Figure 1

Phase profiles of (a) the transforming and (b) the phase-correcting optical element. $d$ is the length of the transformed beam. In (b) only that part of the phase-correcting element is shown, that is illuminated by the transformed beam. In the experiment, the phase profiles are displayed on the spatial light modulators (SLMs) with $2\pi$ phase modulation. (c) Schematic overview of the setup. We use SLMs to both generate Laguerre-Gaussian beams (SLM1) and create the desired phase profiles for the transforming and phase-correcting optical elements (SLM2 and SLM3, respectively). L1 is the Fourier-transforming lens and L2 focuses the transformed beams. We use beam splitters to ensure perpendicular incidence on the SLMs.Reuse & Permissions

Figure 2

Modeled and observed phase and intensity profiles at various planes in the optical system. From left to right, the images show the modeled phase and intensity distribution of the input beam just before the transforming optical element and just after the phase-correcting element, and the modeled and observed images in the CCD plane for five different values of $\ell$. The final row shows the results for an equal superposition of $\ell =-1$ and $\ell =2$. The last two columns are $6\times$ magnified with respect to the first two columns.Reuse & Permissions

Figure 3

Total intensities in all detector regions for pure input OAM states from $\ell =-5$ to $\ell =5$, for both the (a)  modeled and (b) observed results. The regions all have the same size and are chosen such that they fill the entire aperture. The intensities are shown as a fraction of the total intensity in the input beam.Reuse & Permissions