Fig. 1. Optical MPLC setup considered in our work. Two spatially seperated Gaussian input spots are incident to the SLM. After two reflection passages between SLM and mirror (M), the output beams are imaged by a 4f-telescope onto a camera where intensity images are recorded. Both the FMFs facet and the camera are at a distance d ≈ 1.5 cm from the SLM. A smart calibration based on artificial intelligence (AI) is implemented to generate proper SLM phase masks in order to shape desired output modes.

Fig. 2. Structure of the envisioned NN architecture. (a) Training of a single-layer Model-NN. Training data consists of 2k uniformly distributed random SLM phase masks and the corresponding intensity images measured at the MPLC output. This generates a digital twin of the MPLC setup. (b) Another single-layer called Actor-NN is trained on 2k intensity images according to the EMNIST data set. The Actor-NN is used to predict phase masks, which are the input for the Model-NN. When training the Actor-NN, the Model-NN is fixed. (c) The predicted phase mask of the trained Actor-NN is applied to the SLM and the intensity is measured. We achieve a correlation of Γ = 0.65 compared to the Model-NNs predicted intensity.

Fig. 3. Structure of the NN, images are consisting of 8bit images with values from 0 to 1. The resolution is 32 × 32 and 150 × 150 for phase masks and intensity images, respectively.

Fig. 4. Training progress of both Model-NN and Actor-NN. Experimental data (i.e. SLM phase masks and intensity camera images) is used for the Model-NN, while EMNIST data base is used for the Actor-NN. We used 2k data each, where 1600 samples are used for training and 400 for test, respectively. Both NNs comprise of a single-layer structure with sigmoid activation function. MSE is used as loss function with adam optimizer, wheres fidelity is used as performance indicator. Convergence is observed in all scenarios that are training (solid) and test data (dashed) for Model-NN (red) and Actor-NN (blue), respectively.

Fig. 5. Example of dual-input beam configuration. Simulation data is shown. (a) and (b) show heatmaps of 1k images using 1k different random SLM phase masks. (c) overlap between (a) and (b).

Fig. 6. Results from the Actor-Model approach. All samples shown are images from the EMNIST data set. Left column: Ground truth images used as Actor-NN input. Middle left: phase mask predictions resulting from the Actor-NN. Middle right: predictions from the Model-NN after the Actor-NN was trained. The correlation between Model-NN prediction and ground truth is Γ ≈ 0.7. Right: experimental results. Using the trained Actor-NN, SLM phase masks are generated that are employed for driving the MPLC. The images shown are camera recordings capturing the MPLC output. Note, that a single-beam and single-passage configuration is considered. The correlation between experiment and Model-NN prediction is Γ ≈ 0.65.