Graphene plasmons in nanostructured environments

This thesis explores the combination of electromagnetism with electrons in graphene. Graphene is a one atom thick layer of carbon atoms which contains electrons that exhibit rather special properties in terms of their conduction abilities. The combination of electromagnetism with electrons gives rise to new solutions to the governing equations --- solutions with characteristics not quite like normal electromagnetic radiation and not quite like electrons. These solutions, which also exist in normal conductors, are hybrids between electromagnetism and matter, and are usually referred to as plasmons. This thesis is a theoretical study of plasmons in graphene. <br /><br />Graphene plasmons are investigated by calculating the conductivity of graphene, starting from a Hamiltonian describing the low-energy graphene electrons. The conductivity is calculated using linear response theory in terms of Green's functions. In order to probe graphene plasmons with electromagnetic radiation, we consider a subwavelength dielectric grating as a coupling structure. We develop the necessary theory to calculate electromagnetic scattering from the combined system of graphene and grating. The techniques considered are a scattering matrix method and a finite element method. Both are applied to compute the scattering coefficients, which contain information about the graphene plasmons and are also obtainable in experiments. We use these techniques to study various aspects of graphene plasmons, such as their nonlocal properties and the effects of impurities. In addition, we examine the response of graphene plasmons to changes in the surrounding environment and apply this for sensing purposes. Finally, we show that graphene plasmons can be controlled using a DC current in the graphene sample