ABSTRACT
In the previous chapter, we discussed various aspects of scalar wave propagation, including numerical techniques to model scalar wave propagation. Most importantly, we discussed the unidirectional and bidirectional beam propagation method and applied it to various cases of determining beam propagation in homogeneous and inhomogeneous media, including media where the induced refractive index is a function of the intensity of the beam. In this chapter, we start from Maxwell’s equations and analyze plane wave solutions of electromagnetic (EM) waves in various media. We show that the constitutive relations that relate the EM želd variables in the frequency domain play an important part in the behavior of EM waves. Particularly, we bring out the distinction between phase, energy, and group velocities, and show the characteristics of wave propagation in negative index media, i.e., media where the phase and group velocities may be counterdirected due to possible negative values of the permittivity and permeability over a certain frequency range. We also discuss wave propagation through chiral media, where the constitutive relations allow for coupling between the electric and magnetic želds. Finally, we also derive the transfer matrix approach to EM propagation through a layer of a material, which can be described by arbitrary dispersive permittivity and permeability, and show how this technique can be effectively used to model EM plane wave propagation through inhomogeneous materials.
