Effects of astigmatic aberration in holographic generation of Laguerre-Gaussian beam

The Laguerre-Gaussian (LG) beam is an optical beam with a phase singularity that propagates along its axis. We have previously reported the fabrication of blazed transmission phase holograms to generate beams with phase singularities. A common problem encountered in the generation of a phase singularity with high charge is that the singularity tends to split into m individual charge 1 singularities, where m is the charge of the original singularity. We have found through numerical simulation that astigmatic aberration can cause a higher-charge phase singularity to split. We have also found that strong astigmatic aberrations make the resulting beam close to a Hermite-Gaussian beam rather than an LG beam. Experimental investigation of these phenomena agree with the numerical simulation.