Problem

The increasing energy demands of artificial intelligence motivate the development of energy-efficient computing paradigms, with optical computing emerging as a promising solution due to light's parallelism and speed. However, implementing essential nonlinear activation functions at low optical power levels remains a significant challenge, as optical systems are typically governed by linear wave physics. While Spiking Neural Networks (SNNs) offer an energy-efficient neuromorphic approach, their translation into the optical domain, particularly for robust spike generation or thresholding, presents a key hurdle. Current optical SNN implementations often rely on complex device-level excitability or specific materials.

Method

This work proposes an optical spiking neural network that employs free-space diffraction for synaptic integration and programmable rogue-wave (caustic) events for spike generation. The core idea is to establish a mathematical equivalence (homomorphism) between the spatial integration occurring during optical diffraction and the temporal integration in biological neuron models, specifically the Spike Response Model. Input data is encoded into the amplitude of a coherent light field, while synaptic weights are implemented as a phase mask controlled by a Spatial Light Modulator (SLM). The firing mechanism is based on a rogue-wave statistical criterion, where a spike is generated if the local optical intensity exceeds twice the significant wave intensity (the average of the top one-third of the speckle distribution). To enable training, a differentiable digital twin model, utilizing the Angular Spectrum Method, was developed. This allowed for end-to-end co-optimization of the optical phase mask and a lightweight electronic readout layer. A soft sigmoid function approximated the discontinuous rogue wave threshold for gradient-based training, using an Adam optimizer and Cross-Entropy Loss.

Results

Numerical simulations confirmed that the system could reliably generate rogue waves even with deterministic input data, ensuring the viability of the thresholding mechanism. Experimental validation on the BreastMNIST dataset for binary classification yielded an accuracy of 82.45%, demonstrating performance competitive with established digital models like ResNet-18, ResNet-50, and LeNet-5, and proving the system's robustness against experimental noise. Furthermore, the model achieved 95.00% accuracy on the more complex multi-class Olivetti Faces dataset. These results highlight that the optical front-end efficiently performs high-dimensional feature extraction and nonlinear thresholding passively, requiring only a simple electronic readout. Crucially, the experimental outcomes showed strong agreement with the numerical predictions.

Implications

This research demonstrates that extreme-event physics, such as optical rogue waves, can be effectively utilized as a fundamental computational primitive. It offers a novel approach to achieving nonlinear activation in optical computing without the need for device-level excitability, providing a valuable complement to existing photonic SNN implementations. The established principles are not confined to free-space optics and could be extended to temporal domains using optical fibers or integrated photonic circuits, potentially leading to the development of ultrafast neuromorphic processors. By leveraging the inherent complexity of natural phenomena, this work paves the way for a new generation of "physically enhanced" computing architectures that derive computational advantages from physics itself.