Five-vortex spot patterns generated by diffraction of azimuthally X-shaped beam from a fork-shaped grating

By theoretical and experimental methods it is demonstrated how a beam whose amplitude profile is X-modulated in azimuthal direction, with central dark non-vortex core, can be transformed into an array of five-vortex spot patterns. This beam undergoes Fraunhofer diffraction by a fork-shaped grating with integer topological charge (TC) p. The results show an interesting phenomenon: while the incident beam is without topological charge, in the output array of spots a five-vortex modulation on the higher-diffraction-order patterns is evident. It consists of a central vortex (whose value and sign of its TC depend on the diffraction order m) and four “satellite” vortices situated in the apices of a rotated square (whose signs depend on the diffraction order of the spot m, in which they are nested). An exception is made in the case when the product of the diffraction order and the fork-shaped grating TC is equal to two; Then, the central vortex is absent, but, the four ”satellite” vortices are present. The interference patterns of the diffracted wave field and a slightly inclined plane wave are obtained experimentally and numerically, confirming the presence of the vortices predicted by the theory and registering the value and sign of their TCs.