## 2 Procedure of Operation
### Generating Arbitrary Light Fields Using a Phase-Only SLM  
Electromagnetic waves are completely described by amplitude and phase information. With the development of SLMs, the spatial modulation of both the phase and amplitude of light became possible by using a gadget. This possibility has had a huge impact on several optical engineering techniques. It opened the door for coping with optical distortions in flow measurements, investigations of nonlinear phenomena in MMFs or neural networks by shaping the light in a proper way, which is called _adaptive wavefront shaping_ (AWS) [15; 16; 17; 18]. Within the presented work, AWS is used for an accurate mode excitation by shaping the MMF input wavefield with an SLM. For an ideal mode excitation, the light field projected onto the input facet should correspond to the numerical field distribution as accurately as possible. However, there are no modulators manufactured that are directly intended to shape light's amplitude and phase at the same time. Several techniques have been published that show how to shape a laser beam in amplitude and phase using either an amplitude-only or a phase-only modulator. In [19], a technique is presented, where neighboring modulator pixels form a superpixel to generate a desired complex pointer. In that work, they use a nematic liquid crystal SLM (NLCSLM) to implement a method to control light's amplitude and phase independently. In most NLCSLMs, the phase modulation occurs as a polarization modulation, too. This makes polarization-dependent communication through an MMF difficult. In [20], an amplitude-only modulator based on digital micromirrors is used to achieve a light field modulation. However, a micromirror-based application requires more pixel than a liquid crystal on Silicon (LCoS) SLM to achieve the same degree of freedom in modulation. In this paper, a superpixel technique comparable to the procedure shown in [21; 22] using a phase-only LCoS SLM is presented. In this work, it is assumed that a desired complex field distribution is given as a complex 2D data map that has to be applied on an incident Gaussian laser beam that illuminates the modulator's surface. In the following section, it is explained how the pixelated 2D data map has to be transferred into a 2D superpixel map that can be displayed at the modulator surface to generate a desired complex wavefront. It is understood that the spatially separated modulation of light of two neighbored SLM pixels is interfering with each other. Depending on the grayscale of the SLM pixels and, hence, the phase shift between the light fractions, the degree of constructive and destructive interference is controlled. Additionally, the resulting phase level is given by the average phase value of the neighbored SLM pixels. Since the SLM plane is imaged on the input fiber facet, one would actually map the individual SLM pixel on the fiber facet. To only map the intensity modulated light, a spatial low-pass filtering is applied [20]. The reflected light is optically Fourier transformed by lens L1. The diffraction orders are spatially separated. Here, the first diffraction order is required and a pinhole (IB) is used to perform low pass filtering (Figure 2). Figure 2: Optical setup for investigation of the superpixel method. This is a sub-setup from the setup shown in Figure 1. For this procedure, BS6 is used to generate a hologram on CMOS1. The notation of a physical plane wave as a single complex pointer and, furthermore, arbitrary wavefronts being represented by a spatial superposition of several complex pointers are fundamental techniques concerning high frequency engineering. Since visible light is a high frequency electromagnetic wave, it can be described as a complex pointer. Complex pointers having an arbitrary phase and amplitude can always be represented by a superposition of two other pointers being different from each other, as seen in Figure 3a.