Lyon, Keenan2014-08-112014-08-112014-08-112014http://hdl.handle.net/10012/8620This thesis is broken into two parts, both dealing with the role of two-dimensional graphene in electronic and optical applications. The first section develops a phenomenological relationship for the polarizability of the graphene sheet using a hybrid semi-classical and QFT-derived (Quantum Field Theory) model for different energy regimes. Fits are made and our results are compared to data from two distinct experimental setups. The effects of contamination and rippling of the sheet are considered. The second section shows a phenomenological model for the rough surfaces of graphene and its underlying substrate for a sheet grown on a conducting material. Three different perturbative mathematical models are then explored to justify the shift in the plasmon frequency and the energy loss dispersion due to roughness, using input from experimental roughness data. The models are compared and corrected to include physical effects like crumpling.engrapheneplasmonsplasmonicsroughnessspectroscopyMaster ThesisApplied Mathematics