![]() ![]() Scaling properties of superoscillations and the extension to periodic signals. Unusual properties of superoscillating particles. Superoscillations: Faster than the Nyquist rate. Prolate spheroidal wave functions, Fourier analysis and uncertainty - I. Spectral analysis of the finite Hankel transform and circular prolate spheroidal wave functions. Realising superoscillations: A review of mathematical tools and their application. Mathematical method for designing superresolution lenses using superoscillations. Superoscillations with arbitrary polynomial shape. Adaptation of Schelkunoff’s superdirective antenna theory for the realization of superoscillatory antenna arrays. Direct construction of superoscillations. New methods for creating superoscillations. Mathematical concepts of optical superresolution. Super-resolution without evanescent waves. Construction of Aharonov–Berry’s superoscillations. ![]() A simple model of Aharonov-Berry’s superoscillations. Superoscillations and supershifts in phase space: Wigner and Husimi function interpretations. Evolution of quantum superoscillations and optical superresolution without evanescent waves. Superlenses to overcome the diffraction limit. Negative refraction makes a perfect lens. We review the fundamental properties of superoscillatory optical fields and examine emerging technological applications.Ītwater, H. Far-field, label-free, non-intrusive deeply subwavelength super-resolution imaging and metrology techniques that exploit high light localization and rapid variation of phase in superoscillatory fields have also been developed, including new approaches based on artificial intelligence. Dielectric, metallic and metamaterial nanostructured superoscillatory lenses have been introduced that are able to create hotspots smaller than allowed by conventional lenses. In recent years, the understanding of superoscillatory light has led to the development of superoscillatory lensing, imaging and metrology technologies. The discovery of superoscillations stimulated a revision of the limits of classical electromagnetism - in particular, the studies of phenomena such as unlimitedly small energy hotspots, phase singularities, energy backflow, anomalously high wavevectors and their intriguing similarities to the evanescent plasmonic fields on metals. Optical superoscillations are rapid, subwavelength spatial variations of the intensity and phase of light, occurring in complex electromagnetic fields formed by the interference of several coherent waves. ![]()
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