Partitionable Diffractive Neural Networks (PDNNs)

• PDNNs are optical neural architectures that utilize nanostructured metasurfaces to enable reconfigurable and multi-task inference.
• They employ partitioning strategies—such as spatial segmentation, spectral/polarization multiplexing, and layer permutation—to multiplex functionalities.
• Advanced training methodologies and diffraction-based propagation models deliver high speed, low power consumption, and hardware-efficient performance.

Multifunctional Partitionable Diffractive Neural Networks (PDNNs) are optical neural architectures that exploit the wave nature of light and the physical degrees of freedom available in nanostructured metasurfaces to enable high-speed, ultralow-power, multi-task inference and functional reconfigurability. By leveraging partitioned diffractive layers—either physically segmented or multiplexed in spectral, polarization, or spatial channels—PDNNs address the limitations of fixed-functionality conventional all-optical diffractive neural networks (D2NNs) and provide pathways to hardware-efficient, versatile, and truly multitasking optical artificial intelligence systems. This entry details the principles, implementations, multiplexing strategies, training methodologies, and performance trade-offs of PDNNs, as grounded in experimental and computational research.

1. Physical Architecture and Partitioning Strategies

PDNNs consist of cascaded diffractive layers (often realized as phase-only metasurfaces or DOEs), with each layer discretized into subwavelength-scale “neurons” (pixels, nanopillars, or nanofins). These physical neurons impart spatially varying phase delays to the optical field, which then propagates between layers via free-space diffraction described by the Rayleigh–Sommerfeld or Fresnel integral (Luo et al., 2021, Behroozinia et al., 2024, Tian et al., 25 Jan 2026, Motz et al., 2024, Tian et al., 23 Jun 2025, Chen et al., 2022).

Partitionability is achieved by one or more of the following mechanisms:

• In-plane segmentation: The diffractive layer is divided into distinct spatial regions (e.g., quadrants), each trained as an independent submodule for a specific task. These submodules can be activated individually (via masks) or horizontally stacked for composite functionalities. For instance, quadrant-based PDNNs demonstrated both independent and combined holography/classification tasks by switching masking configurations or rotating quadrants (Tian et al., 25 Jan 2026).
• Spectral and polarization multiplexing: The metasurface architecture can realize channel-dependent phase responses—distinct for each polarization or wavelength—enabling simultaneous implementation of fully independent DNNs. Polarization multiplexing assigns different phase maps (e.g., φx, φy) to x- and y-polarizations, while spectral multiplexing exploits wavelength-dependent responses for each task (Luo et al., 2021, Behroozinia et al., 2024, Motz et al., 2024, Chen et al., 2022).
• Layer permutation: Modular diffractive layers can be physically rearranged or permuted in the optical stack, so that the sequence of layers is task-selective. By reconfiguring the order (e.g., {layer 1 → layer 2} or {layer 2 → layer 1}), the same hardware can implement distinct functions (Tian et al., 23 Jun 2025).
• In-depth (longitudinal) multiplexing: Different subsets of layers are trained for separate channels, or the same set of phase masks is trained so that their effective modulation is channel-dependent (e.g., via wavelength) (Chen et al., 2022, Motz et al., 2024).

Channels are generally defined by physical degrees of freedom: spatial partition, polarization, wavelength, or, in advanced cases, angle of incidence and orbital angular momentum.

2. Optical Propagation and Phase Modulation Models

All PDNN implementations are governed by first-principles optical diffraction. The complex field propagation from layer ℓ to ℓ+1 is modeled as:

$$U_{\ell+1}(x, y) = \iint U_\ell(x', y') \cdot h(x - x', y - y', z) \cdot e^{i \phi_\ell(x', y')} dx' dy'$$

Where $h(\Delta x, \Delta y, z)$ is the diffraction kernel, accounting for the geometry and wavelength, and $\phi_\ell(x, y)$ encodes the locally applied phase by each neuron (Luo et al., 2021, Behroozinia et al., 2024, Tian et al., 25 Jan 2026).

For metasurface-based architectures, each optical neuron’s phase delay is set by its geometrical parameters (e.g., nanofin width, orientation, or local thickness), and may independently control multiple phase channels (e.g., along x and y axes for birefringent nanopillars). Under wavelength or polarization multiplexing, the transmission coefficient generalizes to $$T_{p, \lambda}(x, y) = |T_{p, \lambda}| \exp[i \phi_{p, \lambda}(x, y)]$$ with $p$ the polarization, and $\lambda$ the wavelength (Luo et al., 2021, Behroozinia et al., 2024, Motz et al., 2024, Chen et al., 2022).

Physical constraints, such as phase quantization or fabrication-dictated thickness limits, are incorporated via parameterizations and regularization terms. Phase-only modulation is dominant due to higher transmittance and fabrication tractability (Chen et al., 2022, Behroozinia et al., 2024).

3. Multiplexing Schemes and Functional Reconfiguration

Multifunctional PDNNs realize several concurrent or switchable inference tasks by multiplexing independent “channels” through:

• Polarization multiplexing: Birefringent architectures encode independent phase maps for orthogonal polarizations. In Jones-matrix formalism, $J_{meta}(x,y)$ acts as a diagonal matrix with entries $e^{i\phi_x(x,y)}$ and $e^{i\phi_y(x,y)}$. Experimental platforms achieved dual-channel classification (MNIST vs. Fashion-MNIST) at high density ($6.25 \times 10^6$ neurons/mm²/channel) with >99% simulation and ≃96% experimental accuracy per channel (Luo et al., 2021).
• Wavelength multiplexing: Distinct tasks are addressed by encoding channel-selective phase profiles, exploiting the wavelength-dependence of metasurface transmission. Three-task PDNNs were demonstrated, with selective activation by incident λ (e.g., 457 nm, 532 nm, 633 nm) (Behroozinia et al., 2024, Motz et al., 2024, Chen et al., 2022). Crosstalk is minimized by design of meta-atom responses, confirmed by negligible detector cross-energy.
• Spatial partitioning: Physical quadrants or blocks of metasurface layers act as functionally isolated submodules. These can be activated individually (by masks) or jointly (by unmasking), and even re-combined by rotation or lateral translation for new tasks. One experiment used four quadrants each outputting a letter shape, where removing masks yielded composite digits not present in any basis quadrant (Tian et al., 25 Jan 2026).
• Layer permutation: Mechanically rearranging metasurface layers unlocks different task orderings, yielding up to M! configurations with M layers. Weighted multi-task loss enables tailoring performance trade-offs for tasks of differing complexity (Tian et al., 23 Jun 2025).

Functional reconfiguration occurs purely through optical adjustments—changing incident polarization, wavelength, or physical arrangement—without slow or energy-intensive electronic tuning.

4. Training Methodologies and Loss Formulations

PDNNs are trained using end-to-end differentiable physics models. The core approach is to minimize a composite loss $L$ aggregating the task-wise losses over all channels, with:

$L = \sum_{c=1}^{C} L_c$

For classification, $L_c$ is typically cross-entropy between the measured and target intensities integrated over the assigned detector regions. For imaging or holography, mean-squared error (MSE) in normalized intensity is used. Partitioned modules may be trained sequentially (submodule-wise), then jointly fine-tuned in composite mode (Tian et al., 25 Jan 2026).

Multiplexed channels (e.g., polarization, wavelength) are trained by defining a global loss function summing over all tasks, with task-specific weighting for preferential accuracy (e.g., $L_{total} = \sum_t \lambda_t L_t$, adjusting $\lambda_t$ for emphasis) (Tian et al., 23 Jun 2025, Luo et al., 2021). For metasurface hardware, surrogate neural networks can embed the full COMSOL-derived meta-atom response to accurately propagate gradients through physical constraints (Behroozinia et al., 2024).

Backpropagation proceeds through the propagation integrals, phase transmission functions, and quantum yield/efficiency measures, with update rules based on SGD, Adam, or momentum-augmented methods. Training is tractable on standard GPUs, with convergence in minutes to hours for mm-scale devices (Luo et al., 2021, Tian et al., 25 Jan 2026, Motz et al., 2024).

5. Performance Metrics and Experimentally Realized Systems

Performance is evaluated along several axes:

Metric	Reported Values/Reference	Context
Diffraction efficiency η	46–48% per submodule (sim.), 14–28% (exp.) (Tian et al., 25 Jan 2026)	Holography and combined imaging tasks
Classification accuracy	>99% sim., ≃96% on-chip exp. (dual-task) (Luo et al., 2021); 95–100% (Tian et al., 25 Jan 2026); 96–98% (3-task) (Motz et al., 2024)	MNIST, Fashion-MNIST, EMNIST
Throughput/latency	Inference <1 ns (optical), limited by CMOS/frame rate (Luo et al., 2021)	Speed-of-light operation
Reconfigurability	Up to M! functions by layer permutation (Tian et al., 23 Jun 2025)	Physical stacking of layers
Crosstalk	<0.1 contrast loss per task (no significant leakage) (Motz et al., 2024)	Wavelength/polarization-encoded PDNNs

Experimentally, PDNNs have demonstrated dual- and triple-task classification at visible to THz frequencies, with segmentations as fine as 400 nm pitch and active areas of 5+ mm² (Luo et al., 2021, Tian et al., 25 Jan 2026, Behroozinia et al., 2024, Tian et al., 23 Jun 2025, Chen et al., 2022, Motz et al., 2024). Output matching to simulation remains within a few percent, and aggregation of submodules yields hardware-efficient expansion in task repertoire with negligible additional latency or energy consumption.

6. Comparative Analysis and Scaling Behavior

Conventional D2NNs are hardware-static; a new function demands network-wide retraining and full refabrication. PDNNs, by contrast, achieve:

• Functional multiplexing: K submodules and their combinations yield substantially more than K functions, e.g., 5–8 operations realized with four spatial quadrants (Tian et al., 25 Jan 2026).
• Hardware re-use: The same physical device realizes multiple tasks without active elements or energetic cost.
• Task scalability: Dual- and triple-channel PDNNs maintain >80% per-task accuracy. For higher channel counts, performance is preserved by end-to-end joint physical-constraint-aware optimization (Behroozinia et al., 2024).
• Power and latency invariance: Multi-task and composite operations incur no penalty in inference time or optical power, all being single-pass diffraction-limited processes.

Limitations include diminished imaging/classification accuracy under increased crosstalk, especially if physical constraints force suboptimal phase assignments as multiplexing channel count rises. Joint optimization frameworks and weighted loss functions help mitigate these effects (Behroozinia et al., 2024, Tian et al., 23 Jun 2025).

7. Outlook and Generalization

PDNNs are extensible to a wide variety of physical multiplexing modes: polarization, spectral, spatial, angular (incident angle), and orbital angular momentum. Integration of dynamic meta-atoms (e.g., phase-change or liquid-crystal elements) is anticipated to add truly on-demand reconfigurability (Behroozinia et al., 2024). Scaling engineering suggests adding more layers, increasing neuron density, and adopting more sophisticated meta-atom designs to enhance expressivity, provided fabrication constraints are met (Chen et al., 2022).

Open pathways include hybrid electronic–optical inference, calibration for robustness against fabrication errors, and leveraging nonplanar or three-dimensional networks for increased task density. PDNNs thus offer a compelling architecture for next-generation, high-speed, hardware-efficient, and multifunctional optical AI systems that can bridge the gap between the limited task set of static D2NNs and the complexity of SLM-based programmable photonic systems (Tian et al., 23 Jun 2025, Luo et al., 2021, Tian et al., 25 Jan 2026).

---

References:

(Luo et al., 2021, Tian et al., 25 Jan 2026, Tian et al., 23 Jun 2025, Behroozinia et al., 2024, Chen et al., 2022, Motz et al., 2024)