PERSPECTIVES
Computing with Fiber-Optics solitons
learning machines( ELMs) have emerged as particularly well suited to implementation in optical systems due to their simplicity. In contrast to deep neural networks, ELMs avoid iterative training of hidden layers: the input weights are fixed by the physics of the medium, while only the output weights are optimized in a linear step. This approach maps naturally onto nonlinear fiber propagation, where data encoded on ultrashort pulses evolves under the nonlinear Schrödinger equation, producing a complex and high-dimensional representation of the input in a single pass. Essentially, the fiber acts as a physical“ kernel generator,” projecting input data into a rich feature space that can then be linearly processed for learning or classification tasks.
Soliton dynamics provide particularly powerful routes for this kind of dimensionality expansion. Indeed, processes such as soliton fission, dispersive wave generation, and Ramaninduced frequency shifts diversify the temporal and spectral content of the light field in a highly nonlinear yet deterministic manner. These mechanisms effectively create a broad set of nonlinear kernels, where the resulting spectral( and temporal) patterns are both high dimensional and sensitive to the encoded input. Such features directly correspond with the requirements of machine learning, providing natural bases for classification, regression, and other data-driven tasks. In this way, soliton-induced dynamics transform optical fibers into functional learning machines, bridging nonlinear wave physics with modern computational standards.
IMPLEMENTATION Recent advances by several groups have provided both experimental and numerical evidence that soliton dynamics can serve as the basis for optical machine learning. In our own recent experimental study [ 2 ], highly nonlinear fibers were
Figure 1. Concept of soliton-based optical computing. Input data encoded onto ultrashort pulses propagates through a nonlinear fiber where soliton dynamics expand the dimensionality of the signal. The resulting high-dimensional spectral features are processed by a linear readout enabling machine learning tasks such as digit classification.
used to implement an extreme learning machine, where input data encoded onto the spectral phase of femtosecond pulses was transformed through nonlinear propagation( see Figure 1 for a concept illustration). Task-independent analysis based on principal component analysis( PCA) showed that the effective computational dimensionality depends strongly on fiber length, dispersion regime, and input power, with up to 100 independent components generated under optimal conditions. These intrinsic metrics highlight how nonlinear propagation enriches the feature space, even though maximal spectral broadening does not necessarily correspond to maximal dimensionality. Task-dependent evaluation, using the MNIST digit recognition benchmark, confirmed that performance is optimum at intermediate power levels where dimensionality expansion is balanced by output consistency. The MNIST database is a widely used machine learning dataset consisting of 70,000 images of handwritten digits 0 – 9. Using this task, the system achieved a classification accuracy of 88 % exceeding the linear baseline 82 % when encoding 40 PCA and demonstrating that reliable computational features emerge before the onset of nonlinear instabilities.
Complementary numerical simulations [ 3 ], based on the generalized nonlinear Schrödinger equation, provided further insight. A realistic numerical model of a fiber-ELM reproduced classification accuracies exceeding 90 % and showed how parameters such as dispersion profile, encoding strategy, and readout bandwidth shape performance. The simulations also studied the role of intrinsic noise, with anomalous-dispersion soliton fission suffering more from noise penalties, while normal-dispersion operation proved more robust.
Similar conclusions were reached in other recent demonstrations of neuromorphic computing based on soliton dynamics [ 4 ] where the coherent cascade of nonlinear dynamics enabled digital operations such as XOR, efficient classification of benchmark datasets, and even real-world tasks such as COVID-19 diagnosis in a compact fiber platform. More broadly, supercontinuum generation has been benchmarked as an analog computing element [ 5 ] with detailed parameter scans showing that the rich spectral diversity of the continuum acts as a universal function approximator and improves neural tasks such as autoencoding. The concept of nonlinear inference capacity was also recently introduced in fiber-optical extreme learning machines [ 6 ], showing that increasing optical nonlinearity can scale the computational depth to a level that can compete with deep neural networks.
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