Space-time couplings in ultrashort lasers with arbitrary nonparaxial focusing

Space-time separability is commonly assumed in the theoretical description of laser beams. However, recent progresses have demonstrated that this assumption often breaks down for ultrashort realistic pulses, giving rise to spatio-temporal effects that modify both the spatial and temporal characteristics of the laser field. In this work, we introduce semi-analytical and numerical diffraction integral models to investigate these spatio-temporal effects in tightly focused configurations. In particular, we investigate how the TM₀₁ beam mode is modified at the focus by chromatic angular dispersion, curvature, and spatial chirp. We compare the two formalisms, thus creating a toolset for modeling extreme localization of structured electromagnetic beams in time and space.