Radiation forces on Rayleigh particles using a focused anomalous vortex beam under paraxial approximation

The radiation forces of focused anomalous vortex beams acting upon a Rayleigh dielectric sphere are studied theoretically and numerically, based on the Rayleigh scattering theory, within the framework of paraxial approximation. It is shown that a focused anomalous vortex beam with a suitable mode order and topological charge can be used to trap and manipulate a dielectric sphere whose refractive index is smaller or bigger than the ambient one at the focal point. The influences of the topological charges and the beam orders on the radiation force are also discussed. Furthermore, the stability conditions for effective trapping the Rayleigh particles are analyzed.