Theoretical Methods to Control Reflection Using Graded-Index Structures

Manipulating the scattering of electromagnetic radiation is the cornerstone of many modern technologies; from radar and communications to energy har- vesting. Of particular interest is the control over the reflection properties of materials. With a proposed desired effect, we can analytically determine what material parameters would be required to obtain said effect - for example how a structure reflects incident waves at given angles. In this thesis, we explore the scattering properties of materials through their permittivity and permeability. The structures considered will either be stratified media: alternating layers of homogeneous dielectric layers, or media whose properties vary in space: graded-index media. We propose solutions to three distinct problems. Firstly, we design materials that do not reflect electromagnetic waves at grazing incidence. By designing structures whose index varies in a single di- mension, we ensure that a so-called half-bound state is supported in this limit. These states are akin to waveguide modes with infinite decay length. Such modes allow for a ‘transmission’ resonance, leading to zero reflection. Secondly, we calculate the thermal emission from heated multi-layer struc- tures. Using two approaches: the fluctuation-dissipation theorem and Kir- choff’s law of thermal radiation, we derive expressions for the power flow of heated multi-layer structures, and verify that the two approaches are equivalent in the limit that the structure is at a single temperature. We fit both models to experimental data of the thermal emission of graphene-based mid-infrared emitters. We then use the models to explore how to change the properties of the devices to control e.g. the peak emission frequency and/or total emission using only numerical simulations. Finally, we extend our analysis to the complex frequency plane. Poles in reflection in the lower complex frequency plane support quasi–normal modes. These modes are directly related to the spectral response of a structure. Us- ing inverse-design methods, we formulate an eigen-permittivity procedure to control the complex frequency of a single quasi-normal mode, by finding a ho- mogeneous background permittivity shift, which when superimposed onto the original structure, will support a quasi-normal mode at the desired frequency, and thus controlling the frequency and linewidth of an isolated resonance.