Adaptation of Schelkunoff´s Superdirective Antenna Theory for the Realization of Superoscillatory Antenna Arrays

We have adapted Schelkunoff´s method of antenna pattern synthesis to the design of superoscillatory waveforms. Our method stems from the observation that superdirectivity and superoscillation are dual phenomena in the space and spectral domains; it can be applied to construct any periodic superoscillatory wave functions. Using this method, we designed two subwavelength focusing schemesin free space and within a waveguideat an image distance of five wavelengths. We first describe how we extend the concept of superdirectivity toward constructing superoscillatory waveforms, then provide in-depth formulations as they apply to each design example. We also report full-wave simulation results verifying subwavelength focusing to 0.6 times that of the diffraction limit at a distance five wavelengths away from the source.