On-chip input-hidden-layer-degenerate optical diffractive nonlinear neural network

Integrated photonic computing offers compelling advantages, including high speed, compact footprint, and low power consumption, positioning it as a promising platform for artificial intelligence (AI) applications. However, the input scale of current photonic computing chips remains fundamentally constrained by their one-dimensional interface. Here, we propose and experimentally demonstrate an input-hidden-layer-degenerate optical diffractive nonlinear neural network (IHD-ODN3), which expands the input dimension of on-chip optical networks from N to N^2 within a compact footprint. By structurally merging the input layer with linear diffractive hidden layers, input data are directly encoded into optical neurons. Leveraging the intrinsic properties of diffraction, multilayer diffraction interactions among these neurons promote sufficient data mixing, thereby executing an equivalent nonlinear function and mapping the data into a high-dimensional space with a footprint of 0.5 mm2. We validate the nonlinear computational capability of IHD-ODN³ through four-class spiral and handwritten digit classification tasks, achieving accuracies of 88% and 98%, respectively. Furthermore, we demonstrate high-performance image compression and reconstruction, with a compression ratio up to 256:1. This input-hidden-layer-degenerate architecture not only unlocks N^2 dimensional input encoding, but also delivers low-power, highly integrated and programmable optical nonlinear computing with linear photonic hardware. Our approach is fully compatible with mainstream linear optical neural network architectures, paving the way for next-generation of large-scale, highly integrated nonlinear optical deep neural networks.