A novel physics- and data-driven deep-learning (PDDL) method is proposed to execute complete mode decomposition (MD) for few-mode fibers (FMFs). The PDDL scheme underlies using the embedded beam propagation model of FMF to guide the neural network (NN) to learn the essential physical features and eliminate unexpected features that conflict with the physical laws. It can greatly enhance the NN’s robustness, adaptability, and generalization ability in MD. In the case of obtaining the real modal weights (ρ2) and relative phases (θ), the PDDL method is investigated both in theory and experiment. Numerical results show that the PDDL scheme eliminates the generalization defect of traditional DL-based MD and the error fluctuation is alleviated. Compared with the DL-based MD, in the 8-mode case, the errors of ρ2 and θ can be reduced by 12 times and 100 times for beam patterns that differ greatly from the training dataset. Moreover, the PDDL maintains high accuracy even in the 8-mode MD case with a practical maximum noise factor of 0.12. In terms of adaptation, with a large variation of the core radius and NA of the FMF, the error keeps lower than 0.43% and 2.08% for ρ2 and θ, respectively without regenerating new dataset and retraining NN. The experimental configuration is set up and verifies the accuracy of the PDDL-based MD. Results show that the correlation factor of the real and reconstructed beam patterns is higher than 98%. The proposed MD-scheme shows much potential in the application of practical modal coupling characterization and laser beam quality analysis.
The matrix analytic algorithm (MAA) offers excellent abilities in fast mode decomposition (MD) of multimode fibers. However, with the growth of the number of superposition modes, the residual error of the MAA becomes enlarged. In this case, it is not able to realize satisfactory MD due to the trade-off between the number of modes and the decomposition accuracy. In this paper, we propose a new, to the best of our knowledge, MD algorithm by introducing the stochastic parallel gradient descent (SPGD) algorithm to MAA. Specifically, the approximate value of the amplitude and relative phase is first obtained by MAA; then, the approximate value is used to obtain the accurate amplitude and relative phase iteratively through the SPGD method. The MAA-SPGD is helpful in avoiding accuracy degradation as the number of modes increases. With the introduction of SPGD, at the mode number of 50, the average value of the cross-correlation between the original and reconstructed image reduces from 0.25 to 0.02 for the difference from 1. Due to the appropriate initial iteration value from the MAA, the MAA-SPGD eliminates the local optimum, which reveals the stability and reliability features in MD.
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