Localization and migration of phase singularities in the edge-diffracted optical-vortex beams

When a circularly-symmetric light beam with optical vortex (OV) diffracts at an opaque screen with the sharp edge, the OV core is displaced from the beam axis and, in case of the m-charged incident OV, decomposed into vertical bar m vertical bar single-charged ones. By means of numerical simulations and based on examples of incident beams with topological charges vertical bar m vertical bar = 1, 2, 3 we show that, while the screen edge monotonously advances towards the beam axis, the OVs in the diffracted beam cross section move away from the incident beam axis along spiral-like trajectories. The trajectories contain fine structure details that reflect the nature and peculiar spatial configuration of the diffracting beam. For the Kummer beams' diffraction, the trajectories contain self-crossings and regions of 'backward' rotation (loops); in the case of Laguerre-Gaussian beams, the trajectories are smoother. The numerical results are supported by analytical approximations and conform to experiments. The general shape of the trajectories and their local behavior show high sensitivity to the diffraction conditions (spatial structure of the diffracting beam, its disposition with respect to the screen edge, etc), which can be used in diverse metrological applications.