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Orbital angular momentum holography for high-security encryption


Holography has been identified as a vital platform for three-dimensional displays, optical encryption, microscopy and artificial intelligence through different physical dimensions. However, unlike the wavelength and polarization divisions, orbital angular momentum (OAM) of light, despite its helical wavefront being an independent physical dimension, has not been implemented as an information carrier for holography due to the lack of helical mode index selectivity in the Bragg diffraction formula. Here, we demonstrate OAM holography by discovering strong OAM selectivity in the spatial-frequency domain without a theoretical helical mode index limit. As such, OAM holography allows the multiplexing of a wide range of OAM-dependent holographic images with a helical mode index spanning from −50 to 50, leading to a 10 bit OAM-encoded hologram for high-security optical encryption. Our results showing up to 210 OAM-dependent distinctive holographic images mark a new path to achieving ultrahigh-capacity holographic information systems harnessing the previously inaccessible OAM division.

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Fig. 1: Principle of OAM holography through the spatial-frequency domain.
Fig. 2: Design principle of OAM-preserved and -selective holograms.
Fig. 3: Holographic encoding of independent OAM information channels for a multiplexed display.
Fig. 4: Experimental demonstration of using a 10 bit OAM-multiplexing hologram for high-security holographic encryption.

Data availability

All data related to the experiments described in this article are archived on a lab computer at RMIT University. All data are available from the corresponding author upon reasonable request.

Code availability

The code used for the hologram design is available from the corresponding author upon reasonable request.


  1. 1.

    Bragg, W. L. The X-ray microscope. Nature 149, 470–471 (1942).

    ADS  Article  Google Scholar 

  2. 2.

    Gabor, D. A new microscopic principle. Nature 161, 777–778 (1948).

    ADS  Article  Google Scholar 

  3. 3.

    Sur, B., Rogge, R. B., Hammond, R. P., Anghel, V. N. P. & Katsaras, J. Atomic structure holography using thermal neutrons. Nature 414, 525–527 (2001).

    ADS  Article  Google Scholar 

  4. 4.

    Denisyuk, Y. N. The manifestation of the optical properties of an object in the wave field of the radiation it scatters. Dokl. Akad. Nauk SSSR 144, 1275–1278 (1962).

    Google Scholar 

  5. 5.

    Leith, E. N. & Upatnieks, J. Reconstructed wavefronts and communication theory. J. Opt. Soc. Am. 52, 1123–1130 (1962).

    ADS  Article  Google Scholar 

  6. 6.

    Ozaki, M., Kato, J. & Kawata, S. Surface-plasmon holography with white-light illumination. Science 332, 218–220 (2011).

    ADS  Article  Google Scholar 

  7. 7.

    Mueller, J. P. B., Rubin, N. A., Devlin, R. C., Groever, B. & Capasso, F. Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization. Phys. Rev. Lett. 118, 113901 (2017).

    ADS  Article  Google Scholar 

  8. 8.

    Wen, D. D. et al. Helicity multiplexed broadband metasurface holograms. Nat. Commun. 6, 8241 (2015).

    ADS  Article  Google Scholar 

  9. 9.

    Li, X. P. et al. Athermally photoreduced graphene oxides for three-dimensional holographic images. Nat. Commun. 6, 6984 (2015).

    ADS  Article  Google Scholar 

  10. 10.

    Li, X. et al. Multicolor 3D meta-holography by broadband plasmonic modulation. Sci. Adv. 2, e1601102 (2016).

    ADS  Article  Google Scholar 

  11. 11.

    Lim, K. T. P., Liu, H., Liu, Y. & Yang, J. K. W. Holographic colour prints for enhanced optical security by combined phase and amplitude control. Nat. Commun. 10, 25 (2019).

    ADS  Article  Google Scholar 

  12. 12.

    Shen, X. A., Nguyen, A. D., Perry, J. W., Huestis, D. L. & Kachru, R. Time-domain holographic digital memory. Science 278, 96–100 (1997).

    Article  Google Scholar 

  13. 13.

    Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C. & Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992).

    ADS  Article  Google Scholar 

  14. 14.

    Wang, J. et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photon. 6, 488–496 (2012).

    ADS  Article  Google Scholar 

  15. 15.

    Bozinovic, N. et al. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science 340, 1545–1548 (2013).

    ADS  Article  Google Scholar 

  16. 16.

    Ren, H. R., Li, X. P., Zhang, Q. M. & Gu, M. On-chip noninterference angular momentum multiplexing of broadband light. Science 352, 805–809 (2016).

    ADS  Article  Google Scholar 

  17. 17.

    Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001).

    ADS  Article  Google Scholar 

  18. 18.

    Fickler, R. et al. Quantum entanglement of high angular momenta. Science 338, 640–643 (2012).

    ADS  Article  Google Scholar 

  19. 19.

    Hemsing, E., Marinelli, A. & Rosenzweig, J. B. Generating optical orbital angular momentum in a high-gain free-electron laser at the first harmonic. Phys. Rev. Lett. 106, 164803 (2011).

    ADS  Article  Google Scholar 

  20. 20.

    Goodman, J. W. Introduction to Fourier Optics (Roberts & Company, 2005).

  21. 21.

    Gu, M. Advanced Optical Imaging Theory (Springer Verlag, 2000).

  22. 22.

    Yang, Y. & Blake, R. Broad tuning for spatial frequency of neural mechanisms underlying visual perception of coherent motion. Nature 371, 793–796 (1994).

    ADS  Article  Google Scholar 

  23. 23.

    Gibbs, A. J. & Rowe, A. J. Reconstruction of images from transforms by an optical method. Nature 246, 509–511 (1973).

    ADS  Article  Google Scholar 

  24. 24.

    Zernike, F. Phase contrast, a new method for the microscopic observation of transparent objects: Part II. Physica 9, 974–986 (1942).

    ADS  Article  Google Scholar 

  25. 25.

    Kotlyar, V. V., Kovalev, A. A. & Porfirev, A. P. Astigmatic transforms of an optical vortex for measurement of its topological charge. Appl. Opt. 56, 4095–4104 (2017).

    ADS  Article  Google Scholar 

  26. 26.

    Li, J. X. et al. Addressable metasurfaces for dynamic holography and optical information encryption. Sci. Adv. 4, eaar6768 (2018).

    ADS  Article  Google Scholar 

  27. 27.

    Jin, L. et al. Noninterleaved metasurface for (26 – 1) spin- and wavelength-encoded holograms. Nano Lett. 18, 8016–8024 (2018).

    ADS  Article  Google Scholar 

  28. 28.

    Yu, N. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011).

    ADS  Article  Google Scholar 

  29. 29.

    Maguid, E. et al. Photonic spin-controlled multifunctional shared-aperture antenna array. Science 352, 1202–1206 (2016).

    ADS  Article  Google Scholar 

  30. 30.

    Wang, Q. et al. Optically reconfigurable metasurfaces and photonic devices based on phase change materials. Nat. Photon. 10, 60–65 (2016).

    ADS  Article  Google Scholar 

  31. 31.

    Smalley, D. E. et al. A photophoretic-trap volumetric display. Nature 553, 486–490 (2018).

    ADS  Article  Google Scholar 

  32. 32.

    Rosen, J. & Brooker, G. Non-scanning motionless fluorescence three-dimensional holographic microscopy. Nat. Photon. 2, 190–195 (2008).

    ADS  Article  Google Scholar 

  33. 33.

    Heanue, J. F., Bashaw, M. C. & Hesselink, L. Volume holographic storage and retrieval of digital data. Science 265, 749–752 (1994).

    ADS  Article  Google Scholar 

  34. 34.

    Hesselink, L. et al. Photorefractive materials for nonvolatile volume holographic data storage. Science 282, 1089–1094 (1998).

    ADS  Article  Google Scholar 

  35. 35.

    Grier, D. G. A revolution in optical manipulation. Nature 424, 810–816 (2003).

    ADS  Article  Google Scholar 

  36. 36.

    Psaltis, D., Brady, D., Gu, X. G. & Lin, S. Holography in artificial neural networks. Nature 343, 325–330 (1990).

    ADS  Article  Google Scholar 

  37. 37.

    Lin, X. et al. All-optical machine learning using diffractive deep neural networks. Science 361, 1004–1008 (2018).

    ADS  MathSciNet  MATH  Article  Google Scholar 

  38. 38.

    Chrapkiewicz, R., Jachura, M., Banaszek, K. & Wasilewski, W. Hologram of a single photon. Nat. Photon. 10, 576–579 (2016).

    ADS  Article  Google Scholar 

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We thank H.T. Luan and H.C. Yang for technical assistance with the experiment and B.K. Wang, Y. Zhang, C. Xu, T.X. Wang and J.T. Ma for useful discussions. M.G. acknowledges support from the Australian Research Council (ARC) through the Discovery Project (DP180102402). X.F. acknowledges support from a scholarship from the China Scholarship Council (CSC no. 201706190189). H.R. acknowledges funding support from a Victoria Fellowship and a Humboldt Research Fellowship from the Alexander von Humboldt Foundation.

Author information




M.G. and H.R. proposed the idea and conceived the experiment. X.F. and H.R. performed the theoretical calculations. X.F. constructed the experiment, acquired the data and carried out the data analysis. X.F., H.R. and M.G. completed the writing of the paper.

Corresponding author

Correspondence to Min Gu.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Notes 1–11 and Figs. 1–15

Supplementary Video 1

OAM-switched dynamic display.

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Fang, X., Ren, H. & Gu, M. Orbital angular momentum holography for high-security encryption. Nat. Photonics 14, 102–108 (2020).

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