Exact Complex Source Point Beam Expansions for Electromagnetic Fields

Complex source point (CSP) beams (or CSPBs) are known to be exact solutions of Maxwell's equations. Hence they can be used as basis functions to represent the electromagnetic fields generated by arbitrary sources. In this work, it is shown that any fully vector electromagnetic field can be represented exactly as an expansion of CSPBs originating from a relatively arbitrary surface enclosing the sources. Three different variants of the CSPB representation are first considered for a spherical expansion surface and their properties are discussed. It is shown that the CSPB expansion set can be conveniently truncated by selecting only the significantly contributing beams for efficient field calculations. The CSPB representations are next extended to the case of relatively arbitrary expansion surfaces. Numerical results are presented to demonstrate and compare the convergence and efficiency of the three approaches.