Periodic Trajectories Obtained With an Active Tractor Beam Using Azimuthal Polarization: Design of Particle Exchanger

We analytically calculate the forces generated on the near field by a focused azimuthally polarized Hermite-Gauss beam after passing a complex mask formed by two annular pupils. The resultant optical tractor beam shows two transport channels that move trapped objects upstream or downstream along the conveyor. From the analysis of the phase diagrams, we theoretically demonstrate that, depending on illumination inten- sity, the 3-D behavior of nanoparticles in this conveyor shows a limit cycle between trans- port channels. This limit cycle appears as a consequence of diffraction that produces spatially limited optical forces. We theoretically demonstrate the possibility of using the limit cycle to design a particle exchanger between channels.