Propagation Dynamics of Phase Singularities Generated by a Grating With Two Lines of Embedded Dislocations

ABSTRACT

We study the near‐field propagation dynamics of phase singularities (optical vortices) generated by Fresnel diffraction of a light beam from a phase grating containing two spatially separated lines of embedded fork‐shaped dislocations with opposite topological charges. Using a combination of analytical methods based on a hydrodynamic approach and full numerical simulations of the Fresnel diffraction integral, we analyze the evolution of the singularities positions over the propagation. Depending on the relative horizontal shift between the two dislocation lines, the trajectories of positive and negative vortices either intersect and cross each other or annihilate upon meeting. Furthermore, we uncover a periodicity in the propagation direction, where the characteristic distance is determined not by the primary grating period but by the spacing between adjacent dislocations along the grating, which was interpreted as quasi Talbot effect. These findings provide insight into the control of optical vortex arrays in structured diffractive elements and extend the understanding of singular optics in periodic systems.