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The scattering of electromagnetic waves by a perfectly conducting infinite cylinder
Author(s) -
Colton David,
Monk Peter
Publication year - 1990
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670120605
Subject(s) - cylinder , scattering , perpendicular , mathematics , plane wave , plane (geometry) , electromagnetic radiation , near and far field , physics , field (mathematics) , geometry , mathematical analysis , inverse scattering problem , magnetic field , optics , quantum mechanics , pure mathematics
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.