Volumetric Optical Scattering Neural Networks

Optical neural networks offer a route to low-latency and energy-efficient inference by encoding computation in light propagation. However, most existing implementations rely on planar photonic circuits or discretely spaced diffractive layers, restricting volumetric integration and imposing stringent alignment requirements. Here we demonstrate a volumetric optical scattering neural network (OSNN) in which densely packed weak scatterers form a three-dimensional, locally connected optical computing medium. In contrast to fully connected diffractive architectures, the OSNN uses near-field scattering interactions, described under the first-Born approximation, to compress optical interconnections into a monolithic volume. We implement this concept using resilient inverse design and two-photon nanolithography, yielding OSNN devices with a volume of ~$3.8*10^{-4}mm^{3}$ and a record-breaking neuron density of $1.0*10^{9}/mm^{3}$. Experimentally, the fabricated classifier achieves $94.8\%$ blind-test accuracy on MNIST, while the imager performs optical compressed imaging with a $1-{\mu}m$ effective resolution and average FSIM values of $0.93$ on Fashion-MNIST and $0.91$ on VesselMNIST3D. OSNN paves the way for ultra-dense, ultra-compact, and efficient optical computing, creating a universal platform for embedded optical intelligence and promising widespread application in AI fields ranging from autonomous driving to medical diagnosis.