Spatial profile and singularities of the edge-diffracted beam with a multicharged optical vortex

We analyze the edge diffraction of circular Laguerre-Gaussian beams LG02 and LG03 carrying multicharged optical vortices (OVs), with special attention to spatial properties and evolution of the diffracted beam. The problem is considered numerically within the frame of paraxial approximation and the Fresnel diffraction theory. The diffracted beam evolution is interpreted on the basis of the incident beam symmetry breakdown and decomposition of a higher-order OV into a set of single-charged secondary OVs. Upon propagation, the separate OVs describe specific trajectories within the diffracted beam cross section but in the far field they are localized on the symmetry axis parallel to the screen edge. The OVs' positions in each cross section reflect information of the screen edge position with respect to the incident beam axis. If the incident OV is stopped by the screen, the diffracted beam possesses no OV just behind the screen but in the course of its further propagation, single-order OVs appear consecutively so that in the far field the number of OVs equals to the absolute topological charge of the incident OV. Possible applications for the remote measurements of small linear displacements are discussed.