Learning highly oscillatory optical fields with Fourier feature networks

Accurately modelling physical perturbations in optical systems is critical for photonic device design, yet existing characterization methods are often computationally prohibitive. We introduce a data-efficient machine learning framework that learns the perturbation-dependent transmission matrix of a multimode fiber. To circumvent the spectral bias that prevents standard neural networks from resolving high-frequency phase changes, we explicitly encode perturbations into a Fourier Feature basis. This approach enables a compact multi-layer perceptron to learn the mapping from sparse training data with high fidelity. Using experimental data from a mechanically deformed fiber, our model achieves a 0.996 complex correlation with the ground truth, improving phase accuracy by an order of magnitude over standard networks while using significantly fewer parameters. This framework transforms the transmission matrix into a continuous, differentiable "digital twin" of the system, providing a robust tool for characterizing complex media in rapidly evolving environments.