Subject of study. Laser vector vortex beams and their tight focusing are investigated, specifically the spin–orbit transformation effect at the focus. Aim of study. The aim is to theoretically analyze and numerically simulate the features of the spin–orbit effect that arise during tight focusing of optical vortices with circular polarization. Method. Theoretical and numerical investigations were performed using the Debye-integral-based Richards–Wolf method. Main results. The transverse and longitudinal components of the Poynting vector (energy flow), spin angular momentum (SAM), and orbital angular momentum (OAM), averaged over the beam cross-section in the focal plane, were calculated. Practical significance. For the first time, this study shows that, contrary to common assumptions, during the spin–orbit transformation, a portion of the longitudinal SAM does not transform into longitudinal OAM. The total SAM is conserved during focusing and only redistributed—a part of the longitudinal component is converted into a transverse (azimuthal) component. The generation of OAM at the focus is attributed to a circularly polarized beam producing two optical vortices at the focus—a transverse vortex with a topological charge of 2 and a longitudinal vortex with a charge of 1. These vortices generate azimuthal energy flow in the focal plane.
Kotlyar et al. (2025) studied this question.