Mathematical modeling of metamaterials

Metamaterials are artificially structured nano materials with negative refraction index. The successful construction of such metamaterials in 2000 triggered a great interest in study of metamaterials by researchers from different areas. The discovery of metamaterials opened a wide potential for applications in diverse areas such as cloaking, sub-wavelength imaging, solar cell design and antennas. In this thesis, we investigate the most popular Drude metamaterial model. More specifically, we first present a brief overview of metamaterials and their potential applications, then we discuss the well-posedness of this model, and develop several numerical schemes to solve it. We implement our schemes using MATLAB, and demonstrate their effectiveness through numerical simulations of the negative refraction and cloaking phenomena