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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.


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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).

Author information




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 or Junsuk Rho or Stefan A. Maier.

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Competing interests

The authors declare no competing interests.

Additional information

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.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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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