Wave Scattering from Structures that Display Areas of Small Radii of Curvature in the Presence of an Extended Planar Surface

In many applications, it is necessary to simulate wave scattering from surfaces that have small radii of curvature relative to the incident wavelength. Surface features smaller than an electromagnetic wavelength are known to create diffracted fields over a wide range of scattering angles. In this thesis, the significance of such effects at low grazing angles with the presence of an extended planar surface is considered. The magnetic field integral equation (MFIE) describing the currents on such surfaces is used to solve for the bistatic scattered fields. The integral equations are discretized using the moment method and solved using the Method of Ordered Multiple Interactions (MOMI) iterative procedure. This thesis will concentrate on normal incidence and low grazing angle (LGA) incidence, specifically an incident angle of 80 degrees. The surface used in the analysis is a one-dimensional, perfectly-conducting wedge-on-a-plane with a varying radius of curvature at the wedge tip and Gaussian tails that smoothly extend the wedge to the plane surface. This surface displays continuous first and second derivatives over the entire surface. The radius of curvature at the wedge tip is varied between 0.0125 wavelengths and 8 wavelengths. The form of the bistatic scattered fields will be investigated for three different wedge height to wedge width geometries. The surface scattering mechanisms and their respective location and form in the scattered field will be discussed. The dependence of the scattered field pattern on the radius of curvature at the wedge tip and the beam width of the incident field will be considered. The difficulties associated with using a numerical technique on extended surfaces where a significant source of diffracted energy is present will also be examined. This includes the issue of sampling a surface that contains areas of small radii of curvature and the issue of surface truncation when significant currents due to tip diffraction are produced well outside the illuminated area. Both TE (VV) and TM (HH) polarization will be considered.

This thesis also analyzes the scattered fields for a perfect electric conducting (PEC) ridge and well in the presence of an extended planar surface for an incident angle of 70 degrees. The dual-surface magnetic field integral equation (DMFIE) formulation for a one-dimensional extended surface will be used to solve for the unknown currents on the surface of the scatterer. The DMFIE formulation leads to a second kind integral equation that can be solved via the MOMI series with the proper choice of the parameters appearing in the DMFIE formulation. The bistatic scattered fields for several ridge and well geometries are examined for both TE and TM polarization.