The radiation operator

The concept of the radiation operator is introduced to assist in the analysis of various problems involving sources and their radiation fields. It gives the field outside the source region as operating on the field of a point source. Because there is a simple connection between the radiation vector describing the far-field and the radiation operator, it can be used to define fields anywhere outside the source region from their values in the far-field zone. Another important properly of the radiation operator is its ability to express sources of fields given their radiation pattern and polarization in the far zone. The source of such a field can be written in the form of radiation operator operating on a current element, the delta function source. To interpret this in terms of computable functions, existing tables of operational rules for different classes of operators can be applied. Examples of radiation operators corresponding to different sources are given together with examples of sources corresponding to given radiation field patterns. Finally it is shown that the radiation operator allows a considerable simplification to the derivation of the multipole expansion theory when compared to the classical recursion-formula derivation through spherical harmonic eigenfunctions