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. 2022 Jan 20;12:1053. doi: 10.1038/s41598-022-05017-0

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© The Author(s) 2022

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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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The phase and electric field distributions of Q-PVs. (a,e,i) The simulated phase distribution after the metasurface when l equals 1, 5, and 10, respectively. The insets show the designed phase distributions. (b,f,j) The longitudinal section of the Q-PV light field on the xOz plane; (c,g,k) The simulated electric field intensity distributions in the focal planes and the insets represent the corresponding phase distributions; (d,h,l) The theoretical light field calculated by Fresnel integration diffraction theory. All the simulated light field distributions were normalized.