Electromagnetic Scattering by an Ellipsoid in the Third Approximation

Abstract

The method previously described of solving electromagnetic scattering problems as power series in k is here applied to the ellipsoid, the first three terms in the series being obtained. The second term in the series for the wave zone field (that proportional to k3) vanishes, and the same is true of any body possessing a center of symmetry. Thus the terms in k2, k4 in the wave zone field are here obtained. The direction and polarization of the incident wave, and the electromagnetic constants of the ellipsoid, are arbitrary. The final results are expressed in terms of certain elliptic integrals which are functions of the three principal axes of the ellipsoid. These integrals can all be expressed simply in terms of just two such integrals; they become elementary integrals in the case of a spheroid. Various special cases are considered, including that of a perfectly conducting elliptical disk and the complementary problem of diffraction through an elliptical hole in a perfectly conducting screen.