Propagation of electromagnetic radiation in some linear and nonlinear dielectric stacks

In this dissertation, we study the propagation of electromagnetic radiation in dielectric stacks, a class of structures made up of layers of dielectric which we assume to be lossless and nondispersive. We consider stacks composed of linear dielectrics with and without a nonlinearity. For computational simplicity, we often consider two specific types of dielectric stacks which we refer to as alternating and impurity stacks. Successive layers in an alternating stack alternate between two different types of dielectrics. The impurity stack is defined to be an alternating stack with one layer modified to create an impurity layer;We first study the propagation of steady-state radiation in linear alternating and impurity stacks. Exact solutions for the electric field in alternating and impurity stacks with an infinite number of layers are obtained. There are ranges of frequencies and angles of incidence for which both stacks have physically allowed and forbidden solutions. The infinite impurity stack also has a localized solution which is exponentially localized about the impurity layer. Expressions for the transmissivity of alternating and impurity stacks with a finite number of layers are derived. There are ranges of frequencies and angels of incidence for which both types of stacks have high and low transmissivity. There is also an isolated transmission peak for impurity stacks due to the localized solution. We also discuss an experiment which verifies the existence of localized solutions;We next study pulses of radiation in arbitrary linear stacks. We derive a general solution for the radiation transmitted through a class of stacks. If incident radiation is of finite duration, transmitted radiation will decay exponentially with a decay time characteristic of the given stack. We find that the decay times of impurity stacks are anomalously longer than those of alternating stacks. This is due to the occurrence of localized solutions in impurity stacks;We next include a single delta function Kerr nonlinearity in the center of alternating and impurity stacks. For incident steady-state radiation, these systems can exhibit bistability. We find that the localized solution in the impurity stack enhances bistability. Necessary conditions for the occurrence of bistability in a single dielectric layer with a single nonlinearity are derived;Finally, we study pulses of radiation incident on a single delta function Kerr nonlinearity in vacuum. We obtain approximate analytic solutions as well as the complete numerical solution. We also briefly discuss the serious obstacles involved with studying arbitrary stacks with a delta function nonlinearity