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 schemes—in free space and within a waveguide—at 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.