  Spin angular momentum, an elementary dynamical property of classical
electromagnetic fields, plays an important role in spin-orbit and light-matter
interactions, especially in near-field optics. The research on optical spins
has led to the discovery of phenomena such as optical spin-momentum locking and
photonic topological quasiparticles, as well as applications in high-precision
detection and nanometrology. Here, we investigate spin-momentum relations in
paraxial optical systems and show that the optical spin angular momentum
contains transverse and longitudinal spin components simultaneously. The
transverse spin originates from inhomogeneities of field and governed by the
vorticity of the kinetic momentum density, whereas the longitudinal spin
parallel to the local canonical momentum is proportional to the polarization
ellipticity of light. Moreover, the skyrmionlike spin textures arise from the
optical transverse spin can be observed in paraxial beams, and their topologies
are maintained free from the influence of the Gouy phase during propagation.
Interestingly, the optical singularities, including both phase and polarization
singularities, can also affect the spin-momentum properties significantly. Our
findings describe the intrinsic spin-momentum properties in paraxial optical
systems and apply in the analysis of the properties of spin-momentum in optical
focusing, imaging, and scattering systems.
