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Almost one and a half centuries ago, Ernst Abbe [1] and shortly after Lord Rayleigh [2] showed that when an optical lens is illuminated by a plane wave, a diffraction-limited spot with a radius 0.61*lambda/sin(alpha) is obtained, where…

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…

Mathematical Physics · Physics 2016-08-03 Eugene Tang , Lovneesh Garg , Achim Kempf

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…

Mathematical Physics · Physics 2018-03-02 Achim Kempf

Light scattering is one of the most established wave phenomena in optics, lying at the heart of light-matter interactions and of crucial importance for nanophotonic applications. Passivity, causality and energy conservation imply strict…

Optics · Physics 2022-11-23 Seunghwi Kim , Sergey Lepeshov , Alex Krasnok , Andrea Alù

The possibility of focusing light to an ever tighter spot has important implications for many applications and fields of optics research, such as nano-optics and plasmonics, laser-scanning microscopy, optical data storage and many more. The…

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…

Optics · Physics 2008-12-10 Mark R. Dennis , Alasdair C. Hamilton , Johannes Courtial

The ability to create dynamic, tailored optical potentials has become important across fields ranging from biology to quantum science. We demonstrate a method for the creation of arbitrary optical tweezer potentials using the broadband…

Optics · Physics 2020-07-16 A. T. M. Anishur Rahman , P. F. Barker

Lenses are crucial to light-enabled technologies. Conventional lenses have been perfected to achieve near-diffraction-limited resolution and minimal chromatic aberrations. However, such lenses are bulky and cannot focus light into a hotspot…

Optics · Physics 2017-01-25 Guang Hui Yuan , Edward T. F. Rogers , Nikolay I. Zheludev

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…

Optics · Physics 2020-04-08 Barbara Šoda , Achim Kempf

Optical super-oscillation enables far-field super-resolution imaging beyond diffraction limits. However, the existing super-oscillatory lens for the spatial super-resolution imaging system still confronts critical limitations in performance…

Diffraction limits the behaviour of light in optical systems and sets the smallest achievable line width at half the wavelength. With a novel subwavelength plasmonic lens to reduce the diffraction via an asymmetry and to generate and…

Optics · Physics 2009-01-30 K. R. Chen

Two transformation-optics inspired flat lenses are used to build up an optical system capable to transpose an area surrounding the object focal point in a magnified area surrounding the image focal point. The object and image focal points…

Optics · Physics 2018-08-10 Mircea Giloan , Robert Gutt

We present squeezed light that is robust against spatial mode mismatch (beam displacement, tilt, and beam-size difference), which is generated from a self-imaging optical parametric oscillator below the threshold. We investigate the quantum…

Quantum Physics · Physics 2021-10-12 Chan Roh , Geunhee Gwak , Young-Sik Ra

I propose a superoscillation measurement method for subdiffraction incoherent optical sources, with potential applications in astronomy, remote sensing, fluorescence microscopy, and spectroscopy. The proposal, based on coherent optical…

Quantum Physics · Physics 2022-10-10 Mankei Tsang

Light beams can be characterized by their complex spatial profiles in both intensity and phase. Analogous to time signals, which can be decomposed into multiple orthogonal frequency functions, a light beam can also be decomposed into a set…

A light beam propagating with an infinite anti-diffracting distance requires infinite power to preserve its shape. However, the fundamental barrier of finite power in free space has made the problem of diffraction insurmountable over the…

For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available.…

Optics · Physics 2011-01-11 Michael Mazilu , Joerg Baumgartl , Kishan Dholakia

Hyperuniform metasurfaces promise an unusual form of wave control: the suppression of elastic scattering over extended angular ranges without periodic order. Here, we present a comprehensive experimental and theoretical study of 2D stealthy…

In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…

Numerical Analysis · Mathematics 2013-07-16 Wolfgang Erb , Sonja Mathias

Analogous to time signals that can be composed of multiple frequency functions, we use uniquely structured orthogonal spatial modes to create different beam shapes. We tailor the spatial structure by judiciously choosing a weighted…