Learning the matrix of few-mode fibers for high-fidelity spatial mode transmission

Few-mode fibers (FMFs) are promising for advancements in transmission capacity classical and quantum communications. However, the inherent modal crosstalk limits practical application of FMF. One reliable way to overcome this obstacle is measurement complex matrix (TM), describing light propagation behavior fiber. The TM can be obtained by performing mode decomposition (MD) spatial modes at output MD techniques require retrieval both amplitude phase components detected field, which commonly done using holography. provision a reference wave highly unfavorable implementation holography-based communication technology, especially long fibers. Using deep neural networks process intensity-only images, drawback overcome. We introduce transformer network, perform on 23 has been trained offline synthetic data. Experimentally, we demonstrate, first time, not only an FMF but also inversion learning-based method. For transmission, achieve average fidelity 97%. short duration determination allows overcoming time-varying effects due to, e.g., mechanical stress or temperature fluctuations. proposed reference-less calibration fiber with single photons, such as key distribution.