A full wave finite-difference time-domain method (FDTD) combined with thin-wire and thin-slot algorithms to analyze a metamaterial fabricated with periodic mushroom structures, is proposed in this dissertation. This proposed method is suitable for analyzing problems involving large structures with fine structural details. A periodic analysis for mushroom structures is presented. Only a single unit mushroom cell is required to present the phenomena of infinite periodicity with the help of periodic boundary conditions (PBCs). The composite right-/left-handed (CRLH) transmission line (TL) approach is introduced and used to approximate CRLH metamaterial through lumped L and C. Finally, several CRLH metamaterial mushroom-based structures are investigated. A 19 by 8 flat microwave lens and a parabolic microwave lens structure composed of 410 unit mushroom cells are investigated. These structures demonstrate negative refractive index (NRI) characteristics while operate in the left-hand (LH) region. The simulation and measurement results of one- and two-dimensional CRLH mushroom-based structures are compared.

The conventional mushroom-like Sievenpiper structure is re-visited in this thesis and a relationship is established between the dispersion and reflection phase characteristics of the structure. It is shown that the reflection phase frequency at which the structure behaves as a Perfect Magnetic Conductor (PMC) can be predicted for varying angles of incidence from the modal distribution in the dispersion diagrams and corresponds to the supported leaky modes within the light cone. A methodology to independently tune the location of the PMC frequency point with respect to the surface wave band-gap location is then presented. The influence of having said PMC frequency point located inside or outside the surface wave band-gap on a dipole radiation pattern is then studied numerically. It is demonstrated that the antenna exhibits a higher gain when the PMC frequency and band-gap coincide versus when they are separated. Two design cases are then presented for when the aforementioned properties coincide and are separated and a gain improvement of 1.2 dB is measured for the former case.

The conventional mushroom-like Sievenpiper structure is re-visited in this thesis and a relationship is established between the dispersion and reflection phase characteristics of the structure. It is shown that the reflection phase frequency at which the structure behaves as a Perfect Magnetic Conductor (PMC) can be predicted for varying angles of incidence from the modal distribution in the dispersion diagrams and corresponds to the supported leaky modes within the light cone. A methodology to independently tune the location of the PMC frequency point with respect to the surface wave band-gap location is then presented. The influence of having said PMC frequency point located inside or outside the surface wave band-gap on a dipole radiation pattern is then studied numerically. It is demonstrated that the antenna exhibits a higher gain when the PMC frequency and band-gap coincide versus when they are separated. Two design cases are then presented for when the aforementioned properties coincide and are separated and a gain improvement of 1.2 dB is measured for the former case.

The thesis deals with basic principles of metamaterials, which exhibit unusual properties in microwave applications (e.g., negative permittivity and permeability). Different type of metamaterial antennas and parameters of such antennas are described in the thesis.