(A) Theoretical Study of Optical Constants of Two Dimensional Carbon Based Materials

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The electromagnetic response of two dimensional carbon based systems is studied using basic classical tools. The most interesting and important carbon based system known till today is the by now well-known two-dimensional material DGrapheneD. This material is special in several ways, indeed, its very existence is an enigma. Graphene and a few of graphene based systems are studied using theoretical techniques. The key point of this work is the theoretical formulation of monolayer free-standing graphene. This formulation acts as the reference for the subsequent studies done in various graphene based systems. In this formulation monolayer free standing graphene is modelled as a conducting medium of one atom thickness such that the media is non-refracting. The emergent electric field of the system has been calculated by solving the fundamental equations of electromagnetism, DMaxwellDs EquationsD which consists of reflected and transmitted fields. Three physically important and experimentally measurable quantities are derived analytically, viz. coefficient of reflection, coefficient of transmission and polarization of reflection. The energy conservation theorem has been derived for the system using which the loss also has been calculated to make sure of the correctness of the formalism. The results obtained for some of these quantities with fixed values of various parameters show an excellent agreement with the experimental observations available in this field. For most of the device and technological applications, graphene has to be deposited on a substrate. For this reason, we next study a related system - substrate graphene. Theoretical modelling of this system has been done by regarding graphene as a conducting medium deposited on top of a purely dielectric material characterized by a dielectric constant. MaxwellDs equations for this combined system has been solved using the boundary conditions and derived equations for the two parts of emergent field, reflection and transmission which has been made use to study the optical properties of this system. The linearly polarized limit of incident light in this system is important because of a well-known phenomenon in optics, DBrewsterDs phenomenonD. The most interesting feature of BrewsterDs phenomenon related to substrate graphene is the azimuthal angle dependence of the Brewsters minimum. The next immediate system related to graphene is the combination of two single graphene sheets separated by a distance of a few Angstroms. With the monolayer results as reference, the optical constants of the bilayer system has been solved using series summation methods used in many fundamental optics books (such as [142]). Presence of an extra layer leads to multiple reflection phenomena....
Supervisor: G. S. Satlur