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. 2017 Aug 30;7:10055. doi: 10.1038/s41598-017-09523-4

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© The Author(s) 2017

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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Tunable Luneburg Lens for a defocused source located at the right side. The spacing between the layers is 160 nm (≈λ/10) which is within the effective medium region. (a–d) Demonstrate the results of the wavefronts, required refractive index, effective permittivity and applied bias across the radial direction of the metamaterial for different focal lengths of 1.5R _lens, 2R _lens, 2.5R _lens and 3R _lens, respectively. The wavefronts leaving the lens are planar demonstrating tunable beam collimating. The structure can also be used to concentrate the incoming plane waves with a tunable focal length.