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. 2022 Apr 6;12:5832. doi: 10.1038/s41598-022-09680-1

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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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Numerical design map optimization of the metasurface waveguide glass, showing the metasurface optical waveguide display diffraction efficiencies for input/output MOE in the waveguide propagation direction for different positions in the waveguide x, fill factor (FF), and height parameters. Rigorous coupled-wave analysis (RCWA) numerical simulation is used in each design point of the 2D maps. (a) The height is fixed at 0.35 nm. Color scale bar denotes total intensity input–output propagation efficiencies in percentage. (b) Top panel for a fill factor (FF) of 0.4 and bottom panel for a fill factor of 0.5, with varying waveguide heights. The same color scale bar is used. In this implementation, optimal regions for the waveguide heights, fill factors and refractive indices of the metasurface are denoted. (c) Fill factor 0.46 and SiN_x refractive index of 2.14 (at wavelength 521 nm) with wavelengths of 447 nm, 521 nm, and 644 nm for blue, green, and red, respectively and the combined average.