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Superoscillation in speckle patterns.

Mark R Dennis1, Alasdair C Hamilton, Johannes Courtial

  • 1H.H. Wills Physics Laboratory, University of Bristol, Bristol, UK. mark.dennis@physics.org

Optics Letters
|December 17, 2008
PubMed
Summary
This summary is machine-generated.

Random optical speckle patterns exhibit superoscillations, areas where wave phase changes rapidly. This study quanties the fraction of these superoscillatory regions in speckle patterns, finding it to be 1/3 for monochromatic waves and 1/5 for a disk spectrum.

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Area of Science:

  • Wave physics
  • Optics
  • Statistical mechanics

Background:

  • Superoscillations occur when local wave properties exceed spectral limits.
  • Random optical speckle patterns are formed by the superposition of many waves.
  • Understanding the spatial distribution of wave properties in random fields is crucial.

Purpose of the Study:

  • To quantify the superoscillatory area fraction in random optical speckle patterns.
  • To analyze the influence of the wave spectrum on superoscillation occurrence.
  • To compare the stability of naturally occurring superoscillations with designed ones.

Main Methods:

  • Derivation from the joint probability density function of intensity and phase gradient.
  • Analysis of isotropic Gaussian random wave superpositions.
  • Consideration of different wavenumber spectra (monochromatic and disk spectrum).

Main Results:

  • The superoscillatory area fraction is 1/3 for a superposition of waves with the same wavenumber.
  • The superoscillatory area fraction is 1/5 for a disk spectrum.
  • These naturally occurring superoscillations are more stable during paraxial propagation than designed superoscillations.

Conclusions:

  • A significant fraction of random optical speckle patterns exhibit superoscillations.
  • The spectral content of the wave superposition dictates the prevalence of superoscillations.
  • Superoscillations in random fields offer a stable phenomenon for potential applications.