Dynamic spatiotemporal beams that combine two independent and controllable orbital-angular-momenta using multiple optical-frequency-comb lines

Novel forms of beam generation and propagation based on orbital angular momentum (OAM) have recently gained significant interest. In terms of changes in time, OAM can be manifest at a given distance in different forms, including: (1) a Gaussian-like beam dot that revolves around a central axis, and (2) a Laguerre-Gaussian (LGl,p) beam with a helical phasefront rotating around its own beam center. Here we explore the generation of dynamic spatiotemporal beams that combine these two forms of orbital-angular-momenta by coherently adding multiple frequency comb lines. Each line carries a superposition of multiple LGl,p modes such that each line is composed of a different l value and multiple p values. We simulate the generated beams and find that the following can be achieved: (a) mode purity up to 99%, and (b) control of the helical phasefront from 2-6 pi and the revolving speed from 0.2-0.6THz. This approach might be useful for generating spatiotemporal beams with even more sophisticated dynamic properties.