Beam quality factor of aberrated Laguerre-Gaussian optical beams

The influence of aberrations on the beam quality factor of Laguerre-Gaussian beams is investigated. We derive analytical expressions for the beam quality factor due to astigmatism and spherical aberration. We show that the width of a Laguerre-Gaussian beam is a significant parameter that determines the aberration effects on the beam quality factor. For each aberration, we derive an expression for the width that separates the region where the beam quality factor changes infinitesimally and where it changes drastically. The validity of the analytical expressions is assessed by performing numerical simulations. There is excellent agreement between the analytical and numerical results.