Simultaneous Generation of Multiple Three-Dimensional Tractor Curve Beams

A tractor beam, which has the ability to attract objects, is a class of special optical beams. Currently, people are using the holographic technology to shape complex optical tractor beams for both fundamental research and practical applications. However, most of the work reported is focusing on generating two-dimensional (2D) tractor beams and simple three-dimensional (3D) tractor beams, which has limitations in the further development on mechanism and application of beam shaping. In the present work, we are introducing our study in designing multiple 3D tractor beams with spatial location regulated independently. Meanwhile, each individual beam could be prescribed along arbitrary geometric curve and twisted at arbitrary angles as desired. In our method, the computer-generated hologram (CGH) of each curve is calculated, and all the CGHs are multiplexed and encoded into one phase-only hologram by adding respective linear phase grating such that different 3D curves appeared in the different positions of the focal regions. We experimentally prove that the generation of optical tractor beams at 3D configuration can be readily achieved. The generated beams in the present study are especially useful for applications such as multiple micro-machining optical trapping and complex 3D manipulation.