spite of the great use that he made of it; we now accept it as natural, but have we come any nearer than Newton to understanding it?

Introduction

Optical processors hold tremendous potential for processing many information channels in parallel, each at very high bandwidth, and in small volumes with low power consumption (VanderLugt, 1992). Major classes of operations that optics can perform include integral transformations such as Fourier transforms and correlations, and matrix operations, e.g. vector–matrix multiplication (Lee, 1987). Many, but not all, of these are made possible by the remarkable property that a ‘Fourier transform lens’ generates, at the back focal plane, the two-dimensional (2-D) Fourier transform of phase and amplitude information input at the front focal plane.

Initial feasibility demonstrations of optical signal processors are usually performed in the laboratory using existing components, but these often do not come close to fully exploiting the potential of the optical processor, and often disregard practical implementation issues such as: how much phase distortion is permissible in a critical lens, or what will be the effect of vibration or temperature changes in the field, and is it feasible to have a given dynamic range and information capacity in the same processor? Therefore the aim of most subsequent optical hardware development is to answer these questions and overcome any deficiencies.

Much effort has gone into the development of the critical active optical devices, such as infrared laser diodes, spatial light modulators (SLMs) and photodetector arrays, and new device concepts and improvements on existing devices continue to occur (Lee & VanderLugt, 1989).

Introduction

This chapter is dedicated to the evaluation of optical interconnects between electronic processors in multiprocessor systems. Each processor is fully electronic except for the incorporation of a number of photodetectors and optical signal transmitters (e.g., laser diodes, light emitting diodes (LEDs) or optical modulators).

The motivation for this analysis stems from fundamental advantages of optics as well as those of electronics. While electrons are charged fermions, subject to strong mutual interactions and strong reactions to other charged particles, photons are neutral bosons, virtually unaffected by mutual interactions and Coulomb forces. Thus, unlike electrons, multiple beams of photons can cross paths without significant interference. This property allows holographic interconnects to achieve a 3-D (three-dimensional) connection density with only 2-D optical elements. Similarly, photons can propagate through transparent materials without appreciable attenuation or power dissipation. Thus, neglecting speed of light delays, the speed of an optical link is limited only by the switching speed and capacitance of the transmitters and detectors. (For a 10 cm connection length, and a 50° hologram deflection angle, the speed-of-light delay is 0.5 ns.) Hence, the speed and power requirements of an optical interconnect are independent of the connection length. Since electrical very large scale integration (VLSI) connections have a switching energy directly proportional to the line length and an RC delay that grows quadratically with line length, for long enough communication links, optical connections will dissipate less power and provide faster data rate communication.

Introduction

When a scientist or engineer is provided with a given processing problem and asked whether optical processing techniques can solve it, how does he answer the question and approach the problem? To address this, he first considers the basic operations possible. They are often not a direct match to a new problem. Hence new algorithms arise to allow new operations to be performed (often on a new optical architecture). The final system is thus the result of an interaction between optical components, operations, architectures, and algorithms. This chapter describes these issues for the case of image processing. By limiting attention to this general application area, specific examples can be provided and the role for optical processing in most levels of computer vision can be presented. (Other chapters address other specific optical processing applications.)

Section 1.2 presents some general and personal philosophical remarks. These provide guidelines to be used when faced with a given data processing problem and to determine if optical processing has a role in all or part of a viable solution. Section 1.3 describes optical feature extractors. These are the simplest optical systems. This provides the reader with an introduction and summary of some of the many different operations possible on optical systems and how they are of use in image processing. A major application for these simple systems, product inspection, is described to allow a comparison of these optical systems and electronic systems to be made.

Section 1.4 addresses the optical correlator architecture, since it is one of the most powerful and most researched architectures. The key issues in such a system used for pattern recognition are noted.