During solution of the practical problems related to the construction of the field radiators or receivers, the important problem is to "match" them with the free space. The bad matching leads to the formation of the undesired reactive field in the near zone of the corresponding antenna. The investigations show that, the best matching can be achieved by putting the sources in the points of singularities of the far field's analytical continuation. By this could be achieve the minimal area of the reactive field. If the sources, which describes the far field, are distributed outside the singularities, then in the near zone the reactive field with the high amplitude is created, which doesn't make such a radiator optimal. In the given work the sources are distributed initially outside the singularity points. The goal is to study main properties of the excited reactive field and to study the far field formation mechanism, when the sources of the radiation are singularities points out.