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. 2018 Mar 2;9:909. doi: 10.1038/s41467-018-03330-9

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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. 4 — Far-field spectroscopy of topological edge states. a Schematic optical setup for far-field mapping of photonic bands corresponding to edge states in a topological meta-grating. Meta-grating is formed by stitching 12 unit cells of alternating topological/expanded (orange) and trivial/shrunken (light blue) domains of the metasurface with 30 domain walls in total. b SEM image of the proximity to one of the domain walls overlaid with the computed field profile (electromagnetic energy density) of the edge state. c The results of CMT calculations of the scattering from topological meta-grating. Periodic conditions are imposed on the outer interfaces. d Measured far-field reflectance spectra revealing edge states within the bulk bandgap. The parameters used in CMT model are: on-site energy ω₀ = 173.61 THz, intra-cell tunneling amplitude K = 33.00 THz, inter-cell tunneling amplitude J = 23.00 THz, radiative loss γ_r = 0.25 THz, and non-radiative loss γ₀ = 0.30 THz