# Four aspects of superoscillations

@article{Kempf2018FourAO, title={Four aspects of superoscillations}, author={Achim Kempf}, journal={Quantum Studies: Mathematics and Foundations}, year={2018}, volume={5}, pages={477-484} }

A function f is said to possess superoscillations if, in a finite region, f oscillates faster than the shortest wavelength that occurs in the Fourier transform of f. I will discuss four aspects of superoscillations: (1) Superoscillations can be generated efficiently and stably through multiplication. (2) There is a win–win situation in the sense that even in circumstances where superoscillations cannot be used for superresolution, they can be useful for what may be called superabsorption, an… Expand

#### 19 Citations

Evolution of Superoscillations in the Dirac Field

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Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. The study of the evolution of superoscillations as initial datum of field… Expand

Evolution of Superoscillations in the Klein-Gordon Field

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Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. There is nowadays a large literature on the evolution of superoscillations under… Expand

Holomorphic functions, relativistic sum, Blaschke products and superoscillations

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Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. The notion of superoscillation is a particular case of that one of supershift. In… Expand

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- Journal of Optics
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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… Expand

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Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time dependent Schrödinger equation is an important and… Expand

Evolution by Schrödinger equation of Aharonov–Berry superoscillations in centrifugal potential

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- Proceedings of the Royal Society A
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In recent years, we have investigated the evolution of superoscillations under Schrödinger equation with non-singular potentials. In all those cases, we have shown that superoscillations persist in… Expand

Schrödinger evolution of superoscillations with $δ$- and $δ'$-potentials

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- 2019

In this paper, we study the time persistence of superoscillations as the initial data of the time-dependent Schrödinger equation with δand δ′-potentials. It is shown that the sequence of solutions… Expand

How superoscillating tunneling waves can overcome the step potential

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- 2020

Abstract We consider the Cauchy problem for the Schrodinger equation with step potential with jump V 0 at the origin and whose initial datum is a superoscillatory function F n that is traveling from… Expand

Aharonov–Berry superoscillations in the radial harmonic oscillator potential

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- Quantum Studies: Mathematics and Foundations
- 2019

In this paper, we study the evolutions of Aharonov–Berry superoscillations under the radial harmonic oscillator potential. For this model, we know the Green function and, taking advantage of it, we… Expand

Synthesis of Super-Oscillatory Point-Spread Functions with Taylor-Like Tapered Sidelobes for Advanced Optical Super-Resolution Imaging

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- 2021

Recently, the super-oscillation phenomenon has attracted attention because of its ability to super-resolve unlabelled objects in the far-field. Previous synthesis of super-oscillatory point-spread… Expand

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