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Most solutions for electromagnetic wave diffraction by obstacles and apertures assume plane wave incidence or omnidirectional local sources. Solutions to diffraction problems for local directive sources are needed. The complex source point representation of directive beams together with uniform solutions to high frequency diffraction problems is a powerful combination for this. Here the method is applied to beam diffraction by planar structures with edges, such as the half-plane, slit, strip, wedge and circular aperture. Previously used restrictions to very narrow beams and paraxial regions, are removed here and the range of validity increased. Also it is shown that the complex source point method can give a better approximation to broad antenna beams than the Gaussian function. The solution derived for the half-plane problem is uniform, accurate and valid for all beam orientations. This solution can be used as a reference solution for other uniform or asymptotic solutions and is used to solve for the wide slit and complementary strip problems. Uniform solutions for omidirectional sources are developed and extended analytically to become solutions for directive beams. The uniform theory of diffraction is used to obtain uniform solutions where there are no simple exact solutions, such as for the wedge and circular aperture. Otherwise rigorously correct solutions at high frequencies for singly diffracted far fields are used, such as for the half-plane, slit and strip. The geometrical theory of diffraction and equivalent line currents are used to include interaction between edges. Extensive numerical results including the limiting cases; e.g. plane wave incidence, line and point sources are given. These solutions are compared with previous solutions, wherever possible and good agreement is evident Beam diffraction by a wedge with its edge on the beam axis is analysed. This solution completes a previous asymptotic solution which is infinite on the shadow boundaries and inaccurate in the transition regions. Finally, the diffraction by a circular aperture illuminated by normally incident acoustic beam, is derived and the singularity along the axial caustic is removed using Bessel functions and a closed form expression for multiple diffraction is derived. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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This thesis deals with the theoretical analysis of the effect of the water droplets in the atmosphere on the propagation of a linearly polarized plane wave. These effects are (1) scattering - it is found that the scattered power is proportional to the sixth power of the radius of the droplet, also the scattered power varies as the fourth power of the frequency. (2) Absorption - it is found that the dielectric loss is much greater than the conductivity loss in the frequency range 10 M Hz. to 300 M Hz. The absorbed power is found to be much greater than the scattered power in the frequency range 10 M Hz. to 300 M Hz. Multiple scattering is neglected because scattered power is very small compared with the power absorbed. At the end of the thesis an expression for the attenuation constant is derived for homogeneous distribution of rain-drops of particular size falling at a particular rainfall rate. / M.S.

The electromagnetic diffraction problem is formulated in terms of either the electric or magnetic Hertz potential. This approach is equivalent to traditional methods based on the vector form of Green's theorem, but it is less widely known. The components of the Hertz potentials are independent, and each satisfies a scalar wave equation. The formal solutions for these components are therefore given by two equations referred to as the Rayleigh formulas, which are familiar from scalar diffraction theory. A physical interpretation of the Rayleigh solution shows that the diffracted wave may be thought of as a superposition of elementary, electromagnetic Huygens wavelets. Depending on the type of Green's function that is chosen, these wavelets have the same form as fields radiated by dipoles of different orientations (D-theory) or by special types of quadrupoles (Q-theory). Using techniques which are well known from scalar theory, it is shown that the diffracted wave can be represented as an angular spectrum of electromagnetic plane waves, and that this description is equivalent to the Q-theory approach. The use of approximate, Kirchhoff-type boundary conditions in the Hertz potential formalism is investigated. When these boundary conditions are used in the D-theory, the diffracted wave is found to be identical with the results of more traditional theories that apply the boundary conditions directly to the fields in the aperture. Using these boundary conditions in the Q-theory yields different results, because they are applied to the Hertz potentials rather than to the fields themselves. The differences between the two approaches are most apparent when the aperture is small in comparison with the wavelength. To determine which theory is more appropriate for Kirchhoff-type boundary conditions, an experiment to measure the diffraction from subwavelength-diameter pinholes is performed. The Q-theory shows better agreement with the results. It is also determined that the best agreement is obtained when the magnetic rather than electric Hertz potential is used.

In this dissertation, a novel approach to modeling the scattered field of a periodic corrugated cylinder, from an oblique incident planewave, is presented. The approach utilizes radial waveguide approximations for fields within the corrugations, which are point matched to approximated scattered fields outside of the corrugation to solve for the expansion coefficients. The point matching is done with TMz and TEz modes simultaneously, allowing for hybrid modes to exist. The derivation of the fields and boundary conditions used are discussed in detail. Axial and radial propagating modes for the scattered fields are derived and discussed. Close treatment is given to field equations summation truncation and conversion to matrix form, for numerical computing. A detailed account of the modeling approach using Mathematica® and NCAlgebra for the noncommutative algebra, involved in solving for the expansion coefficients, are also given. The modeling techniques offered provide a full description and prediction of the scattered field of a periodic corrugated cylinder. The model is configured to approximate a smooth cylinder, which is then compared against that of a textbook standard smooth cylinder. The methodology and analysis applied in this research provide a solution for computational electromagnetics, RF communications, Radar systems and the like, for the design, development, and analysis of such systems. Through the rapid modeling techniques developed in this research, early knowledge discovery can be made allowing for better more effective decision making to be made early in the design and investigation process of an RF project. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection