Optical vortex generated with an asymmetric forked grating

Over 30 years ago a simple laboratory tool for optical-vortex beams generation was reported as a synthesized 'forked' diffraction grating. We renew the issue, addressing specific properties of such a grating in the sense of geometrical transformation of the grating shape. Stretching or compressing the grating scale results in the astigmatic optical vortex appearance in the first diffraction order. In the case of the induced vortex topological charge higher than unity, the astigmatism forces the optical vortex to separate into a line of unity-charged vortices. The initial splitting occurs along an azimuth angle, depending on the topological charge of the vortex. We show the rotation of the pattern in the free space propagation in simulations and analytical consideration.