Superoscillation in speckle patterns

Details Superoscillation in speckle patterns Superoscillation in speckle patterns

2008-10-10

arxiv.org/abs/0810.1948v2

Optics Letters 33 (2008) 2976-2978

Physics

Optics

3 pages, two figures, Optics Letters style

Scientific paper

10.1364/OL.33.002976

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.

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