Focusing properties and deep learning-based efficient tuning of symmetric butterfly beams

In this Letter, we report what we believe to be a new type of abruptly autofocusing beams, termed symmetric butterfly Gaussian beams (SBGBs). The proposed beams appear to have a high degree of tunability for their focal position, focal length, focal intensity, and propagation trajectory. In addition, we propose a deep learning-based model for quick and accurate predictions of the propagation properties of SBGBs, achieving an average relative error of no more than 2.1% and being 8000 times faster than that of split-Fourier transform algorithms. This work may open a new platform for optical manipulation, optical communication, and biomedical applications.