Ghosh, Amartya2017-04-112017-04-112016-12https://hdl.handle.net/11299/185561University of Minnesota M.S. thesis. December 2016. Major: Electrical Engineering. Advisor: Anand Gopinath. 1 computer file (PDF); viii, 66 pages.An electromagnetic study of sub-wavelength structures made with graphene and gold is done with a concentration on the electro-magnetic coupling of these structures. The aim of the thesis is to analyze the reflection and transmission coefficients from the numerical simulations done with the help of COMSOL. Then homogenize these periodic array of structures for varying thicknesses so that it behaves as a continuous medium in the long wavelength limit. The next goal is to retrieve the effective electromagnetic parameters like the permittivity, permeability and refractive index from this homogenized structure. This will lead to tuning the electromagnetic properties according to the requirements-the property which is not available in naturally occurring materials, because the electrical or magnetic properties in naturally occurring materials are fixed. This new kind of material is defined as the metamaterial. The effective parameters of these materials are dependent on the properties of the basic materials with which the periodic array of structures are made - for example, it will be seen later how the effective properties is different when graphene is used instead of gold. The approach here is to use a normally incident wave on these periodic arrangement of graphene or gold structures and extract the scattering coefficients. Then invert these reflection and transmission data using basic Maxwell's equations to determine the refractive index and the impedance of the multilayered slab. From here the self consistent equations, the permittivity and permeability is determined. When the metamaterial is made with graphene it is found that the continuous slab behaves as an optical non magnetic material while with gold it behaves as a magnetic material. Some studies are also done on the dispersion of graphene nanoribbons and the electromagnetic modes associated with it.enBianisotropyGrapheneKubo ConductivityMagnetoelectric couplingMetamaterialsSplit ring resonatorThesis or Dissertation