An exact CSP beam representation for EM wave radiation

It is known that complex source point beams are exact solutions of the Maxwell's equations everywhere in in space. By using this property, it is shown in this work that any fully vector EM field can be exactly expanded in terms of CSP beams launched from an arbitrary surface enclosing the EM sources. The approach is based on the analytical extension of the surface equivalence theorem to the case in which the equivalent surface becomes complex. Three different variations of the surface equivalence theorem are considered, and the properties of each are discussed. Numerical results are presented to demonstrate the exactness and efficiency of the approach. The resulting CSP beam expansion is expected to be useful in the solution of the EM radiation/scattering problems involving complicated environments, such as reflector problems and radome problems.