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.