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

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.