Analytical analysis of the beam propagation factor of elegant Hermite-Gaussian and elegant Laguerre-Gaussian beams with astigmatism

Abstract

The impact of astigmatism on the beam propagation factor (M2) of elegant Hermite–Gaussian and elegant Laguerre–Gaussian beams is examined. We derive closed-form expressions for M2 when the optical beams are aberrated with astigmatism. The analysis shows that the beam radius is crucial to the degree of impact astigmatism has on M2. To this extent, we derive the beam radius that separates the region where the M2 is negligibly affected and the region where it becomes severely affected. For the elegant Laguerre-Gaussian beams, we establish a parameter that determines a set of beams that are impacted equally by astigmatism. The analytical results are validated with numerical simulations.