The scattering of electromagnetic waves by a perfectly conducting infinite cylinder

✍ Scribed by David Colton; Peter Monk

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 602 KB
• Volume: 12
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670120605

✦ Synopsis

Abstract

We consider the scattering of a plane time‐harmonic electromagnetic wave by a perfectly conducting infinite cylinder with axis in the direction k, where k is the unit vector along the z axis. Suppose the incident wave propagates in a direction perpendicular to the cylinder. For a given observation angle θ, let F~D~(θ, α)k be the far‐field pattern of the electric field corresponding to an incident wave with direction angle α polarized perpendicular to the axis and let F~N~(θ; α)k be the far‐field pattern of the magnetic field corresponding to an incident wave with direction angle α polarized parallel to the z axis. Let {α~n~}~n=1~^∞^ be a distinct set of angles in [ − π, π] and μ a complex number. Then, necessary and sufficient conditions are given for the set {(1 − μ)F~D~(θ;α~n~) + μ__F__~N~(θ;α~n~)}~n = 1~^∞^ to be complete in L^2^[ − π, π]. Applications, together with numerical examples, are given to the inverse scattering problem of determining the shape of the cylinder from a knowledge of the far‐field data.