Angular momentum of a strongly focused Gaussian beam

A circularly polarized paraxial Gaussian laser beam carries ±¯h angular momentum per photon as spin, with zero orbital angular momentum. Focusing the beam with a rotationally symmetric lens cannot change this angular momentum flux, yet the focused beam must have spin |Sz | < ¯h per photon. The remainder of the original spin is converted to orbital angular momentum, manifesting itself as a longitudinal optical vortex at the focus. We investigate the nature of this orbital angular momentum