Investigating the degree of paraxiality in light–atom quadrupole interactions

We examine the applicability and limitations of several established measures of paraxiality in the context of electric quadrupole interactions between light and trapped atoms. Focusing on Laguerre–Gaussian beams, we compare analytical predictions—particularly transition amplitudes and selection rules—derived under the paraxial assumption with full numerical solutions obtained via diffraction integrals that account for the complete vectorial field structure. This comparison allows us to assess the validity and relevance of these measures across a range of beam parameters. We also investigate the role of the power-series expansion in the paraxial parameter in bridging paraxial and nonparaxial regimes.