Uniform asymptotic solution for electromagnetic reflection and diffraction of an arbitrary Gaussian beam by a smooth surface with an edge

Abstract

Abstract. A closed form solution is obtained to describe, in a physically appealing manner, the reflection and diffraction of a general astigmatic Gaussian beam which is incident on an arbitrary smooth, electricaJly large, slowly varying curved, perfectly conducting screen (or reflector). This dosed form solution is obtained via an asymptotic evaluation of the radiation integral for the fields scattered from the reflector, to within the physical optics approximation that remains valid for the present situation. The analysis developed here is particularly well suited for the fast analysis of electrically large reflector antennas by representing the feed illumination by a relatively small set of Gaussian beams launched from the feed plane. Each of these Gaussian beams after being launched undergoes reflection and diffraction at the reflector; the expressions for the reflected and diffracted fields are developed in this paper and utilized by Chou [1996] to compute the radiation pattern of large reflector antennas in a matter of a few seconds as compared to the conventional numerical physical optics integral method which takes hours on the same computer.

Electromagnetic Scattering of a Field Known on a Curved Interface Using Conformal Gaussian Beams

“…The radius of curvature of the quadric are that of the original surface at O. Therefore, z can approximated by [5]:…”

“…where k is the wave number and Q f the complex curvature matrix of the elementary currents, analogue to that of conventional elliptical Gaussian Beam field formulation [5].…”

“…Some approaches may use different basis functions involving Gaussian Beams (GBs) for tracking fields in complex environments [4][5][6][7][8][9]. Various formulations based on Gaussian Beams are reviewed in [10].…”

Deastigmatism and Circularization of an Elliptical Gaussian Beam by Off-Axis Ellipsoid Reflector Based Off-Focus Configuration

“…F 1 and F 2 are the actual intersections of the incident and reflected directions with the x axis, respectively. [ [6][7][8][9][10][11][12][13][14] algorithm based on the configurations described above, including off-axis reflector based conventional configuration, astigmatic off-axis reflector based configuration, and off-axis reflector based off-focus configuration. DGBA algorithm has nearly the same calculation efficiency with PO [6].…”

Fast SDM for Shaped Reflector Antenna Synthesis via Patch Decompositions in Po Integrals

“…These techniques are most widely employed in the reflector antenna analysis for practical applications. Either Fast Fourier Transform (FFT) or expansions over the integrands using properly selected bases, such as Gaussian beams (GB) [4,5,15], are performed with endurable sacrifice of accuracy. Previously, successfully employed synthesis techniques are referenced in [3,[8][9][10][11][12][16][17][18] including genetic algorithm (GA) [11], steepest decent method (SDM) [3,5,8,9], successive projection method (SPM) [10][11][12]17] and particle swarm optimization (PSO) [18].…”