Generation of optical vortices by converting elegant hermite gaussian beams

We have derived that an optical vortex of charge l can be generated in an arbitrary position over the transverse cross section of the light beam by converting a tailored elegant Hermite Gaussian beam of order l [J. Opt. Soc. Am. 63 (1973) 1093] using an astigmatic mode converter. We have indeed generated a quasi-elegant Hemite Gaussian beam of order 1 by superposing two Gaussian beams copropagating with a spatial separation, and converted it into a vortex beam. The vortex moves by varying the relative amplitude and phase of the Gaussian beams, which agrees well with the theoretical predictions.