Line-integral representation of the field radiated by a modal rectangular current distribution

Reducing surface radiation integrals into line-integrals is important for problems of horn and open ended waveguide antennas. Indeed, the aperture distribution can be represented in terms of the modes which are used as basis functions in a method of moments (MoM) solution, and the near field calculation is the basic step of the analysis. Reduction of this radiation integral into a line-integral provides a drastic saving of the time for filling the MoM matrix. Previously, a method was suggested for obtaining the aperture field in terms of a line-integral for an arbitrary shaped modal distribution which is based on the theorem demonstrated by Maci, Ufimtsev and Tiberio (see IEEE Trans. Antenna Propag., vol.45, no.1, p.183-4, 1997). This latter formulation, involves an asymptotic evaluation, so that it could not be applied for very near field calculations (as for the self-reaction integral). In this paper, a formulation is carried out, which does not involve any asymptotic derivation; however, it is valid only for rectangular modes.