Spin angular momentum density in the tight focus of a light field with phase and polarization singularities

For a light field with both phase and polarization singularities at its center, expressions are obtained that describe the distribution of the spin angular momentum (SAM) density in the sharp focal spot of an aplanatic system. These expressions include the radial, azimuthal, and longitudinal SAM components. As special cases, focusing of optical vortices with radial, azimuthal, and saddle polarizations is studied. Using a narrow annular as an example, it is shown that in some areas in the focal plane the longitudinal SAM component is zero (resulting in a photonic wheel), while in others it is an order of magnitude less than the transverse component.