Determining the vortex densities of random nondiffracting beams.

The evolutionary and statistical properties of the optical vortices that exist in random nondiffracting beams (RNDBs) are analyzed. It is found that the phase singularities (PSs) in the RNDBs originate from the zero rings of Bessel beams with the same ring-shaped spatial spectrum structure (but with zero phase fluctuations) as those of the RNDBs provided. It is also found that the average PS density or vortex density is determined by the average duration of the zero rings of the corresponding Bessel function. According to this model, we successfully derived, for the first time to our knowledge, an analytical formula for quantitatively predicting the PS density of the RNDBs. This formula could be helpful for understanding and designing RNDBs in their applications.