Study of Superoscillating Functions Application to Overcome the Diffraction Limit with Suppressed Sidelobes

The problem of overcoming the diffraction limit does not have an unambiguously advantageous solution because of the competing nature of different beams’ parameters, such as the focal spot size, energy efficiency, and sidelobe level. The possibility to overcome the diffraction limit with suppressed sidelobes out of the near-field zone using superoscillating functions was investigated in detail. Superoscillation is a phenomenon in which a superposition of harmonic functions contains higher spatial frequencies than any of the terms in the superposition. Two types of superoscillating one-dimensional signals were considered, and simulation of their propagation in the near diffraction zone based on plane waves expansion was performed. A comparative numerical study showed the possibility of overcoming the diffraction limit with a reduced level of sidelobes at a certain distance outside the zone of evanescent waves.