Laguerre-Gaussian (LGmn) modes have several unique properties that lend them to applications in materials processing [1] and particle manipulation [2], among others. One characteristic that lends these modes to such applications is their ability to carry orbital angular momentum (OAM), as opposed to the spin angular momentum of beams that are circularly polarised. There are several techniques for creating these; one popular one exploits the Gouy phase shift through the use of cylindrical lenses [3]. The Gouy phase shift causes a phase shift in a Gaussian beam as it passes through a focus and is dependent on the Rayleigh range of the beam. Using cylindrical lenses to create an astigmatic focal point you can create a relative phase shift between the sagittal and tangential planes of the beam. As a LG 01 can be modelled as two orthogonal first order Hermite-Gaussian (HG 01 ) modes, π out of phase with each other, you can exploit this to convert between the two modes. Furthermore, depending on whether the HG 01 mode is at +45° or −45° to the astigmatic axis it will create an LG 01 mode with either clockwise or anticlockwise orbital angular momentum.
