Abstract: This dissertation deals with periodic structures that are used as free-space electromagnetic filters. Two types of periodic structures are treated, namely the so called frequency selective surface (FSS) and the artificial puck plate (APP) structure. The FSS structure consists of one or several periodic arrays of identical elements embedded in an arbitrary number of dielectric layers. The APP structure, on the other hand, consists of a thick conducting structure which is perforated with apertures. So called pucks are located in these apertures and an arbitrary number of dielectric layers are attached on either side of the conducting structure. Free-space electromagnetic filters are used in stealth radome applications where the radome is designed to be transparent within the frequency range of the enclosed antenna, while it is reflective otherwise. By this technique, the radar cross section is reduced which provides the ability to see, but not to be seen. The filters are also used in dichroic reflector antenna applications, where a reflector is either reflective or transparent dependent of the frequency and/or polarisation of the incident field. This technique provides compact antennas with high performance. Furthermore, the filters are also used in the walls of office buildings to prevent the signals transmitted by wireless network devices to leak out of the office building, while the walls still are transparent for mobile phone signals. Specifically, this dissertation introduces methods for the electromagnetic analysis of the above mentioned filter structures. The method of moments, which is a well known and widely used method for electromagnetic analysis in general, is used to calculate the reflection and transmission properties of the structures, which are assumed to be plane and infinite in two dimensions. Basis functions are used to expand the surface current of the FSS (or the APP). A continuity condition for basis functions used in FSS calculations is derived in the dissertation. The dissertation also presents a new set of so called V-dipole basis functions which can be applied to fairly general FSS element geometries. Moreover, methods that admit complex media to be included in the analysis are presented. This is useful when it comes to glass fibre composites which is an example of a complex media with different properties in different spatial directions.
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