## 2 Procedure of Operation
### Specific Alignment Techniques  
In this section, a step-by-step instruction that describes how one can image the SLM plane to the input MMF facet plane properly, considering that the planes are aligned in parallel, is presented. The introduced alignment procedure was inspired by the work from [25]. 1. Spatial filtering of the modulated light field In Section 2.1, it is explained that the derived superpixel distribution needs to be superimposed with a diffraction grating to filter the modulated signal that is located in the 1 st diffraction order secluded from the center of the Fourier plane. It is necessary that the filtered signal (first diffraction order) is located on the optical axis to avoid unwanted optical aberrations, which can be achieved by tilting the SLM plane. After conduction, the passed light from IB in Figure 2 propagates through the center of L2. 2. Guiding the laser beam through microscope objective 1 (MO1) The utilized subsetup for aligning the laser beam through MO1 is shown in Figure 6. After the IFFT executed by L2, the beam is guided along a desired hole line on the optical bench using two mirrors M3 and M4 and two pinholes (HIB1 and HIB2). Now, L3 can be positioned in the beam path, which should not disturb the beam direction. Finally, the microscope objective can be positioned. In general, microscope objectives magnify small alignment deviations and therefore it is advisable to mount MO1 on a stage with \(\upmu\)m precision. Eventually, the beam should propagate through HIB1 and HIB2 after every component was set in the path. Furthermore, it is mandatory for a proper mode excitation, that the IFFT with L2 and the telescope involving L3 and MO1 is performing correctly. This depends on the correct distances between the optical components and can be verified by modulating an image with the SLM. In this case, an axicon was used as a target test field. After propagation through the setup, the image behind MO1 can be monitored with a screen. On the screen, the phase boundaries should completely disappear. Figure 5: Investigation of superpixel influences on spatial frequencies and resulting fidelity. (**a**) Scheme to illustrate the dependency between spatial frequency movement and superpixel size. (**b**) Measured fidelity of generating a \(LP_{02}\) mode by varying superpixel size. Parallel imaging of the SLM plane to MO1 For a proper mode excitation, the SLM plane has to be imaged onto to the input fiber facet. Deviating incident angles could lead to inappropriate mode excitation and should be neglected. Therefore, a non-invasive method to verify a parallel imaging of the mentioned planes was developed. The utilized sub-setup is shown in Figure 7a. The beam propagating through MO1 is split into a second path by BS2, propagates through L4 and is reflected by an auxiliary mirror M5, so that the reflected light is imaged on CMOS1 by another telescope involving L4 and L5. At first, the correct distances between the optical components should be ensured to provide a sharp image of the SLM plane on CMOS1. This was verified by modulating an axicon with the SLM once more. The captured intensity image of the axicon under proper conditions is shown in Figure 7b, where the boundary lines are of minimum thickness. Afterwards, by displaying the sheer diffraction grating on the SLM, the pure modulator plane is imaged on CMOS1 (see Figure 7c). Now, a retro reflector without beam displacement has to be placed in front of MO1 as shown in Figure 7a. Perpendicular alignment of the optical components causes concentric interference rings on CMOS1, as shown in Figure 7d. 4 Alignment of the MMF With the use of the auxiliary sub-setup introduced in step 3, the MMF can be aligned and a parallel imaging of the SLM plane to the input fiber facet plane is ensured. In the first instance, the MMF has to be set in its place of destination, as shown in Figure 8a. In the next step, light has to be coupled into the fiber at the actual output by using the reference beam. For the alignment, M2, BS5 and M6 can be tilted as desired.