近日，北京大学杜朝海团队研究了广义斯涅尔定律中的谐波动力学缺失：揭示梯度超曲面的全通道特性。相关论文于2025年9月15日发表在《光：科学与应用》杂志上。

传统的广义斯涅尔定律（GSL）由经典的光学反射和折射定律推导而来，它通过相位梯度控制波前操作，但忽略了由超表面上元原子之间相互耦合激发的高阶空间谐波。

通过将相位梯度控制与Floquet周期性统一起来，研究组提出了空间谐波扩展GSL （SH-GSL）框架，将空间谐波作为独立的自由度而不是传统的寄生扰动。SH-GSL框架严格地识别了元曲面固有的内在谐波动力学，这是GSL中缺乏的一个关键特征。

此外，该框架进一步揭示了所有梯度相位元表面由于全空间谐波而固有地作为多通道平台，这种多功能性根植于非局部Floquet-Bloch模态相互作用。实验验证表明：异常空间谐波反射具有角精度（<5°偏差），通过特定谐波和补偿波矢量之间的关系进行多波束分裂（双/四组配置），以及一个完美的三通道后向反射器，其效率高达99%，其中寄生谐波仅限于近场等离子体状态。

该框架建立了一个确定性的Floquet工程动量补偿机制，以同时激活目标谐波通道，同时将寄生谐波限制在近场等离子体区域。实验验证证实了该框架的准确性和可扩展性，将动量空间物理与实际的元等离子体系统连接起来。这项工作重新定义了超表面工程范式，通过谐波分复用解锁了超密集波束形成、传感和元光子学的进步。

附：英文原文

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

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

Issue&Volume: 2025-09-15

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.

DOI: 10.1038/s41377-025-02009-3

Source: https://www.nature.com/articles/s41377-025-02009-3