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<p>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 ( &lt; 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月15日

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

摘要

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.