Superoscillation in speckle patterns

Dennis, M.R., Hamilton, A. and Courtial, J. (2008) Superoscillation in speckle patterns. Optics Letters, 33(24), pp. 2976-2978. (doi: 10.1364/OL.33.002976)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Courtial, Dr Johannes and Hamilton, Mr Alasdair
• Authors: Dennis, M.R., Hamilton, A., and Courtial, J.
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Journal Name: Optics Letters
• Publisher: Optical Society of America
• ISSN: 0146-9592
• ISSN (Online): 1539-4794
• Copyright Holders: Copyright © 2008 Optical Society of America
• First Published: First published in Optics Letters 33 (24): 2976-2978
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher