Three-dimensional analysis of optical forces generated by an active tractor beam using radial polarization

We theoretically study the three-dimensional behavior of nanoparticles in an active optical conveyor. To do this, we solved the Langevin equation when the forces are generated by a focusing system at the near field. Analytical expressions for the optical forces generated by the optical conveyor were obtained by solving the Richards and Wolf vectorial diffraction integrals in an approximated form when a mask of two annular pupils is illuminated by a radially polarized Hermite-Gauss beam. Trajectories, in both the transverse plane and the longitudinal direction, are analyzed showing that the behavior of the optical conveyor can be optimized by conveniently choosing the configuration of the mask of the two annular pupils (inner and outer radius of the two rings) in order to trap and transport all particles at the focal plane. (C) 2014 Optical Society of America