Convolutional Neural Network Combined With Stochastic Parallel Gradient Descent to Decompose Fiber Modes Based on Far-Field Measurements

Modal decomposition (MD) of fiber modes based on direct far-field measurement combining the convolutional neural network (CNN) with a stochastic parallel gradient descent (SPGD) algorithm is investigated both numerically and experimentally. For obtaining the modal coefficients of fiber modes guided in a large-mode-area fiber, the fiber modes are decomposed into a finite number of Hermite gaussian modes, the initial conditions of the modal coefficients are obtained through the CNN, and further optimization of them are carried out through the SPGD. The ambiguity problem that may happen in the CNN owing to the existence of the pair-beam field is resolved by properly labelling the phase differences with a single-valued parameter set in consideration of the mode-order indices. The feasibility and effectiveness of the proposed MD method is verified both numerical simulations and experimental demonstrations with both recorded image data and online real-time image data. The correlation error incurred by the proposed method is below $6.6 \times {10}^{ - 4}$ and $8.7 \times {10}^{ - 3}$ in the numerical simulations and the experimental demonstrations, respectively. The online real-time operation of the proposed method is also experimentally demonstrated at a decomposing rate of ∼2 Hz.