Electromagnetic waves in material media

Abstract In Chapter 9 we studied electromagnetic waves propagating in vacuum. In this chapter we study how electromagnetic waves are affected by the properties of the medium in which the propagate, described by frequency-dependent constitutive relations such as those studied in the previous chapter, or by non-trivial boundary conditions, as in the case of electromagnetic waves propagating in waveguides. We introduce the refraction index, the dispersion relations of electromagnetic waves in materials, phase and group velocity. We study the propagation of em waves in metals; we find transverse electromagnetic waves, which penetrates a metal up to a distance caracterized by the skin depth, as well as longitudinal waves at the plasma frequency, and we study the corresponding plasma oscillations. We then discuss the propagation of electromagnetic waves in waveguide and the corresponding TE, TM and TEM modes.