4-18-2019 Roadmap on Superoscillations

Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to Journal of Optics J. Opt. 21 (2019) 053002 (35pp) https://doi.org/10.1088/2040-8986/ab0191 19 Guest editors of the Roadmap. 20 Author to whom any correspondence should be addressed. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 2040-8978/19/053002+35$33.00 © 2019 IOP Publishing Ltd Printed in the UK 1 optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments.

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