Programmable spatiotemporal OAM optical toroidal beams with completely tunable properties

Spatiotemporal toroidal orbital angular momentum (OAM) beams are a developing class of spatiotemporal beams which have key applications within quantum physics, metrology, imaging and optical manipulation. However, the full realization of these applications require complete configurability within tunable temporal duration, 3D geometric structure and OAM charge of these beams along with amplitude, phase and polarization control. In this paper, we demonstrate complete configurability of programmable, polarization-resolved OAM toroidal beams after propagation through a multimode optical fiber (MMF) supporting 90 spatial/polarization modes. We show high fidelity control: temporally with beams spanning 2.3 ps - 6.8 ps, geometrically with toroidal aspect ratios spanning 1.5-2.7 and with up to $|l|=13$ OAM topological charge. In total this system supports 25,000 spatiotemporal and polarization degrees of freedom which enables the independent control of all physical and geometric properties of these 3D toroidal beams. By utilizing an MMF, this system also enables toroidal beam delivery to previously inaccessible regions, paving the way for applications including optical manipulations, sensing and imaging through complex photonics media such as scattering biological tissues.