Superoscillation in speckle patterns

Abstract

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 density function of intensity and phase gradient for isotropic gaussian random wave superpositions. Strikingly, this fraction is 1/3 when all the waves in the two-dimensional superposition have the same wavenumber. The fraction is 1/5 for a disk spectrum. Although these superoscillations are weak compared with optical fields with designed superoscillations, they are more stable on paraxial propagation.Comment: 3 pages, two figures, Optics Letters styl

Optimising superoscillatory spots for far-field super-resolution imaging

“…Superoscillatory spots have been produced in a number of ways, for example by a quasi-periodic array of nanoholes in a metal screen [18], binary ring masks [21], using micro/nanofibre arrays [22] and in random speckle patterns [23]. Theoretical techniques for designing superoscillatory functions with particular properties have also been demonstrated, for example by manipulating zeros [24], by prescribing values of the superoscillatory function and minimising total energy [25,26] or energy yield [27], and by using variational techniques to find minimum energy solutions that satisfy specified constraints on the amplitude and/or derivative of the desired superoscillatory function [19,28].…”

Representing fractals by superoscillations

“…They have been applied to quantum weak measurements [9][10][11], speckle [12,13], superresolution microscopy [14][15][16][17][18][19][20], radar superdirectivity [21,22], and optical vortices [23,24].…”

Experimental generation of arbitrarily shaped diffractionless superoscillatory optical beams

“…Berry explored superoscillatory functions, which, in finite, yet arbitrarily large regions of space oscillate faster than the fastest (highest) Fourier component of the entire function. Such superoscillations occur naturally in optics near optical phase singularities [5] or in random optical speckle patterns [6], wherever the local gradient of the phase of the field exceeds the maximum Fourier component of the spectrum of the entire field. Further, it is possible to design superoscillatory optical fields.…”