Spiral-Like Trajectories of Singularities at Fresnel Diffraction on Double Fork-Shaped Gratings

Abstract

Fresnel diffraction on double fork-shaped gratings is studied. The trajectories of singularities are found to form two groups of nested spirals, with one originating from each dislocation. The number of spirals nested in each group is found to be equal to the topological charge of the dislocation from which it originates. The influence of the initial distance between dislocations on the trajectories of singularities is examined in detail, and the distinctive characteristics of this dependence are highlighted. The trajectory of the displacement of centroids of singularities from one group of nested spirals during the propagation for various topological charges is investigated. The results demonstrate that the higher the topological of the second dislocation is, the faster the centroid from the first dislocation will shift along the $y$ axis during the propagation. This finding indicates that the trajectory of singularities displacement is not defined by the singularity itself, but rather by the background field, which correlates well with the hydrodynamic approach.