Using the state of a physically constrained machine learning model trained on the output intensity images to reconstruct the eigenmodes of an optical fiber

In this work, the architecture of a machine learning model which is strongly constrained by the physical boundary conditions of the observed optical fibers is presented. The procedure of extraction of the physical relevant information from the trained model is shown. This work aims to estimate the eigenmodes of an optical fiber with the main focus on fibers with few guided modes. We will give an overview of the transit scheme of the expected electromagnetic field properties in a system with low eigenstates by introducing conform ML-Model architecture and corresponding merit (loss) functions for the learning procedure. The introduced ML-Model is proposed as a glass box, where the internal states are equivalent or equivalent up to an isomorphism to the corresponding physical model. The model itself will be presented as a trainable transfer function of a few modes or, in general multimode, optical fiber. The proposed training procedure is equivalent to the approximation of a transfer function of a certain physical system with a limited number of eigenstates, which are finally extractable from the trained model. The presented model contains physically motivated dot-product layers in the complex plane. The gradient-descent-based learning procedure is performed with the Wirtinger derivative technique. The presented estimation technique can be applied in a wide range of tasks, where the eigenstates are unknown or the system is only partially temporal invariant e.g., for analyzing the effect of Transverse Mode Instabilities (TMI) in optical fibers.