Pith. sign in

REVIEW 4 major objections 5 minor 48 references

Metasurface-empowered freely-arrangeable multi-task diffractive neural networks with weighted training

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read By swapping the order of two phase-only metasurface layers, a single trained optical network classifies both handwritten digits and fashion items, at simulated accuracies close to two dedicated networks that use twice the hardware.

desk verdict Layer-order permutation as a task selector is a genuinely new idea and the simulation evidence largely supports it, but the paper never isolates the mechanism and the experiment is too thin to carry the load. read the letter →

arxiv 2506.18242 v1 pith:K2TDQITN submitted 2025-06-23 physics.app-ph physics.optics

Yudong Tian , Haifeng Xu , Yuqing Liu , Xiangyu Zhao , Jingzhu Shao , Jierong Cheng , Chongzhao Wu This is my paper · ORCID
classification physics.app-phphysics.optics
keywords opticalneuralnetworksdiffractivedeepmulti-tasklearningmetasurfacesterahertzlayerrearrangementPancharatnam-Berryphase
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper sets out to show that a diffractive neural network — an optical computer built from stacked phase-modulating layers — can be switched between tasks simply by reordering its already-designed layers, with no retraining and no new hardware. Using two phase-only metasurface layers trained once with a weighted multi-task loss, the authors demonstrate that the order $\{\varphi_1, \varphi_2\}$ classifies handwritten digits while the swapped order $\{\varphi_2, \varphi_1\}$ classifies fashion items, reaching simulated test accuracies of 88.9% and 81.8% against 91.0% and 84.4% for two dedicated two-layer networks. Because light encounters the same two modulators in a different sequence, each arrangement behaves as a distinct network, turning layer arrangement into a reconfiguration mechanism that costs nothing extra in fabrication. A proof-of-concept experiment at 0.291 THz confirms both orderings focus light onto the correct detection regions, though with lower accuracy than simulation. If the claim holds, static diffractive hardware can serve many tasks at a fraction of the hardware and training cost.

What carries the argument

The load-bearing object is the ordered sequence of diffractive layers, treated as a permutation of shared phase-only metasurfaces. In a D2NN each layer multiplies the propagating optical field by its phase profile, and diffraction between layers is modeled with the angular spectrum method; since propagation from layer A to layer B is not identical to propagation from B to A, each ordering composes the same modulators into a different classifier. Training couples the orderings through a weighted multi-task loss, $\mathcal{L}_{\mathrm{multi}} = \mathcal{L}(\theta_1; X_1, Y_1) + \beta\mathcal{L}(\theta_2; X_2, Y_2)$, so one backpropagation updates the shared phase profiles for both tasks and $\beta$ trades accuracy between them. On the physical side, the layers are silicon metasurfaces whose rotation-angle-controlled Pancharatnam–Berry phase gives full $0$–$2\pi$ phase coverage, designed by FDTD parameter sweeps and fabricated by photolithography, so one fabricated wafer pair realizes both task configurations by mechanically swapping layer order.

What would settle it

Measure the output-plane field of the two fabricated metasurfaces in both orders on the same input set: the permutation mechanism predicts that each ordering routes energy to a different class region with classification accuracy near the trained values, so statistically indistinguishable confusion matrices across orderings, or unchanged outputs when the layers are swapped with an unrelated trained pair, would refute the claim that layer order carries the reconfiguration.

Watch

Extended reading notes

Core claim

The central claim is that permutation of trained diffractive layers is itself a task-selection mechanism. The authors construct a two-task A-DNN from two phase-only metasurfaces with phase profiles $\varphi_1$ and $\varphi_2$, define the two configurations $\theta_1 = \{\varphi_1, \varphi_2\}$ and $\theta_2 = \{\varphi_2, \varphi_1\}$, and train both at once by minimizing the weighted sum $\mathcal{L}_{\mathrm{multi}} = \mathcal{L}(\theta_1; X_1, Y_1) + \beta \mathcal{L}(\theta_2; X_2, Y_2)$ in a single backpropagation pass. After training, the network scores 88.9% test accuracy on MNIST and 81.8% on FashionMNIST, versus 91.0% and 84.4% for two separately trained two-layer D2NNs — halving the trainable diffractive units and roughly halving training time. The weight $\beta$ acts as an accuracy dial, moving performance toward FashionMNIST when increased and toward MNIST when decreased. A three-task variant built from four layers raises the hardware-efficiency gain to 66.7% and cuts training time to one-third of the dedicated-network baseline.

Load-bearing premise

The scheme assumes that the angular-spectrum, phase-only optical model used during training predicts how the fabricated metasurfaces actually transform light; the paper's own experiment shows accuracy dropping from 93.1% to 75% for digits and from 87.2% to 70% for fashions, so that fidelity is only partly met.

Editorial extensions

If this is right

  • Reconfiguration no longer requires refabrication or retraining: any permutation of a trained stack is a candidate new configuration, so a single fabricated set of metasurfaces can be physically reordered for different jobs.
  • Hardware cost shrinks with the task-to-layer ratio: two tasks on two shared layers use half the diffractive units of two dedicated networks, and four layers hosting three tasks save 66.7% of hardware while cutting training time to one-third.
  • The weight parameter $\beta$ gives an operator an explicit accuracy dial, allowing a harder or more valuable task to be prioritized at the expense of another.
  • The authors note the framework composes with other optical multiplexing techniques, so layer arrangement could be combined with wavelength- or spatial-multiplexing to enlarge the number of tasks per device.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Only the two-layer, two-task case is demonstrated in the main text, so the promise that larger stacks host many permutations as usable tasks is an extrapolation; a natural test is training a three- or four-layer stack and evaluating all $N!$ orderings to see how many reach usable accuracy.
  • The simulation-to-experiment accuracy gap (93.1% to 75% for digits, 87.2% to 70% for fashions) indicates the forward optical model's fidelity, not the permutation idea itself, is the current bottleneck; the paper's own suggested remedies, repeating identical nano-fins per pixel and inverse design, could be tested directly by replacing ideal phase profiles with measured complex transmission in simu
  • If layer order is a genuine task selector, the number of tasks a stack can host grows factorially with layer count, but accuracy per ordering may degrade as the same modulators are asked to do more; measuring that accuracy-versus-permutations tradeoff would tell whether the mechanism scales beyond a few tasks.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes an arrangeable diffractive neural network (A-DNN) in which two phase-only metasurface layers are trained jointly under a weighted multi-task loss (Eq. 7); at inference, swapping the physical order of the two layers switches the network between MNIST digit and FashionMNIST fashion classification. Simulations on 10-class tasks report test accuracies of 88.9% (MNIST) and 81.8% (FashionMNIST), versus 91.0% and 84.4% for two dedicated two-layer D2NNs, using one shared pair of layers (Table 1). A 5-class proof-of-concept experiment at 0.291 THz with 80x80 metasurfaces reports simulated accuracies of 93.1% and 87.2% but measured accuracies of 75% and 70% on 40 fabricated input samples. The paper also presents a beta-sweep showing task-weight control and robustness tests against phase noise and layer misalignment.

Significance. The central idea, if confirmed, is attractive: layer-order permutation is a zero-hardware-cost reconfiguration mechanism that turns one trained diffractive pair into two classifiers, and the weighted-loss formulation gives a simple way to trade off task performance. The manuscript has real strengths: results are measured on standard external benchmarks; the beta trade-off is swept openly; the training code is promised to be available; and a full metasurface fabrication and THz measurement is reported. The significance is nevertheless moderate: the simulations show a small but real accuracy penalty relative to dedicated D2NNs, the experimental demonstration rests on 40 samples with a large simulation-to-experiment drop, and the mechanism is not isolated by ablations.

major comments (4)
  1. [Sec. 3.2, Eq. (7)] The central claim that swapping layer order creates two distinct classifiers is not isolated by the experiments. Training under Eq. (7) optimizes a shared phase pair against both orderings simultaneously, so the same pair could in principle solve both tasks without the swap being causally important (e.g., one layer could dominate each task, or the pair could multiplex the two tasks in a way that is insensitive to order). I request (i) a control in which the same two layers are trained on both tasks with a fixed order (using a combined output plane) and evaluated without any reconfiguration, (ii) a control in which a single-task-trained pair is evaluated after swapping its layers on the other task, (iii) a similarity measure between the optimized phase profiles, and (iv) training from at least five random initializations with mean and standard deviation for every reported accuracy. Without (i)-(iv), the 88.9%/81.8% results could reflect a favorable initialization or an implicit multiplexing effect rather than the permutation mechanism.
  2. [Sec. 3.4, Figs. 7-8] The experimental demonstration does not support the quantitative accuracy comparison. The text says 40 samples were fabricated but does not state the per-task split. For a five-class task, chance is 20%, and 30 correct out of 40 gives a 95% Wilson interval of roughly 59-86%, so the reported 75% and 70% values are not precise estimates of deployment accuracy. The simulation-to-experiment drop (93.1% to 75% for digits, 87.2% to 70% for fashions) is attributed to forward-design errors (Sec. 4, Fig. S8) without a quantitative error budget. Please report per-class counts, confidence intervals, and either a larger experimental test set or a simulation that uses measured meta-atom phase and amplitude responses to reproduce the experimental accuracies.
  3. [Sec. 3.2, Table 1] The claims of '50% improvement in hardware efficiency' and 'saving nearly half of the training time' are not demonstrated by the reported measurements. Table 1 compares parameter counts, but A-DNN's per-iteration forward cost includes two ordered propagations (one per task), and no wall-clock training time or energy measurement is reported. The comparison also varies the number of tasks by construction (one multi-task network versus two single-task networks), so the claimed savings need a direct timing comparison with the same optimizer and hardware. Please either report actual training times or energy or restrict the claim to parameter count.
  4. [Sec. 3.3] The robustness analysis does not test the sensitivity of the permutation mechanism itself. The Gaussian phase-noise and misalignment tests show that the trained A-DNN tolerates fabrication errors, but they do not address whether the classification of each task remains tied to the correct layer order, nor how the mechanism degrades as the two phase profiles become more correlated. A direct test would be to perturb one layer and measure the accuracy of both orderings, or to interpolate between the two optimized phase profiles and report the accuracy of each task; this would show whether the swap is a true functional switch rather than a fortuitous property of the optimized pair.
minor comments (5)
  1. [Sec. 2, Fig. 2] Eq. (1) presents a Rayleigh-Sommerfeld propagator, while Fig. 2 states that forward propagation is computed with the angular-spectrum method; clarify which model is implemented in the training code and confirm the two are used consistently.
  2. [Sec. 3.1, Fig. 3d] The 'overall test accuracy' in Fig. 3d is not defined; specify whether it is the mean of the MNIST and FashionMNIST accuracies and add error bars across seeds before claiming that moderately increasing beta improves overall accuracy.
  3. [Sec. 3.4] The accuracies 93.1% and 87.2% are for five-class subsets, while Table 1 reports 88.9% and 81.8% for ten-class tasks; state the class count at every occurrence to avoid confusion.
  4. [Data Availability] The code link is given as 'Atrf/Arrangeable-multi-task-diffractive-neural-network' without a full URL or DOI; provide a persistent link that reviewers can access.
  5. [Fig. 5 caption and Sec. 3.3] The caption says x, y, and z represent the dimensions of the diffraction layer, while the text says x and y are side lengths and z is the layer distance; align the caption with the text.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the A-DNN multi-task claim is tested against external MNIST/FashionMNIST benchmarks with an openly specified weighted loss, so the central result is not equivalent to its inputs.

full rationale

The paper's central derivation chain consists of (i) a weighted multi-task loss over the same two phase-only metasurface layers in two orders, Eq. (7); (ii) a single backpropagation training run; and (iii) evaluation on external MNIST and FashionMNIST test sets, reported in Table 1 and Figs. 4, 7, and 8. The multi-task loss is a training objective, not a hidden fit to the test results: beta is swept openly in Sec. 3.1 and the headline comparison uses beta = 1, and the test accuracies are measured against labels that are not used as trainable parameters. No parameter is fitted to the reported accuracies, and no result is asserted on the authority of a self-citation: the optical model (Rayleigh-Sommerfeld / angular spectrum) is standard and the experimental metasurface design uses FDTD meta-atom sweeps that are openly parameterized. The acknowledged simulation-to-experiment drop (93.1%/87.2% to 75%/70%) is a fidelity limitation, not circularity. The lack of seed repetition and ablations would bear on robustness or conclusiveness, but it does not make any predicted number equivalent to the inputs by construction. Accordingly, no circular step satisfies the evidence bar, and the appropriate score is 0.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central result rests on standard diffraction physics plus a set of design hyperparameters and the empirical premise that joint training yields order-selective behavior. No hidden fitted constants beyond network weights and the reported hyperparameters are used. No new physical entities are introduced.

free parameters (4)
  • Task weight beta = beta = 1 for main results; swept in Fig. 3
    Weight on the FashionMNIST loss in Eq. 7, chosen by hand to control the task accuracy tradeoff; the central comparison uses beta = 1.
  • Metasurface nanofin length and width = L = 90 um, W = 465 um
    Selected from FDTD parameter sweeps over 50-500 um in 5 um steps to maximize cross-polarization conversion efficiency (91.2%).
  • Layer sizes and interlayer distances = 200x200 pixels with 10 cm spacing for 10-class; 80x80 pixels with 1.5 cm spacing for the experiment
    Architecture hyperparameters chosen by the authors; they directly affect the achievable classification accuracy.
  • Training hyperparameters = learning rate 0.5, batch size 32, Adam optimizer, 5 epochs for the experimental design
    Standard training choices reported in the Experimental Section; not derived from theory.
assumptions (5)
  • standard math Light propagation between diffractive layers follows the Rayleigh-Sommerfeld diffraction integral (Eq. 1) and is simulated with the angular spectrum method.
    Used throughout Sec. 2 and Fig. 2 as the forward model for training; standard scalar diffraction theory with stated assumptions.
  • domain assumption Each neuron is a phase-only modulator with unit amplitude transmission, so the amplitude term in Eq. 2 is a constant.
    The D2NN framework assumes ideal phase-only masks; the fabricated PB metasurface approximates this for circular polarization with 91.2% conversion efficiency.
  • domain assumption The fabricated metasurface realizes the trained phase profile through PB geometric phase with negligible co-polarized leakage.
    Invoked in Sec. 3.4 and Fig. 6; the paper attributes part of the simulation-to-experiment accuracy drop to forward-design errors, so this is only approximately satisfied.
  • ad hoc to paper The global minimum or a good local minimum of the weighted multi-task loss in Eq. 6 yields phase profiles for which both layer orderings classify accurately.
    This is the load-bearing premise of the A-DNN concept; it is validated empirically by the reported simulations and experiments, not proven analytically.
  • domain assumption The class prediction is the detection region with the highest integrated intensity at the output plane.
    Standard D2NN readout, stated in Sec. 2 and used for both confusion matrices and experiments.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Metasurface-empowered freely-arrangeable multi-task diffractive neural networks with weighted training." pith.science (2026). https://pith.science/paper/K2TDQITN

@misc{pith2026250618242,
  author       = {Pith},
  title        = {Pith review of: Metasurface-empowered freely-arrangeable multi-task diffractive neural networks with weighted training},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K2TDQITN}},
  note         = {Machine review of arXiv:2506.18242}
}
read the original abstract

Recent advancements in optical computing have garnered considerable research interests owing to its ener-gy-efficient operation and ultralow latency characteristics. As an emerging framework in this domain, dif-fractive deep neural networks (D2NNs) integrate deep learning algorithms with optical diffraction principles to perform computational tasks at light speed without requiring additional energy consumption. Neverthe-less, conventional D2NN architectures face functional limitations and are typically constrained to single-task operations or necessitating additional costs and structures for functional reconfiguration. Here, an arrangea-ble diffractive neural network (A-DNN) that achieves low-cost reconfiguration and high operational versa-tility by means of diffractive layer rearrangement is presented. Our architecture enables dynamic reordering of pre-trained diffractive layers to accommodate diverse computational tasks. Additionally, we implement a weighted multi-task loss function that allows precise adjustment of task-specific performances. The efficacy of the system is demonstrated by both numerical simulations and experimental validations of recognizing handwritten digits and fashions at terahertz frequencies. Our proposed architecture can greatly expand the flexibility of D2NNs at a low cost, providing a new approach for realizing high-speed, energy-efficient ver-satile artificial intelligence systems.

Figures

Figures reproduced from arXiv: 2506.18242 by the authors.

Figure 1
Figure 1. Framework of the arrangeable diffractive neural network (A [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Flowchart of weighted training process for the two-task A-DNN. The forward propagation of the input light wave is computed using the angular spectrum method. As the light wave propagates through each diffractive layer, the complex field is modulated by multiplying the corresponding phase profile. Subsequently, losses of different tasks are combined through weighted summation, enabling parameter updates via a single … view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 45 canonical work pages

  1. [1]

    LeCun, Y

    Y. LeCun, Y. Bengio, G. Hinton, Nature 2015, 521, 436

    work page 2015

  2. [2]

    Russakovsky, J

    O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Karpathy, A. Khosla, M. Bernstein, A. C. Berg, L. Fei-Fei, Int. J. Comput. Vis. 2015, 115, 211

    work page 2015

  3. [3]

    Krizhevsky, I

    A. Krizhevsky, I. Sutskever, G. E. Hinton, Commun. ACM 2017, 60, 84

    work page 2017

  4. [4]

    X. Zhao, L. Wang, Y. Zhang, X. Han, M. Deveci, M. Parmar, Artif. Intell. Rev. 2024, 57, 99

    work page 2024

  5. [5]

    Han, ACM Trans

    L. Han, ACM Trans. Asian Low-Resour. Lang. Inf. Process. 2023, 3616373

    work page 2023

  6. [6]

    Z. Chen, S. Wang, Y. Qian, K. Yu, in ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020, pp. 6574–6578

    work page 2020

  7. [7]

    X. Han, D. Simig, T. Mihaylov, Y. Tsvetkov, A. Celikyilmaz, T. Wang, 2023, DOI 10.48550/arXiv.2306.15091

    arXiv doi:10.48550/arxiv.2306.15091 2023

  8. [8]

    Y. Jia, C. D. W. Lee, M. H. Ang, in Intelligent Autonomous Systems 18 (Eds.: S.-G. Lee, J. An, N. Y. Chong, M. Strand, J. H. Kim), Springer Nature Switzerland, Cham, 2024, pp. 43–55

    work page 2024

Show all 48 references
  1. [9]

    S. Doll, N. Hanselmann, L. Schneider, R. Schulz, M. Cordts, M. Enzweiler, H. P. A. Lensch, 2024, DOI 10.48550/arXiv.2406.06264

    2024 doi arXiv

  2. [10]

    Markram, Nat

    H. Markram, Nat. Rev. Neurosci. 2006, 7, 153

    2006

  3. [11]

    Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr -Jones, M. Hochberg, X. Sun, S. Zhao, H. Laro- chelle, D. Englund, M. Soljačić, Nat. Photonics 2017, 11, 441

    2017

  4. [12]

    Wetzstein, A

    G. Wetzstein, A. Ozcan, S. Gigan, S. Fan, D. Englund, M. Soljačić, C. Denz, D. A. B. Miller, D. Psaltis, Nature 2020, 588, 39

    2020

  5. [13]

    Genty, L

    G. Genty, L. Salmela, J. M. Dudle y, D. Brunner, A. Kokhanovskiy, S. Kobtsev, S. K. Turitsyn, Nat. Photonics 2021, 15, 91

    2021

  6. [14]

    J. Liu, Q. Wu, X. Sui, Q. Chen, G. Gu, L. Wang, S. Li, PhotoniX 2021, 2, 5

    2021

  7. [15]

    T. Fu, J. Zhang, R. Sun, Y. Huang, W. Xu, S. Yang, Z. Zhu, H. Chen, Light: Sci. Appl. 2024, 13, 263

    2024

  8. [16]

    T. Wang, M. M. Sohoni, L. G. Wright, M. M. Stein, S. -Y. Ma, T. Onodera, M. G. Anderson, P. L. McMahon, Nat. Photonics 2023, 17, 408

    2023

  9. [17]

    X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, A. Ozcan, Science 2018, 361, 1004

    2018

  10. [18]

    C. Qian, X. Lin, X. Lin, J. Xu, Y. Sun, E. Li, B. Zhang, H. Chen, Light: Sci. Appl. 2020, 9, 59

    2020

  11. [19]

    Y. Luo, D. Mengu, A. Ozcan, Sci. Rep. 2022, 12, 7121

    2022

  12. [20]

    Mengu, A

    D. Mengu, A. Tabassum, M. Jarrahi, A. Ozcan, Light: Sci. Appl. 2023, 12, 86

    2023

  13. [21]

    Mengu, A

    D. Mengu, A. Ozcan, Adv. Opt. Mater. 2022, 10, 2200281

    2022

  14. [22]

    X. Xu, S. Guo, J. Chen, X. Bai, Opt. Laser Technol. 2024, 176, 110937

    2024

  15. [23]

    Y. Luo, D. Mengu, N. T. Yardimci, Y. Rivenson, M. Veli, M. Jarrahi, A. Ozcan, Light: Sci. Appl. 2019, 8, 112

    2019

  16. [24]

    Huang, P

    Z. Huang, P. Wang, J. Liu, W. Xiong, Y. He, J. Xiao, H. Ye, Y. Li, S. Chen, D. Fan, Phys. Rev. Appl. 2021, 15, 014037

    2021

  17. [25]

    M. Veli, D. Mengu, N. T. Yardimci, Y. Luo, J. Li, Y. Rivenson, M. Jarrahi, A. Ozcan, Nat. Commun. 2021, 12, 37

    2021

  18. [26]

    Ç. Işıl, D. Men gu, Y. Zhao, A. Tabassum, J. Li, Y. Luo, M. Jarrahi, A. Ozcan, Sci. Adv. 2022, 8, eadd3433

    2022

  19. [27]

    B. Bai, X. Yang, T. Gan, J. Li, D. Mengu, M. Jarrahi, A. Ozcan, Light: Sci. Appl. 2024, 13, 178

    2024

  20. [28]

    P. Tang, W. Wei, B. Xu, X. Zhao, J. Shao, Y. Tian, C. Wu, J. Lightwave. Technol. 2025, 43, 71

    2025

  21. [29]

    M. S. Sakib Rahman, A. Ozcan, ACS Photonics 2021, 8, 3375

    2021

  22. [30]

    J. Chen, Q. Zeng, C. Li, Z. Huang, P. Wang, W. Xiong, Y. He, H. Ye, Y. Li, D. Fan, S. Chen, Opt. Commun. 2023, 537, 129433

    2023

  23. [31]

    A. V. Kildishev, A. Boltasseva, V. M. Shalaev, Science 2013, 339, 1232009

    2013

  24. [32]

    Meinzer, W

    N. Meinzer, W. L. Barnes, I. R. Hooper, Nat. Photonics 2014, 8, 889

    2014

  25. [33]

    J. Zhu, W. Wei, B. Chen, P. Tang, X. Zhao, C. Wu, ACS Photonics 2024, 11, 1857

    2024

  26. [34]

    W. Wei, P. Tang, J. Shao, J. Zhu, X. Zhao, C. Wu, NANOPHOTONICS 2022, 11, 2921

    2022

  27. [35]

    N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. -P. Tetienne, F. Capasso, Z. Gaburro, Science 2011, 334, 333

    2011

  28. [36]

    S. Chen, Z. Li, Y. Zhang, H. Cheng, J. Tian, Adv. Opt. Mater. 2018, 6, 1800104

    2018

  29. [37]

    B. Xu, W. Wei, P. Tang, J. Shao, X. Zhao, B. Chen, S. Dong, C. Wu, Adv. Sci. 2024, 11, 2309648

    2024

  30. [38]

    Badloe, S

    T. Badloe, S. Lee, J. Rho, Adv. Photonics 2022, 4, 064002

    2022

  31. [39]

    C. Liu, Q. Ma, Z. J. Luo, Q. R. Hong, Q. Xiao, H. C. Zhang, L. Miao, W. M. Yu, Q. Cheng, L. Li, T. J. Cui, Nat. Electron. 2022, 5, 113

    2022

  32. [40]

    T. Zhou, X. Lin, J. Wu, Y. Chen, H. Xie, Y. Li, J. Fan, H. Wu, L. Fang , Q. Dai, Nat. Photonics 2021, 15, 367

    2021

  33. [41]

    C. He, D. Zhao, F. Fan, H. Zhou, X. Li, Y. Li, J. Li, F. Dong, Y. -X. Miao, Y. Wang, L. Huang, OEA 2024, 7, 230005

    2024

  34. [42]

    Y. Li, R. Chen, B. Sensale-Rodriguez, W. Gao, C. Yu, Sci. Rep. 2021, 11, 11013

    2021

  35. [43]

    H. Chi, X. Zang, T. Zhang, G. Wang, Z. Fan, Y. Zhu, X. Chen, S. Zhuang, Laser Photon. Rev. 2025, 19, 2401178

    2025

  36. [44]

    X. Luo, Y. Hu, X. Ou, X. Li, J. Lai, N. Liu, X. Cheng, A. Pan, H. Duan, Light: Sci. Appl. 2022, 11, 158. [45]X. Zhang, T. Li, H. Zhou, Y. Li, J. Li, X. Li, Y. Wang, L. Huang, Laser Photon. Rev. 2024, 18, 2300887

    2022

  37. [46]

    Lecun, L

    Y. Lecun, L. Bottou, Y. Bengio, P. Haffner, Proc. IEEE 1998, 86, 2278

    1998

  38. [47]

    H. Xiao, K. Rasul, R. Vollgraf, 2017, DOI 10.48550/arXiv.1708.07747

    2017 doi arXiv

  39. [48]

    J. W. Goodman, Introduction to Fourier Optics, Roberts And Company Publishers, 2005

    2005

  40. [49]

    M. V. Berry, Proc. R. Soc. Lond. A. 1984, 392, 45

    1984

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.