A direct non redundant complex source point expansion of the electromagnetic field radiated by an arbitrary source

A simple closed-form expression for a non-redundant Complex Source Point (CSP) beam expansion of an arbitrary electromagnetic field is derived. The expansion process consists of two steps: first, a particular form of the equivalence principle is applied to a sphere enclosing the real sources, and a continuous equivalent electric current distribution is obtained; then, the continuous current is extended to complex space and properly filtered and sampled to generate the discrete set of CSP coefficients. The final result is an exact field representation suitable for arbitrary radiated fields, and optimal if the source is highly directional and/or the observation domain is restricted.