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ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity
Ziang Yin, Qi Jing, Raktim Sarma, Rena Huang, Yu Yao, Jiaqi Gu
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Summary
The paper introduces ReDON (Recurrent Diffractive Optical Neural Processor), a novel architecture that enhances Diffractive Optical Neural Networks (DONNs) by integrating reconfigurable, recurrent self-modulated nonlinearity. ReDON overcomes the static, linear limitations of traditional DONNs by sensing intermediate optical fields and using lightweight electro-optic modulation to dynamically adjust phase or intensity in downstream metasurfaces. Inspired by Gated Linear Units (GLUs) in large language models, this approach enables input-dependent, highly expressive nonlinear transformations with negligible power overhead, achieving up to 20% accuracy improvement in image recognition and segmentation tasks compared to prior methods.
Entities (6)
Relation Signals (5)
ReDON → improves → DONN
confidence 95% · ReDON improves test accuracy and mean intersection-over-union (mIoU) by up to 20% compared with prior DONNs
ReDON → inspiredby → GLU
confidence 92% · Inspired by the gated linear unit (GLU) used in large language models, ReDON senses a fraction of the propagating optical field
ReDON → uses → Metasurface
confidence 90% · As a non-von Neumann architecture in which the primary weighting elements (metasurfaces) remain fixed
ReDON → controls → SLM
confidence 88% · use it to control the spatial-light modulator (SLMs) to modulate the phase or intensity
DONN → limitedby → Metasurface
confidence 85% · their computational expressivity is constrained by static, passive diffractive phase masks
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Abstract
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.
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- Source: https://arxiv.org/abs/2602.23616v3
- Canonical: https://arxiv.org/abs/2602.23616v3
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ReDON:RecurrentDiffractiveOpticalNeural Processor with Reconfigurable Self-Modulated Nonlinearity ZIANG YIN, Arizona State University, USA QI JING, Arizona State University, USA RAKTIM SARMA, Center for Integrated Nanotechnologies, Sandia National Laboratories, USA ZHAORAN RENA HUANG, Rensselaer Polytechnic Institute, USA YU YAO, Arizona State University, USA JIAQI GU, Arizona State University, USA Diffractive optical neural networks (DONNs) have demonstrated unparalleled energy efficiency and paral- lelism 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 reprogramma- bility. To address these limitations, we introduce 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) in large language models,ReDONsenses 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 with the main weighting units (metasurfaces) being fixed, we substantially extend the DONN’s nonlinear representational capacity and task adaptability via recurrent optical hardware reuse and dynamically tunable nonlinearity. We systematically investigate various self- modulation configurations to uncover the trade-offs between hardware efficiency and expressivity. On image recognition and segmentation tasks,ReDONimproves test accuracy and mIoU by up to 20% over prior DONNs with optical or digital nonlinearities at comparable complexity and negligible power overhead. This work establishes a new paradigm for reconfigurable nonlinear optical computing, uniting the benefits of recurrence and self-modulation in non-von Neumann analog processors. 1 Introduction Diffractive optical neural networks (DONNs) have emerged as a promising platform for high- throughput, low-power neuromorphic processing [5,6,11,16,19,20,31]. By encoding neural weights directly into phase elements in the fabricated diffractive masks (e.g., metasurfaces), DONNs realize massively parallel in-memory computing, where weights are stored physically in sub- wavelength optical structures and applied to input with sub-nanosecond optical readout. This non-von Neumann computational physical system, where computation and memory are co-located, has enabled ultra-efficient optical inference for applications including computer vision, sensing, holography, generative AI, and scientific computing [5, 16, 19, 25, 31]. Despite these advantages, DONNs remain fundamentally limited by two key challenges: weak optical nonlinearity and a lack of reconfigurability, both rooted in the static, passive, and linear nature of diffractive metasurfaces.➊Weak Nonlinearity: Deep neural networks (DNNs) are fundamentally highly nonlinear functions for feature transformation. Yet DONNs are inherently (near) linear systems: cascaded passive diffractive layers reduce to a single global linear operator, with only weak square-law detection at photodetectors, dramatically restricting expressivity and limiting DONNs to tasks solvable by shallow NNs. Researchers have explored several strategies to Authors’ Contact Information: Ziang Yin, Arizona State University, Tempe, AZ, USA, ziangyin@asu.edu; Qi Jing, Arizona State University, Tempe, AZ, USA, qjing1@asu.edu; Raktim Sarma, Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM, USA, rsarma@sandia.gov; Zhaoran Rena Huang, Rensselaer Polytechnic Institute, Troy, NY, USA, huangz3@rpi.edu; Yu Yao, Arizona State University, Tempe, AZ, USA, yuyao@asu.edu; Jiaqi Gu, Arizona State University, Tempe, AZ, USA, jiaqigu@asu.edu. , Vol. 1, No. 1, Article . Publication date: March 2026. arXiv:2602.23616v3 [physics.optics] 10 Mar 2026 Ziang Yin, Qi Jing, Raktim Sarma, Zhaoran Rena Huang, Yu Yao, and Jiaqi Gu 휎(⋅) Linear Spatial light modulator (SLM) ℳ′ splitter Readout sensors sensor Light in Couple out Ψ ! 1 3 2 1 2 3 Linear Linear 푦 휶푬 풊 ′ 푬 풋 Gated Linear Units (GLU) in LLM 풊-th 풋-th ReDON: Diffractive Self-Modulated Nonlinearity gate up down Inspire Couple light out layer 풊 Transform Self-modulate layer 풋 1 2 3 × 푬 풊$ퟏ 푬 풊 ⋯ ⋯ ⋯ Fig. 1. Inspired by GLU in LLMs, we propose a diffractive self-modulated nonlinear unit inReDON. A small fraction of the light is sensed and self-modulates downstream metasurfaces. introduce nonlinearity. Prior work has explored all-optical nonlinearity (e.g., saturable absorbers, 휒(2)/휒(3) nonlinear materials to build nonlinear optical encoder with enhanced accuracy, but often require unrealistically high optical power to trigger (100 kW/cm 2 ), have low energy efficiency (0.1%), rooted in the shallow interaction depths (<1휇푚) in free-space DONNs [12,23,24]. Structure nonlinearity, such as repeatedly encoding inputs [32] or using cavity feedback [29], provides high-order nonlinearity but lacks parametric control and acts more like fixed optical reservoirs than programmable activations. To date, no solution offers efficient, programmable, low-latency nonlinear processing while maintaining DONNs’ speed and energy advantages. ➋Restricted Reconfigurability: A second major limitation of DONNs is their reconfigura- bility. Traditional DONNs depend on static metasurfaces whose nanostructures encode a fixed set of optical weight banks determined at fabrication time (similar to read-only memory). While this enables extremely fast, low-power inference (similar to memory readout), it prevents multi- channel, multi-layer neural computing and task adaptation in dynamic, evolving AI tasks. Hybrid optical-electronic architectures treat DONNs as static optical encoders and rely on digital backends for task adaptation. Multi-dimensional reconfiguration frameworks [31] and multi-task learning method [14,34] explore mechanical rotation, permutation, and wavelength/polarization tuning to introduce system-level reconfigurability, but mechanical actuation still shows limited reliability and speed. As an active research topic, programmable metasurfaces can potentially offer per-element programmability but face substantial fabrication complexity, high insertion loss, and limited ma- turity for large-scale deployment [1]. Overall, existing DONNs lack a scalable mechanism for input-dependent, high-expressivity computation without re-fabricating diffractive layers. Inspired by the dynamic gating mechanisms of modern gated linear units (GLUs) [22], we introduceReDON, a diffractive optical neural processor that hybridizes fixed passive metasurfaces with a lightweight electro-optic self-modulation mechanism.ReDONsenses a small fraction of the propagating optical field, processes it through a learnable parametric function, and uses the output to modulate the phase or amplitude of downstream diffractive layers. This introduces strong, tunable, input-dependent nonlinearity far beyond traditional pointwise, static activations, like ReLU, while requiring negligible inference overhead. Crucially,ReDONapplies this modulation recurrently to reinforce nonlinearity and expand effective network depth. This in-situ recurrence follows diffusion-style iterative refinement: the system composes multiple simple optical nonlinear steps into highly expressive mappings. By hybridizing non-volatile metasurfaces with dynamic electro-optic self-modulation,ReDONovercomes long-standing limitations in nonlinearity and reconfigurability while preserving the efficiency and massive parallelism of diffractive optical in-memory computing. Our main contributions are summarized as follows: , Vol. 1, No. 1, Article . Publication date: March 2026. ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity •Tunable, Self-Modulated Electro-Optic Nonlinearity: We introduce a novel diffractive optical nonlinear mechanism that senses intermediate optical fields and applies a learnable, GLU-inspired gating function to modulate downstream transmission, providing input-dependent, reprogrammable nonlinear transmission. •Recurrent Diffractive Optical Processing: We introduce in-situ recurrence to reinforce the DONN nonlinearity by reusing the same hardware system with dynamic parameter tuning, incrementally composing deep neural representations for highly expressive transformations. • Hybrid Reconfigurable Optical Processor Architecture:ReDONunifies static, non-volatile metasurface weight banks with lightweight electro-optic self-modulation to enable dynamic, reconfigurable computation in a non-von Neumann optical setting. • Comprehensive Design Space Exploration: We systematically analyze different architectural design settings and characterize their trade-offs in nonlinear expressivity, parameter efficiency, and hardware complexity. On classification and segmentation applications, ourReDONdemon- strates an average of 20% higher accuracy with superior task adaptability and negligible power overhead compared to existing linear/nonlinear DONNs. 2 Preliminary A diffractive optical neural network (DONN) [16,19,31] implements computation through cascaded free-space propagation and metasurface modulation. Let푥 in ∈C 푁 denote the input optical field. Each diffractive layer푖applies a diagonal transfer matrix푇 푖 = diag(exp(푗휙 푖 ))representing spatially varying phase modulation, and propagation over distance푧 푖 is modeled by a linear operator푈 푖 (푧 푖 ) derived from the Fresnel diffraction integral. The end-to-end transformation is ℎ out (푥 in )= 퐾 Ö 푖=1 푈 푖 (푧 푖 )푇 푖 ! 푈 0 푥 in , 푦=|ℎ out | 2 ,(1) where the square-law detection at the output plane provides the only nonlinearity. Thus, once the metasurfaces are fabricated, the DONN implements a single fixed global linear operator in the field domain, followed by a static, uncontrollable intensity nonlinearity. The absence of tunable or distributed nonlinear mechanisms fundamentally limits expressivity and task adaptivity. Existing Optical Nonlinearity Mechanisms. Recent work has explored several directions to introduce nonlinearity into diffractive or optical neural systems [27,28,30]. Structural nonlinearity reuses the same linear diffractive elements multiple times so that the optical field is re-encoded and re-scattered through a static medium [15]. Through repeated interaction and interference, the resulting intensity response effectively approximates a polynomial mapping [29]. These methods preserve low power and remain fully optical, but the nonlinear mapping is implicitly determined by the fixed geometry and cannot be shaped or tuned after fabrication. 2.1 Gated Linear Units Modern deep learning models, particularly large language models, increasingly rely on gated linear units (GLUs) [22] and related gating variants to achieve expressive, input-dependent transforma- tions, e.g., SwigLU, SiLU. A GLU augments a linear projection with a learnable multiplicative gating function that modulates the output as 푧=퐺퐿푈(푥)=(푊 up 푥 +푏 up )⊙ 휎 (푊 gate 푥 +푏 gate ) ; 푦=(푊 down 푧+푏 down ),(2) where휎(·)is typically Swish or GELU. The gating branch conditions the main signal, provid- ing a flexible mechanism for selective amplification, suppression, and routing, offering dynamic modulation while maintaining computational and parameter efficiency. , Vol. 1, No. 1, Article . Publication date: March 2026. Ziang Yin, Qi Jing, Raktim Sarma, Zhaoran Rena Huang, Yu Yao, and Jiaqi Gu LC-SLM splitter Camera Sensor Couple out 휓 ! LC-SLM Input encoding Backend Processors (EIC or PIC) 푥−휂ℱ !"#$% (푥) ×휂 PWConv 퐖 &'() ReDON ℱ !"#$% (푥,Θ * ,Φ) - PWConv 퐖 &+, recurrence head ReDON block N ReDON block 2 ReDON block 1 ... Share Φ Recurrence ReDON Map to backend processor Map to ReDON Software model Hardware architecture Fig. 2.ReDONsoftware–hardware correspondence. Top: software abstraction of a titlename block, where the optical operatorF titlename (·)is integrated with lightweight pointwise layers and a compact digital head; recurrence reuses the same optical core with shared metasurface phasesΦand iteration-dependent modulation parametersΘ 푟 . Bottom: a corresponding optoelectronic realization using an input encoder (e.g., LC-SLM), passive metasurface stack, intermediate optical sensing (coupling ratio훼), and a lightweight electronic processor that computesΨ(·,Θ) to drive a modulation plane for self-modulated nonlinearity. 3 Recurrent Diffractive Optical Processor (ReDON) We presentReDON, a recurrent diffractive optical neural processor. Unlike existing DONNs with fixed functionality and weak nonlinearity only at the photodetector arrays,ReDONintroduces an electro-optic self-modulated nonlinearity and recurrent inference mechanism that simultaneously enables strong nonlinear expressivity and reconfigurability for non-von Neumann diffractive optical in-memory computing. As summarized in Fig. 2,ReDONadmits a direct software-hardware correspondence: in software, a ReDON block wraps the optical operatorF ReDON (·) with lightweight pointwise layers and a compact digital head, while in hardware the same computation is realized by sensing an intermediate optical field, computing a parametric transformΨ(·,Θ)on a lightweight electronic backend, and driving a modulation plane (e.g., SLM / tunable metasurface) to self- modulate downstream transmission. Recurrence reuses the same fabricated metasurface stack across iterations by updating onlyΘ while keepingΦ shared. 3.1 Diffractive Self-Modulated Nonlinearity Inspired by the powerful and parameter-efficient GLU mechanism in LLMs (Eq.(2)), we design ReDONwith a diffractive self-modulation mechanism to introduce a dynamic input-dependent nonlinear response to DONNs. As illustrated in Fig. 1 and Fig. 2, we augment standard multi-layer DONNs with an auxiliary modulation branch that couples out and senses a small fraction (훼) of intermediate light field퐸 푖 at the푖-th metasurface, and convert it into electrical signals훼|퐸 푖 | 2 . In the electrical domain, we perform a lightweight parametric transformation function on the sensed signal Ψ(퐸,Θ)and use it to control the spatial-light modulator (SLMs) to modulate the phase or intensity for the main branch light field at subsequent metasurface layer(s). As a simplified illustration, we assume the SLM modulates the푗-th metasurface. Let퐸 푖 denote the complex amplitude of the optical , Vol. 1, No. 1, Article . Publication date: March 2026. ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity 92.77% 91.31% 70.26%72.72% 74.87% 73.73% 68.88%71.44% 50% 60% 70% 80% 90% 100% Ph a seAm p li t ud eIntensityComplex QuickDraw - 10 Acc (%) Train Accura cy Test Accura cy 01 0 10 1 01 Input Encoding Function E ! =ℰ(푥) Fig. 3. Compare different input encoding functions forReDONon QuickDraw-10 classification. Phase and intensity encoding show the best effects. field on the푖-th metasurface output plane near-field, and푈 푖 (휆,푧 푖 )denotes the linear diffraction matrix parameterized by wavelength휆and diffraction distance푧 푖 between two metasurfaces. Each metasurface is a broadband phase mask that applies phase shifts푒 푗Φ 푖 to the incident light field. The formulation of an 퐿-layer ReDON system transmission is as follows couple-out layer 푖 : 퐸 ′ 푖 =푈(푧 푖 /2)퐸 푖−1 , 퐸 푖−1 = 푖−1 Ö 푘=1 (푒 푗Φ 푘 푈 푘−1 )퐸 0 ,퐸 0 =E(푥) parametric transform:M 푗 =Ψ(훼|퐸 ′ 푖 | 2 ,Θ), M ′ = 푓(M) self-modulate layer푗 : 퐸 푗 = √ 1− 훼M ′ 푗 ⊙ 푗 Ö 푘=푖 (푒 푗Φ 푘 푈 푘−1 )퐸 푖−1 ; transform after layer 푗 :푦=F ReDON (푥)=(1− 훼) 푈 퐿 퐿 Ö 푘=푗+1 (푒 푗Φ 푘 푈 푘−1 )퐸 푗 2 ; (3) where the input푥 ∈ [0,1]is first encoded as the incident light field퐸 0 via an input encoding function E(·), e.g., phase encoding퐸 0 = 푒 푗휋푥 , amplitude encoding퐸 0 = 푥, etc.훼|퐸 ′ 푖 | 2 is the intermediate light intensity coupled out between푖−1 and푖-th metasurfaces. Here,Ψ(·,Θ)generates control signals from the sensed light intensity, while푓(·):M →M ′ maps these signals to either phase shifts or attenuation factors at the modulated metasurface(s).” For phase self-modulation,M ′ will be extra phase shifts within[−휋/2,휋/2]; for intensity self-modulation,M ′ will be mapped to real-valued attenuation factors. M ′ phase = 푓 phase (M)= 푒 푗(M%휋−휋/2) M ′ intensity = 푓 intensity (M)= Clip(M, 0, 1). (4) 3.2 Nonlinear Expressivity Investigation Input Encoding Investigation. The expressivity of theReDONsystem is strongly influenced by the input encoding function퐸 0 =E(푥). Figure 3 compares several commonly used encoding methods, including phase, amplitude, intensity, and complex-valued encoding. Among them, phase encoding consistently achieves the highest accuracy on classification tasks, whereas intensity and complex encodings exhibit noticeable training instability. This observation aligns with prior findings [15], which show that phase encoding preserves more optical energy and introduces a natural nonlinear dependence in the photodetection process. For these reasons, all subsequent experiments adopt the phase-encoding schemeE(푥)= 푒 푗휋푥 ,푥 ∈ [0, 1]. , Vol. 1, No. 1, Article . Publication date: March 2026. Ziang Yin, Qi Jing, Raktim Sarma, Zhaoran Rena Huang, Yu Yao, and Jiaqi Gu -0.5 0 0.5 1 1.5 00.51 -0.5 0 0.5 1 1.5 00.51 GELU Linear DONN ReDON ReLU Linear DONN ReDON -0.5 0 0.5 1 1.5 00.51 -0.5 0 0.5 1 1.5 2 00.51 Tanh Linear DONN ReDON Swish Linear DONN ReDON Input 푥 Input 푥 Input 푥 Input 푥 Output 푦 Output 푦 Output 푦 Output 푦 Metasurface SLM Image sensor Ψ Θ Linear DONN setup: trainable vars Φ ReDON setup: trainable vars (Φ,Θ) 3 ×3image sensor array Output 푦 in the center detector Scalar nonlinear activation setup Inputs 111 1푒 푗 1 111 diffraction diffraction diffraction diffraction Φ Φ 푦 Inputs 111 1푒 푗 1 111 Fig. 4. Evaluation of nonlinear expressivity by fitting popular activation functions. We simulate a 3×3 phase- encoded input where only the center pixel sweeps phase푥 ∈ [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 polynomialΨand residual readout푥 −휂F ReDON (푥)) approximates common nonlinear activations, while a linear DONN fails. Scaled Differential Residual Output. Since the output detection plane measures only optical intensity, the resulting features are strictly non-negative, which limits representational richness and causes numerical instability during training. A common workaround in prior optical neural networks is to use two parallel optical paths to form a differential signal, but this doubles the hardware cost. To overcome the non-negative readout and avoid doubling hardware overhead, we instead form a scaled, differential residual path between the input image and the detector readout, 푦= 푥−휂F ReDON (푥) . The scaling factor휂controls the overall magnitude(norm) of the residual branch and compensates for the limited modulation range of phase-encoded diffractive propagation. This formulation restores sign flexibility to the features while avoiding additional optical paths. Nonlinear Activation Expressivity. The proposed self-modulation mechanism is fully learnable, enabling input-dependent nonlinear responses. To probe its expressivity, Fig. 4 considers a minimal single-layerReDONsetup with 3×3 input resolution and asks whether it can fit common nonlinear activation curves (compared to a linear DONN baseline). We synthesize controlled interference patterns by sweeping only the center input phase,푥 ∈ [0,1](field푒 푗휋푥 ), while keeping the remaining eight inputs at unit amplitude and zero phase. We then form a scalar output by reading the center photodetector intensity (normalized), yielding a 1D mapping푥 ↦→ 푦; in contrast, aggregating all detector intensities is uninformative in our (approximately) lossless simulation because total optical power is conserved and thus nearly constant. By jointly optimizing the metasurface phasesΦand the coefficientsΘof a second-order polynomial modulation functionΨ(·,Θ),ReDONaccurately reproduces a variety of widely used nonlinear activations in Fig. 4. Existing linear DONNs, despite weak inherent nonlinearity, fail to approximate these functions and are constrained to nonnegative outputs under intensity-only readout. With the residual-output formulation,ReDONcan realize sign-changing nonlinear mappings and, more generally, is not restricted to canonical pointwise activations; it can discover task-adaptive nonlinear functions during training. 3.3 Expressivity Augmentation with Multi-Layer Self-Modulation and Recurrent Architecture Multi-Layer Self-Modulation. In a standard GLU, only a single multiplicative gating operation is applied. In a standard GLU, only a single multiplicative gating operation is applied. To further , Vol. 1, No. 1, Article . Publication date: March 2026. ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity strengthen the nonlinear capacity of our diffractive system, we extend this idea by allowing the same sensed intermediate signal to modulate multiple downstream metasurface layers. As illustrated in Fig. 5(b), the optical field is coupled out at layer푖, processed through individualΨfunctions, and used to control any subsequent metasurface layer(s)푗, where푗 ≥ 푖. For example, one may couple out at푖=1 to modulate layers푗=2,3,5. Increasing the number of modulated layers naturally strengthens nonlinear expressivity but also incurs higher hardware cost. In Sec. 4.2.3, we systematically evaluate this design space and quantify the trade-off between hardware complexity and expressivity gains achieved through multi-layer self-modulation. Recurrent Network Architecture. Figure 2(top) shows the overall model architecture using ReDONas the basic building block. Lightweight pointwise convolutions are used for channel mixing and dimension matching, while theReDONmodule performs per-channel spatial transformation. MultipleReDONblocks can be stacked to form a deeper backbone (with푁blocks), followed by a compact digital head for downstream tasks. To further enhance nonlinear expressivity and maximize the utility of the non-volatile passive metasurfaces, we introduce a recurrent inference mechanism. Each feature map is passed through the sameReDONsystem for푅iterations, effectively composing multiple nonlinear transformations in situ. During recurrence, the metasurface phases Φremain entirely shared and fixed, while we update per-channelΘcoefficients per recurrence iteration, which are stored in local SRAM and streamed to the modulation plane. That is, each hidden channel receives a distinct set of parameters at each recurrence iteration, i.e., Θ 푟,푐 ,푟 ∈ [푅],푐 ∈ [퐶 푖푛 ]. With a fixed layer depth (i.e., constant푅× 푁), we find thatrecurrenceof 푅=2achievesthebestexpressivityandlatency, while more recurrence gives saturated gain. 3.4 Parameter-Efficient Coefficient Sharing The parametric functionΨintroduces dynamically tunable weightsΘ, which must be stored in local SRAM and reloaded every inference. This incurs additional data movement, memory footprint, and compute overhead. To reduce these costs while preserving high nonlinear expressivity, we explore two simple yet effective parameter-sharing strategies forΨ. Figure 5 summarizes the two approaches. Spatial Group-wise Coefficient Sharing. Here, the퐻 ×푊pixels on the modulation plane are divided into푝×푞spatial groups, each of size푟×푐. If푝= 퐻,푞=푊, each pixel has its own independent set of coefficientsΘin theΨfunction, yielding maximal flexibility but the highest parameter count. At the opposite extreme, when푝=푞=1, a single set of coefficients is shared across all modulated pixels. By adjusting the group setting푝and푞, we can smoothly trade expressivity for reduced memory and compute complexity, achieving up to 푟푐 times reduction in parameters. Cross-layer Coefficient Sharing. This strategy becomes relevant when the sensed signal from layer푖modulates multiple downstream metasurface layers푗. Instead of assigning distinct parameters Θfor multiple modulated layers, we can potentially share theΘcoefficients for all layers to reduce the parameter count and compute cost by 퐿 times, where 퐿 is the number of modulated layers. 3.5 Implementation Practicality Justification Figure 6 illustrates two feasible implementations of the proposedReDONarchitecture. In the reflective design (Fig. 6(a)), both the diffractive layers and light path are integrated within a single substrate. The back plane employs a gold reflector, while the intermediate optical field at layer푖is partially coupled out through a beam splitter and detected by an on-chip image sensor array. A small number of high-speed ADCs can sequentially read out the sensed intensities in a time-multiplexed fashion, amortizing ADC cost. The sensed signal훼|퐸| 2 can be transformed byΨ(·,Θ)in situ, either through compact analog circuits (for simple operations such as scaling, shifting, ReLU, or small-kernel convolutions) or lightweight digital units. The resulting control signal directly drives the modulation , Vol. 1, No. 1, Article . Publication date: March 2026. Ziang Yin, Qi Jing, Raktim Sarma, Zhaoran Rena Huang, Yu Yao, and Jiaqi Gu 푚 !! 푚 !" 푚 #! 푚 #" v 푝 groups v v v v v v v v v v v v 푞 groups Each group shares the same modulation 푚 (low control complexity and parameter count) Group size=1x1 Group size=풓 × 풄 Ψ ( Ψ ! $ Ψ ! % Ψ ! & ... ... Metasurfaces share the same modulation ℳ′ (low control complexity and parameter count) (a) (b) Separate control Shared control 푳푯푾|휽 풊풋 | 푳푯푾휽 풊풋 /(풓풄)푳푯푾|휽 풊풋 |푯푾|휽 풊풋 | #param Fig. 5. (a) Group-wise and (b) layer-wise parameter sharing on metasurface modulation. Metasurface Gold reflectorSLM Image sensor 퐼∝훼퐸′ ! 1 − 훼 퐸 " ′ splitter 퐸 # 퐸 "$% 퐸 " 훼퐸 " ′ 휓⋅ can realize a handful of function, e.g. Bias, Polynomial, Max Pooling, Conv2d ℳ # & =푓(Ψ(E,Θ) Liquid crystal ITO electrode v1 푚 % 푚 ! 푚 ' 푚 ( reflect v v v ... Ψ ) ( ⋅ ) ... v2 Self-modulated nonlinear unit Tunable metasurface to control SLM input encoder 퐸 " ′ (a) Folded reflective implementation (b) Transmissive implementation Ψ ) (⋅) recurrence recurrence ℳ # & =푓(Ψ(E,Θ) input encoder Fig. 6. (a) Folded reflective and (b) transmissive example implementations ofReDONarchitecture. The self- modulation mechanism can be realized by image sensors and SLM. applied at the downstream metasurface layer(s)푗. Alternatively, a transmissive implementation (Fig. 6(b)) can be constructed by engineering metasurface푖to redirect a small fraction of the incident light (훼%) toward an intermediate image sensor, while allowing the remaining light to propagate forward. Multiple metasurfaces can be fabricated on separate substrates with precise optical alignment. Modulation Plane. A key hardware component is the tunable modulation plane at layer(s)푗. Commercial liquid-crystal spatial light modulators (LC-SLMs) already support reprogramming rates near 10 kHz, phase modulation exceeding휋, and more than 8-bit precision, sufficient for many proof-of-concept real-time AI systems [18]. Looking forward, emerging technologies in actively programmable metasurfaces [1,21], promise significantly higher speeds and tighter integration. Electro-optic modulation in particular can reach modulation rates in the gigahertz range with per-element tunability with compact footprints, which in principle, raise the achievable throughput , Vol. 1, No. 1, Article . Publication date: March 2026. ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity 85.01% 88.96% 87.04% 92.77% 70.75%73.67%70.17% 74.87% 50% 60% 70% 80% 90% 100% f(x)x - f(x )f(x) * etax - f(x ) * e ta QuickDraw - 10 Acc (%) Train Accuracy Test Accuracy ℱ !"#$% (푥)푥−ℱ !"#$% (푥)휂ℱ !"#$% (푥) 푥−휂ℱ !"#$% (푥) Fig. 7. Compare different readout strategies. Our differential, scaled residual shows the best accuracy on QuickDraw-10. by 2–3 orders of magnitude over LC-SLM-based prototypes. Indium-tin-oxide (ITO) transparent electrodes can be used to minimize optical loss. 4 Evaluation 4.1 Evaluation Setup 4.1.1 Model and Dataset. As a case study, we assume ourReDONsystem has up to 5 cascaded metasurfaces and 1ReDONblock. We couple out훼=5% of light. The hidden dimension is 3. For classi- fication on CIFAR-10 [13] and QuickDraw-10/50 [8], the head is FC512ReLU-FC128ReLU-FC32ReLU- FC10. For segmentation on binarized Stanford Background [9], the head is Conv2DC128K3ReLU- Conv2DC64K3ReLU-Conv2DC2K1. All 5 metasurfacesΦare shared across all blocks. Others parameters, includingW 푝푟푒 ,W 푝표푠푡 ,휂,Θare independently learned for eachReDONblock. Each metasurface has 32×32 meta-atoms. We use wavelength휆=532 nm, meta-atom size푠=400 nm, and metasurface spacing 푧= 8.42 휇푚 as used in the literature [19, 31]. 4.2 Ablation Study 4.2.1 Scaled, Differential Residual Output. Figure 7 compares our proposed residual formulation 푥 −휂F(푥)against several alternatives on the QuickDraw-10 classification task. Both the explicit scaling factor and the differential residual path substantially improve expressivity and training stability. 4.2.2Parametric FunctionΨSelection. The design of the parametric functionΨplays a crucial role in balancing expressivity and hardware efficiency. Figure 8 presents a comprehensive comparison across a wide range of candidates, including polynomials, common nonlinear operators (Tanh, ReLU, MaxPool), and lightweight operators such as 3x3 convolutions, evaluated under both phase and intensity self-modulation. The functions are ordered by decreasing accuracy, revealing a trend consistent with their computational complexity. Importantly, all candidates are implementable on compact digital logic, and several, such as scaling, bias, or small convolutions, can even be realized directly in the analog electrical domain without ADCs. A key observation is that even the simplest affine transformations (scale + bias) significantly outperform the passive baseline (i.e., no self- modulation). This demonstrates that our self-modulation mechanism itself contributes the most to the expressivity, not relying on any complicatedΨfunction. For further evaluation, we select two nonlinear functions (third-order polynomial and scaled Tanh) and two linear functions (affine transform and simple bias) as representatives spanning a range of hardware costs. 4.2.3Modulation Layer Exploration. We next examine how the choice of modulation layers affects expressivity and hardware cost. Figure 9 enumerates all combinations of coupling-out layers 푖 ∈ [1,5]and modulated layers푗 ∈ [푖,5]. For phase self-modulation, we observe two conclusions. (1) Later modulation layers yield higher accuracy: For any fixed couple-out index푖, accuracy , Vol. 1, No. 1, Article . Publication date: March 2026. Ziang Yin, Qi Jing, Raktim Sarma, Zhaoran Rena Huang, Yu Yao, and Jiaqi Gu maxpool(푥+푏) Tanh(푘 1 푥+푏) 70%80%90%100% 푘 2 푥 2 +푘 1 푥+푏 Tanh(푘 2 푥 2 +푘 1 푥+푏) ReLU(푘 1 푥+푏) 푘 1 푥+푏 푏 passive: 0 Intensity self-modulation Conv3x3푥+푏 70%75%80%85%90%95%100% 푘 3 푥 3 +푘 2 푥 2 +푘 1 푥+푏 푘 2 푥 2 +푘 1 푥+푏 Tanh(푘 1 푥+푏) ReLU(푘 1 푥+푏) 푘 1 푥+푏 푏 passive: 0 maxpool(푥+푏) 70% 75% 80% 85% 90% 95% 100% Phase Train AccPhase Test AccIntensity Train AccInten Phase self-modulation Train acc Test acc Tanh(푘 2 푥 2 +푘 1 푥+푏) ReLU(푘 2 푥 2 +푘 1 푥+푏) Conv3x3푥+푏 ReLU(푘 2 푥 2 +푘 1 푥+푏) 푘 3 푥 3 +푘 2 푥 2 +푘 1 푥+푏 Compute Complexity Compute Complexity Fig. 8. Compare the expressivity of differentΨ(퐸,Θ)functions on phase and intensity self-modulation.Ψ(·,Θ) are ordered by computing complexity. Each highlighted function represents the highest-accuracy model at different complexity levels. 83% 88% 93% 98% 0 2000 4000 6000 12345 12131415232425343545 123124125134135145234235245345 23451234123512451345 12345 2345 232425343545 234235245345 2345 345 343545 345 45 45 5 Num ParameterTrain Acc 83% 88% 93% 98% 0 2000 4000 6000 푖=1 푖=2푖=3푖=4푖=5 #params #params Accuracy Accuracy Phase Intensity 풋= Fig. 9. Parameter count and accuracy comparison with different sensing layer푖to modulated layers푗using phase and intensity self-modulation. Phase self-modulation shows better accuracy than intensity. The blue markup shows the best setting under different #layers in푗. These results motivate our choice of phase self-modulation and multi-layer modulation in the main experiments. increases as the modulation target푗moves deeper into the stack, with푗=5 consistently offering the best performance.This suggests that a longer linear transformation path between layers푖 and푗provides richer interference structure for modulation, whereas transformations occurring after modulation have comparatively limited impact. (2) Modulating more layers increases expressivity: The strongest performance is achieved when all five layers are modulated, i.e.,푖=1 and 푗= 1, 2, 3, 4, 5. While for intensity self-modulation, however, increasing the number of modulated layers drastically reduces accuracy. Unlike phase modulation, intensity modulation inherently attenuates optical power, and repeated attenuation across layers significantly limits expressivity due to compounded energy loss (and consequently low optical efficiency). Based on these observations, , Vol. 1, No. 1, Article . Publication date: March 2026. ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity 80% 81% 82% 83% 84% 10100100010000 Train Accuracy #Parameters 풊 = 3, 풋 = 5 in Ψ(⋅,Θ) 32x32 16x16 8x8 1x32 4x4 2x2 Sharing group: 푝 x 푞 32x1 16x1 1x16 (a) 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 12024036048050010002000 Power (mW) Desired FPS SRAM Write SRAM Read Head TIA DAC ADC Psi PWConv PD SLM Freq. SLM Modu Req. Freq. (kHz) Commercial LC-SLM operating freq. (10 kHz) Ψ(⋅) (b) Fig. 10. (a) Accuracy and #Params Pareto-front selection with different parameter sharing group sizes푝×푞on phase self-modulation with푖=1,푗=1,2,3,4,5 on QuickDraw-50. (b) Power breakdown and scaling with higher FPS. 1 10 100 1000 10000 100000 70% 75% 80% 85% 90% 95% 3 to 5 2 to 2 3 1 to 245 1 to 1345 1 to 12345 3 to 5 2 to 2 3 1 to 245 1 to 1345 1 to 12345 3 to 5 2 to 2 3 1 to 245 1 to 1345 1 to 12345 3 to 5 2 to 2 3 1 to 245 1 to 1345 1 to 12345 Psi ParametersTrain AccTest Acc Accuracy 32x32 16x16 32x12x2푝×푞= #Params #Params in Ψ Fig. 11. With the best modulation layer settings (푖to푗) from Fig. 9, we explore #Params vs. accuracy trade-off with different sharing group 푝,푞. we select representative configurations across different hardware budgets for later experiments: 3 to 5, 2 to (2,3), 1 to (2,4,5), 1 to (1,3,4,5), and 1 to (1,2,3,4,5). 4.2.4 Parameter Sharing Strategy. Figure 10 evaluates different spatial parameter-sharing group sizes in the accuracy-parameter-count trade-off, using푖=3,푗=5 as a representative configuration. Along the Pareto front, we identify four representative operating points, 32×32, 8×8, 32×1, and 2×2, that provide well-balanced trade-offs between expressivity and model compactness. Depending on the available on-chip memory budget for storing theΘparameters, one can choose an appropriate group size to meet system-level constraints. Figure 11 further combines the optimal group-sharing configurations (from Fig. 10) with the best-performing modulation-layer settings (from Fig. 9) to reveal the overall accuracy-parameter- count landscape. A clear trend emerges: modulating more layers has a stronger positive impact on expressivity than simply reducing the parameter-sharing group size. For instance, comparing 32×32 3-to-5 vs. 16×16 1-to-12345, with similar parameter counts, the latter consistently achieves higher accuracy. It indicates that modulating more diffractive layers contributes more to expressivity than increasing per-pixel parameter granularity, suggesting a practical design rule for future nonlinear DONNs. , Vol. 1, No. 1, Article . Publication date: March 2026. Ziang Yin, Qi Jing, Raktim Sarma, Zhaoran Rena Huang, Yu Yao, and Jiaqi Gu 4.2.5System Hardware Cost Analysis.ThroughputAnalysis. The primary throughput limitation of the proposed system stems from the modulation speed of commercially available spatial light modulators (SLMs), which currently operate at a maximum of퐹 SLM,max ≈10kHz. Although our self-modulation mechanism substantially enhances nonlinear expressivity, its reliance on SLM reprogramming makes it the dominant inference speed bottleneck. On the digital side, the detection head contains a total of 814,058 trainable parameters, corresponding to only 1.6×10 6 FLOPs, negligible compared with the DONN part. To characterize the SLM modulation speed requirement, we model the required modulation frequency as퐹 SLM,req = 푅 · 푁 · 퐶 mid · FPS, where푅is the number of recurrent iterations,푁is the number ofReDONblocks,퐶 mid denotes the hidden-channel dimension, andFPSis the target application frame rate. The system, using a commercial liquid-crystal SLM, remains feasible when 퐹 SLM,req ≤ 퐹 SLM,max ≈ 10 kHz. Given the SLM speed limit and a spatial resolution of 32×32, the maximum digital throughput after photodetection and readout from the CMOS sensor is bounded by푓 sample = 푆 · 퐹 SLM,req ,where 푆is the total number of pixel readout samples. Under our typical configuration, this corresponds to 푓 sample ≈2.95MS/s,which is well within the capability of modern ADC/DAC hardware, commonly supporting sampling rates on the order of 10–14 GS/s [4, 17]. Overall, with fourReDONblocks (푁=4) and fewer than two recurrent iterations (푅=2) per block, the system can process a 32×32 spatial input with 3 hidden channels at up to 416 FPS, or 78 FPS when using 16 hidden channels. These results demonstrate thatReDONremains compatible with real-time throughput. As mentioned in the next section, one can potentially enable much higher throughput using a programmable metasurface that supports GHz modulation speed. PowerBreakdown. We further analyze the power overhead related to the self-modulated circuitry. The introduced power overhead is overall negligible (<1 mW) compared to the laser power (>100 mW) of the DONN system. We estimate data-converter power using a standard figure-of-merit style scaling where power grows approximately linearly with sampling rate and exponentially with resolution (number of quantization levels). For a푏 in -bit DAC and푏 out -bit ADC operating at sampling rate 푓 , we model: 푃 퐷퐴퐶 (푏 푖푛 , 푓)= 푃 0,퐷퐴퐶 2 푏 푖푛 푏 푖푛 + 1 푓,(5) 푃 퐴퐷퐶 (푏 표푢푡 , 푓)= 푃 0,퐴퐷퐶 2 푏 표푢푡 푏 표푢푡 + 1 푓,(6) where푃 0,퐷퐴퐶 and푃 0,퐴퐷퐶 are technology- and architecture-dependent constants derived from representative high-speed converter designs. We estimate the power of the lightweight digital blocks (PWConv,Ψwhen implemented digitally, and the classification/segmentation head) by converting their required MAC throughput into power using an energy-per-MAC model. Using a 45 nm INT8 MAC energy of퐸 MAC ≈0.23 pJ/MAC [10], the corresponding efficiency is 휂 MAC = 1/퐸 MAC ≈ 4.35× 10 12 MAC/J. Therefore, 푃 digital = MAC/s 휂 MAC =(MAC/s)· 퐸 MAC .(7) In Fig. 10(b), we show the power scaling with increased target FPS. With a commercial liquid- crystal SLM that supports 10 kHz modulation rate, ourReDONcan achieve over 400 FPS throughput. A higher FPS can be realized using advanced electro-optic tunable metasurfaces [2,3,26]. We can see SRAM (45 nm) access takes the largest proportion of power, while sensor array, TIA, ADC/DAC, and digital (PWConv/head) (45 nm), due to time-multiplexing and low cost, only take less than 3% of the power overhead. OurReDONsystem (푁=1) can potentially support over 1000 FPS end-to-end , Vol. 1, No. 1, Article . Publication date: March 2026. ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity Table 1. Comparison across different nonlinearity designs on 3 benchmarks, our proposedReDONwith scaled Tanh asΨconsistently achieves the best performance.ReDONsharesΘacross all 5 modulated layers. With more recurrence (푅) and blocks (푁),ReDONshows 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. CIFAR-10QuickDraw-50 Stanford Background Seg. Binarized Seg Different Nonlinear Strategy Train Acc. Test Acc.Train Acc. Test Acc.Train mIoUTest mIoU Saturable Absorption [33]61.9%61.1%80.1%71.3%72.2%47.1% Reflection Coating [7]58.4%58.3%76.6%68.5%68.3%41.3% Encoding (Phase) [15]61.2%60.2%79.4%70.4%76.1%53.4% Encoding (Intensity) [15]58.3%58.6%76.5%68.7%66.4%46.9% Encoding (Complex) [15]59.7%59.6%77.9%69.8%68.2%44.3% Digital activation (Log)60.1%58.1%78.3%68.3%69.5%38.2% Digital activation (Square)61.4%60.4%79.6%70.6%72.1%51.7% Digital activation (Tanh)62.6%60.7%80.7%70.9%77.2%55.6% ReDON 푖=1, 푗 =1,2,3,4,5 Tanh(푘 1 푥 +푏) cross-layer share 푝×푞=32×32, 푅= 1, 푁= 1 74.4%64.8%86.7%76.7%83.3%68.7% ReDON Diffractive Only 푅= 2, 푁= 4 70.7%61.2%82.9%73.1%70.9%58.2% ReDON Digital Tanh 푅= 2, 푁= 4 77.4%66.4%91.8%77.6%85.4%63.8% ReDON 푖=1, 푗 =1,2,3,4,5 Tanh(푘 1 푥 +푏) cross-layer share 푝×푞=32×32, 푅= 2, 푁= 4 83.6%74.5%98.8%81.33%89.2%72.4% inference with only∼1 mW electrical power overhead compared to passive DONNs, showing its potential for low-power edge deployment on real-time inference tasks. 4.3 Main Results Using the optimal settings identified through our ablation studies, Table 1 compares our self- modulated nonlinearity with prior optical and hybrid nonlinear mechanisms. We report both training accuracy (reflecting expressivity) and test accuracy (reflecting generalization). For fully optical nonlinearities, we benchmark against saturable absorbers and reflection-based nonlinear coatings. We also compare against natural nonlinearities arising from input encoding [15], as well as digital nonlinear activations (logarithmic, square, Tanh). All baselines use the same metasurface stack, input resolution, and digital head; only the nonlinearity mechanism differs. Across CIFAR-10, QuickDraw-50, and Stanford Background segmentation, ourReDONachieves substantially higher accuracy (+20% on average) and mIoU, even with a single block (푁=1) and a lightweight scaled TanhΨfunction. Notably, prior DONNs with a single diffractive stage typically achieve <60% accuracy on CIFAR-10 in the literature. To our knowledge,ReDONis the first to reach∼65% accuracy using only one block, highlighting its markedly improved expressivity. In the lower half of Table 1, we perform a controlled ablation by keeping all architectural components identical but replacing our self-modulation mechanism with either (1) a purely linear DONN or (2) a DONN augmented with digital nonlinear activation. Compared to simply adding digital activations, the self-modulation learns task-specific nonlinear functions with much higher accuracy, explaining the clear gain from self-modulation over the digital activation function at the same recurrence/block depth. It also shows its benefits compound when scaling to deeper architectures. Our evaluation focuses on modest-scale inputs for proof-of-concept evaluation, , Vol. 1, No. 1, Article . Publication date: March 2026. Ziang Yin, Qi Jing, Raktim Sarma, Zhaoran Rena Huang, Yu Yao, and Jiaqi Gu Table 2. Transferability evaluation ofReDON(푅=2,퐵=4). On Fasion-MNIST→QuickDraw-10, we show classifi- cation test accuracy. On Darcy flow→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. Design Accuracy↑Mean-Square Error (MSE)↓ FMNIST QuickDraw-10 adapt from FMNIST Darcy Navier-Stokes adapted from Darcy Saturable Absorption [33]80.1%53.1%0.0950.1822 ReDON95.1%87.2%0.0150.1035 (a) Stanford cars binarized image segmentation (b) Darcy flow PDE solving (c) Navier-Stokes PDE solving InputPred. by Ground truth Mask overlay Input Pred. by Ground truth Input Pred. by Ground truth Fig. 12. Visualization of representative inference results ofReDONon (a) Stanford cars image segmentation, (b) Darcy flow, and (c) Navier-Stokes PDE solving tasks. also due to training resource limitations. ExtendingReDONto high-resolution vision tasks is an important direction for future work. Task Adaptability of ReDON. We assessReDON’s task adaptability on both classification and PDE solving, as summarized in Table 2. After training on a source task, we freeze all metasurfaces and adapt only the head, PWConv, and the tunableΨ(·,Θ)functions on new tasks. Under this constraint, ReDONachieves substantially better transfer performance: on QuickDraw, it improves accuracy by 34% over the baseline, and on Navier-Stokes it reduces the adapted solution error by 40%. We further compareReDONto a nonlinear DONN based on saturable absorption [33], which can only finetune the head with a fixed diffractive optical encoder, which severely limits its transferability. ReDON Inference Visualization . Figure 12 visualizes the inference results ofReDONon advanced learning tasks, including image segmentation and PDE solving, demonstrating the high expressivity and inference quality of ReDON in real-world complex tasks beyond simple classification. ReDON Robustness Study. Practical diffractive optical systems inevitably suffer from physical non-idealities such as diffractive layer misalignment, random perturbations on the readout due to input/sensor noises, and fabrication-induced metasurface phase response deviations. We evaluate , Vol. 1, No. 1, Article . Publication date: March 2026. ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity Designed Fabricated MisalignmentRandom Noise on Readout Metasurface Fabrication Error Horizontal (E / W) & vertical (N / S) misalignment N E W Φ ! Φ "#$%& Sensor noise System noise (Input noise, etc) 훿푥 S 훿푥 훿푥 훿푥 Meta-atom size variation Fig. 13. Robustness evaluation settings under practical non-idealities. Left: random horizontal/vertical mis- alignment of diffractive planes up to±1 pixel/meta-atom size. Middle: additive Gaussian noise with휎=0.01 applied to sensed light intensities. Right: fabrication-induced phase error modeled as i.i.d. Gaussian phase perturbations with 휎 휙 = 0.01 푟푎푑 on metasurface phase responses. 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. 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 (휎 )0.040.060.080.1 Averaged test accuracy93.1%92.4%91.2%89.1% Std. of test accuracy0.00290.00280.00290.0033 Fabrication Error (FE) Injected phase error 휎(훿휙)0.20.40.60.8 Averaged test accuracy90.3%88.2%82.3%76.3% Std. of test accuracy0.00460.00520.00540.0062 Combined: MA + RN + FE Combined system errorMA 0.5 + RN 0.04 + FE 0.2MA 1 + RN 0.06 + FE 0.4MA 1.5 + RN 0.08 + FE 0.6MA 2 + RN 0.1 + FE 0.8 Averaged test accuracy88.1%86.2%79.1%71.8% Std. of test accuracy0.00520.00540.00510.0059 Noise-injected inference (Noise-aware Training) Misalignment (MA) Misaligned pixel size0.511.52 Averaged test accuracy91.9%91.7%91.6%91.7% Std. of test accuracy0.00410.00490.00420.0044 Readout Noise (RN) Injected Gaussian noise (휎 )0.040.060.080.1 Averaged test accuracy91.1%91.0%92.7%92.0% Std. of test accuracy0.00280.00290.00310.0034 Fabrication Error (FE) Injected phase error 휎(훿휙)0.20.40.60.8 Averaged test accuracy91.8%91.2%91.3%91.2% Std. of test accuracy0.00510.00570.00550.0048 Combined: MA + RN + FE Combined system errorMA 0.5 + RN 0.04 + FE 0.2MA 1 + RN 0.06 + FE 0.4MA 1.5 + RN 0.08 + FE 0.6MA 2 + RN 0.1 + FE 0.8 Averaged test accuracy91.6%91.1%91.5%91.1% Std. of test accuracy0.00490.00440.00510.0052 robustness on Fashion-MNIST classification using a 5-layerReDONsystem without recurrence to isolate the physical sensitivity of the optical front-end. As illustrated in Fig. 13, we consider three non-ideality sources: (i) misalignment, modeled as a random lateral shift of each diffractive plane, where the shift direction (horizontal or vertical) and sign are randomly selected, and the shift magnitude is set to the specified misalignment level (in pixel units with pixel size푠=400nm); (i) readout noise, modeled as additive i.i.d. Gaussian noiseN(0,휎 2 )applied to the sensed intensities; , Vol. 1, No. 1, Article . Publication date: March 2026. Ziang Yin, Qi Jing, Raktim Sarma, Zhaoran Rena Huang, Yu Yao, and Jiaqi Gu and (i) fabrication error, modeled as i.i.d. Gaussian phase perturbations훿휙 ∼N(0,휎 2 )added to each meta-atom phase response. For e-beam lithography fabricated metasurfaces, the average phase error experimentally observed is typically around 5 to 10 degrees, which justifies the practicality of phase error injection strength later in Table 3. Table 3 summarizes the resulting test accuracy under inference-time noise injection. For each noise setting in Table 3, we perform 5 independent evaluation iterations over the test set. Within an iteration, the injected noise realization is held fixed, while a new noise realization is resampled for the next iteration. Therefore, the evaluation is stochastic across iterations, and Table 3 reports the mean and standard deviation of accuracy over 5 iterations. Under standard (noise-free) training,ReDONremains relatively resilient to moderate MA and RN, but becomes increasingly sensitive to FE, and especially to compound system-level errors. In the most severe combined setting (MA 2 + RN 0.1 + FE 0.8), accuracy drops substantially. To mitigate this, we perform noise-aware training by injecting the combined system noise (MA 2 + RN 0.1 + FE 0.8) during training to encourage a more robust model. This noise-aware model slightly reduces noise-free accuracy (92.9%), but markedly improves robustness, maintaining 91-92% accuracy across the tested ranges of MA/RN/FE and recovering most of the accuracy under harsh combined-noise conditions. 5 Conclusion We presentReDON, a recurrent diffractive optical neural processor that overcomes the weak nonlin- earity and rigidity of conventional DONNs through a self-modulated electro-optic nonlinearity. By sensing a small portion of the optical field and dynamically modulating downstream meta- surfaces,ReDONprovides a strong, tunable, input-dependent nonlinear response with minimal overhead while preserving the speed and parallelism of optical in-memory computing. Through extensive design-space exploration, we show thatReDONconsistently delivers far higher nonlinear expressivity with balanced efficiency compared to prior nonlinear mechanisms. This makesReDON a promising candidate for adaptive front-end encoders in optical machine learning systems. It establishes a new direction toward reconfigurable, recurrent, nonlinear diffractive in-memory computing. Acknowledgments R.Sarma and Y. Yao acknowledge support from the Laboratory Directed Research and Development program at Sandia National Laboratories and Sandia University Partnerships Network (SUPN) program. This work was performed in part at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE’s National Nuclear Security Administration under Contract No. DE-NA-0003525. 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