Aperture theory and the equivalence theorem

The equivalence theorem provides an elegant method for analysing electromagnetic radiation and scattering from structures. A specific class of problems is where a source is enclosed within a structure which forms a cavity with an aperture. From a radiation point of view, the fields within the cavity are not of any real interest, only the ´external´ fields radiated from the aperture. If the field distribution in the aperture is known (even if only approximately), this a priori knowledge can be exploited to limit calculations to the ´external´ part of the problem. This technique is commonly referred to as ´aperture theory´. This paper deals with the methods in which the equivalent aperture current densities are incorporated into the surface equivalence theorem. It is shown that the application of image theory to problems involving radiation from apertures in a half-space is incorrect and that the conventional formulation of aperture theory violates a basic condition of the equivalence principle. A new aperture theory formulation is presented. The method is very simple to implement and is shown to be exact in as far as the exact aperture fields are known.