Mode decomposition (MD) is essential to reveal the intrinsic mode properties of multimode fibers (MMFs). Real-time MD provides a powerful tool to analyze the dynamics in MMFs. In this paper, we demonstrated that real-time MD can be achieved with the help of deep learning technique. We use large amounts of simulated beam intensity profiles of MMFs to train a convolutional neural network (CNN) and then evaluated this trained CNN on both simulation and experimental data. When testing on the simulated beam profiles, the averaged correlation between the reconstructed patterns and measured patterns is above 0.9842 and the decomposing rate can reach about 200 Hz. While for the experimental case, the averaged correlation is above 0.8896 and the decomposing rate for modal weights is 29.9 Hz, which is restricted by the maximum frame rate of the CCD camera. The results of both simulation and experiment show the superb real-time ability of the deep learning-based MD methods.

Mode decomposition (MD), detecting the mode content of a laser beam, is an important technique that has wide applications in research and industry areas. This paper demonstrated a novel non-iterative mode decomposition method, called deep mode decomposition (DeepMD), which relies on a deep neural network with unsupervised learning for the first time. A trained network can directly compute the accurate modal coefficients of the eigenmodes propagating in the fibers, including the modal weights and relative phases with only one near-field intensity image. Regardless of the number of modes, the decomposing rate is similar in simulations, around 571.4 Hz, benefiting real-time applications. The quantitative results of both simulation and real-time experiments show the superiority of our method.

This study introduced a differential polarization division multiplexing (DPDM) scheme for all-fiber high-accuracy spectral measurement. Launching two orthogonal linearly polarized light beams into multimode fibers, the DPDM elegantly reconstructs the input spectra from the differential speckle, which is more comprehensive spectral-to-spatial encoding with fewer noises and better contrast. A spectral measurement with 2 pm resolution and 2000 channels was achieved. Compared with traditional transmission matrix and polarization division multiplexing schemes, the proposed DPDM approach reduced the spectral reconstruction error by 77% and 69%, respectively, offering a simple and effective solution for highly accurate spectral measurements.

The speckle field yielded by disordered media is extensively employed for spectral measurements. Existing speckle reconstructive spectrometers (RSs) implemented by neural networks primarily rely on supervised learning, which necessitates large-scale spectra-speckle pairs. However, beyond system stability requirements for prolonged data collection, generating diverse spectra with high resolution and finely labeling them is particularly difficult. A lack of variety in datasets hinders the generalization of neural networks to new spectrum types. Here we avoid this limitation by introducing PhyspeNet, an untrained spectrum reconstruction framework combining a convolutional neural network (CNN) with a physical model of a chaotic optical cavity. Without pre-training and prior knowledge about the spectrum under test, PhyspeNet requires only a single captured speckle for various multi-wavelength reconstruction tasks. Experimentally, we demonstrate a lens-free, snapshot RS system by leveraging the one-to-many mapping between spatial and spectrum domains in a random medium. Dual-wavelength peaks separated by 2 pm can be distinguished, and a maximum working bandwidth of 40 nm is achieved with high measurement accuracy. This approach establishes a new paradigm for neural network-based RS systems, entirely eliminating reliance on datasets while ensuring that computational results exhibit a high degree of generalizability and physical explainability.