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. 2023 Nov 14;14:7347. doi: 10.1038/s41467-023-42449-2

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© The Author(s) 2023

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. 3 — a A finite-size photonic TI. The parameters are the same as those in Fig. 2a, b. The ratio between the running averaged edge LDOS over the running averaged bulk LDOS (left panel), the ratio between the running averaged corner LDOS over the running averaged bulk LDOS (left panel), and the ratio between the running averaged corner LDOS over the running averaged edge LDOS (left panel) are presented respectively. The solid (dashed) blue and orange lines represent the measured (simulated) ratio for the OI and TI, respectively. c The upper (lower) panels show the LDOS of a single frequency at 4.04, 5.04, 5.88, 7.08, and 7.52 GHz for OI and TI, respectively. For the ordinary insulator (OI), the LDOS is homogeneously distributed over the entire bulk area (EBA) at all frequencies. For the topological insulator (TI), at 4.04, 5.04, 5.88, 7.08, and 7.52 GHz, the LDOS is dominant at the interior bulk area (IBA), edge and IBA, corner, edge and IBA, edge and IBA, respectively (encircled by dashed blue lines) which clearly reveals the multidimensional partition of the LDOS.