A diffractive spiral axicon can be used for the generation of a vortex beam with orbital angular momentum. The coaxial superposition of multiple vortices can generate a complex field with off-axis optical vortices. These fields are known as optical vortex lattices. In general, this superposition is done by the use of spatial light modulators. Discretization of the continuous spiral in radial and azimuthal direction introduces additional degrees of freedom and thus, more complex fields are

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... ted. Methods and Results: Here, we discuss the basic theory for discretized spiral axicons. Then, as an example, we consider a discretized multi-pronged element where radial and azimuthal coordinates are discretized. Simulations of the near-field distribution show the occurrence of additional off-axis vortices with anisotropic character. The number of off-axis vortices depends on the number of discretization steps in azimuthal direction. Theory is confirmed by experiments. The diffractive element used in the experiments was fabricated lithographically. For instance, a Shack-Hartmann sensor was used to measure orbital momentum of on-and off-axis vortices. Conclusion: Optical vortex fields can be achieved due to the discretization of the continuous spiral axicon. The resulting field distribution can be seen as superposition of different non-diffracting fundamental vortex modes.