An intuitive view of the origin of orbital angular momentum in optical vortices

A modulated laser beam by a phase pattern exp(ilθ) can be focused by an objective into a ring-like optical vortex, where l is a constant and θ is the azimuth angle. The vortex is capable of trapping the particles nearby and circulating them along the ring. This phenomenon is often explained involving Fourier optics and the transfer of orbital angular momentum (OAM). Although Fourier optics transforms the electric field distribution of the modulated laser beam behind the phase pattern to that of the vortex, it does not include both the path and OAM of the photons of the electromagnetic wave. Therefore, it is difficult to further trace the transfer of OAM from the photons to the particles in the vortex. In this paper, we propose a simple and intuitive view to the origin of optical vortex. By analyzing the relationship of the intensity distributions between the phase of the phase pattern and the intensity of the vortex by utilizing Fourier transform, we propose that the phenomenon of vortex also involve the transfer of linear momentum on the vortex plane transversely.