The role of modes in nonlinear fiber optical computing

Abstract

We investigate the nonlinear propagation of light in graded-index multimode fiber, utilizing it as an optical computing unit, and quantify how it employs waveguide modes to process information. Using a time-dependent spatiotemporal propagation model with modal decomposition, we evaluate several benchmark regression and classification tasks and study the modal content of the generated speckles, which couples with a simple digital layer to perform optical computing. Analysis of modal entropy and energy-based mode counts reveals that effective computation is confined to a low-dimensional modal subspace, whose identity depends on the task and propagation regime. This also sets a trade-off between modal richness and nonlinear beam self-cleaning. These results establish modal statistics as practical design metrics for fiber-based optical computers.

Figures (4)

• Figure 1: Schematic of the fiber optical computing unit and performance on regression and classification tasks. (a) System architecture. (b) and (c) Sinc regression task before and after optical computing. (d) and (e) BreastMNIST classification task before and after optical computing.
• Figure 2: Modal power fraction matrices for the BreastMNIST task at different propagation regimes. Each panel shows the normalized modal power fractions $p_{m,n}$ on a logarithmic scale for (a) near the input (after a single propagation step, 555 µ m), (b) 5.55 mm with 3 MW peak powers, and (c) a longer propagation distance (2.75 cm) with reduced peak power (600 kW).
• Figure 3: Dataset-dependent modal power fraction matrices. Normalized modal power fractions $p_{m,n}$ on a logarithmic scale for (a) BreastMNIST, (b) Sinc, and (c) small-CIFAR (airplane, cat, and dog classes) after 5.55 mm fiber length with 3 MW peak powers, enabling direct comparison of modal occupancy across tasks.
• Figure 4: Statistics of modal usage. (a) Distributions of modal Shannon entropy across samples and datasets. (b) Distributions of the number of modes required to capture $90\%$ of the total energy, quantifying how many modes are effectively used by the nonlinear optical computer.