Accurate mode decomposition with the combination of the matrix analytic and the SPGD algorithm

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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.