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.

We have not provided answers to all the exercises in this book. Some (such as exercise 1.1) do not require an answer from us, while others (e.g. 3.3) are intended as an opportunity for you to practise a piece of extended stylistic analysis. In the latter cases, lengthy answers from us are not practical, since there are a number of potential analytical perspectives that such texts can be analysed from. A speculative answer from us would not necessarily cover the issues you have investigated. Instead we have concentrated on providing sample answers to those exercises that focus on fairly specific issues. Nonetheless, it should be borne in mind that even here we are not claiming to provide complete answers.

Chapter 2

The commentaries that follow are not comprehensive, but indicate the kinds of statements that can be made about literary style, using the tools of analysis provided by linguistics.

Keats's famous poem is written in the most common metre of English verse, iambic pentameter, and has a relatively regular, though complex, rhyme scheme. There are three stanzas of eleven lines each, which have the pattern ababcde in the first seven lines and the patterns dcce (first stanza) and cdde (second and third stanzas) in the final four lines. This complexity allows what is in effect a regular use of full rhymes (sun-run; hook-brook-look and so on) to sound musical without becoming monotonous, and thus reflecting the natural world rather than the human-made one.

This book, in the ‘red’ series, is one that we are very proud to have been given the opportunity to write. We have both been teaching stylistics courses at different levels of University education for a number of years, and have found that the sheer variety and diversity of practice that it encompasses causes problems in introducing the field to students for the first time. Equally, this diversity is part of its attraction as a discipline which can interest students from all areas of English Studies, from English Language through Literature to Creative Writing, as well as those coming to text analysis from a Linguistics background.

There are very many excellent books on stylistics already in existence of course, and we pay tribute to these in the pages of this book. Many of these books have been written by significant figures in the Poetics and Linguistics Association (PALA), which has been an extremely important player in the development of the field. Most of these books are the product of a particular personal view (of the author) or represent a particular stage in the development of the field, and for this reason, we felt there was room for another, more eclectic book, which would try to sum up the state of the art as it reaches approximately its centenary.

In planning the book, we felt that it was important to engage readers early, but that this could not come before we had set out some of the principles of the field as we see them.

Cognitive stylistics

In this chapter and in Chapter 6 we focus on an area of stylistics in which interest has grown considerably over the last decade or so. This is an area which has come to be known generally as cognitive stylistics (‘cognitive poetics’ is another term currently in use, though there is arguably no significant difference between what the two terms signify). Cognitive stylistics focuses primarily on hypothesising about what happens during the reading process and how this influences the interpretations that readers generate about the texts they are reading. It proceeds on the assumption that reading is an active process and that readers consequently play an active role in constructing the meaning of texts. Cognitive stylistics has drawn considerable influence from work in areas such as cognitive science generally, psychology, computing and artificial intelligence. Although Stockwell (2002a: 1) claims that cognitive stylistics (he calls it cognitive poetics) ‘is all about reading literature’, there is in principle no reason why cognitive stylistics should not also deal with non-literary texts (the arguments for why stylistics generally is appropriate for the analysis of both fiction and non-fiction writing can be found in Chapter 1).

In recent years, the theories and analytical frameworks of cognitive stylistics have been outlined in a number of key texts (see Tsur 1992, Semino and Culpeper 2002, Stockwell 2002a and Gavins and Steen 2003), though the roots of such work may be traced back much further.

Methodological considerations

Teaching people to ‘do’ stylistics is a very difficult task. This is partly because stylistics draws on a wide range of theories and methods from linguistics, and as a result does not have a single set of parameters which define the discipline. This eclecticism is not a weakness, but a theoretically-legitimate strength. The purpose of theories is to shed light on the subject under consideration and as a result they tend to produce models which are simpler in some respects than the data they relate to. This is in order to generate fuller understanding of particular aspects of the data separately. Trying to capture the whole ‘truth’ about the data in one single unified theory of textual meaning would be unilluminating in its complexity.

As a result of this theoretical eclecticism, the question of how to go about a stylistic study is a complicated one, and requires the researcher to answer a number of questions, which will be introduced and discussed in the sections below. Note that any piece of stylistic research should aim to make clear the basis on which the analysis and interpretation is made, so that others are in a position to judge the results with an understanding of where they originated. This requirement – that stylistics should be as objective as possible in being rigorous and transparent – has at times been questioned by those who saw in this desire for clarity a claim to be ‘scientific’.

What is style?

The previous chapter was a general introduction to stylistics, and many of its topics will be explored in more detail in later chapters. Here, we will introduce some of the core activities of stylistics by considering the beginnings of stylistics as it arose from a combination of some of the principles of Russian formalism and the emerging descriptive techniques of linguistics. Though the remainder of this book will demonstrate that stylistics has developed a rich array of further techniques and principles since this starting point, the principles and techniques with which it began are still very much in evidence in contemporary stylistics, and remain relevant for the close study of literary – and non-literary – language. We will draw the majority of our examples in this chapter from literary works, and especially poems, since these were the principal objects of study of early stylistics. Nonetheless, all of the techniques described in this chapter are applicable to non-literary texts too.

In section 1.5.3, we considered the question of whether we were interested in the style of an author or a genre, and concluded that stylisticians are interested in all aspects of style, whatever their scope. Here, the question of what constitutes style addresses the assumption in earlier criticism that literary language was somehow set apart from the ‘everyday’ or elevated above the mundane uses of language in, say, shopping transactions or workplace documents.

Texts as discourse

In Chapter 2 we considered the origins of stylistics in Russian formalism, and the progress made in the analysis of literary texts in response to the developments of descriptive linguistics in the first half of the twentieth century. Many of the insights of the theory of foregrounding, and its various realisations in the analysis of form, are still relevant to stylistic analysis and have been refined and added to as linguistics has increasingly considered context and function as part of its scope. This chapter will introduce some of the main ways in which the consideration of function in language study has affected the way in which stylistics approaches the study of literary and other texts, and will begin by tracing the debates and controversies that accompanied some of these developments.

Stylistics has, on occasion, been the target of attacks from literary critics for what has been seen as an excessive concern with the linguistic form of (literary) texts at the expense of social, historical and other contextual factors that also play a role in a text's meaning. (Similarly, stylisticians have found themselves accused of failing to take adequate account of the important relationship between writer and reader which is mediated by the text. Recent advances in cognitive stylistics have addressed this criticism directly; see Chapters 5 and 6.) While no stylistician would accept that an analysis can incorporate too much linguistic detail, there is perhaps some truth to the point that stylistics has sometimes neglected contextual factors involved in meaning-making.