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Abstract
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In this thesis, we investigated the utilization of different absorbing boundary conditions in the finite difference time domain method (FDTD) for stimulating various physical phenomena. We present relevant formulation in frequency and time domains to be used for code development. Different approaches such as perfect absorbing boundary conditions, periodic boundary conditions, and the perfectly matched layer (PML) are considered. It is shown that one could choose the proper boundary condition for different problems in Nano-Optics. To validate our approaches, we have considered regular problems in Optics for which analytical solutions are available. First of all, we examine the cases where no object is within the boundaries, so that one can employ perfect absorbing conditions. For instance, light interaction with one-dimensional multilayers can be modelled with this kind of boundary condition. Then we try dielectric materials inside boundaries and investigate the reflection from a thin layer deposited on a dielectric substrate. In this case a regular PML is used. Finally, we consider dispersive materials filling the boundaries. In this case, it is important to find suitable models for describing the optical properties of the dispersive material and implement it in the FDTD method. Then we need to extend our PML formulation to include these models. In this work, we have considered Gold, Silver and copper as dispersive materials within PML and investigated the plasmonic modes excited in these materials.
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