Determination of an optical vortex topological charge using an astigmatic transform

It It is shown both theoretically and experimentally that if a cylindrical lens is placed into a laser beam, having an optical vortex with integer topological charge n and on-axis intensity , then at the double focal distance behind the lens, the n -fold degenerate intensity is split into n isolated intensity s. These intensity s lie on a straight line in the transverse plane at an angle of + 45 or - 45 degrees to the axis of the cylindrical lens, depending on the vortex helicity direction (i.e. sign of the topological charge). Experiments show that such a method can be used to determine higher-order topological charges up to n = 100.