An exact non redundant Complex Source Point beam representation of an EM field obtained from a spherical wave expansion

A non-redundant representation of the field radiated in a certain angular region. In terms of electric type Complex Source Point (CSP) beams is analytically derived from the spherical wave expansion (SWE) of the field. This is done by first applying a particular form of the equivalence principle to a sphere enclosing the real sources and then extending the sphere to complex space. The properties of the SWE combined with the CPS angular selectivity allow one to minimize the number of wave objects needed for the field representation.