Abstract
In the previous chapter, we have introduced Maxwell’s equations and studied the behavior of electromagnetic waves in free space and dielectrics. We have also introduced the concept of permittivity and permeability. In this chapter, we will take this further and primarily study two concepts: origin of permittivity and electromagnetic waves in conductors (metals). By origin of permittivity, we mean the dependence of permittivity on the fundamental parameters of the material (dielectric or conductor). We will derive the expression for permittivity starting from Newton’s force equation and try to understand its behavior in various frequency ranges. The nature of electromagnetic waves in metals is very different from that in dielectrics due to the presence of free electrons. These free electrons lead to a non-zero conductivity which manifests as the imaginary part of the effective permittivity which is now complex (unlike the dielectric case where it is real for most frequencies). Due to this, the electromagnetic waves in conductors are spatially damped and lead to loss of electromagnetic energy. As we will see, there is also a frequency range in which the permittivity of conductors becomes approximately real and negative. It is this frequency range (usually around the optical or ultraviolet region) that is of primary interest in the context of plasmonics.