Fourier Feature Networks for High-Fidelity Prediction of Perturbed Optical Fields

Abstract: Modelling the effects of perturbations on optical fields often requires learning highly oscillatory complex-valued functions. Standard multi-layer perceptrons (MLPs) struggle with this task due to an inherent spectral bias, preventing them from fitting high-frequency sinusoids. To overcome this, we incorporate Fourier features - a set of predefined sinusoids dependent on the perturbation - as an additional network input. This reframes the learning problem from approximating a complex function to finding a linear combination of basis functions. We demonstrate this method by training a Fourier Feature Network to predict the transmission matrix of a multimode fibre under mechanical compression. Compared to a standard MLP, our network reduces prediction error in the output field's amplitude and phase by an order of magnitude, achieving a mean complex correlation of 0.995 with the ground truth, despite using 85% fewer parameters. This approach offers a general and robust method for accurately modelling a wide class of oscillatory physical systems.