| 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 FD(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 FN(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 {αn}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)FD(θ;αn) + μFN(θ;αn)}n = 1∞ to be complete in L2[ ? 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. |
