physics.opticsFeb 27, 2026

ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity

Authors: Ziang Yin, Qi Jing, Raktim Sarma, Rena Huang, Yu Yao, Jiaqi Gu

Organizations: Arizona State University, Tempe, AZ, USA · Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM, USA · Rensselaer Polytechnic Institute, Troy, NY, USA

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Abstract

Diffractive optical neural networks (DONNs) have demonstrated unparalleled energy efficiency and parallelism by processing information directly in the optical domain. However, their computational expressivity is constrained by static, passive diffractive phase masks that lack efficient nonlinear responses and reprogrammability. To address these limitations, we introduce the Recurrent Diffractive Optical Neural Processor (ReDON), a novel architecture featuring reconfigurable, recurrent self-modulated nonlinearity. This mechanism enables dynamic, input-dependent optical transmission through in-situ electro-optic self-modulation, providing a highly efficient and reprogrammable approach to optical computation. Inspired by the gated linear unit (GLU) used in large language models, ReDON senses a fraction of the propagating optical field and modulates its phase or intensity via a lightweight parametric function, enabling effective nonlinearity with minimal inference overhead. As a non-von Neumann architecture in which the primary weighting elements (metasurfaces) remain fixed, ReDON substantially extends the nonlinear representational capacity and task adaptability of conventional DONNs through recurrent optical hardware reuse and dynamically tunable nonlinearity. We systematically investigate various self-modulation configurations to characterize the trade-offs between hardware efficiency and computational expressivity. On image recognition and segmentation benchmarks, ReDON improves test accuracy and mean intersection-over-union (mIoU) by up to 20% compared with prior DONNs employing either optical or digital nonlinearities at comparable model complexity and negligible additional power consumption. This work establishes a new paradigm for reconfigurable nonlinear optical computing, uniting recurrence and self-modulation within non-von Neumann analog processors.

Figures & tables

Figure 1. Inspired by GLU in LLMs, we propose a diffractive self-modulated nonlinear unit in ReDON . A small fraction of the light is sensed and self-modulates downstream metasurfaces.
Figure 2. ReDON software–hardware correspondence. Top: software abstraction of a titlename block, where the optical operator Ftitlename(⋅)\mathcal{F}_{\text{titlename}}(\cdot) is integrated with lightweight pointwise layers and a compact digital head; recurrence reuses the same optical core with shared metasurface phases Φ\Phi and iteration-dependent modulation parameters Θr\Theta_{r} . Bottom: a corresponding optoelectronic realization using an input encoder (e.g., LC-SLM), passive metasurface stack, intermediate optical sensing (coupling ratio α\alpha ), and a lightweight electronic processor that computes Ψ(⋅,Θ)\Psi(\cdot,\Theta) to drive a modulation plane for self-modulated nonlinearity.
Figure 3. Compare different input encoding functions for ReDON on QuickDraw-10 classification. Phase and intensity encoding show the best effects.
Figure 4. Evaluation of nonlinear expressivity by fitting popular activation functions. We simulate a 3×33\times 3 phase-encoded input where only the center pixel sweeps phase x∈[0,1]x\in[0,1] (others fixed at unit amplitude and zero phase) and read out only the center detector intensity to form a scalar mapping. ReDON (with a second-order polynomial Ψ\Psi and residual readout x−ηFReDON(x)x-\eta\mathcal{F}_{\text{ReDON}}(x) ) approximates common nonlinear activations, while a linear DONN fails.
Figure 5. (a) Group-wise and (b) layer-wise parameter sharing on metasurface modulation.
Figure 6. (a) Folded reflective and (b) transmissive example implementations of ReDON architecture. The self-modulation mechanism can be realized by image sensors and SLM.
Figure 7. Compare different readout strategies. Our differential, scaled residual shows the best accuracy on QuickDraw-10.
Figure 8. Compare the expressivity of different Ψ(E,Θ)\Psi(E,\Theta) functions on phase and intensity self-modulation. Ψ(⋅,Θ)\Psi(\cdot,\Theta) are ordered by computing complexity. Each highlighted function represents the highest-accuracy model at different complexity levels.
Figure 9. Parameter count and accuracy comparison with different sensing layer ii to modulated layers jj using phase and intensity self-modulation. Phase self-modulation shows better accuracy than intensity. The blue markup shows the best setting under different #layers in jj . These results motivate our choice of phase self-modulation and multi-layer modulation in the main experiments.
Figure 10. (a) Accuracy and #Params Pareto-front selection with different parameter sharing group sizes p×qp\times q on phase self-modulation with ii =1, jj =1,2,3,4,5 on QuickDraw-50. (b) Power breakdown and scaling with higher FPS.
Figure 11. With the best modulation layer settings ( ii to jj ) from Fig. 9 , we explore #Params vs. accuracy trade-off with different sharing group p,qp,q .
 CIFAR-10QuickDraw-50Stanford Background Seg. Binarized Seg
Different Nonlinear StrategyTrain Acc.Test Acc.Train Acc.Test Acc.Train mIoUTest mIoU
Saturable Absorption ( Zhang et al., 2025 )61.9%61.1%80.1%71.3%72.2%47.1%
Reflection Coating ( Dong et al., 2025 )58.4%58.3%76.6%68.5%68.3%41.3%
Encoding (Phase) ( Li et al., 2024 )61.2%60.2%79.4%70.4%76.1%53.4%
Encoding (Intensity) ( Li et al., 2024 )58.3%58.6%76.5%68.7%66.4%46.9%
Encoding (Complex) ( Li et al., 2024 )59.7%59.6%77.9%69.8%68.2%44.3%
Table 1. Comparison across different nonlinearity designs on 3 benchmarks, our proposed ReDON with scaled Tanh as Ψ\Psi consistently achieves the best performance. ReDON shares Θ\Theta across all 5 modulated layers. With more recurrence ( RR ) and blocks ( NN ), ReDON shows higher expressivity. We replace our self-modulation with standard DONN or DONN with a digital Tanh activation function, which shows much worse results than our self-modulation.
DesignAccuracy ↑\uparrowMean-Square Error (MSE) ↓\downarrow
FMNISTQuickDraw-10 adapt from FMNISTDarcyNavier-Stokes adapted from Darcy
Saturable Absorption ( Zhang et al., 2025 )80.1%53.1%0.0950.1822
ReDON95.1%87.2%0.0150.1035
Table 2. Transferability evaluation of ReDON ( RR =2, BB =4). On Fasion-MNIST →\rightarrow QuickDraw-10, we show classification test accuracy. On Darcy flow →\rightarrow Navier-Stokes PDE solving, we show test mean-square error (MSE). We train on the initial task and adapt to the second task, reusing fabricated metasurfaces.
Figure 12. Visualization of representative inference results of ReDON on (a) Stanford cars image segmentation, (b) Darcy flow, and (c) Navier-Stokes PDE solving tasks.
Figure 13. Robustness evaluation settings under practical non-idealities. Left : random horizontal/vertical misalignment of diffractive planes up to ±1\pm 1 pixel/meta-atom size. Middle : additive Gaussian noise with σ=0.01\sigma=0.01 applied to sensed light intensities. Right : fabrication-induced phase error modeled as i.i.d. Gaussian phase perturbations with σϕ=0.01 rad\sigma_{\phi}=0.01~rad on metasurface phase responses.
Noise-injected inference (Standard Training)Misalignment (MA)
Misaligned pixel size0.511.52
Averaged test accuracy92.6%91.3%90.1%88.2%
Std. of test accuracy0.00480.00510.00490.0053
Readout Noise (RN)
Injected Gaussian noise ( σ\sigma )0.040.060.080.1
Averaged test accuracy93.1%92.4%91.2%89.1%
Table 3. Robustness of a 5-layer ReDON system (no recurrence) on Fashion-MNIST under misalignment (MA), readout noise (RN), fabrication error (FE), and their combination. The noise-free test accuracy is 95.1%. The noise-aware model is trained with combined system errors (MA 2 + RN 0.1 + FE 0.8) injected during training; we report the average and std. of test accuracy over 5 iterations under inference-time noise injection.

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