Superoscillation in speckle patterns

MR Dennis, AC Hamilton, J Courtial

Research output: Contribution to journalArticle (Academic Journal)peer-review

86 Citations (Scopus)


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.
Translated title of the contributionSuperoscillation in speckle patterns
Original languageEnglish
Pages (from-to)2976 - 2978
Number of pages3
JournalOptics Letters
Publication statusPublished - Dec 2008

Bibliographical note

Other: Arxiv: 0810.1948


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