Creation of a controllable three dimensional optical chain by TEM01 mode radially polarized Laguerre–Gaussian beam

Three dimensional (3D) multi sites optical trapping requires multi focal spots in the focal region, which is not easy to achieve. In this paper, we present a novel design to create a controllable 3D optical chain that can stably trap and deliver particles purposely. On the basis of the vector diffraction theory, the complex pupil filters (CPF) is successfully designed to modulate the phase of TEM01 mode radially polarized Laguerre–Gaussian beams. With the optimized parameters of CPF, the 3D optical chains with two and five focal spots are created, respectively. Also, the 3D optical chain with five focal spots is periodical and moves forward (i.e., the direction far away the aplanatic system) with the increasing of the phase ψ of the outer zone of CPF. Moreover, the movement of the 3D optical chain can be well controlled by changing ψ purposely, which makes particle manipulation more controllable and flexible. This work is important for micromanipulation, micromachines, and microscopy.