Astigmatic transformation of a set of edge dislocations embedded in a Gaussian beam

It is theoretically shown how a Gaussian beam with a finite number of parallel lines of intensity s (edge dislocations) is transformed using a cylindrical lens into a vortex beam that carries orbital angular momentum (OAM) and has a topological charge (TC). In the initial plane, this beam already carries OAM, but does not have TC, which appears as the beam propagates further in free space. Using an example of two parallel lines of intensity s symmetrically located relative to the origin, we show the dynamics of the formation of two intensity s at the double focal length: as the distance between the vertical lines of intensity s is being increased, two optical vortices are first formed on the horizontal axis, before converging to the origin and then diverging on the vertical axis. At any distance between the zero-intensity lines, the optical vortex has the topological charge TC = -2, which conserves at any on-axis distance, except the initial plane. When the distance between the zero-intensity lines changes, the OAM that the beam carries also changes. It can be negative, positive, and at a certain distance between the lines of intensity s OAM can be equal to zero. It is also shown that for an unlimited number of zero-intensity lines, a beam with finite OAM and an infinite TC is formed.