Generation of complex source point expansions from radiation integrals

This paper discusses methods for expanding fields radiated by arbitrary sources enclosed by a certain minimum sphere in terms of Complex Source Point (CSP) beams. Two different approaches are reviewed; the first one is based on a spectral radiation integral, where the Fourier-spectrum is obtained by far field matching. The second approach consists of two steps: first, the equivalence principle is applied to a sphere enclosing the real sources, and a continuous equivalent electric current distribution is obtained in terms of spherical waves; then, the continuous current is extended to complex space and its SW components are properly filtered and sampled to generate the discrete set of CSPs. In both cases, the final result is a compact finite series representation with a number of terms that matches the degrees of freedom of arbitrary radiated fields; it is particularly efficient when the fields are highly directional and the observation domain is limited to a given angular sector. The fact that the CSPs rigorously respect Maxwell's equations ensures the validity of the expansion from near to far zone and allows one to incorporate the CSP representation in a generalized admittance matrix formalism for the analysis of complex problems.