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. 2018 Apr 24;9:1632. doi: 10.1038/s41467-018-04103-0

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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 — Formation of high-quality Airy beam. a, b Amplitude profile in a and phase profile in b at the surface of the LAM for generating the Airy beam. The LAM consists of 80 discrete unit cells (triangles). c, d Simulated pressure fields of Airy beams produced by the APM in c and PM in d. Scale bar, 10 cm. e, f Distributions of pressure amplitude on the dashed lines in c and d. The result for the perfect Airy beam is calculated by Eq. (7), which is displayed for comparison (red lines)