A series representation for the intermediate-field transmittance between apertures

A recent communication provided a model for the transmittance between two antennas supporting Orbital Angular Momentum modes. That formulation involved a single integral along the radial spectral coordinate. That approach actually also applies to any pair of apertures supporting arbitrary distributions. Asymptotically, for far field conditions, an analytical expression has been developed, as a power of the near-field parameter, corresponding to the ratio between the far-field limit and the distance between antennas. This expansion is extended to the intermediate-field region, as a polynomial of the near-field parameter. The convergence of this method is discussed, along with the corresponding time savings and limitations.