47:. Chremmos and Fikioris have proposed a method for constructing superoscillations that approximate a desired polynomial with arbitrary accuracy within a given interval. In 2013 experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams has been demonstrated. Two years later, in 2015, it was shown experimentally that super-oscillations can generate features that are many-fold smaller than the diffraction limit. The experiment was done using visible light, demonstrating enhanced resolution of 35 nm. Kempf and Ferreira proved that superoscillations come at the expense of a dynamical range that has to increase exponentially with the number of superoscillations and polynomially with the frequency of the superoscillations.
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In 2007, Huang experimentally observed optical superoscillation phenomenon in the diffraction patterns of light transmitted through quasi-periodic nanohole arrays. Optical foci much smaller than the diffraction limit were observed. The results matched simulations without evanescent waves. In 2009,
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Huang et al further developed theoretical models to design superoscillation masks that can achieve extreme light concentration and imaging with arbitrary resolution. A practical method for constructing superoscillations and a discussion of their potential for quantum field theory were given by
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Berry, M V, 1994, 'Faster than
Fourier', in 'Quantum Coherence and Reality; in celebration of the 60th Birthday of Yakir Aharonov' (J S Anandan and J L Safko, eds.) World Scientific, Singapore, pp 55-65.
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Superoscillatory wave forms are being considered as a possible practical tool for engineering applications, such as optical superresolution, i.e., resolution beyond the diffraction limit.
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Huang, Fu Min; Zheludev, Nikolay; Chen, Yifang; Javier Garcia De Abajo, F. (2007). "Focusing of light by a nanohole array".
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Huang, Fu Min; Zheludev, Nikolay I. (2009). "Super-Resolution without
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Berry, M. V.; Dennis, M. R. (2009). "Natural superoscillations in monochromatic waves in
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can contain local segments that oscillate faster than its fastest
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Kempf, Achim (2000). "Black holes, bandwidths and
Beethoven".
31:, and has been made more popularly known through the work of
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Zheludev, Nikolay I. (2008). "What diffraction limit?".
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189:"Optical super-resolution through super-oscillations"
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is a phenomenon in which a signal which is globally
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492:"Superoscillations: Faster Than the Nyquist Rate"
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