## 3 Results  
The number of fiber modes in MMFs determines the available degrees of freedom (channels) for transmitting the information. An input image is mapped to the fiber modes basis. Therefore, a MMF with only few modes would not be able to transmit a complex signal. Figure 3 shows how the image of the digit 5 selected from the MNIST database would be reconstructed through MMFs with the same NA that support different total number of spatial modes. It is apparent in Figure 3 that, below a certain number of modes, the features of the images would not be preserved. Therefore, it is important to evaluate the classification performance of the DNN at different wavelengths in the range of the tunable laser to assess its dependence on the number of supported modes in each case. In particular, in order to test the performance of DNNs in the presence of wavelength drift, it is essential that the classification accuracy is firstly determined for the different wavelengths within the drift bandwidth in no-drift conditions. In this way, it can be assumed that any change in the classification performance  
Figure 2: Schematic representation of the deep neural network (DNN) architecture used for the classification of the speckle patterns recorded at the fiber output for different phase inputs. The VGG-type network is trained to receive the image of a speckle pattern intensity and provide a label for the input digit. is attributed to the induced \"noise\" in the dataset caused by the wavelength perturbation and not to the inherent incapability of the system to support the input images because of the low number of supported modes at a certain wavelength. Phase-encoded images of handwritten digits from the MNIST database are projected by the SLM on the GRIN fiber facet, and the corresponding intensity images of the resulted speckle patterns are collected. We collect datasets for different wavelengths covering the range of the tunable laser ranging from 700 to 1000 nm with a 50 nm increment. The classification accuracy of the system is determined by training the VGG DNN for each case [30,31]. The training and test set consist of images captured at a single wavelength, without any drift during recording, for this preliminary assessment. It has been shown in our previous work that with increasing fiber length, slight environmental perturbations can cause severe speckle drifts [16]. For the 10-cm long GRIN fiber used in the experiments, no further instabilities because of mechanical or thermal changes are observed. In Figure 4a, the average classification accuracy obtained at the different wavelengths is presented together with the normalized confusion matrices for the two ends of the wavelength range, namely 700 nm (Figure 4b) and 1000 nm (Figure 4c). No significant change in the classification accuracy is observed for the datasets across the studied range. Hence, we can assume that the total number of spatial modes supported within this wavelength scanning range is sufficient to represent the input information and it does not affect the performance of the VGG classifier. As a next step, we explore the effect of wavelength drift on the DDN performance for different bandwidths of 6, 12, 24, 48, 72 and 96 nm for a central wavelength at 800 nm (Figure 5). We investigate two different cases of drifting noise [30,31]. The same GRIN fiber of 62.5 \(\upmu\)m core and length of 10 cm is used for all the measurements. In the first case, the DNNs are trained with data acquired with the laser wavelength fixed at 800 nm, and then tested on speckle patterns recorded at different wavelengths far from the 800 nm one at which the training set is obtained.