UCLA's single-layer diffractive surface achieves universal nonlinear optical computing

UCLA researchers led by Aydogan Ozcan have broken the long-held assumption that nonlinear optical computing requires cascaded layers or nonlinear materials. In a new paper, they introduce the encoder-decoder co-localization (E+D) architecture: a single phase-only diffractive plane integrates an input-dependent dynamic encoder and a static optimized decoder. Under coherent illumination, free-space propagation and interference between the encoder and decoder fields, combined with intensity detection at the detector plane, generates programmable nonlinear input-output mappings. The team proves mathematically that this single-layer system is a universal approximator for any real-valued band-limited nonlinear function, and identifies key physical factors that govern approximation fidelity—including decoder degrees of freedom, detector aperture size, and axial propagation distance. They also show that adding a trained, frozen phase bias to the encoder region boosts expressivity and provides robustness against coarse phase quantization on spatial light modulators.

To validate their theory, the researchers built a visible-light experimental setup and used in situ learning to train the diffractive surface to approximate nine different nonlinear functions simultaneously in a single optical forward pass. This includes commonly used neural network activation functions (e.g., ReLU, tanh) and even complex-valued nonlinear functions. The results demonstrate that the E+D architecture can replace bulky multi-layer optical systems with a single, compact diffractive layer, dramatically reducing both hardware complexity and alignment challenges. This work opens the door to practical, scalable analog optical processors that can perform real-time nonlinear computation for applications in machine learning, image processing, and communications, all without the power and latency overhead of electronic converters or nonlinear crystals.