Complex electromagnetic responses from simple geometries

The electromagnetic properties of a material arise from its intrinsic microstructure, which may often be very complex. However, materials are usually characterized more simply using macroscopic material parameters, electric permittivity and magnetic permeability. This thesis considers the principles of material modeling from the electromagnetics point of view. The analysis is mostly based on electrostatics. The aim of the thesis is to enhance the understanding of the interaction between matter and the electromagnetic fields, and further, the relation between matter and geometry. The contents of the thesis can be divided into three parts. The first part discusses the concepts of polarization and polarizability and considers the electric reponses of particles with different geometries. Polarizabilities of a three-dimensional hemisphere and a two-dimensional half-disk are solved. The second part studies negative material parameters. The emphasis lies on negative permittivity. Interfaces between permittivities of opposite signs are found supporting surface plasmons, or electrostatic resonances. The occurrence of these resonances is especially studied for a hemisphere and a half-disk. Moreover, it is showed that sharp edges with negative permittivity may support unphysically singular field modes, which in numerical simulations can result in non-convergent solutions. The most efficient way to overcome this problem in computational modeling is to slightly round all sharp corners. The third part focuses on homogenization of composite media. Effective material parameters modeling the response of a thin dielectric composite slab are retrieved. Computational homogenization techniques and their limitations are studied. The results indicate that for a successful homogenization, the unit cells of the slab must remain very small compared with the wavelength. Also, the boundary layers of the slab show higher effective permittivity than the corresponding bulk medium.