Superoscillation in speckle patterns

TL;DR

This paper investigates the occurrence and stability of superoscillations in random optical speckle patterns, revealing that a significant fraction of the pattern exhibits superoscillatory behavior, which is more stable during propagation.

Contribution

It provides a theoretical analysis of superoscillatory regions in speckle patterns based on the joint probability density of intensity and phase gradient, highlighting their prevalence and stability.

Findings

Superoscillatory area fraction is 1/3 for uniform wavenumber superpositions.

Superoscillatory area fraction is 1/5 for disk spectrum superpositions.

Superoscillations in speckle patterns are more stable during paraxial propagation.

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.