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Optics Letters

Optics Letters


  • Editor: Alan E. Willner
  • Vol. 33, Iss. 24 — Dec. 15, 2008
  • pp: 2976–2978

Superoscillation in speckle patterns

Mark R. Dennis, Alasdair C. Hamilton, and Johannes Courtial  »View Author Affiliations

Optics Letters, Vol. 33, Issue 24, pp. 2976-2978 (2008)

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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.

© 2008 Optical Society of America

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(260.3160) Physical optics : Interference
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Coherence and Statistical Optics

Original Manuscript: October 10, 2008
Revised Manuscript: November 3, 2008
Manuscript Accepted: November 4, 2008
Published: December 9, 2008

Mark R. Dennis, Alasdair C. Hamilton, and Johannes Courtial, "Superoscillation in speckle patterns," Opt. Lett. 33, 2976-2978 (2008)

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