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. 2020 Jul 23;11:3681. doi: 10.1038/s41467-020-17529-2

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© The Author(s) 2020

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 — a Microstructural design of the active Willis meta-layer. Geometric and material parameters of the design are given in Supplementary Fig. 4 and Supplementary Table 2. b Working principles of the active meta-layer. c, d Designed amplitudes and phases of electrical transfer functions, (c) H₁ and (d) H₂ of a transmission-type meta-layer (R_l = 0) with the amplitude of the transmission coefficient, T_l varied from 0 to 2 (horizontal axis) and with a full 2π phase change coverage (vertical axis). Source data are provided as a Source Data file. e Differences between numerically calculated transmission and reflection coefficients and their prescribed values to be achieved with the corresponding transfer functions in (c) and (d). Source data are provided as a Source Data file.