Diffraction Theory for Polygonal Apertures
Abstract
We explain and describe diffraction from polygonal apertures over a wide range of sizes and observation distances. In the first case considered, a small square aperture (2a X 2a, ka << 1, where k = 2pi/lambda is the wavenumber) in a perfectly conducting plane screen of vanishing thickness diffracts a normally incident, linear polarized, monochromatic plane wave. Within the vector framework of Maxwell's equations, we hypothesize a solution for the dominant component of the electric field. Subsequently, by means of an integro- differential equation formulation of the diffraction problem applied to small apertures, we substantiate the solution. The solution represents the first three terms in a more general expansion for the aperture field. Physical intuition and the solutions for circular aperture field. Physical intuition and the solutions for circular apertures and slits motivate use to propose this expansion. Numerical calculations validate the solution over most of the aperture except in the close vicinity of the corners of the aperture. This limited expansion does not achieve an accurate description of the field near the corners. In the remainder of the investigation we treat diffraction within the realm of Fourier optics. We develop a Gaussian beam expansion and use it to describe diffraction from a plane-screen corner of arbitrary angle.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1988
- Accession Number
- ADA203778
Entities
People
- R. E. English Jr
Organizations
- University of Rochester