Electromagnetic source transformations using superellipse equations

Transformation optics can be used to design media with unique properties for the manipulation of electromagnetic waves. The transformation optical approach can be used not only to control the path of light, but also to change the way that currents and charges (or sources) behave when they interact with light. The interaction of electromagnetic waves is fundamental in the design of antennas.  In the latest issue of Applied Physics Letters, Jeffery Allen and colleagues demonstrate several examples of transforming space in the presence of sources to make interesting radiating structures. Using a general class of coordinate transformations, Allen and colleagues show how the current from a dipole antenna can be redistributed over cylindrical shells with arbitrary cross section. By surrounding the transformed current distribution with an appropriate medium determined from the coordinate transformation, the radiation pattern of the original dipole is precisely replicated as seen by an outside observer. This recent work illustrates the applicability of source transformations to conformal antenna design.