Helical tractor beam: analytical solution of Rayleigh particle dynamics.

We analyze particle dynamics in an optical force field generated by helical tractor beams obtained by the interference of a cylindrical beam with a topological charge and a co-propagating temporally de-phased plane wave. We show that, for standard experimental conditions, it is possible to obtain analytical solutions for the trajectories of particles in such force field by using of some approximations. These solutions show that, in contrast to other tractor beams described before, the intensity becomes a key parameter for the control of particle trajectories. Therefore, by tuning the intensity value the particle can describe helical trajectories upstream and downstream, a circular trajectory in a fixed plane, or a linear displacement in the propagation direction. The approximated analytical solutions show good agreement to the corresponding numerical solutions of the exact dynamical differential equations.