Pushing the limits of optical information storage using deep learning

Abstract

Diffraction drastically limits the bit density in optical data storage. To increase the storage density, alternative strategies involving supplementary recording dimensions and robust readout schemes must be explored. Here, we propose to encode multiple bits of information in the geometry of subwavelength dielectric nanostructures. A crucial problem in high-density information storage concepts is the robustness of the information readout with respect to fabrication errors and experimental noise. Using a machine-learning-based approach in which the scattering spectra are analysed by an artificial neural network, we achieve quasi-error-free readout of sequences of up to 9 bits, encoded in top-down fabricated silicon nanostructures. We demonstrate that probing few wavelengths instead of the entire spectrum is sufficient for robust information retrieval and that the readout can be further simplified, exploiting the RGB values from microscopy images. Our work paves the way towards high-density optical information storage using planar silicon nanostructures, compatible with mass-production-ready complementary metal–oxide–semiconductor technology.

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Fig. 1: Sketch of the nanostructure geometry and the 1D convolutional ANN.
Fig. 2: Experimental dark-field spectra training data set for 4 bits.
Fig. 3: Training convergence and readout accuracy of the ANN trained on the full scattering spectra.
Fig. 4: Accuracy of network trained on reduced spectral information.
Fig. 5: Neural-network based data readout via the RGB colour values.
Fig. 6: Information encoding with 9 bits per nanostructure.

Code availability

The authors declare that all software used to obtain the results of this work is publicly accessible as open-source software: python including SciPy, TensorFlow, as well as pyGDM46, our own implementation of the GDM. Our scripts can be made accessible from the corresponding author upon reasonable request.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. The experimental and simulated scattering data sets are available under https://doi.org/10.6084/m9.figshare.7326842.v1.

References

  1. 1.

    Zhang, J., Gecevičius, M., Beresna, M. & Kazansky, P. G. Seemingly unlimited lifetime data storage in nanostructured glass. Phys. Rev. Lett. 112, 033901 (2014).

    Article  Google Scholar 

  2. 2.

    Gu, M., Li, X. & Cao, Y. Optical storage arrays: a perspective for future big data storage. Light Sci. Appl. 3, e177 (2014).

    CAS  Article  Google Scholar 

  3. 3.

    Satoh, I., Ohara, S., Akahira, N. & Takenaga, M. Key technology for high density rewritable DVD (DVD-RAM). IEEE Trans. Magn. 34, 337–342 (1998).

    Article  Google Scholar 

  4. 4.

    Borg, H. J. et al. Phase-change media for high-numerical-aperture and blue-wavelength recording. Jpn J. Appl. Phys. 40, 1592 (2001).

    CAS  Article  Google Scholar 

  5. 5.

    Zeng, B. J., Ni, R. W., Huang, J. Z., Li, Z. & Miao, X. S. Polarization-based multiple-bit optical data storage. J. Opt. 16, 125402 (2014).

    Article  Google Scholar 

  6. 6.

    Tominaga, J., Nakano, T. & Atoda, N. An approach for recording and readout beyond the diffraction limit with an Sb thin film. Appl. Phys. Lett. 73, 2078–2080 (1998).

    CAS  Article  Google Scholar 

  7. 7.

    Mottaghi, M. D. & Dwyer, C. Thousand-fold increase in optical storage density by polychromatic address multiplexing on self-assembled DNA nanostructures. Adv. Mater. 25, 3593–3598 (2013).

    CAS  Article  Google Scholar 

  8. 8.

    Strickler, J. H. & Webb, W. W. Three-dimensional optical data storage in refractive media by two-photon point excitation. Opt. Lett. 16, 1780–1782 (1991).

    CAS  Article  Google Scholar 

  9. 9.

    van Heerden, P. J. Theory of optical information storage in solids. Appl. Opt. 2, 393–400 (1963).

    Article  Google Scholar 

  10. 10.

    Psaltis, D. & Burr, G. W. Holographic data storage. Computer 31, 52–60 (1998).

    Article  Google Scholar 

  11. 11.

    Girard, C. Near fields in nanostructures. Rep. Prog. Phys. 68, 1883–1933 (2005).

    Article  Google Scholar 

  12. 12.

    Novotny, L. & Hecht, B. Principles of Nano-Optics (Cambridge Univ. Press, Cambridge, 2006).

    Google Scholar 

  13. 13.

    Maier, S. Plasmonics: Fundamentals and Applications (Springer, New York, 2010).

  14. 14.

    Kuznetsov, A. I. et al. Optically resonant dielectric nanostructures. Science 354, aag2472 (2016).

    Article  Google Scholar 

  15. 15.

    Cao, L., Fan, P., Barnard, E. S., Brown, A. M. & Brongersma, M. L. Tuning the color of silicon nanostructures. Nano Lett. 10, 2649–2654 (2010).

    CAS  Article  Google Scholar 

  16. 16.

    Wiecha, P. R. et al. Evolutionary multi-objective optimization of colour pixels based on dielectric nanoantennas. Nat. Nanotechnol. 12, 163–169 (2017).

    CAS  Article  Google Scholar 

  17. 17.

    Mansuripur, M. et al. Plasmonic nano-structures for optical data storage. Opt. Express 17, 14001–14014 (2009).

    CAS  Article  Google Scholar 

  18. 18.

    Chen, W. T. et al. Manipulation of multidimensional plasmonic spectra for information storage. Appl. Phys. Lett. 98, 171106 (2011).

    Article  Google Scholar 

  19. 19.

    Cui, Y., Phang, I. Y., Hegde, R. S., Lee, Y. H. & Ling, X. Y. Plasmonic silver nanowire structures for two-dimensional multiple-digit molecular data storage application. ACS Photon. 1, 631–637 (2014).

    CAS  Article  Google Scholar 

  20. 20.

    El-Rabiaey, M. A., Areed, N. F. F. & Obayya, S. S. A. Novel plasmonic data storage based on nematic liquid crystal layers. J. Lightwave Technol. 34, 3726–3732 (2016).

    CAS  Article  Google Scholar 

  21. 21.

    Zijlstra, P., Chon, J. W. M. & Gu, M. Five-dimensional optical recording mediated by surface plasmons in gold nanorods. Nature 459, 410–413 (2009).

    CAS  Article  Google Scholar 

  22. 22.

    Taylor, A. B., Kim, J. & Chon, J. W. M. Detuned surface plasmon resonance scattering of gold nanorods for continuous wave multilayered optical recording and readout. Opt. Express 20, 5069–5081 (2012).

    CAS  Article  Google Scholar 

  23. 23.

    Taylor, A. B., Michaux, P., Mohsin, A. S. M. & Chon, J. W. M. Electron-beam lithography of plasmonic nanorod arrays for multilayered optical storage. Opt. Express 22, 13234–13243 (2014).

    CAS  Article  Google Scholar 

  24. 24.

    Li, X., Cao, Y., Tian, N., Fu, L. & Gu, M. Multifocal optical nanoscopy for big data recording at 30 TB capacity and gigabits/second data rate. Optica 2, 567–570 (2015).

    CAS  Article  Google Scholar 

  25. 25.

    Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photon. 5, 1365–1369 (2018).

    CAS  Article  Google Scholar 

  26. 26.

    Albella, P. et al. Low-loss electric and magnetic field-enhanced spectroscopy with subwavelength silicon dimers. J. Phys. Chem. C 117, 13573–13584 (2013).

    CAS  Article  Google Scholar 

  27. 27.

    Nielsen, M. A. Neural Networks and Deep Learning (Determination Press, 2015); http://neuralnetworksanddeeplearning.com/

  28. 28.

    Goodfellow, I., Bengio, Y. & Courville, A. Deep Learning (MIT Press, Cambridge, 2016).

  29. 29.

    Szegedy, C., Ioffe, S., Vanhoucke, V. & Alemi, A. Inception-v4, inception-ResNet and the impact of residual connections on learning. Preprint at https://arxiv.org/abs/1602.07261 (2016).

  30. 30.

    Mamoshina, P., Vieira, A., Putin, E. & Zhavoronkov, A. Applications of deep learning in biomedicine. Mol. Pharm. 13, 1445–1454 (2016).

    CAS  Article  Google Scholar 

  31. 31.

    Shimobaba, T. et al. Convolutional neural network-based data page classification for holographic memory. Appl. Opt. 56, 7327–7330 (2017).

    Article  Google Scholar 

  32. 32.

    Jo, Y. et al. Holographic deep learning for rapid optical screening of anthrax spores. Sci. Adv. 3, e1700606 (2017).

    Article  Google Scholar 

  33. 33.

    Malkiel, I. et al. Plasmonic nanostructure design and characterization via deep learning. Light Sci. Appl. 7, 60 (2018).

    Article  Google Scholar 

  34. 34.

    Peurifoy, J. et al. Nanophotonic particle simulation and inverse design using artificial neural networks. Sci. Adv. 4, eaar4206 (2018).

    Article  Google Scholar 

  35. 35.

    van der Maaten, L. & Hinton, G. Visualizing high-dimensional data using t-SNE. J. Mach. Learn. Res. 9, 2579–2605 (2008).

    Google Scholar 

  36. 36.

    Feichtner, T., Selig, O., Kiunke, M. & Hecht, B. Evolutionary optimization of optical antennas. Phys. Rev. Lett. 109, 127701 (2012).

    Article  Google Scholar 

  37. 37.

    Rivenson, Y. et al. Deep learning enhanced mobile-phone microscopy. ACS Photon. 5, 2354–2364 (2018).

    CAS  Article  Google Scholar 

  38. 38.

    Orth, A., Wilson, E. R., Thompson, J. G. & Gibson, B. C. A dual-mode mobile phone microscope using the onboard camera flash and ambient light. Sci. Rep. 8, 3298 (2018).

    CAS  Article  Google Scholar 

  39. 39.

    Wei, Q. et al. Plasmonics enhanced smartphone fluorescence microscopy. Sci. Rep. 7, 2124 (2017).

    Article  Google Scholar 

  40. 40.

    Flauraud, V., Reyes, M., Paniagua-Domínguez, R., Kuznetsov, A. I. & Brugger, J. Silicon nanostructures for bright field full color prints. ACS Photon. 4, 1913–1919 (2017).

    CAS  Article  Google Scholar 

  41. 41.

    González-Alcalde, A. K. et al. Optimization of all-dielectric structures for color generation. Appl. Opt. 57, 3959–3967 (2018).

    Article  Google Scholar 

  42. 42.

    Duan, X., Kamin, S. & Liu, N. Dynamic plasmonic colour display. Nat. Commun. 8, 14606 (2017).

    CAS  Article  Google Scholar 

  43. 43.

    Guerfi, Y., Carcenac, F. & Larrieu, G. High resolution HSQ nanopillar arrays with low energy electron beam lithography. Microelectron. Eng. 110, 173–176 (2013).

    CAS  Article  Google Scholar 

  44. 44.

    Guerfi, Y., Doucet, J. B. & Larrieu, G. Thin-dielectric-layer engineering for 3D nanostructure integration using an innovative planarization approach. Nanotechnology 26, 425302 (2015).

    CAS  Article  Google Scholar 

  45. 45.

    Martin, O. J. F., Girard, C. & Dereux, A. Generalized field propagator for electromagnetic scattering and light confinement. Phys. Rev. Lett. 74, 526–529 (1995).

    CAS  Article  Google Scholar 

  46. 46.

    Wiecha, P. R. pyGDM—a python toolkit for full-field electro-dynamical simulations and evolutionary optimization of nanostructures. Comput. Phys. Commun. 233, 167–192 (2018).

    CAS  Article  Google Scholar 

  47. 47.

    Girard, C., Dujardin, E., Baffou, G. & Quidant, R. Shaping and manipulation of light fields with bottom-up plasmonic structures. New J. Phys. 10, 105016 (2008).

    Article  Google Scholar 

  48. 48.

    Edwards, D. F. In Handbook of Optical Constants of Solids (ed. Palik, E. D.) 547–569 (Academic, Burlington, 1997).

  49. 49.

    Draine, B. T. The discrete-dipole approximation and its application to interstellar graphite grains. Astrophys. J. 333, 848–872 (1988).

    CAS  Article  Google Scholar 

  50. 50.

    Abadi, M. et al. TensorFlow: Large-scale Machine Learning on Heterogeneous Distributed Systems. https://www.tensorflow.org/ (2015).

  51. 51.

    Ioffe, S. & Szegedy, C. Batch normalization: accelerating deep network training by reducing internal covariate shift. Preprint at https://arxiv.org/abs/1502.03167 (2015).

  52. 52.

    Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. Preprint at https://arxiv.org/abs/1412.6980 (2014).

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Acknowledgements

The authors thank A. Arbouet and C. Girard for their advice, for their help and for discussing and proofreading the manuscript, and F. Carcenac for his help with EBL and automatic SEM images. This work was supported by Programme Investissements d’Avenir under the program ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT, by the LAAS-CNRS micro and nanotechnologies platform, a member of the French RENATECH network, and by the computing facility centre CALMIP of the University of Toulouse under grant P12167.

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P.R.W. conceived the idea and designed the research together with G.L. G.L. and A.L. developed the fabrication techniques. A.L. fabricated the nanostructures and performed the electron microscopy with the help of N.M. P.R.W. carried out the optical experiments, did the simulations and the data analysis, and implemented the machine-learning part. P.R.W. wrote the manuscript with contributions from G.L. P.R.W and G.L. discussed the results and all authors commented on the manuscript at every stage.

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Correspondence to Peter R. Wiecha.

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Wiecha, P.R., Lecestre, A., Mallet, N. et al. Pushing the limits of optical information storage using deep learning. Nat. Nanotechnol. 14, 237–244 (2019). https://doi.org/10.1038/s41565-018-0346-1

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