Determination of an optical vortex topological charge using an astigmatic transform

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 null, then at the double focal distance behind the lens, the $n$-fold degenerate intensity null is split into n isolated intensity nulls. These intensity nulls 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 $n = 100$.