The null field approach to the antenna boundary value problem

The diffraction of electromagnetic waves by a perfectly conducting body is considered from a computational viewpoint. The paper utilizes the null field method and extends the ideas of Bates and Wall (1977) to vector diffraction problems. The 'spheroidal' null field applied to the rotationally symmetric antenna problem is considered. By use of an expansion of the free-space Green's tensor in terms of spheroidal wave functions, the extinction theorem is satisfied within the spheroid inscribed by the antenna. It is demonstrated numerically that for the 'prolate spheroidal' null field method this procedure ensures numerical stability in situations where the 'spherical' null field method leads to computational instabilities. In conclusion, it is emphasized that apart from rotational symmetry the shape of the antenna can be arbitrary.