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Complex-amplitude metasurface-based orbital angular momentum holography in momentum space


Digital optical holograms can achieve nanometre-scale resolution as a result of recent advances in metasurface technologies. This has raised hopes for applications in data encryption, data storage, information processing and displays. However, the hologram bandwidth has remained too low for any practical use. To overcome this limitation, information can be stored in the orbital angular momentum of light, as this degree of freedom has an unbounded set of orthogonal helical modes that could function as information channels. Thus far, orbital angular momentum holography has been achieved using phase-only metasurfaces, which, however, are marred by channel crosstalk. As a result, multiplex information from only four channels has been demonstrated. Here, we demonstrate an orbital angular momentum holography technology that is capable of multiplexing up to 200 independent orbital angular momentum channels. This has been achieved by designing a complex-amplitude metasurface in momentum space capable of complete and independent amplitude and phase manipulation. Information was then extracted by Fourier transform using different orbital angular momentum modes of light, allowing lensless reconstruction and holographic videos to be displayed. Our metasurface can be three-dimensionally printed in a polymer matrix on SiO2 for large-area fabrication.

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Fig. 1: Principle of ultrahigh-dimensional OAM-multiplexing holography based on a large-scale COMH.
Fig. 2: Design principle of a complex-amplitude hologram for OAM holography in momentum space.
Fig. 3: The physical mechanism of complex-amplitude-based OAM-multiplexing holography and its application in a holographic video display.
Fig. 4: Design and optimization of a 3D metasurface for the complete and independent manipulation of both amplitude and phase responses of transmitted light.
Fig. 5: Experimental demonstration of ultrahigh-dimensional OAM-multiplexing holography based on a large-scale COMH.

Data availability

The data that support the figures and other findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

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


  1. Downing, E., Hesselink, L., Ralston, J. & Macfarlane, R. A three-color, solid-state, three-dimensional display. Science 273, 1185–1189 (1996).

    CAS  Google Scholar 

  2. Tay, S. et al. An updatable holographic three-dimensional display. Nature 451, 694–698 (2008).

    CAS  Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  8. Lin, D., Fan, P., Hasman, E. & Brongersma, M. L. Dielectric gradient metasurface optical elements. Science 345, 298–302 (2014).

    CAS  Google Scholar 

  9. Arbabi, A., Horie, Y., Bagheri, M. & Faraon, A. Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission. Nat. Nanotechnol. 10, 937–943 (2015).

    CAS  Google Scholar 

  10. Ni, X., Kildishev, A. V. & Shalaev, V. M. Metasurface holograms for visible light. Nat. Commun. 4, 2807 (2013).

    Google Scholar 

  11. Huang, L. et al. Three-dimensional optical holography using a plasmonic metasurface. Nat. Commun. 4, 2808 (2013).

    Google Scholar 

  12. Zheng, G. et al. Metasurface holograms reaching 80% efficiency. Nat. Nanotechnol. 10, 308–312 (2015).

    CAS  Google Scholar 

  13. Wang, L. et al. Grayscale transparent metasurface holograms. Optica 3, 1504–1505 (2016).

    Google Scholar 

  14. Hu, Y. et al. 3D-integrated metasurfaces for full-colour holography. Light. Sci. Appl. 8, 86 (2019).

    Google Scholar 

  15. Chen, W. T. et al. High-efficiency broadband meta-hologram with polarization-controlled dual images. Nano Lett. 14, 225–230 (2014).

    Google Scholar 

  16. Wang, H. et al. Ultrathin planar cavity metasurfaces. Small 14, 1703920 (2018).

    Google Scholar 

  17. Montelongo, Y. et al. Plasmonic nanoparticle scattering for color holograms. Proc. Natl Acad. Sci. USA 111, 12679–12683 (2014).

    CAS  Google Scholar 

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

    Google Scholar 

  19. Huang, Y. et al. Aluminium plasmonic multicolour meta-hologram. Nano Lett. 15, 3122–3127 (2015).

    CAS  Google Scholar 

  20. Wang, B. et al. Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms. Nano Lett. 16, 5235–5240 (2016).

    CAS  Google Scholar 

  21. Kamali, S. M. et al. Angle-multiplexed metasurfaces: encoding independent wavefronts in a single metasurface under different illumination angles. Phys. Rev. X 7, 041056 (2017).

    Google Scholar 

  22. 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).

    Google Scholar 

  23. Zhao, R. et al. Multichannel vectorial holographic display and encryption. Light. Sci. Appl. 7, 95 (2018).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  29. Ren, H. et al. Metasurface orbital angular momentum holography. Nat. Commun. 10, 2986 (2019).

    Google Scholar 

  30. Lee, G. et al. Complete amplitude and phase control of light using broadband holographic metasurfaces. Nanoscale 10, 4237–4245 (2018).

    CAS  Google Scholar 

  31. Overvig, A. C. et al. Dielectric metasurfaces for complete and independent control of the optical amplitude and phase. Light. Sci. Appl. 8, 95 (2018).

    Google Scholar 

  32. Deng, Z. et al. Full-color complex-amplitude vectorial holograms based on multi-freedom metasurfaces. Adv. Funct. Mater. 30, 1910610 (2020).

    CAS  Google Scholar 

  33. Smalley, D. E., Smithwick, Q. Y. J., Bove, V. M., Barabas, J. & Jolly, S. Anisotropic leaky-mode modulator for holographic video displays. Nature 498, 313–317 (2013).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  35. Hirayama, R., Plasencia, D. M., Masuda, N. & Subramanian, S. A volumetric display for visual, tactile and audio presentation using acoustic trapping. Nature 575, 320–323 (2019).

    CAS  Google Scholar 

  36. Makey, G. et al. Breaking crosstalk limits to dynamic holography using orthogonality of high-dimensional random vectors. Nat. Photonics 13, 251–256 (2019).

    CAS  Google Scholar 

  37. Bomzon, Z., Biener, G., Kleiner, V. & Hasman, E. Space-variant Pancharatnam–Berry phase optical elements with computer-generated subwavelength gratings. Opt. Lett. 27, 1141–1143 (2002).

    Google Scholar 

  38. Saha, S. K. et al. Scalable submicrometer additive manufacturing. Science 366, 105–109 (2019).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  40. Huang, C. et al. Ultrafast control of vortex microlasers. Science 367, 1018–1021 (2020).

    CAS  Google Scholar 

  41. Wang, B. et al. Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum. Nat. Photonics (2020).

  42. Zhang, Z. et al. Tunable topological charge vortex microlaser. Science 368, 760–763 (2020).

    CAS  Google Scholar 

  43. Rivenson, Y., Wu, Y. & Ozcan, A. Deep learning in holography and coherent imaging. Light. Sci. Appl. 8, 85 (2019).

    Google Scholar 

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

    CAS  Google Scholar 

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H.R. acknowledges funding support through a Humboldt Research Fellowship from the Alexander von Humboldt Foundation. S.A.M. acknowledges funding support from the Deutsche Forschungsgemeinschaft and the Lee-Lucas Chair in Physics. J.R. acknowledges the Samsung Research Funding & Incubation Center for Future Technology (grant SRFC-IT1901-05) funded by Samsung Electronics, and the National Research Foundation (NRF; grants NRF-2019R1A2C3003129, CAMM-2019M3A6B3030637, NRF-2019R1A5A8080290, NRF-2018M3D1A1058997 and NRF-2015R1A5A1037668) funded by the Ministry of Science and ICT (MSIT) of the Korean government. J.J. acknowledges the Hyundai Motor Chung Mong-Koo Foundation fellowship, an NRF fellowship (NRF-2019R1A6A3A13091132) funded by the Ministry of Education of the Korean governent and the NRF-DAAD Summer Institute program funded by the NRF and German Academic Exchange Service (DAAD). X.F. acknowledges funding support from Shanghai Rising-Star Program (20QA1404100) and Zhangjiang National Innovation Demonstration Zone (ZJ2019-ZD-005).

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Authors and Affiliations



H.R. and S.A.M. proposed the idea and conceived the experiment; X.F. and H.R. calculated the complex-amplitude OAM-multiplexing holograms; J.J., J.R. and H.R. performed the numerical simulation of the 3D meta-atoms; H.R. and J.B. carried out 3D laser printing of large-scale 3D metasurfaces; H.R. and J.B. performed the optical characterization of the metasurface holograms; H.R., J.R. and S.A.M. contributed to the data analysis; all the authors contributed to the writing of the paper.

Corresponding authors

Correspondence to Haoran Ren, Junsuk Rho or Stefan A. Maier.

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Competing interests

The authors declare no competing interests.

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Peer review information Nature Nanotechnology thanks Xianzhong Chen, Tim Wilkinson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Notes 1–4 and Figs. 1–18.

Supplementary Video 1

Numerical results of a holographic video display in an image plane z=z1.

Supplementary Video 2

Numerical results of a holographic video display in an image plane z=z2.

Supplementary Video 3

Experimental results of a holographic video display in an image plane z=z1.

Supplementary Video 4

Experimental results of a holographic video display in an image plane z=z2.

Source data

Source Data Fig. 2

The source data for Fig. 2b and Fig. 2d.

Source Data Fig. 4

The source data for Fig. 4.

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Ren, H., Fang, X., Jang, J. et al. Complex-amplitude metasurface-based orbital angular momentum holography in momentum space. Nat. Nanotechnol. 15, 948–955 (2020).

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