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 studied the effect of astigmatic aberration on LG beams through numerical simulation and experiment. An LG beam with astigmatic aberration can undergo various transformations. An LG beam with astigmatic aberration can be expanded in terms of Hermite-Gaussian(HG) beams whose horizontal and vertical axes are aligned with the axes of the astigmatism. By redefining the expansion coefficients to include the Gouy phase of the HG beams, the coefficients can be reduced to a single parameter that depends on the propagation distance. It can be shown that the various transformations of the LG beam is governed by this parameter. This presents us with a simple method of estimating the beam profile and positions of the split phase singularities at any given propagation distance. The estimations show good agreement with intensity and phase distributions calculated with the angular spectrum method.