Ultraprecision, high-capacity, and wide-gamut structural colors enabled by a mixture probability sampling network

Zeyong Wei; Weijie Xu; Siyu Dong; Xiaojia Liang; Jingyuan Zhu; Hui Zhang; Kaixuan Li; Lei Jin; Zhanshan Wang; Yuzhi Shi; Gang Yan; Cheng-Wei Qiu; Xinbin Cheng

doi:10.1038/s41377-025-02122-3

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Ultraprecision, high-capacity, and wide-gamut structural colors enabled by a mixture probability sampling network

Original Articles

- Ultraprecision, high-capacity, and wide-gamut structural colors enabled by a mixture probability sampling network
- Ultraprecision, high-capacity, and wide-gamut structural colors enabled by a mixture probability sampling network
- Light: Science & Applications 2026年15卷第4期页码：1076-1088
- Affiliations：
  
  1.School of Physics Science and Engineering, Tongji University, Shanghai, China
  2.Institute of Precision Optical Engineering, School of Physics Science and Engineering, Tongji University, Shanghai, China
  3.MOE Key Laboratory of Advanced Micro-Structured Materials, Shanghai, China
  4.Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai, China
  5.Shanghai Frontiers Science Center of Digital Optics, Shanghai, China
  6.Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
  7.School of Electronics and Information Engineering, Hangzhou Dianzi University, Hangzhou, China
  8.Shanghai Eye Diseases Prevention & Treatment Center, Shanghai Eye Hospital, Shanghai, China
- Author bio：
  
  Yuzhi Shi (yzshi@tongji.edu.cn)
  Gang Yan (gyan@tongji.edu.cn)
  Cheng-Wei Qiu (chengwei.qiu@nus.edu.sg)
  Xinbin Cheng (chengxb@tongji.edu.cn)
- Funds：
- DOI：10.1038/s41377-025-02122-3
  中图分类号：
- 收稿：2025-07-05，
  
  修回：2025-10-08，
  
  录用：2025-11-05，
  
  网络首发：2026-03-11，
  
  纸质出版：2026-04-30
- Accepted：
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Zeyong Wei, Weijie Xu, Siyu Dong, 等. Ultraprecision, high-capacity, and wide-gamut structural colors enabled by a mixture probability sampling network[J]. Light: Science & Applications, 2026,15(4):1076-1088.

Wei, Z. Y. et al. Ultraprecision, high-capacity, and wide-gamut structural colors enabled by a mixture probability sampling network. Light: Science & Applications, 15, 1076-1088 (2026).
Zeyong Wei, Weijie Xu, Siyu Dong, 等. Ultraprecision, high-capacity, and wide-gamut structural colors enabled by a mixture probability sampling network[J]. Light: Science & Applications, 2026,15(4):1076-1088. DOI： 10.1038/s41377-025-02122-3.

Wei, Z. Y. et al. Ultraprecision, high-capacity, and wide-gamut structural colors enabled by a mixture probability sampling network. Light: Science & Applications, 15, 1076-1088 (2026). DOI： 10.1038/s41377-025-02122-3.

摘要

Abstract

The advancement of nanophotonic devices is significantly dependent on achieving high-precision inverse design capabilities

which are critical for identifying optimal structural configurations that enable enhanced and multifunctional performances. The process of inverse design confronts a one-to-many relationship due to the complex mapping between optical performance and structure. Though several approaches

including tandem networks

mixture density networks (MDN)

and conditional generative adversarial networks

have shown promising outcomes

they still face accuracy limitations when confronted with structures with higher degrees of freedom. Here

we propose a sampling-enhanced MDN called a mixture probability sampling network (MPSN)

that outputs mixture Gaussian distributions (MGDs) of structural parameters through an end-to-end framework. The results of multiple samples drawn from the MGDs are fed into a pre-trained network

and the sample that minimizes the error relative to the real data is selected for network training. We benchmark the high performance in nanophotonics through the structural color design

achieving a high precision of up to 99.9% and a mean absolute error of less than 0.002. This work paves the way for resolving intricate inverse design problems in nanophotonics.

关键词

Keywords

references

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