2475905 - CHAPTER TWO PLANEWAVES 2.1MAXWELLSEQUATIONS theoreticalbasis.Inoptics, areavailable.Intheoldertheor


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CHAPTER TWO R.R.A.Syms and J.R.Cozens Optical Guided Waves and Devices 1 ELECTROMAGNETIC FIELDS AND PLANE WAVES 2.1  MAXWELL’S EQUATIONS The understanding of any field of physics or electrical engineering requires a suitable theoretical basis. In optics, we are fortunate that two highly developed and accurate theories are available. In the older theory  - often described as the 'classical theory' - the behaviour of light is described in terms of electromagnetic fields and waves. This is particularly appropriate for the analysis of passive devices, where the absorption and emission of radiation is unimportant, and consequently where the interaction of a wave with matter may represented in a somewhat phenomenological way. In the newer theory - the  quantum theory  - a different model is employed. Light is considered to be composed of photons, which are the elementary units or quanta of radiation. The interaction of light and matter is then understood in terms of exchanges of energy between photons and electrons. For example, the generation of a photon may be identified with the transition of a single electron between two energy levels. Quantum theory is therefore directly applicable to active optical devices. The development of this alternative model, and of its later incarnation, quantum electrodynamics, occupied the first half of the century, and involved many of the world's foremost physicists. Quantum theory may also describe situations that do not involve matter at all, but are still not accurately represented by classical theory. One example is provided by low light levels, where the photon flux may be extremely small and the arrival of radiation in discrete units is important. However, for a high enough photon flux, the two theories are equivalent. We shall encounter both of them in this book. Since our early discussions will centre on passive devices, we shall begin with a classical approach, turning only to the quantum theory at a much later stage (Chapter 11). In classical theory, the laws of electricity and magnetism are described by  Maxwell's equations . These represent the result of a synthesis of several existing theories and experimental observations by James Clerk Maxwell (1831-1879). In effect, Maxwell's equations are a set of relations linking the values of a number of quantities that describe electric and magnetic fields. These are the  electric flux density   D , the  magnetic flux density   B , the  electric field strength E , the  magnetic field strength   H , and the  current density J . All are vector quantities, and are functions not only of the three spatial coordinates x, y and z but also of time t.  Of these parameters, 
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