Efficient prediction for arbitrary trajectories of butterfly vortex beams using a deep neural network.

Longitudinal particle manipulation by beams relies on the guidance of particle motion through propagation trajectory design. However, a single trajectory cannot satisfy the requirements for longitudinal particle manipulation in different directions, and the offset position of the light spot at different propagation distances is difficult to predict accurately using numerical methods. In this Letter, we propose butterfly vortex beams (BVBs) with arbitrary trajectories. Experimental results demonstrate that the BVBs exhibit adjustable propagation trajectories and the ability to guide particles. Furthermore, a deep learning-based model is proposed to accurately predict the position of the light spot. The model achieves a mean square error approaching 0.01. Our work may advance the application of deep learning in particle manipulation and biomedicine.