Creating optical vortex modes with a single cylinder lens

Optical vortex (Laguerre-Gauss) modes can be created by introducing a π/2 phase shift between orthogonal components of Hermite-Gauss (HG) modes. The well-known astigmatic mode converter design described by M.W. Beijersbergen et al. [Optics Communications 96 pgs. 123 132, 1993] achieves this condition by manipulating the differing Gouy phases along orthogonal axes between a matched pair of cylinder lenses. Apparently not well known is that quite useful mode conversions can easily be achieved with a single cylinder lens. We explain the operating principle of such a single lens mode converter, and describe and illustrate how to match the input HG mode to the required Rayleigh range z_Η = f_cyl with one additional spherical lens. Setting up and optimizing such a simplified mode converter is an excellent exercise for undergraduate students, and the resulting optical vortex beams can be used for a variety of instructional experiments.