Related papers: Reconstructing Superoscillations Buried Deeply in …
We introduce a new numerically stable method for constructing superoscillatory wave forms inan arbitrary number of dimensions. The method allows the construction of superoscillatory square-integrable functions that match any desired smooth…
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…
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…
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 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…
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…
Robustly manipulating waves on subwavelength scales can be achieved by, firstly, designing a structure with a subwavelength band gap and, secondly, introducing a defect so that eigenfrequencies fall within the band gap. Such frequencies are…
We show that it is possible to construct spectrally lower bound limited functions which can oscillate locally at an arbitrarily low frequency. Such sub-oscillatory functions are complementary to super-oscillatory functions which are…
Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time…
We use compressed sensing to demonstrate theoretically the reconstruction of sub-wavelength features from measured far-field, and provide experimental proof-of-concept. The methods can be applied to non-optical microscopes, provided the…
Frequency combs have revolutionized the field of optical spectroscopy, enabling researchers to probe molecular systems with a multitude of accurate and precise optical frequencies. While there have been tremendous strides in direct…
We further develop the concept of supergrowth [Jordan, Quantum Stud.: Math. Found. $\textbf{7}$, 285-292 (2020)], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function being higher than its…
We report a method for constructing bandpass functions that approximate a given analytic function with arbitrary accuracy over a finite interval. A corollary is that bandpass functions can be obtained that oscillate arbitrarily slower than…
Optical frequency combs are key to optical precision measurements. While most frequency combs operate in the near-infrared regime, many applications require combs at mid-infrared, visible or even ultra-violet wavelengths. Frequency combs…
Optical frequency combs combine ultrashort pulse duration and phase stability, making them powerful resources for high-precision ranging even when affected by atmospheric dispersion. It has been established that by classical modal…
Advanced digital signal processing techniques in combination with ultra-wideband balanced coherent detection have enabled a new generation of ultra-high speed fiber-optic communication systems, by moving most of the processing…
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…
Optical frequency combs can potentially provide an efficient light source for multi-terabit-per-second optical superchannels. However, as the bandwidth of these multi-wavelength light sources is increased, it can result in low per-line…
Acoustic frequency combs leverage unique properties of the optical frequency comb technology in high-precision measurements and innovative sensing in optically inaccessible environments such as under water, under ground or inside living…