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

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 M(2 )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 M-2. To this extent, we derive the beam radius that separates the region where the M(2 )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.