The direct measurement of the radiation pattern of an antenna is often unreachable. A near-field sampling followed by a near-field/far-field (NF/FF) transformation is therefore substituted. This process is, in most cases, applied to antennas placed in free-space or over a perfect electric conductor. On the contrary, few results concern real environment conditions. Nevertheless, it is well known that the nature of the soil can drastically change the radiating characteristic of an antenna. The lack of information about the behavior of the antenna in real conditions can give rise to substantial errors in the evaluation of the performances of electromagnetic devices. The aim of this paper is then to propose a new NF/FF transformation able to reliably supply the field radiated by an antenna placed over a plane, homogeneous, dielectric, and lossy interface. The method is based on the cylindrical-wave expansion of the electric field. The real soil is taken into account by means of its reflection coefficients. First results are given for simple antennas and for both transverse magnetic and transverse electric polarizations.

Band-limited acoustic sources of small spatial extent produce radiation patterns well approximated by those of multi-poles. Assumed limits on dimensionless size Ka and source efficiency lead to explicit rules for the necessary length of the multi-pole series.