Electric-Magnetic Uniaxial Lossy Medium and its Applications to Boundary Conditions and Metamaterials

In this dissertation, properties of a general electric-magnetic uniaxial lossy medium and its applications to boundary conditions and metamaterials are investigated. In the first part of the dissertation, electromagnetic reflection from the interface of an electric-magnetic uniaxial lossy medium is studied. It is assumed that the uniaxial medium is characterized by complex permittivity and permeability tensors, and has an arbitrarily directed optic axis. The propagation of both homogeneous and inhomogeneous waves in the uniaxial lossy medium is discussed. Many metamaterials proposed in literature can be homogenized as electric-magnetic uniaxial media. We investigate their characteristics and try to understand their limitations due to presence of the material losses. The interface of the uniaxial medium with a simple isotropic medium is analyzed by applying the general soft-and-hard and DB boundary conditions. The reflection is investigated under different circumstances by considering various orientations of the plane of incidence with respect to the plane containing the optic axis of the medium. The results obtained in the lossy case are compared with those of lossless one, available in the literature. Subsequently, we present a reflection analysis of a plane wave striking on an interface of a novel uniaxial medium characterized by extreme constitutive parameters: very large transverse and very small longitudinal components of the diagonal permittivity and permeability tensors. The novelty of the medium is specified by enforcing particular conditions on the material properties. The reflection is studied by assuming that the optic axis of the uniaxial material is arbitrarily oriented. We discuss the effect of the direction of the optic axis on the reflection characteristics and emphasize on its importance for the realization of electromagnetic absorbers. The behavior of the medium is also examined by varying the direction of the plane of incidence with respect to the plane of the optic axis. It is observed that, in this case, there exists a Brewster-like angle where the interface activates zero reflection for the co-component of the incident field while total reflection for the cross-component. An analytical expression for this angle is also presented. From the numerical results it is noticed that the medium shows very interesting properties of behaving as a perfect reflector, a perfect transmitter and a polarization inverter depending upon the direction of the optic axis and the plane of incidence. The second part of the thesis focuses on a numerical analysis of the three-dimensional unit-cell structure proposed for practical realization of the metamaterial, satisfying the DB boundary conditions. The realization of the DB boundary conditions require cancellation of the normal components of electric flux density vector \textbf{D} and magnetic flux density vector \textbf{B} on the boundary surface. The cancellation of these components happens if the components of both permittivity and permeability orthogonal to the interface are zero. We present free-space computer simulation results for the unit-cell structure consisting of two circular split-ring resonators and a metallic wire immersed in an ordinary dielectric medium. Moreover, a new composite design based on rectangular split-ring resonators which can imitate the DB behavior is also presented. From numerically calculated reflection and transmission parameters all components of the effective permittivity and permeability tensors, characterizing the DB material, are retrieved both in the axial as well as in the orthogonal directions to the metamaterial boundary. Such effective constitutive parameters are extracted using the scattering parameters inversion technique for a plane wave obliquely incident on a metamaterial slab.