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. 2019 Jul 19;10:2986. doi: 10.1038/s41467-019-11030-1

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — Design and fabrication of an OAM-conserving meta-hologram. a Numerical characterization of OAM-dependent spatial frequency sampling of an OAM-conserving meta-hologram. Insets show that a spatial frequency analysis of a spiral phase plate that is used for the generation of an incident OAM beam leads to a doughnut-shaped intensity distribution in the image plane, which further determines the sampling constant (p) of an OAM-conserving meta-hologram. Avoiding interference between OAM pixels in the image plane is required to maintain the OAM information. This indicates that the image sampling size has to increase with the OAM topological charges. b Schematic design of an OAM-conserving meta-hologram through multiplying an object image with an OAM-dependent 2D Dirac comb function (a constant periodicity: p) in the image plane. c Characterization of transmission efficiency and phase response of GaN nanopillars as a function of nanopillars radius at a wavelength of 632 nm, respectively. d The optical image of a fabricated OAM-conserving meta-hologram, where the top- and oblique-view scanning electron microscopy images of enlarged areas in the meta-hologram are presented. The scale bar in the inset is 2 µm. e Experimental characterization of the lensless reconstruction of OAM-carrying holographic images from different OAM-conserving meta-holograms through using incident OAM beams with topological charges of l = ± 1 and ± 2, respectively. The original “disc”, “car”, and “rocket” images were obtained from Flaticon, Free Icons Library, and Interactivecoding websites, respectively