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...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.展开更多
基金supported by the National Natural Science Foundation of China(62271011)and(62405009)the National Science Key Lab Fund(2024CXPTGFJJ020010401)+1 种基金the National Key Research and Development Program of China(2021YFA1600302)the Beijing Science Foundation for Distinguished Young Scholars(JQ21011).
文摘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.
