Polarizability analysis of canonical dielectric and bi-anisotropic scatterers

Solutions for simple, canonical problems are important in electromagnetics, because they can be often utilized in more complicated problems. This thesis consists of analyses of some basic canonical objects and fundamental principles of electromagnetic theory. One of the fundamental objects analyzed in this thesis is an ellipsoid, and especially a layered ellipsoid. Although it is a basic and classical object in electromagnetics, some new properties of the layered ellipsoid can still be found. Very important concept in static electromagnetics is polarizability, which simply is the connection between the incident field and the dipole moment that is induced in an object. The polarizability of a dielectric sphere and ellipsoid is well known and can be calculated with simple formulas, but for a more complicated object the evaluation of the polarizability requires more effort. This thesis presents an analysis of one particular class of objects, namely the Platonic polyhedra. The thesis also describes how inhomogeneous materials can be modelled with mixing formulas, in which the polarizability is a key parameter.