Electromagnetic Waves

Abstract

The topic of electromagnetism is extensive and deep. Nevertheless, we have endeavoured to restrict coverage of it to this chapter, largely by focusing only on those aspects which are needed to illuminate later chapters in this text. For example, the Maxwell equations, which are presented in their classical flux and circulation formats in Eqs. (2.1)–(2.4), are expanded into their integral forms in Sect. 2.2.1 and differential forms in Sect. 2.3. It is these differential forms, as we shall see, that are most relevant to the radiation problems encountered repeatedly in ensuing chapters. The process of gathering light from the sun to generate ‘green’ power generally involves collection structures (see Chap. 8) which exhibit smooth surfaces that are large in wavelength terms. The term ‘smooth’ is used to define a surface where any imperfections are dimensionally small relative to the wavelength of the incident electromagnetic waves, while ‘large’ implies a macroscopic dimension which is many hundreds of wavelengths in extent. Under these circumstances, electromagnetic wave scattering reduces to Snell’s laws. In this chapter, the laws are developed fully from the Maxwell equations for a ‘smooth’ interface between two arbitrary non-conducting media. The transverse electromagnetic (TEM) wave equations, which represent interfering waves at such a boundary, are first formulated, and subsequently, the electromagnetic boundary conditions arising from the Maxwell equations are rigorously applied. Complete mathematical representations of the Snell’s laws are the result. These are used to investigate surface polarisation effects and the Brewster angle. In the final section, the Snell’s laws are employed to examine plane wave reflection at perfectly conducting boundaries. This leads to a set of powerful yet ‘simple’ equations defining the wave guiding of electromagnetic waves in closed structures.

The mind of man has perplexed itself with many hard questions. Is space infinite, and in what sense? Is the material world infinite in extent, and are all places within that extent equally full of matter? Do atoms exist or is matter infinitely divisible?

James Clerk Maxwell