**Authors:** Prabhakar H. Pathak

**Source:**FERMAT, Volume 22, Communication 18, Jul.-Aug., 2017

**Abstract:** It is well known from the independent works of Keller, Deschamps, and Felsen, respectively, that an electromagnetic (EM) point current source positioned in complex space produces a beam wave field which is highly localized about its forward propagation axis. It is noted that the EM field of a complex source beam (CSB) constitutes an exact solution of Maxwell's equations, and it is simply obtained by an analytic continuation of the exact closed form expression of the EM field for a point current in real space, where the real source coordinates are replaced by complex values. In its paraxial region, a CSB automatically reduces to a Gaussian Beam (GB). By controlling the values of the complex source coordinates, one can produce either a CSB with a very broad ( not well focused ) beam or a very narrow ( highly focused ) beam; consequently, such a CSB field can be made to pass smoothly from the field of a real point source to a plane wave field. It is clear that CSBs can serve as highly useful basis functions to represent EM fields, and indeed they have been used in this fashion by some researchers in this area. Here, additional useful methods for developing convergent CSB expansions to represent the fields of EM sources, via appropriate EM equivalence theorems, will be illustrated. Applications of such CSB expansions to analyze a class of electrically large practical antenna and scattering problems will be presented to demonstrate their utility.

**Index Terms:** Ray Optics, Diffraction, GTD, UTD, PTD, Beams, Hybrid Methods

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