Abruptly autofocusing beams (AAFBs) exhibit unique focusing properties that, such beams keep a low intensity profile during propagation, and their intensity can be increased by several orders of magnitude when reaching the focus. Most of previous studies concerned about the trajectory and focusing properties of AAFBs. Here, we propose and demonstrate an alternative method for constructing multi-focus abruptly autofocusing beams (MFAAFBs). This is accomplished by designing the AAFBs of each focus and superimposing the corresponding wavefronts in spatial domain. By modulating the complex amplitude of the light field, we can manipulate the beams to propagate along varied pre-designed trajectories and focus on multiple focal points. Additionally, we show that the number of generated foci, and other characteristics of each focal point (such as position in 3D space, peak intensity, size of the focal spot, and the subsequent oscillation) are tunable. We also discuss several possible experimental means to generate MFAAFBs, among which a diffractive optical element (DOE) with discrete amplitude and phase modulations is practical and effective, verified by our simulation results. This method is expected to further expand the application of AAFBs and the field of photonic integration.
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