Comparison of focusing of short pulses in the Debye approximation

We have examined different types of pulses and features of their frequency spectra. Calculations have shown that a significant distinction between the pulses only takes place at a very short pulse duration (shorter than the oscillation period). In this case, the Gaussian pulse becomes nonphysical and one needs to use other types of pulses, for example, the Poisson pulse. We performed comparative modeling of focusing of short pulses by an aplanatic lens for different polarization states and vortex singularity orders in the Debye approximation. We have shown that the polarization state and the presence of vortex phase singularity essentially affect the distribution in the focal area for a subcycle Poisson pulse.