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On a Uniform Geometrical Theory of Diffraction based Complex Source Beam Diffraction by a Curved Wedge with Applications to Reflector Antenna Analysis
Kim, Youngchel

2009, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
A uniform geometrical theory of diffraction (UTD) solution is developed for describing the high frequency (HF) electromagnetic (EM) fields surrounding an arbitrarily curved, perfect electrically conducting (PEC) wedge, that is illuminated by a point source, in complex space, which generates a complex source beam (CSB). This solution is surprisingly found to be the same as the UTD solution obtained previously for PEC curved wedges illuminated by a real point source after it is analytically continued for dealing with CSB illumination; hence, it is defined here as the CSB-UTD for curved wedges. The solution for curved wedges is developed from canonical HF solutions for a straight wedge with planar faces. For a real point source, the canonical UTD solution is obtained via a simpler asymptotic HF based first order Pauli-Clemmow method (PCM) of steepest descent. However, a CSB field constitutes a complex wave, and the first order PCM is strictly not valid for solving the canonical wedge problem with CSB illumination. Hence, for complex waves, a different, less compact, first order asymptotic approximation, known as the Van der Waerden method (VWM) of steepest decent, needs to be employed. This first order VWM leads to a canonical wedge solution which may be viewed as an extended UTD (or EUTD) wedge solution for the CSB illumination, defined here as the CSB-EUTD solution, because it can be expressed as CSB-EUTD = CSB-UTD + C . However, C is found to be negligible for the wedge case; it is for this reason that a first order PCM based CSB-UTD remains accurate even though PCM is not strictly valid for this case. After having established the fact that the CSB-UTD solution for the canonical wedge is the same as if the canonical UTD wedge solution for a real source excitation is simply and directly analytically continued to deal with a complex source location (or a CSB), the CSB-UTD for the arbitrarily curved wedge can thus also be similarly developed by analytically continuing the corresponding UTD solution for the same curved wedge excited by a real point source, to now deal with the excitation by a point source in complex space (or CSB). The curved wedge CSB-UTD solution is employed to analyze the radiation from an offset parabolic reflector illuminated by a CSB. The CSB-UTD results for this reflector are compared with a numerical physical optics (PO) approach to illustrate the accuracy of the CSB-UTD. The CSB-UTD is extremely fast compared to the numerical PO method; also, the latter becomes increasingly time consuming with increase in frequency, whereas the CSB-UTD remains essentially independent of frequency. The complex points of surface reflection and edge diffraction on the complex extension of the reflector are computed here using a relatively fast and efficient procedure, thus making it very practical to trace complex rays with almost the same speed and efficiency as tracing real rays.
Prabhakar Pathak, Ph.D (Advisor)
Roberto Rojas-Teran, Ph.D (Committee Member)
Robert Burkholder, Ph.D (Committee Member)
230 p.

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Kim, Y. (2009). On a Uniform Geometrical Theory of Diffraction based Complex Source Beam Diffraction by a Curved Wedge with Applications to Reflector Antenna Analysis. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Kim, Youngchel. "On a Uniform Geometrical Theory of Diffraction based Complex Source Beam Diffraction by a Curved Wedge with Applications to Reflector Antenna Analysis." Electronic Thesis or Dissertation. Ohio State University, 2009. OhioLINK Electronic Theses and Dissertations Center. 25 Nov 2017.

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Kim, Youngchel "On a Uniform Geometrical Theory of Diffraction based Complex Source Beam Diffraction by a Curved Wedge with Applications to Reflector Antenna Analysis." Electronic Thesis or Dissertation. Ohio State University, 2009. https://etd.ohiolink.edu/

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