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. 2018 Dec 19;9:5384. doi: 10.1038/s41467-018-07817-3

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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 — Conceptual sketch of the one-way (half-mode) waveguides in 2D and 3D. a Single-mode two-way waveguide. b One-way waveguide at the edge of a 2D topological bandgap material, across which the forward and backward modes are spatially separated. c One-way fiber at the core of a 3D topological bandgap material. The backward mode is spatially separated, from the forward core mode, at the outer surface of the fiber cladding