High-Precision Mode Decomposition for Few-Mode Fibers Based on Multi-Task Deep Learning

A novel mode decomposition (MD) method based on multi-task learning (MTL) is proposed to obtain high-precision modal weights (<italic>ρ<sub>n</sub><sup>2</sup></italic>) and modal relative phases (<italic>θ<sub>n</sub></italic>). Due to the different physical implications between <italic>ρ<sub>n</sub><sup>2</sup></italic> and <italic>θ<sub>n</sub></italic>, we design a multi-output convolutional neural network (CNN) with specialized branched structures for MTL-based MD. A few-mode fiber with complex multi-step refractive index (RI) profile is selected to verify the superiority of the proposed scheme in complex mode coupling analysis. In simulation, compared with the traditional method based on single-task learning (STL), the MTL-based scheme can reduce the modal weights error tenfold and keep the modal relative phases error below 1.6%, while maintaining fast MD processing. Due to the strong learning ability, the precision shows much stability with an increasing mode number. In addition, regardless of a diminishing beam profile image resolution, the MTL-based MD still performs effectively. In experiment, the results obtained by using real beam profile images also demonstrate the effectiveness of the MTL-based scheme in practice.