A Combined Inverse Source and Scattering Technique for Dielectric Profile Design to Tailor Electromagnetic Fields

This article augments existing gradient-based inverse scattering algorithms to enable the design of reflectionless lossless permittivity profiles within a given design domain that can transform an input incident field into an output field of desired characteristics. These desired characteristics are often some user-defined far-field performance criteria, such as main beam directions, null directions, and half-power beamwidth (HPBW). To this end, two extra steps will be performed prior to the inverse scattering step. First, an inverse source algorithm inverts the desired far-field performance criteria to infer a set of equivalent surface currents on a boundary close to the design domain. These equivalent currents are then converted to a set of field values that constitute the required aperture fields. Second, these aperture fields are scaled such that the input incident power to the design domain is approximately equal to the output power leaving the design domain. Finally, the desired scattered fields are formed and then inverted by an inverse scattering algorithm to reconstruct a lossless reflectionless dielectric profile within the design domain. We also show that the inverse scattering algorithm can employ appropriate regularization methods, in particular a binary regularization term, to facilitate the physical implementation of reconstructed dielectric profiles.