Inverse Source Problem for Determining a Surface Impedance: Generating the Field of a Complex Point Source

The radiation from a complex point source has very unusual properties: the field in the near zone closely resembles the far-field pattern, which has a single main beam and no sidelobes. These properties make the complex point-source field desirable in numerous applications in electromagnetics and acoustics. The possible physical realization a complex point-source is explored in two dimensions using an impenetrable impedance surface that is illuminated by an array of real point sources or a plane wave. Such a device can be implemented using a metasurface that is characterized by a transversely inhomogeneous impedance profile. The problem of determining a physically realizable impedance profile is cast in the form of a constrained inverse source problem. An impedance cylinder in the shape of a Cassini oval illuminated by an array of real point source can reproduce the near and far fields of a complex point source to an arbitrarily high degree of accuracy. One of these solutions has 99% efficiency but exhibits both gain and loss locally.