The scattering of electromagnetic waves by a perfectly conducting infinite cylinder

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.