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. 2018 Oct 24;9:4413. doi: 10.1038/s41467-018-06952-1

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© The Author(s) 2018

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. 1 — Principle of OAM nanometrology in a plasmonic topological insulator film. a The schematic design of different GTCs by shifting one half of a circular nanogroove with respect to the other along the breaking line. The GTCs are inspected in the middle of the transverse shifts (∆x/2), where ∆x is the shifting distance. b The linear dependence of the GTC (l_S) on the transverse shift (∆x) of the two semi-circular nanogrooves. λ_SPPs represents the SPPs wavelength. c The intensity cross-sections in the transverse shift direction (the x-axis) of plasmonic fields excited by illuminating optical beams with incident angular momentum modes (l₀ + s) ranging from −6 to +6 on displaced semi-circular nanogrooves with the GTCs (l_S) ranging from +6 to −6, respectively. d The schematic of CMOS-integratable OAM nanometrology. An ultrathin OAM-dispersive plasmonic topological insulator film is constituted by spatially shifted semi-circular nanogrooves and mode-sorting nanoapertures, through which the OAM-superposed beams are spatially separated and directly measured by a CMOS detector in the far-field region. e The multilayer structure of the topological insulator thin film as well as the cross-section of nanogrooves