Generation of structured light by multilevel orbital angular momentum holograms

Structured light has been created by a myriad of near-and far-field techniques and has found both classical and quantum applications. In the case of orbital angular momentum (OAM), continuous spiral phase patterns in dynamic or geometric phase are often employed with the phase patterns existing across the entire transverse plane. Here, we exploit the uncertain relationship between OAM and angle in order to create structured OAM fields by using multilevel OAM holograms. We show theoretically and experimentally that only a multilevel angular phase contour in the near-field is needed to create structured OAM light in the far-field, exploiting the reciprocal nature of angular momentum and angle. We use this approach to demonstrate exotic 3D structured light control to show the Poynting vector's evolution in such fields and to highlight the physics underlying this phenomenon.