Related papers: Superoscillations Made Super Simple
Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics and in many fields of science and technology such as…
Superoscillating functions, i.e., functions that locally oscillate at a rate faster than their highest Fourier component, are of interest for applications from fundamental physics to engineering. Here, we develop a new method which allows…
Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more…
A remarkable phenomenon of superoscillations implies that electromagnetic waves can locally oscillate in space or time faster than the fastest spatial and temporal Fourier component of the entire function. This phenomenon allows to focus…
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…
Superoscillations are a phenomenon where a band-limited wave may locally oscillate faster than its highest Fourier component. They are a product of destructive interference between the wave's constituent harmonics. In this article, we…
Super-oscillation is a counter-intuitive phenomenon describing localized fast variations of functions and fields that happen at frequencies higher than the highest Fourier component of their spectra. The physical implications of the effect…
Superoscillations, i.e., the phenomenon that a bandlimited function can temporary oscillate faster than its highest Fourier component, are being much discussed for their potential for `superresolution' beyond the diffraction limit. Here, we…
Waves are superoscillatory where their local phase gradient exceeds the maximum wavenumber in their Fourier spectrum. We consider the superoscillatory area fraction of random optical speckle patterns. This follows from the joint probability…
It has been found that functions can oscillate locally much faster than their Fourier transform would suggest is possible - a phenomenon called superoscillation. Here, we consider the case of superoscillating wave functions in quantum…
Band-limited functions can oscillate locally at an arbitrarily fast rate through an interference phenomenon known as superoscillations. Using an optical pulse with a superoscillatory envelope we experimentally break the temporal…
Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory…
The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…
We utilize a method using frequency combs to construct waves that feature superoscillations - local regions of the wave that exhibit a change in phase that the bandlimits of the wave should not otherwise allow. This method has been shown to…
We construct a signal from "almost" pure oscillations within some low frequency band. We construct it to produce a superoscillation with frequency above the nominal band limit. We find that indeed the required high frequency is produced but…
In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some…
Superoscillating signals are band--limited signals that oscillate in some region faster their largest Fourier component. While such signals have many scientific and technological applications, their actual use is hampered by the fact that…
Fourier synthesis is one of the foundations of physical optics. Spatial Fourier optics is a basis for understanding optical imaging, microscopy, and holography. In conventional Fourier optics, the complex spatial field distribution in the…
Super oscillating signals are band limited signals that oscillate in some region faster than their largest Fourier component. Such signals have many obvious scientific and technological applications, yet their practical use is strongly…
Superoscillation (SO) wavefunctions, that locally oscillate much faster than its fastest Fourier component, in light waves have enhanced optical technologies beyond diffraction limits, but never been controlled into 2D periodic lattices.…