Numerical mode decomposition for multimode fiber: From multi-variable optimization to deep learning

Multimode fibers are gaining a resurgence of interest in both fundamental and applied research in recent years. Thanks to the ability to see the weights and relative phase of the multimode fiber modes, mode decomposition (MD) has shown tremendous potential in wide applications of mode properties evaluation, mode-related processes measurement and fiber laser beams characterization. Among various MD techniques, numerical methods stand out for their simplicity and low hardware requirements. In this paper, the new horizon opened by the recently developed new numerical MD schemes will be reviewed. First, the background and basic principles of MD will be introduced, and some typical numerical MD methods will be summarized. Second, the multi-variable optimization approaches, including the stochastic parallel gradient descent (SPGD) scheme and genetic algorithm (GA) assisted GA-SPGD strategy, will be presented in details. Third, a novel numerical MD method based on deep learning technique will be discussed, which solves the initial values sensitivity and relatively long-time cost of multi-variable optimization approaches. Last, several novel applications will be given, indicating the versatile applicability of numerical MD.