The complex source point (CSP) concept is utilized in this work to efficiently treat a class of electromagnetic (EM) radiation and scattering problems. A CSP generates a beam field which reduces paraxially to a Gaussian beam (GB). The CSP beam constitutes an exact solution of the Maxwell's equations, hence a complex extension of the equivalence theorem is employed in this work to rigorously expand the EM fields which are generated by arbitrary sources into a set of CSP beam basis elements. The beam like behavior of CSP fields allows one to efficiently compute the fields of arbitrary sources because only a few beams contribute significantly at any given observation point. The work presented here on the CSP beam expansions is useful, e.g., for the rapid analysis of the radiation from large reflector antennas, and also for the fast analysis of such large antennas when they radiate in the presence of larger radome structures. Conventional approaches for solving the above class of problems are highly inefficient. Also this CSP beam expansion provides an efficient and physically appealing technique for performing a near field to far field transformation of spherical near field scanning measurement data. Furthermore, a new hybrid method, combining the Method of Moments (MoM) with the present CSP beam expansion procedure, or CSP-MoM, is developed to numerically solve very large electromagnetic radiation/scattering problems. The key idea in the CSP-MoM is that the elements of the MoM operator matrix are expressed as a superposition of the interactions between a small/compact set of CSP beams radiated from the local domains enclosing these elements. The CSP-MoM does not assume any particular form of the Green's function; therefore it is applicable also to inhomogeneous space problems. It is shown that the operational count and the storage can be reduced to O(N 3/2) by properly choosing the group sizes (N=number of unknowns), as compared to O(N 2) of conventional MoM methods, both for memory and computational time.
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