Abstract

This paper presents a theoretical and numerical investigation of the spatially averaged electric field in the beam of a circular aperture. The investigation leads to closed-form analytical expressions, based on scalar diffraction theory, which describe the spatially averaged electric field in the Fresnel region of a circular aperture excited by a spatially uniform, harmonic plane wave. The expressions ultimately permit rapid, practical, and efficient prediction of certain routine electromagnetic measurements. Because the expressions are valid in the Fresnel region, they are also valid in the near field, the far field, and the Fraunhofer region of a circular aperture. In fact, it is shown that the closed-form expressions contain, as special cases, classic on-axis and far-field results associated with a circular aperture. The analytical expressions are based on a generalization of Fresnel diffraction originally developed by Lommel in the late 1800s. Hence, a thorough review of the literature on the Lommel diffraction formulation is presented. Finally, it is shown that results obtained from the closed-form expressions compare quite favorably to results obtained from the exact solution computed via the dyadic Green's function approach.

Publication Date

2003

Comments

©2003 Institute of Electrical and Electronics Engineers (IEEE). Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. The authors express their deep appreciation to the anonymous referees. Their thorough review contained insightful comments, helpful suggestions, and numerous references, all of which improved our submission significantly.ISSN:0018-926X Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Article

Department, Program, or Center

Chester F. Carlson Center for Imaging Science (COS)

Campus

RIT – Main Campus

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