Complementary Speckle Patterns : deterministic interchange of intrinsic vortices and maxima through Scattering Media

TL;DR

This paper demonstrates that applying a spiral phase delay to a coherent beam behind a diffuser interchanges speckle pattern extrema, enabling control over speckle features and revealing a cyclic permutation of vortices and maxima.

Contribution

It introduces a method to deterministically interchange speckle pattern extrema using spiral phase delays and explores the resulting statistical and structural properties of the patterns.

Findings

Interchanging speckle extrema with spiral phase delays.

Superposition of complementary patterns enlarges speckle grain size by √3.

Observed cyclic permutation of vortices and maxima.

Abstract

Intensity minima and maxima of speckle patterns obtained behind a diffuser are experimentally interchanged by applying a spiral phase delay of charge $\pm 1$ to the impinging coherent beam. This transform arises from the intuitive expectation that a tightly focused beam is so-changed into a vortex beam and vice-versa. The statistics of extrema locations and the intensity distribution of the so-generated "complementary" patterns are characterized by numerical simulations. It is demonstrated experimentally that the incoherent superposition of the three "complementary speckle patterns" yield a synthetic speckle grain size enlarged by a factor $\sqrt{3}$. A cyclic permutation of optical vortices and maxima is unexpectedly observed and discussed.