Analytical Techniques Used to Calculate the Fields due to Refraction and Diffraction of Electromagnetic Waves.

This thesis provides a compendium of analytical techniques which can be used to calculate the fields that are created when an electromagnetic wave is incident upon a physical object. Quasi-optical techniques (Geometrical Theory of Diffraction and Uniform Theory of Diffraction) are analyzed along with the more classical physical and geometrical optics techniques (Kirchoff Diffraction Theorem, Sommerfeld Diffraction Theorem, Fourier optics, and geometrical optics). The approximations that are used in each technique along with the regions of the electromagnetic spectrum where each technique can be applied are emphasized. Each technique is derived and all are shown to be ultimately dependent upon the validity of Maxwell's equations. The Fourier optics and Geometric Theory of Diffraction techniques are shown to be direct mathematical extensions of the Sommerfeld Diffraction Theorem. Each technique is then applied to a simple example problem. The technique of Fourier optics is shown to be very powerful while remaining mathematically simple. The Fresnel and Fraunhoffer approximations are most readily understood when this technique is used. It is also shown that the Geometric Theory of Diffraction and Uniform Theory of Diffraction are capable of giving accurate results when the physical object has a complex geometry. Keywords include: Diffraction; Millimeter waves; and Microwave optics.