Topological stability of optical vortices diffracted by a random phase screen

Here, we theoretically demonstrate that if a Gaussian optical vortex is distorted by a random phase screen (diffuser) then the average intensity distribution in the focus of a spherical lens has a form of a ring with a nonzero value on the optical axis. The radius of the average-intensity ring depends on both the topological charge of an optical vortex and on the diffusing power of the diffuser. Therefore, the value of the topological charge cannot be unambiguously determined from the radius of the average intensity ring. However, the value of the topological charge of the optical vortex can be obtained from the number of points of phase singularity that can be determined using a Shack-Hartmann wavefront sensor. It is also shown that if we use a linear combination of two optical vortices, then the average intensity distribution has local maxima, the number of which is equal to the difference of the topological charges of the two original vortices. The number of these maxima no longer depends on the scattering force of the diffuser and can serve as an indicator for optical vortex identification. Modeling and experiments confirm the theoretical conclusions.