Electromagnetic Scattering by Metallic Structures with Edges Excited by Multiple Plane Waves

The electromagnetic scattering by complex structures is important in a variety of applications: cellular communications; propagation in indoor and outdoor environments; vehicular technology; microwave components and devices; antennas and arrays; radar signatures of ground vehicles, ships, aircraft, missiles and satellites; detection of buried objects; security screening; implanted health-care devices. The scattering behavior of these structures can be studied by analytical, numerical and experimental methods. Among the analytical methods, many results have been obtained via exact solutions or approximate techniques such as low frequency and high-frequency methods. Exact solutions, also called canonical solutions, are available only for relatively simple geometries, materials, and primary sources; however, they are very important because they provide information on the behavior of more complicated structures and because they constitute valuable tools for the validation of computer solvers. Many structures of interest contain sharp metallic edges, which constitute an important source of scattered fields that are often unwanted but difficult to blunt for many reasons such as the shape of the metallic structure, the nature of the incident wave, …etc. This dissertation presents geometrical optics solutions that are exact solutions for the considered boundary value problems. This goal is achieved by selecting the number, polarization, amplitude, phase and direction of incidence of the primary plane waves in such a way that the edges of the metallic structures do not scatter, that the boundary conditions on the surfaces of these structures are satisfied, and that there are no field discontinuities across optical boundaries. Additionally, certain relations among the angle of incidence, wavelength, dimensions of the metallic structure and spacing between the structures (if more than one structure exist) must be satisfied. The resulting exact total field is the sum of the incident fields and sometimes it generates mode(s) propagates in certain directions and/or it consists of standing waves in the space surrounding the structures. It is proven in this work that for the metal structures with strips and right-angle wedges the exact geometrical optics solutions are possible under incidence by multiple plane waves, if certain important conditions are satisfied. This dissertation proposes a method, we call it "Grid Method", which can be introduced as a general procedure developed for obtaining exact geometrical optics (GO) scattering solutions under incidence by multiple primary or imaged plane waves impinging upon a two-dimensional structure consisting of simply or multiply connected perfect electric conductor (PEC) strips either parallel or perpendicular to one another. The grid method provides all the conditions that must be satisfied to assure the existence of the GO solution to the boundary-value problem. The key feature behind applying the grid method is that the edges of the metallic structure will not scatter, which means that the GO solution represents the exact solution to the boundary-value problem. For some structures, we consider the case of a single incident plane wave and nd the solution to scattering by this wave using the Wiener-Hopf theoretic method. Then, the obtained solutions by considering each single incident wave individually, are added to get the total solution to the boundary-value problem, which is the same as the GO solution developed by using the grid method. Next, the two-dimensional problems of scattering by several metallic structures with strips and right angle wedges such as metallic grating, prism, rectangular cylinders … etc are developed based on the proposed grid method. All the required conditions to guarantee the existence of the GO solution are stated and applied. The two-dimensional results obtained by applying the grid method are generalized to the three-dimensional solutions by considering the oblique incidence of the primary waves with respect to the z-axis, when the metallic structures are perpendicularly truncated by a ground metal plate. Numerical results for the surface current densities on the surface of the metallic structures and the truncating plane are shown and discussed. The analysis is carried out in the phasor domain with a time-dependence factor exp(+jwt) omitted throughout. The importance of the proposed grid method is twofold: it provides novel canonical solutions to scattering problems, and it may be a helpful tool in validating both complicated analytical solutions and numerical solutions obtained via commercially available computer solvers.