This book is intended to explain the physical basis of classical optics and to introduce the reader to a variety of wave phenomena and their applications. However, it was discovered at the end of the nineteenth century that the description of light in terms of Maxwell's classical electromagnetic waves was incomplete, and the notion of quantization had to be added. Since then, in parallel to the development of wave optics, there has been an explosive growth of quantum optics, much of it fuelled by the invention of the laser at the end of the 1950s, which also provided a great incentive to reconsider many topics of classical optics, such as interference and coherence theory. It would be inappropriate that this book should ignore these developments; on the other hand, the subject of quantum optics is now so wide that a single chapter can do no justice to the field. In this chapter, we therefore set out modestly to explain the way in which quantum optics is different from classical optics, and give a qualitative introduction to lasers, followed by a taste of some of the new phenomena that have developed in recent years and are currently at the forefront of optics research.

In this chapter we shall discuss:

• how the electromagnetic field can be quantized, by creating an analogy between an electromagnetic wave and a simple harmonic oscillator;

• the concept of the photon, and some of its properties;

• […]

J. B. J. Fourier (1768–1830), applied mathematician and Egyptologist, was one of the great French scientists working at the time of Napoleon. Today, he is best remembered for the Fourier series method, which he invented for representation of any periodic function as a sum of discrete sinusoidal harmonics of its fundamental frequency. By extrapolation, his name is also attached to Fourier transforms or Fourier integrals, which allow almost any function to be represented in terms of an integral of sinusoidal functions over a continuous range of frequencies. Fourier methods have applications in almost every field of science and engineering. Since optics deals with wave phenomena, the use of Fourier series and transforms to analyze them has been particularly fruitful. For this reason, we shall devote this chapter to a discussion of the major points of Fourier theory, hoping to make the main ideas sufficiently clear in order to provide a ‘language’ in which many of the phenomena in the rest of the book can easily be discussed. More complete discussions, with greater mathematical rigour, can be found in many texts such as Brigham (1988), Walker (1988) and Prestini (2004).

In this chapter we shall learn:

• what is a Fourier series;

• about real and complex representation of the Fourier coefficients, and how they are calculated;

• how the Fourier coefficients are related to the symmetry of the function;

• how to represent the coefficients as a discrete spectrum in reciprocal, or wave-vector, space;

• […]

In this chapter we shall meet examples of electromagnetic wave propagation in systems containing fine dielectric structure on a scale of the order of the wavelength, where the scalar-wave approximation is inadequate. Clearly, in these cases we have to solve Maxwell's equations directly. On writing the equations, we shall discover that they bear a close similarity to those of quantum mechanics, where the dielectric constant in Maxwell's equations is analogous to the potential in Schrödinger's equation. This opens up a vast arsenal of methods, both analytical and numerical, which have been developed for their solution.

We first discuss the optical waveguide, already familiar in everyday life as the optical fibre, which has caused a revolution in the communications industry (Agrawal (2002)). The second topic is the dielectric multilayer system which, in its simplest form (the quarter-wave anti-reflection coating) has been with us for more than a century, but can today be used to make optical filters of any degree of complexity (MacLeod (2001)).

Following these examples, we shall briefly discuss their application to photonic crystals, structures with periodic refractive index leading to optical band gaps, whose behaviour can immediately be understood in terms of the quantum analogy (Joannopoulos et al. (2008)). Photonic crystals have always existed.

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 study the past as a guide to the future. Much insight into the great minds of the era of classical physics can be found in books by Magie (1935) and Segré (1984).

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?

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 that 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. Some of the quantum-mechanical ideas behind dispersion will be discussed later in Chapter 14, but most are outside the scope of this book.

In this chapter we shall learn:

• about the way in which a classical dipole atom responds to an oscillating electromagnetic field;

• about Rayleigh scattering, and why sky light is blue and polarized;

• how refractive index, absorption and scattering are related;

• that dispersion, the dependence of refractive properties on frequency, results from atomic resonances;

• about anomalous dispersion near to absorption lines;

• analytical relationships between refractive index and absorption;

• about plasma absorption and magneto-optical effects;

• whether signals can be propagated faster than the speed of light in anomalous-dispersion regions;

• a little about non-linear optical properties, which arise when the wavefields are very intense;

• about harmonic generation, the photo-refractive effect and soliton propagation;

• about optics at interfaces between conventional dielectrics and materials with negative permittivity;

• about surface plasmon resonance.

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 quite appropriate to put this chapter here. Essentially, geometrical optics, which considers light waves as rays that propagate along straight lines in uniform media and are related by Snell's law (§2.6.2 and §5.4) at interfaces, has a relationship to wave optics similar to that of classical mechanics 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. Under these conditions we can neglect diffraction, which otherwise prevents the exact simultaneous specification of the positions and directions of rays on which geometrical optics is based.

Analytical solutions of problems in geometrical optics are rare, but fortunately there are approximations, in particular the Gaussian or paraxial approximation, which work quite well under most conditions and will be the basis of the discussion in this chapter. Exact solutions can be found using specialized computer programs, which will not be discussed here. However, 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.

The difference between Fresnel and Fraunhofer diffraction has been discussed in Chapter 7, where we showed that Fraunhofer diffraction is characterized by a linear change of phase over the diffracting obstacle, contrasting the quadratic phase change responsible for Fresnel diffraction. Basically, Fraunhofer diffraction is the limit of Fresnel diffraction when the source and the observer are infinitely distant from the obstacle. When the wavelength is very short and the obstacles are very small, such conditions can be achieved in the laboratory; for this reason Fraunhofer diffraction is naturally observed with X-rays, electrons, neutrons, etc., which generally have wavelengths less than 1Å. The study of Fraunhofer diffraction has been fuelled by its importance in understanding the diffraction of these waves, particularly by crystals. This has led to our present-day knowledge of the crystalline structures of materials and also of many molecular structures. Figure 8.1 shows a famous X-ray diffraction pattern of a crystal of haemoglobin, from about 1958, whose interpretation was a milestone in visualizing and understanding biological macromolecules. The techniques used in interpreting such pictures will be discussed in the later parts of the chapter.

In optics, using macroscopic objects in a finite laboratory, the linear phase change can be achieved by illuminating the object with a beam of parallel light. It is therefore necessary to use lenses, both for the production of the parallel beam and for the observation of the resultant diffraction pattern.

In Chapter 8 we discussed the theory of Fraunhofer diffraction and interference, emphasizing in particular the relevance of Fourier transforms. In this chapter we shall describe the applications of interference to measurement; this is called interferometry. Some of the most accurate dimensional measurements are made by interferometric means using waves of different types, electromagnetic, matter, neutron, acoustic etc. One current highlight of optical interferometry is the development of detectors that can measure dimensional changes as small as 10−19 m, which should be induced by gravitational waves emitted by cataclysmic events in the distant Universe. A picture of one such interferometer, which has two orthogonal arms each 4 km in length, is shown in Fig. 9.1 and the design of this instrument will be discussed in more detail in §9.7.

An enormous variety of interferometric techniques has been developed during the years, and we shall limit ourselves in this chapter to a discussion of examples representing distinctly different principles. There are several monographs on interferometry that discuss practical aspects in greater detail, for example Tolansky (1973), Steel (1983), Hariharan (2003) and Hariharan (2007).

In this chapter we shall learn about:

• Young's basic two-slit interferometer and its capabilities;

• interference in a reflecting thin film;

• diffraction gratings: how they work and how they are made, their resolving power and their efficiency;

• two-beam interferometers of several types;

• […]

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 polarization vectors, which can be in any two mutually orthogonal directions normal to k. However, when the medium through which the wave travels is anisotropic, which means that its properties depend on orientation, the choice of the polarization vectors is not arbitrary, and the velocities of the two waves may be different. A material that supports two distinct propagation vectors is called birefringent.

In this chapter, we shall learn:

• about the various types of polarized plane waves that can propagate – linear, circular and elliptical – and how they are produced;

• how an anisotropic optical material can be described by a dielectric tensor ∈, which relates the fields D and E within the material;

• a simple geometrical representation of wave propagation in an anisotropic material, the n-surface, which allows the wave propagation properties to be easily visualized;

• how Maxwell's equations are written in an anisotropic material, and how they lead to two particular orthogonally polarized plane-wave solutions;

• […]

This chapter will discuss the electromagnetic wave as a 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 with the steps leading to this formulation will be assumed (see, for example, Grant and Phillips (1990), Jackson (1999), Franklin (2005)). It is well known that Maxwell's formulation included for the first time the displacement current ∂D/∂t, the time derivative of the fictitious displacement field D = ∈0E+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.

In this chapter we shall learn:

• about the properties of electromagnetic waves in isotropic linear media;

• about simple-harmonic waves with planar wavefronts;

• about radiation of electromagnetic waves;

• the way in which these waves behave when they meet the boundaries between media: the Fresnel coefficients for reflection and transmission;

• about optical tunnelling and frustrated total internal reflection;

• about electromagnetic waves in conducting media;

• some consequences of the time-reversal symmetry of Maxwell's equations;

• about electromagnetic momentum, radiation pressure and optical tweezers;

• about angular momentum of waves that have spiral wavefronts, instead of the usual plane wavefronts;

• […]

We use optics overwhelmingly in our everyday life: in art and sciences, in modern communications and medical technology, to name just a few fields. This is because 90% of the information we receive is visual. The main purpose of this book is to communicate our enthusiasm for optics, as a subject both practical and aesthetic, and standing on a solid theoretical basis.

We were very pleased to be invited by the publishers to update Optical Physics for a fourth edition. The first edition appeared in 1969, a decade after the construction of the first lasers, which created a renaissance in optics that is still continuing. That edition was strongly influenced by the work of Henry Lipson (1910–1991), based on the analogy between X-ray crystallography and optical Fraunhofer diffraction in the Fourier transform relationship realized by Max von Laue in the 1930s. The text was illustrated with many photographs taken with the optical diffractometers that Henry and his colleagues built as ‘analogue computers’ for solving crystallographic problems. Henry wrote much of the first and second editions, and was involved in planning the third edition, but did not live to see its publication. In the later editions, we have continued the tradition of illustrating the principles of physical optics with photographs taken in the laboratory, both by ourselves and by our students, and hope that readers will be encouraged to carry out and further develop these experiments themselves.

Optics is the study of wave propagation and its quantum implications, the latter now being generally called ‘photonics’. Traditionally, optics has centred around visible light waves, but the concepts that have developed over the years have been found increasingly useful when applied to many other types of wave, both inside and outside the electromagnetic spectrum. This chapter will first introduce the general concepts of classical wave propagation, and describe how waves are treated mathematically.

However, since there are many examples of wave propagation that are difficult to analyze exactly, several concepts have evolved that allow wave propagation problems to be solved at a more intuitive level. The latter half of the chapter will be devoted to describing these methods, due to Huygens and Fermat, and will be illustrated by examples of their application to wave propagation in scenarios where analytical solutions are very hard to come by. One example, the propagation of light waves passing near a heavy massive body, called ‘gravitational lensing’ is shown in Fig. 2.1; the figure shows two images of distant sources distorted by such gravitational lenses, taken by the Hubble Space Telescope, compared with experimental laboratory simulations. Although analytical methods do exist for these situations, Huygens' construction makes their solution much easier (§2.8).

A wave is essentially a temporary disturbance in a medium in stable equilibrium. Following the disturbance, the medium returns to equilibrium, and the energy of the disturbance is dissipated in a dynamic manner.

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.

Bessel functions come into wave optics because many optical elements – lenses, apertures, mirrors – are circular. We have met Bessel functions in several places (§8.3.4, §8.7, §12.2, §12.6.4 for example), although since most students are not very familiar with them (and probably becoming less so with the ubiquity of computers) we have restricted our use of them as far as possible. The one unavoidable meeting is the Fraunhofer diffraction pattern of a circular aperture, the Airy pattern, which is the diffraction-limited point spread function of an aberration-free optical system (§12.2). Another topic that involves the use of Bessel functions is the Fourier analysis of phase functions, in which the function being transformed contains the phase in an exponent. We met such a situation when we studied the acousto-optic effect, where a sinusoidal pressure wave affects directly the phase of the optical transmission function.

In this appendix we simply intend to acquaint the reader with the results that are necessary for elementary wave optics. The proofs can be found in the treatise by Watson (1958) and other places.

The coherence of a wave describes the accuracy with which it can be represented by a pure sine wave. So far we have discussed optical effects in terms of coherent waves whose wave-vector k and frequency ω are known exactly; in this chapter we intend to investigate the way in which uncertainties and small fluctuations in k and ω can affect the observations in optical experiments. Waves that appear to be pure sine waves only if they are observed in a limited space or for a limited period of time are called partially coherent waves, and we shall see in this chapter how we can measure deviations of such waves from their pure counterparts, and what these measurements tell us about the source of the waves.

The classical measure of coherence was formulated by Zernike in 1938 but had its roots in much earlier work by Fizeau and Michelson in the late nineteenth century. Both of these scientists realized that the contrast of interference fringes between waves travelling by two different paths from a source to an observer would be affected by the size, shape and spectrum of the source. Fizeau suggested, and Michelson carried out, experiments which showed that the angular diameter of a star could indeed be measured by observing the degradation of the contrast of interference fringes seen when using the star as a source of light (§11.8.1).

Stylistics: an interdiscipline

Throughout this book we have argued for a broad view of stylistics as being concerned with the systematic analysis of style in language in all its forms. This is a wider view of stylistics than some stylisticians might hold; as we have seen, stylistics is often defined more narrowly as the study of literary texts using linguistic techniques. However, as we have also noted at various points throughout this book, the techniques of linguistics are just as applicable in the analysis of non-literary (in the sense of non-fiction) texts as they are in the analysis of prototypically literary works. Furthermore, the problem of defining the concept of literariness (see Chapter 2) lends further weight to the view that stylistics should not be seen as concerned with any one particular text-type. While we cannot dismiss the fact that stylisticians generally have concentrated primarily on the analysis of so-called literary texts, this activity has been motivated by a desire to understand the workings of what is defined socio-culturally as literature rather than by an analytical inability on the part of stylistics to deal with other text-types.

Despite the fact that our broad view of stylistics may not be shared by all practitioners of it, one aspect of our definition of the subject that all stylisticians will be in agreement with concerns its development out of the discipline of linguistics. Stylistics is unremittingly linguistic in orientation.

Stylistics and pragmatics

Early work in stylistics focused primarily on the analysis of the formal linguistic elements of texts – for example, grammatical forms, phonological features and propositional meanings (see Chapter 2). It is no surprise that such work also focused mainly on the analysis of poems, since such texts are short (making it possible for the stylistician to analyse a complete text) and relatively straightforward in terms of discourse structure. That is, many poems have a single-tier discourse architecture in which the poet addresses the reader directly (Short 1996: 38). This makes a stylistic analysis of such texts relatively straightforward (at least in methodological terms), since it involves identifying stylistic effects at just one discourse level. This is considerably more straightforward than trying to identify the stylistic effects in a text with multiple discourse levels, such as a novel, which involves an address from the author to the reader, embedded in which is an address from a narrator to a narratee, embedded in which are the characters in the fictional world addressing each other. In texts composed of multiple discourse levels, the task for the analyst is considerably more difficult, since the analysis necessitates identifying and isolating stylistic effects at each of the text's constituent discourse levels. Also, such texts tend to be longer, making it unfeasible to produce analyses of complete texts (though corpus stylistics has alleviated this problem to a certain extent; we will discuss this fully in Chapter 7).

The reading process

In the previous chapter we considered the active role that readers play in the construction of meaning. We focused on the prior knowledge that readers bring to texts and which they use in the process of interpretation, and from this it becomes clear that the process of meaning creation is a result of the interconnection between textual triggers and readers' world knowledge. Or, to restate this in Semino's (1997) terms, texts project meaning while readers construct it. The means by which readers go about constructing meaning is, as we explained in Chapter 5, the central concern of cognitive stylistics. In this chapter we will continue our consideration of this branch of stylistics by focusing on how readers navigate their way though texts. While Chapter 5 considered the stylistic effects that can arise as a result of, say, deviant schemas or novel conceptual metaphors, in this chapter we will focus primarily on a descriptive account of how readers process textual meaning. In so doing we will outline some of the most influential theories of text processing to have been adopted by stylistics. One caveat to the whole cognitive stylistics enterprise, of course, is that it is important that it does not reject the more linguistically and textually orientated approaches described in the earlier chapters of this book. Rather it should seek to enrich these by adding a cognitive layer to the explanation of how readers react to texts.