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. 2018 Apr 10;9:1349. doi: 10.1038/s41467-018-03839-z

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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. 3 — Horn-like space-coiling metamaterial unit cell and its equivalent model. a Horn-like space-coiling metamaterial structure composed of six coils is shown here, where d_n (n = 1:6) represents the channel width at n^th coil and d₇ is the channel width at the output port; channel widths follows the geometrical sequence with common ratio in excess of one (CR > 1). b Equivalent model of the gradient coil structure featuring a horn-shaped channel of length L_eff filled with original medium with refractive index of (n₀)