Tailored holograms for superimposed vortex states

We present the generation, optimization and full control of superimposed optical vortices (SOVs) using tailored computer generated holograms by utilizing a 2D liquid crystal spatial light modulator. To perform full radial and azimuthal control over the targeted SOVs we apply spatial amplitude modulation via window functions as well as radial and azimuthal phases, encoded in the diffraction mask. In particular we discuss the influence of spatial linear and quadratic radial phases, which is supplemented by an analytical description. The developed formalism further permits the direct shaping in k -space which is highlighted by the radial and azimuthal confinement of SOV states. Our technique enables full real-time control over the spatial structure, the symmetry and azimuthal orientation of the generated SOVs in a common path geometry, which is useful in the context of optical information transfer. We also study the topological properties, i.e. the orbital current S ⃗ O to determine the topological charge ℓ of the generated SOVs.