Supergrowing Optical Fields: Subwavelength Imaging and Generation.

A bandlimited function is considered superoscillatory when it locally oscillates at a rate higher than its fastest Fourier component. Superoscillatory optical fields are routinely used for far-field superresolution imaging, i.e., for achieving resolution beyond the Rayleigh limit. The presence of very intense sidelobes limits the effectiveness of such fields in experimental implementations. The appearance of these sidelobes leads to poor imaging quality and unrealistic constraints on the dynamic ranges of the detectors. Supergrowth, a recently introduced concept [Jordan, Quantum Stud.: Math. Found. 7, 285-292(2020)], is a promising candidate for mitigating such issues. Supergrowth is defined as the local amplitude growth rate of a function being higher than its fastest Fourier component. Supergrowing regions can have intensities exponentially higher than superoscillating regions, alleviating the effects of sidelobes. In my talk, I will show that supergrowing and superoscillating optical fields can help us reconstruct subwavelength objects. We will also see that I will show how to generate supergrowing/superoscillating functions robustly.