Accurate mode decomposition in multimode fibers using deep learning with real–imaginary modal weights

Multimode fibers enable high-capacity optical transmission but produce complex speckle patterns due to modal interference, which complicates access to individual modal information. Accurate MD from intensity measurements is therefore essential for practical multimode fiber applications. This work presents a deep learning-based approach that directly predicts complex modal coefficients from speckle intensity patterns, without interferometric setups or iterative reconstruction. To avoid the instability caused by phase periodicity, modal coefficients are represented in real-imaginary form instead of the conventional amplitude-phase representation. Transformer-based architecture is employed to capture global spatial correlations in speckle patterns. Under identical training conditions, the real-imaginary formulation improves the correlation coefficient of reconstructed amplitude distribution by approximately 5% and that of phase distribution by approximately 10%. The proposed method provides modal information relevant for fiber-control tasks and MMF precoding and remains applicable in long and strongly coupled fiber links where modal crosstalk is pronounced.