Investigation of the topological charge stability for multi-ringed Laguerre–Gauss vortex beams to random distortions

We performed a comparative numerical study of the conservation of properties of individual Laguerre-Gauss beams and their superpositions in a random environment. The simulation is based on the extended Huygens-Fresnel principle. Studies have shown that increasing the number of rings of Laguerre-Gauss modes with the same vortex order allows one to increase the ratio of the energy of the minimum informative coefficient to the energy of the maximum parasitic coefficient, which is important when detecting information encoded in the coefficients. In addition, an increase in the number of rings partially compensates for the stronger effect of random fluctuations on beams with high topological charges. Such a positive impact can be explained by the structural redundancy of multi-ring distributions (the vortex phase structure of the beam is repeated in each ring). A similar result was obtained for beams corresponding to a two-mode superposition. The best result on information preservation was obtained for the superposition with duplication of information in complex conjugate coefficients, and the best ratio of informative energy to parasitic one was obtained for beams with the largest area.