Statistical learning method for modal analysis of optical fibers

In this work, a novel data driven approach towards modal analysis of multimode fibers is proposed. Key to this approach is a neural network which was trained to approximate the complex optical transfer function of a given fiber. Afterwards, it can be used to reconstruct the fiber modes. Hence, the network is able to provide approximated solutions to the underlying partial differential equations. Training data was generated by simulating the propagation of various synthetic test patterns through the fiber. During network training the inverse transfer function of the system is found. As the model topology mirrors deterministic approaches, the model is fully interpretable. The approximated eigenstates of the system and for this reason, the modes guided by the fiber, can be extracted from the trained network. These obtained fiber modes are compared to the theoretical modes which are obtained by calculation with finite difference method. This reconstruction was shown to be of high quality as a low mean squared error between the magnitudes of the deterministically calculated and the reconstructed modes was achieved. The influence of the used training data was investigated. It could be shown, that the convergence as well as the generalisation properties of the approach depend heavily on the statistical properties of the excitation amplitudes of the eigenstates in the training data.