Exact solutions for non-Rayleigh nondiffracting speckles

We report on a speckle field that is non-Rayleigh, nondiffracting, and an exact solution to the scalar Helmholtz equation. We have shown that these fields can be directly optimized to a continuous range of contrast values corresponding to the sub-Rayleigh or super-Rayleigh statistics maintaining its nondiffracting characteristics. Besides, this work extends the range of non-Rayleigh statistics of nondiffracting fields, which may find many applications in the areas of solid-state physics, cold atoms, and optical imaging.