相关论文: Analysis of Superoscillatory Wave Functions
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…
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…
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…
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…
Superoscillatory functions represent a counterintuitive phenomenon in physics but also in mathematics, where a band-limited function oscillates faster than its highest Fourier component. They appear in various contexts, including quantum…
In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak…
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…
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…
We present a formal definition of superoscillating function. We discuss the limitations of previously proposed definitions and illustrate that they do not cover the full gamut of superoscillatory behaviours. We demonstrate the suitability…
Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing…
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…
A recipe is presented for constructing band-limited superoscillating functions that exhibit arbitrarily high frequencies over arbitrarily long intervals.
In ordinary circumstances the highest frequency present in a wave is the highest frequency in its Fourier decomposition. It is however possible for there to be a spatial or temporal region of the wave which locally oscillates at a still…
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…
We present a method for constructing superoscillatory functions the superoscillatory part of which approximates a given polynomial with arbitrarily small error in a fixed interval. These functions are obtained as the product of the…
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…
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…
This book chapter gives a selective review of physical implementations and applications of superoscillations and associated phenomena. We introduce the field by reviewing simple examples of superoscillations and showing how their existence…
Superoscillations occur when a globally band-limited function locally oscillates faster than its highest Fourier coefficient. We generalize this effect to arbitrary quantum mechanical operators as a weak value, where the preselected state…