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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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.
The code used for the hologram design is available from the corresponding author upon reasonable request.
Bragg, W. L. The X-ray microscope. Nature 149, 470–471 (1942).
Gabor, D. A new microscopic principle. Nature 161, 777–778 (1948).
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).
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).
Leith, E. N. & Upatnieks, J. Reconstructed wavefronts and communication theory. J. Opt. Soc. Am. 52, 1123–1130 (1962).
Ozaki, M., Kato, J. & Kawata, S. Surface-plasmon holography with white-light illumination. Science 332, 218–220 (2011).
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).
Wen, D. D. et al. Helicity multiplexed broadband metasurface holograms. Nat. Commun. 6, 8241 (2015).
Li, X. P. et al. Athermally photoreduced graphene oxides for three-dimensional holographic images. Nat. Commun. 6, 6984 (2015).
Li, X. et al. Multicolor 3D meta-holography by broadband plasmonic modulation. Sci. Adv. 2, e1601102 (2016).
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).
Shen, X. A., Nguyen, A. D., Perry, J. W., Huestis, D. L. & Kachru, R. Time-domain holographic digital memory. Science 278, 96–100 (1997).
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).
Wang, J. et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photon. 6, 488–496 (2012).
Bozinovic, N. et al. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science 340, 1545–1548 (2013).
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).
Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001).
Fickler, R. et al. Quantum entanglement of high angular momenta. Science 338, 640–643 (2012).
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).
Goodman, J. W. Introduction to Fourier Optics (Roberts & Company, 2005).
Gu, M. Advanced Optical Imaging Theory (Springer Verlag, 2000).
Yang, Y. & Blake, R. Broad tuning for spatial frequency of neural mechanisms underlying visual perception of coherent motion. Nature 371, 793–796 (1994).
Gibbs, A. J. & Rowe, A. J. Reconstruction of images from transforms by an optical method. Nature 246, 509–511 (1973).
Zernike, F. Phase contrast, a new method for the microscopic observation of transparent objects: Part II. Physica 9, 974–986 (1942).
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).
Li, J. X. et al. Addressable metasurfaces for dynamic holography and optical information encryption. Sci. Adv. 4, eaar6768 (2018).
Jin, L. et al. Noninterleaved metasurface for (26 – 1) spin- and wavelength-encoded holograms. Nano Lett. 18, 8016–8024 (2018).
Yu, N. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011).
Maguid, E. et al. Photonic spin-controlled multifunctional shared-aperture antenna array. Science 352, 1202–1206 (2016).
Wang, Q. et al. Optically reconfigurable metasurfaces and photonic devices based on phase change materials. Nat. Photon. 10, 60–65 (2016).
Smalley, D. E. et al. A photophoretic-trap volumetric display. Nature 553, 486–490 (2018).
Rosen, J. & Brooker, G. Non-scanning motionless fluorescence three-dimensional holographic microscopy. Nat. Photon. 2, 190–195 (2008).
Heanue, J. F., Bashaw, M. C. & Hesselink, L. Volume holographic storage and retrieval of digital data. Science 265, 749–752 (1994).
Hesselink, L. et al. Photorefractive materials for nonvolatile volume holographic data storage. Science 282, 1089–1094 (1998).
Grier, D. G. A revolution in optical manipulation. Nature 424, 810–816 (2003).
Psaltis, D., Brady, D., Gu, X. G. & Lin, S. Holography in artificial neural networks. Nature 343, 325–330 (1990).
Lin, X. et al. All-optical machine learning using diffractive deep neural networks. Science 361, 1004–1008 (2018).
Chrapkiewicz, R., Jachura, M., Banaszek, K. & Wasilewski, W. Hologram of a single photon. Nat. Photon. 10, 576–579 (2016).
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.
The authors declare no competing interests.
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Fang, X., Ren, H. & Gu, M. Orbital angular momentum holography for high-security encryption. Nat. Photonics 14, 102–108 (2020). https://doi.org/10.1038/s41566-019-0560-x
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