Generalized sheet transition conditions for metafilm and its applications.

摘要

In this thesis generalized sheet transition conditions (GSTCs) for the average electromagnetic fields across a surface distribution of electrically small scatterers characterized by electric and magnetic polarization densities are derived. We call such an arrangement of scatterers a metafilm ---the two-dimensional equivalent of a metamaterial. The derivation is based on a replacement of the discrete distribution of scatterers by a continuous one, resulting in a continuous distribution of electric and magnetic polarization densities in the surface. This is done in a manner analogous to the Clausius-Mossotti-Lorenz-Lorentz procedure for determining the dielectric constant of a volume distribution of small scatterers. The study was done for a metafilm immersed in one medium of magnetodielectric material and for a metafilm at the interface between two different media. These two media are characterized by different electric permittivities and magnetic permeabilities. First we find the GSTCs for a metafilm in one medium. The result contains as special cases many particular ones found throughout the literature. The GSTCs are expected to have wide applications to the design and analysis of antennas, reflectors and other devices where controllable scatterers are used to form a "smart" surface.; Using the generalized sheet transition conditions (GSTCs) for the average electromagnetic fields across a metafilm, it is expected that a certain level of reflection and transmission is achieved once this metafilm is designed in a specific way. The reflection and transmission coefficients of the metafilm are calculated through the use of the GSTC. The coefficients for both the TM and TE polarized plane waves are obtained with arbitrary incidence angles. The work presented here is of the reflection and transmission properties of the metafilm, which are based on the electric and magnetic polarizabilities of the scatterers themselves. The conditions necessary for the transmission and/or total reflection are derived which leads to finding the polarizabilities of the scatterers. The applicability of the GSTC for the analysis of a metafilm is demonstrated through various illustrations. The work presented also proposes a "smart" and/or "controllable" surface through controlling densities of polarization of the scatterers in the metafilm, so the analytic solution for a controllable metafilm designed from resonant, magnetodielectric particles is presented.; In order to have more controllable characteristics, the case in where the metafilm is placed in between two different materials is studied. However, the Idemen jump conditions for this case need to be understood. A corrected version of Idemen's condition was obtained. Due to the discontinuity of the medium, the Whittaker potential is more suitable to solve the problem of the metafilm at the interface of the two media. Thus, the BC for the Whittaker potentials is obtained. On the other hand, due to the discontinuity of the medium, the normal electric field is discontinuous. To understand how the dipole moment is to be defined, the dipole moment for a static dipole; placed normally in the interface is studied. It is found that the electric field flux is more suitable than the intensity to define the dipole moment. As a matter of duality the magnetic flux density is used to define the magnetic dipole moment. Finally the GSTCs are to be obtained.