Missing harmonic dynamics in generalized Snell's law: revealing full-channel characteristics of gradient metasurfaces

Yueyi Zhang; Fengyuan Han; Yibing Xiao; Ziwen Zhang; Jitao Yang; Yulu Lei; Fei Gao; Hongsheng Chen; Chao-Hai Du

doi:10.1038/s41377-025-02009-3

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Missing harmonic dynamics in generalized Snell's law: revealing full-channel characteristics of gradient metasurfaces

Original Articles

- Missing harmonic dynamics in generalized Snell's law: revealing full-channel characteristics of gradient metasurfaces
- Missing harmonic dynamics in generalized Snell's law: revealing full-channel characteristics of gradient metasurfaces
- Light: Science & Applications 2025年14卷第11期页码：3479-3495
- Affiliations：
  
  1.Center for Carbon-Based Electronics, School of Electronics, Peking University, Beijing 100871, China
  2.State Key Laboratory of Photonics and Communications, School of Electronics, Peking University, Beijing 100871, China
  3.Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310058, China
- Author bio：
  
  Hongsheng Chen (hansomchen@zju.edu.cn)
  Chao-Hai Du (duchaohai@pku.edu.cn)
- Funds：
- DOI：10.1038/s41377-025-02009-3
  中图分类号：
- 收稿：2025-04-08，
  
  修回：2025-07-23，
  
  录用：2025-08-13，
  
  网络出版：2025-09-15，
  
  纸质出版：2025-11-30
- Accepted：
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Yueyi Zhang, Fengyuan Han, Yibing Xiao, 等. Missing harmonic dynamics in generalized Snell's law: revealing full-channel characteristics of gradient metasurfaces[J]. Light: Science & Applications, 2025,14(11):3479-3495.

Zhang, Y. Y. et al. Missing harmonic dynamics in generalized Snell's law: revealing full-channel characteristics of gradient metasurfaces. Light: Science & Applications, 14, 3479-3495 (2025).
Yueyi Zhang, Fengyuan Han, Yibing Xiao, 等. Missing harmonic dynamics in generalized Snell's law: revealing full-channel characteristics of gradient metasurfaces[J]. Light: Science & Applications, 2025,14(11):3479-3495. DOI： 10.1038/s41377-025-02009-3.

Zhang, Y. Y. et al. Missing harmonic dynamics in generalized Snell's law: revealing full-channel characteristics of gradient metasurfaces. Light: Science & Applications, 14, 3479-3495 (2025). DOI： 10.1038/s41377-025-02009-3.

摘要

Abstract

The conventional generalized Snell's law (GSL)

derived from classical laws of optical reflection and refraction

governs wavefront manipulation via phase gradients but neglects higher-order spatial harmonics inherently excited by the mutual coupling among meta-atoms on a metasurface. Here

we introduce a spatial harmonic-expanded GSL (SH-GSL) framework by unifying phase-gradient control with Floquet periodicity

establishing spatial harmonics as independent degrees of freedom rather than conventional parasitic disturbances. The SH-GSL framework rigorously identifies the intrinsic harmonic dynamics inherent to metasurfaces

which is a critical feature absent in GSL. Furthermore

this framework further reveals that all gradient-phase metasurfaces inherently function as multichannel platforms due to full spatial harmonics

with this multifunctionality rooted in nonlocal Floquet-Bloch modal interactions. Experimental validation demonstrates: abnormal spatial-harmonic reflection with angular precision (< 5° deviation)

multi-beam splitting (dual/quad configurations) via the relationship between specific harmonics and compensation wave vectors

and a perfect three-channel retroreflector achieving up to 99% efficiency

where parasitic harmonics are confined to near-field plasmonic regimes. This framework establishes a deterministic Floquet-engineered momentum compensation mechanism to simultaneously activate target harmonic channels while confining parasitic harmonics to near-field plasmonic regimes. Experimental validation confirms the framework's accuracy and scalability

bridging momentum-space physics with practical meta-plasmon systems. This work redefines metasurface engineering paradigms

unlocking advancements in ultra-dense beamforming

sensing

and meta-photonics through harmonic-division multiplexing.

关键词

Keywords

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