| The objective of this thesis is to analyze two aspects of a focused beam measurement system. Specifically, an estimate of the error caused by the plane-wave approximation when this system is used to measure the dielectric constant of a material is fast obtained. Second, the scattering associated with a sharp edge of a sample under investigation, e.g., scattering from a metal plate is analyzed. The setup of the focused beam system for the two types of measurements are slightly different. However, the common feature is that a combination of a horn antenna and a dielectric lens produces a beam that resembles a Gaussian beam. This beam is focused onto a plane that contains the specific sample under investigation. For the analysis in this thesis, it is assumed that the beam produced by the horn antenna and the lens is a Gaussian beam.; The scattering analysis from a sharp edge contains two distinct parts. First, the infitesimally thin perfectly conducting (PEC) half plane is analyzed. This is the canonical geometry for edge scattering, and rigorous formulas for the scattering of a three-dimensional electromagnetic Gaussian beam by the PEC half plane are derived. The beam can be incident from any direction, and the main component of the electric field can point in any direction on the plane of the beam waist. Second, the scattering of a Gaussian beam from an edge of a PEC plate is analyzed. Two commercial software packages are used to simulate the scattering of the beam by the plate. |
