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. 2019 Jul 15;9:10178. doi: 10.1038/s41598-019-46522-z

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© The Author(s) 2019

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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Maps of the leaky wave propagation (a) and attenuation (b) constants, evaluated at 32.05 GHz. The quantities are expressed as a function of m_κ₁ and m_κ₂. The substrate used in this calculations is Rogers RO3010 with ε_r = 10.2 and thickness h_d = 0.635 mm.