Propagation property of the abruptly auto-focusing multi-focus beam

The auto-focusing property of the optical beams plays an important role in contemporary optics. In this work, we introduce a method of abruptly auto-focusing multi-focus beam (AAMB) along the optical axis. The simulation results show that the AAMB can flexibly adjust the normalized focusing intensity, focal length, and the number of focus points by controlling different beam parameters. Experimental results show that our proposed method achieved a beam with double equal-intensity focus or three equal-intensity focus during propagation. The AAMB enriches the existing multi-focal beam. In addition, the flexible and controllable focusing properties of the beam may broaden the potential applications.