Multi-order Hybrid Vector Mode Decomposition in Few-Mode Fibers with DL-based SPGD Algorithm

Multi-mode fibers (MMFs) guiding a serial of spatial transversal modes with unique intensity and polarization distribution have been widely employed in the emerging MMF imaging enabled by deep learning (DL) and mode division multiplexing (MDM) for scaling up the capability, and super-resolution microscopy. Compared with linearly polarized (LP) scalar modes and Laguerre-Gaussian modes, vector modes (VMs) are true eigenvector modes of a circular-core fiber, which can stably propagate in the MMF. However, how to efficiently and accurately measure the modal proportions of multi-order hybrid vector modes (HVMs) remains rarely investigated. Here we propose a DL-based stochastic parallel gradient descent (SPGD) algorithm to precisely obtain the modal coefficients of the HVMs in the few-mode fibers (FMFs). Four typical convolutional neural network (CNN) models are exploited in the HVMs decomposition and the results present that Xception model can invariably provide excellent accuracy for vector modal prediction, keeping the average modal errors below 1.9% for modal weights and 3.5% for modal relative phases, and the average correlations exceeding 99% for the lowest three-order HVM cases. Moreover, the correlations can be greatly improved to reach over 99.999% based on the DL-based SPGD algorithm. Finally, the hybrid zeroth- and first-order vector mode decomposition (MD) is experimentally implemented based on a mode selective coupler (MSC). Both simulation and experimental results quantitatively demonstrate that the proposed method can definitely acquire superb high-precision modal coefficients for multi-order HVM decomposition, which may open up a new perspective for intelligent MDM and MMF imaging enabled by DL-based algorithms.