Random sources generating far fields with ring-shaped array profiles

We introduce a class of planar random source generating ring-shaped array profiles in the far field. The model for spatial correlation function of this new source is composed by the Fourier transform of the Laguerre-Gaussian array function with circular symmetry. The analytical expressions for the spectral density (average intensity) in free space and atmospheric turbulence are derived. The effect of the source parameters on the propagation properties are investigated in detail. Numerical results show that the source can produce a ring-shaped optical array profile consisting of dark-hollow-shaped or Gaussian-like-shaped beamlets at some distance, and then keep shape-invariant for long distances in free space. The number of rings, the position of beamlets, and other features can be conveniently controlled by changing the initial source parameters. In addition, increasing the relative separation distance of each beamlet or decreasing the radius of beamlets can reduce the turbulence-induced degradation.