High-transmission dielectric metasurface with 2π phase control at visible wavelengths
可見光波長下具有 2π 相位控制的高透射介質元表面

1. Introduction

Recent years have witnessed significant research work in the area of optical metamaterials, broadly defined as artificially synthesized media engineered at a size scale much smaller than the wavelength of incident light. In contrast to conventional materials whose intrinsic properties are fixed, metamaterials open up the exciting possibility of tailoring material properties to a specific application. Consequently numerous functionalities and devices have been developed, such as negative refractive index lenses, optical cloaking devices, artificial magnets, nanolasers, spasers and more 1.

Metasurfaces 2, which can be understood as a two-dimensional version of metamaterials, have garnered particular attention due to their advantages of possessing a smaller physical footprint, simpler fabrication and lower losses compared to their bulk counterparts. Crucially, they retain the ability to manipulate the phase, amplitude and polarization of light upon transmission or reflection. Due to their two-dimensional nature, it is therefore possible to realize planar analogs of traditional optical components, such as lenses, beam transformers, broadband pass filters, wave plates and polarization converters 2-4. In addition, new functionalities arising from phase discontinuities at an interface can also be obtained, such as beam deflection 5-7, beam forming 8-12, and holography 13-15.
超表面 2 可以被理解爲超材料的二維版本，由於其具有比體材料更小的物理尺寸、更簡單的製造工藝和更低的損耗等優點，因此受到了特別的關注。最重要的是，它們在透射或反射時仍能操縱光的相位、振幅和偏振。由於它們的二維性質，因此可以實現傳統光學元件的平面模擬，如透鏡、光束轉換器、寬帶通濾波器、波板和偏振轉換器 2-4。 此外，還可以通過界面上的相位不連續性獲得新的功能，如光束偏轉 5-7、光束形成 8-12 和全息 13-15。

Plasmonic-based metasurfaces achieve the required full 2π phase control primarily using two different approaches. The first approach relies on the generation of two resonances, which can be independently tuned, each covering a standard phase range of π. For example, V-shaped antennas with different arm lengths and angles can generate symmetric and asymmetric modes. Full wavefront control can be achieved by varying the geometry of the antennas, which also takes into account material dispersion effects 6, 12. The second approach is based on rotationally asymmetric nanostructures whose resonant modes are polarization dependent. Complete phase control can be achieved by spatially varying the geometric orientation of the nanostructures, due to phase singularity via the Pancharatnam–Berry phase 16. However, the intrinsically high losses of metals at optical frequencies lead to low performance efficiencies for plasmonic metasurfaces, especially in transmission 17, 18. This initiated significant work in developing dielectric analogs of metasurfaces, since many dielectric materials have very low absorption loss in the visible and near-infrared range. If the refractive index of a dielectric material is sufficiently high (e.g. >2) in the spectral range of interest, nanoparticles made of this material may possess strong Mie-type scattering resonances analogous to their plasmonic counterparts 19, 20. Accordingly, various high-index dielectric structures have been proposed and in some cases demonstrated at optical frequencies, but have yet to unequivocally show transmission coefficients and bandwidths significantly superior to their metallic counterparts 8-10, 21-27.
基於等離子體的元表面主要通過兩種不同的方法實現所需的全 2π 相位控制。第一種方法依賴於產生兩個共振，這兩個共振可以獨立調整，各自覆蓋 π 的標準相位範圍。例如，具有不同臂長和角度的 V 形天線可以產生對稱和不對稱模式。通過改變天線的幾何形狀可以實現全面的波前控制，這也考慮到了材料的色散效應 6、12。第二種方法基於旋轉不對稱納米結構，其諧振模式與極化有關。由於 Pancharatnam-Berry 相位 16 的相位奇異性，通過在空間上改變納米結構的幾何方向，可以實現完全的相位控制。然而，金屬在光學頻率上的固有高損耗導致等離子體超表面的性能效率較低，尤其是在傳輸方面 17、18。由於許多介電材料在可見光和近紅外波段的吸收損耗非常低，因此開發介電類元表面的工作也隨之啓動。如果電介質材料的折射率在相關光譜範圍內足夠高（例如大於 2），那麼由這種材料製成的納米粒子就可能具有類似於等離子體的強米氏散射共振 19、20。因此，人們提出了各種高指數介質結構，並在某些情況下在光學頻率上進行了演示，但尚未明確顯示出明顯優於金屬材料的傳輸係數和帶寬 8- 10、21- 27。

In this work, we provide clear theoretical and experimental proof that close-to-unity resonant transmission can be achieved at visible wavelengths using properly designed high-index (amorphous silicon) metasurfaces (Fig. 1). This effect is realized by almost complete suppression of resonant reflection due to destructive interference between electric and magnetic-dipole resonances. These transparent metasurfaces have resonant behavior and allow for precise engineering in 2D of the local transmitted light phase over the whole 2π range. The latter concept is demonstrated by the example of a gradient metasurface having close to 50% transmission into the desired diffraction order. The maximum transmission is limited by material loss and can further be improved, e.g. by using other materials with lower losses in the visible (e.g TiO₂, GaN, etc.).
在這項工作中，我們提供了明確的理論和實驗證明，利用適當設計的高指數（非晶硅）超表面（圖 1），可以在可見光波長下實現接近統一的諧振傳輸。由於電偶極共振和磁偶極共振之間的破壞性干擾，共振反射幾乎被完全抑制，從而實現了這種效果。這些透明的超表面具有共振行爲，可以在整個 2π 範圍內對局部透射光相位進行精確的二維工程設計。後一個概念通過梯度元表面的例子得到了證明，它對所需衍射階的透射率接近 50%。最大透射率受材料損耗的限制，可通過使用其他在可見光下損耗較低的材料（如 TiO ₂ 、氮化鎵等）進一步提高。

It is known 19, 20, 28-32 that in spherical high refractive index dielectric particles, a strong magnetic dipole response is observed in addition to the electric one. This resonance appears when the wavelength of light in a particle is close to the diameter λ / n_mat ≈ D 30. This corresponds to the condition where the polarization of the incident electric field is antiparallel at opposite boundaries of the sphere, which gives rise to strong coupling of light to circulating displacement currents within the particle, resulting in generation of a strong magnetic dipole in the center. Dielectric nanoparticles with a magnetic dipole response can be used as building blocks for metamaterials with nonunity magnetic permeability 19, 28, 29. Additionally, it was theoretically predicted 33 and experimentally demonstrated 34, 35 that at particular wavelengths such particles may possess strong directional forward scattering with almost zero backscattering. This effect appears when the electric and magnetic-dipole resonances have similar amplitudes and phases, interfering constructively in the forward direction while canceling each other in the backscattering direction. This is known as the first Kerker's condition, and was theoretically proposed for spherical particles having nonzero magnetic susceptibility in 1983 36. In addition, recent work on oblate dielectric spheroids 37 and disks 23 has shown that these geometries have significantly greater overlap of electric and magnetic-dipole resonances, resulting in the realization of Kerker's condition across a relatively broad spectral bandwidth. A metasurface composed of such densely packed nanoparticles with zero resonant backscattering may thus have almost zero reflection and transmission close-to-unity over the dipole resonance spectral range, while having a controllable phase shift in transmission over 0–2π due to excitation of two (electric and magnetic) dipoles.
衆所周知 19、20、28- 32，在球形高折射率介電質粒子中，除了電響應外，還能觀察到強磁偶極子響應。當粒子中的光波長接近直徑 λ / n _mat ≈ D 30 時，就會出現這種共振。這相當於入射電場的極化在球體的相對邊界處是反平行的，從而導致光與粒子內循環位移電流的強耦合，從而在中心產生一個強磁偶極子。具有磁偶極子響應的介電納米粒子可用作具有非統一磁導率超材料的構件 19、28、29。此外，根據理論預測 33 和實驗證明 34、35，在特定波長下，這類粒子可能具有很強的定向正向散射，而反向散射幾乎爲零。當電偶極子共振和磁偶極子共振具有相似的振幅和相位時，就會出現這種效應，在前向產生建設性干擾，而在後向則相互抵消。這被稱爲第一凱爾克條件，是 1983 年針對磁感應強度不爲零的球形粒子提出的理論條件 36。此外，最近對扁平介質球體 37 和磁盤 23 的研究表明，這些幾何形狀的電偶極共振和磁偶極共振的重疊程度明顯更高，從而在相對較寬的光譜帶寬上實現了克爾克條件。 因此，由這種具有零共振反向散射的密集納米粒子組成的元表面，在偶極子共振光譜範圍內的反射和透射幾乎爲零，接近統一，同時由於兩個（電和磁）偶極子的激發，在 0-2π 範圍內具有可控的透射相移。

The idea of transparent dielectric metasurfaces with 2π phase control was recently proposed in 23, 24 and an attempt has been made to realize this effect in the near-IR spectral range with silicon on insulator (SOI)-based nanostructures. However, the maximum experimentally achieved broadband resonant transmission was around 55%. Here, we experimentally demonstrate that close to 90% transmission can be achieved with silicon-on-quartz metasurfaces even in the visible spectrum while maintaining 2π phase control. We also verify this by observing highly efficient (close to 50%) beam deflection with such metasurfaces, which is experimentally demonstrated.
23 和 24 最近提出了具有 2π 相位控制的透明介電元表面的想法，並嘗試用基於絕緣體（SOI）硅的納米結構在近紅外光譜範圍內實現這種效果。然而，實驗中實現的最大寬帶諧振傳輸率約爲 55%。在此，我們通過實驗證明，即使在可見光譜範圍內，石英基硅元表面也能實現接近 90% 的傳輸率，同時保持 2π 的相位控制。我們還通過實驗證明，使用這種超表面可以觀察到高效（接近 50%）的光束偏轉，從而驗證了這一點。

2 Near-unity visible transmission of uniform silicon nanodisk arrays
2 一致性硅納米盤陣列的近統一可見光傳輸

Our metasurface (Fig. 1) consists of an array of silicon nanodisks of 130 nm thickness (t) and variable diameters (D = 2R) with subwavelength period (P = D + 90 nm) on a fused silica substrate. The structure is embedded in a poly-dimethyl-siloxane (PDMS) layer from the top. For a certain particle diameter range this configuration fulfills the condition for minimized reflection, which happens when the spectral positions of electric and magnetic-dipole resonances are matched. For materials with a refractive index close to 3.7, this occurs at a ratio of diameter to height of approximately 2 23, 34, 37. PDMS was used as an embedding medium to simulate conditions close to a homogeneous environment that enables better amplitude matching between the two resonant modes. The height of 130 nm was chosen to have the resonances in the red spectral range of 700–800 nm where intrinsic absorption loss of our amorphous silicon is small. The exact values for these parameters were obtained via finite-difference time-domain (FDTD, Lumerical) simulations and optimization sweeps, using experimentally measured refractive-index data of our silicon deposited by chemical vapor deposition (CVD) (see Methods in Supplementary Information).
我們的元表面（圖 1）由熔融石英基底上厚度（t）爲 130 nm、直徑（D = 2R）可變、亞波長週期（P = D + 90 nm）的硅納米盤陣列組成。該結構從頂部嵌入聚二甲基硅氧烷（PDMS）層。在一定的顆粒直徑範圍內，這種結構符合反射最小化的條件，當電偶極子共振和磁偶極子共振的光譜位置相匹配時，反射就會最小化。對於折射率接近 3.7 的材料，當直徑與高度之比約爲 2 時就會出現這種情況 23、34、37。使用 PDMS 作爲嵌入介質，是爲了模擬接近均質環境的條件，使兩種共振模式之間的振幅能更好地匹配。選擇 130 nm 的高度是爲了讓共振出現在 700-800 nm 的紅色光譜範圍內，因爲非晶硅的本徵吸收損耗較小。這些參數的精確值是通過有限差分時域（FDTD，Lumerical）模擬和優化掃描獲得的，使用的是化學氣相沉積（CVD）法沉積的硅的實驗測量折射率數據（見補充信息中的方法）。

Experimentally measured and simulated transmission spectra of the arrays of silicon disks used for the optimization sweeps (with radii varying from 120 nm to 155 nm) are presented in Fig. 2. For smaller sizes of nanodisks (e.g. radius below 130 nm) as shown in Figs. 2a and c (top), it is seen that the electric and magnetic dipoles are spectrally close but not fully overlapped and give a resonant dip in transmission around 680–700 nm. However, as the disk size is increased, the dipole resonances overlap and the transmission at resonance increases. The optimal transmission case is reached for radii of 130–135 nm with peak transmission close to 90% around 700 nm and > 85% transmission across the whole resonant range from 670 nm to 770 nm. With larger disk sizes, the resonances are again detuned, resulting in a characteristic crossing of the resonances 23, 24, 37 and decreased resonant transmission. Figures 2b and c (bottom) show numerically calculated results via FDTD for similar disk sizes. It is seen that the simulated and experimental spectra are in a good agreement, in terms of both feature intensity and position. Magnified views of experimental transmission spectra for different disk radii varied in the range from 120 nm to 175 nm with a step of 5 nm are shown in supplementary materials (Fig. S1). Though the transmission through the arrays at optimized conditions (R = 135 nm) is close-to-unity all nanoparticles are resonantly excited having both spectrally overlapped electric and magnetic-dipole resonances (see Fig. 2d showing resonant electric and magnetic near-fields at the wavelength of transmission maximum of 736 nm).
圖 2 展示了用於優化掃描的硅盤陣列（半徑從 120 納米到 155 納米不等）的實驗測量和模擬透射光譜。對於圖 2a 和 c（上圖）所示的較小尺寸的納米盤（例如半徑小於 130 nm），可以看到電偶極子和磁偶極子在光譜上很接近，但沒有完全重疊，並在 680-700 nm 波長附近產生了透射共振凹陷。然而，隨着磁盤尺寸的增大，偶極子共振重疊，共振時的透射率增加。半徑爲 130-135 nm 時達到最佳傳輸率，700 nm 附近的峯值傳輸率接近 90%，在 670 nm 至 770 nm 的整個共振範圍內傳輸率大於 85%。隨着圓盤尺寸增大，共振再次失諧，導致共振 23、24、37 特性交叉，共振透射率下降。圖 2b 和 c（下圖）顯示了通過 FDTD 對類似尺寸的圓盤進行數值計算的結果。從圖中可以看出，模擬光譜和實驗光譜在特徵強度和位置方面都非常吻合。補充材料（圖 S1）中顯示了不同圓盤半徑的實驗透射光譜放大圖，半徑範圍從 120 nm 到 175 nm，步長爲 5 nm。雖然在優化條件下（R = 135 nm）通過陣列的透射率接近於均勻，但所有納米粒子都被共振激發，具有光譜上重疊的電偶極子共振和磁偶極子共振（見圖 2d，顯示透射最大波長 736 nm 處的共振電場和磁場近場）。

Figure 3a shows in greater detail the experimentally measured transmission for the optimal parameters of the silicon nanoparticle array (corresponding to R = 135 nm in Fig. 2a), while Fig. 3b plots the optimal simulated response (bottom panel) as well as the corresponding electric- and magnetic-dipole contributions (top panel) extracted through the multipole decomposition technique 38, 39 (see Methods in Supplementary Information). One can see a reasonable agreement between the experiment and simulations. Indeed, we observe a peak in transmission close to 90% on resonance, in good agreement with simulated values. However, the experimental transmission over the whole resonant range from 670 nm to 770 nm is surprisingly higher than that in the simulations. This is likely due to the narrower and stronger electric-dipole contribution, which does not fully overlap with the broader magnetic-dipole resonance in the simulated case. In the experiment the electric-dipole resonance broadens due to fabrication tolerances, including surface roughness, size variations and slight sidewall tapering (which could be aperiodic), as well as deviations from bulk-material parameters. All these factors may affect the Q-factor and intensity of the electric-dipole resonance and result in its better matching with the magnetic dipole in the experiment. We also remark that near-field interaction between the nanoparticles in the array strongly influences the spectral positions of both electric and magnetic-dipole resonances. This also results in significant narrowing of the electric-dipole resonance in the array, while the magnetic-dipole resonance shape is less affected due to the stronger field confinement inside the particles. This is illustrated in Fig. S2 in the supplementary materials, where the same simulation is shown for the case of an isolated nanodisk. Thus, small deviations from ideal periodicity could also contribute to better overlap of the resonances.
圖 3a 更詳細地顯示了硅納米粒子陣列最佳參數（對應圖 2a 中的 R = 135 nm）的實驗測量透射率，而圖 3b 則繪製了最佳模擬響應（下圖）以及通過多極分解技術 38、39 提取的相應電偶極子和磁偶極子貢獻（上圖）（見補充信息中的方法）。我們可以看到實驗與模擬之間存在合理的一致性。事實上，我們觀察到共振時的傳輸峯值接近 90%，與模擬值十分吻合。然而，在 670 納米到 770 納米的整個共振範圍內，實驗透射率竟然高於模擬值。這可能是由於電偶極貢獻較窄且較強，與模擬情況中較寬的磁偶極共振並不完全重疊。在實驗中，電偶極共振由於製造公差而變寬，包括表面粗糙度、尺寸變化和輕微的側壁錐度（可能是非週期性的），以及與塊體材料參數的偏差。所有這些因素都可能影響電偶極共振的 Q 因子和強度，並使其在實驗中與磁偶極更好地匹配。我們還注意到，陣列中納米粒子之間的近場相互作用會強烈影響電偶極共振和磁偶極共振的光譜位置。這也導致陣列中的電偶極子共振明顯變窄，而磁偶極子共振的形狀由於粒子內部較強的場約束而受到的影響較小。如圖所示 補充材料中的 S2 顯示了對孤立納米盤的相同模擬。因此，與理想週期性的微小偏差也有助於更好地重疊共振。

Figure 3b also shows the simulated phase change in the silicon nanoparticle array over a full period of 0–2π around the resonance, as expected due to the overlap of the electric- and magnetic-dipole contributions. To design a metasurface with a full phase control at a particular wavelength, one approach is to vary the disk size around the optimized position. This is demonstrated in Fig. 3c both in simulations and experiment for disk radius variations around the central value of 135 nm. Transmission through the arrays with different nanoparticle size is shown at optimized wavelengths, which are slightly different in simulations and experiments, of 736 nm and 720 nm respectively, due to a minor offset in resonance position between the two. A simulated phase change at 736 nm is also shown in Fig. 3c as a function of disk radius. One observes that the phase of the transmitted light varies in the range of 2π when the disk radius is changed from 115 nm to 155 nm, while reasonably high transmission centered at the optimal value can be achieved. Note that the transmission plots as a function of nanoparticle size exhibit a similar behavior to those plotted as a function of wavelength since small variations in size tend to linearly shift the resonance features. This causes the simulated transmission curve in Fig. 3c to exhibit double-dip behavior, similar to Fig. 3b, whereas the experimental curve has a smoother profile, similar to Fig. 3a. Overall, these results demonstrate that with a proper choice of particle sizes, the extension from a uniform array to a metasurface with beam forming capabilities and overall high transmission can be achieved.
圖 3b 還顯示了硅納米粒子陣列在共振周圍 0-2π 全週期內的模擬相位變化，這是由於電偶極子和磁偶極子貢獻的重疊而產生的。要設計出在特定波長下具有全相位控制能力的元表面，一種方法是在優化位置周圍改變圓盤大小。圖 3c 演示了模擬和實驗中圍繞 135 納米中心值的圓盤半徑變化。圖 3c 顯示了不同納米粒子大小的陣列在優化波長下的透射率，模擬和實驗中的波長略有不同，分別爲 736 納米和 720 納米，這是因爲兩者之間的共振位置略有偏移。圖 3c 還顯示了 736 納米波長下的模擬相位變化與圓盤半徑的函數關係。我們可以觀察到，當圓盤半徑從 115 納米變爲 155 納米時，透射光的相位在 2π 的範圍內變化，同時可以實現以最佳值爲中心的較高透射率。請注意，透射率與納米粒子尺寸的函數關係圖與波長的函數關係圖表現出類似的行爲，因爲尺寸的微小變化往往會線性地移動共振特徵。這導致圖 3c 中的模擬透射曲線表現出與圖 3b 相似的雙浸行爲，而實驗曲線則表現出與圖 3a 相似的平滑曲線。總之，這些結果表明，只要適當選擇顆粒大小，就能實現從均勻陣列到具有光束形成能力和整體高透射率的元表面的擴展。

3. Gradient metasurface and beam deflection
3.梯度元面和橫樑偏轉

To validate the phase control effect of these transparent silicon nanodisk arrays, we utilized a gradient metasurface with a supercell containing 8 elements, whose radius is increased from 120 nm to 155 nm in steps of 5 nm. The period of the nanodisk array is fixed at 360 nm and the height of the nanostructures is 130 nm (Fig. 4a). These sizes were chosen to provide the accumulated phase difference of approximately from one neighboring element to the other, resulting in a full 2π phase difference accumulation over the period of the supercell. According to the generalized Snell's law: , 6, where the θ_t/θ_i is the transmitted/incident angle, n_t/n_i is the refractive index of surrounding medium on transmitted/incident sides, λ₀ is the radiation wavelength in vacuum and dФ/dx is the (spatial) phase gradient, we expect that for our experimental configuration (see Methods in Supplementary Information), the metasurface will deflect the transmitted beam at an angle of 10.3° in resonance.
爲了驗證這些透明硅納米盤陣列的相位控制效果，我們使用了一個包含 8 個元素的超級單元的梯度元表面，其半徑以 5 nm 爲單位從 120 nm 增加到 155 nm。納米盤陣列的週期固定爲 360 納米，納米結構的高度爲 130 納米（圖 4a）。選擇這些尺寸是爲了使相鄰元素之間的累積相位差約爲 ，從而在超級電池的週期內實現 2π 的相位差累積。根據廣義的斯涅耳定律：其中，θ _t /θ爲透射/入射角，n _t /n爲透射/入射側周圍介質的折射率，λ ₀ 爲真空中的輻射波長，dФ/dx 爲（空間）相位梯度。我們預計，對於我們的實驗配置（見補充信息中的方法），元表面將在共振時使透射光束偏轉 10.3°。

Experimental measurements of the beam deflection conducted through back-focal plane imaging of light transmitted through the metasurface are shown in Figs. 4b and c (see Methods in Supplementary Information for experimental details). We scan the wavelength of incident beam over the collective (electric and magnetic) resonance position in steps of 10 nm. At shorter wavelengths (see 665 nm in Fig. 4c), a regular diffraction pattern is observed in transmission with significant energy accumulated in the 0^th diffraction order spot (purely transmitted light). Diffraction is natural for such a gradient metasurface design due to the periodicity of the supercell. The relative intensities of the three main diffraction orders (0, −1, +1) measured at different wavelengths and normalized to the incident intensity are shown in Fig. 4b. The higher diffraction orders are significantly weaker and can be neglected. When the wavelength of the incident beam approaches the optimized position of 705–715 nm, the 0^th and all other diffraction orders except −1 are strongly suppressed. The −1 order is, by contrast, enhanced, which corresponds to the transmitted beam deflection to an angle of approximately 10°, in accordance with the theoretical prediction. This is a hallmark of phase-manipulation behavior by a metasurface 6. For larger wavelengths away from the optimized value the effect disappears and a regular diffraction pattern with strong 0^th-order beam spot is again observed (see 775 nm in Fig. 4c).
圖 4b 和 c 顯示了通過對穿過元表面的光進行背焦面成像而對光束偏轉進行的實驗測量（實驗詳情請參見補充信息中的方法）。我們以 10 nm 爲單位掃描集體（電和磁）共振位置上的入射光波長。在較短波長下（見圖 4c 中的 665 納米），透射中觀察到規則的衍射圖樣，在 0 ^th 衍射階光斑（純透射光）中積累了大量能量。由於超級星體的週期性，這種梯度元表面設計自然會產生衍射。圖 4b 顯示了在不同波長下測量到的三個主要衍射階（0、-1、+1）的相對強度，並與入射強度進行了歸一化。較高的衍射階數明顯較弱，可以忽略。當入射光束的波長接近 705-715 納米的優化位置時，0 ^th 和除-1 以外的所有其他衍射階都被強烈抑制。相反，-1 衍射階則增強了，這相當於透射光束偏轉了大約 10° 角，與理論預測相符。這是元表面 6 的相位操縱行爲的特徵。在遠離優化值的更大波長上，這種效應消失了，並再次觀察到帶有強 0 ^th 階光束光斑的規則衍射圖樣（見圖 4c 中的 775 nm）。

From Fig. 4b, one can observe that the efficiency of the metasurface reaches the maximum value of around 45% at 705 nm, i.e. 45% of incident light is transformed into the desired (−1) order. The measured values are in very good agreement with numerical calculations for the same design (Figs. S3 and S4 in Supplementary Information). The obtained efficiency is very high in the context of transmissive metasurfaces. It was recently established that for planar nonmagnetic plasmonic metasurfaces in the lossless case the maximum transmission efficiency is limited to 25% in the crosspolarized beam 40. This limit appears since the full phase control requires the plasmonic structures to be anisotropic and support more than a single resonance. In order to surpass this limit, the authors of 40 proposed to employ stacked structure of 3 planar metasurfaces. This structure operating at mid-IR frequencies was theoretically shown to have transmission efficiencies around 60%. This value is comparable to our experimental result at visible wavelengths.
從圖 4b 可以看出，在 705 納米波長處，元表面的效率達到 45% 左右的最大值，即 45% 的入射光被轉化爲所需的 (-1) 階。測量值與相同設計的數值計算結果非常吻合（補充信息中的圖 S3 和 S4）。就透射式超表面而言，獲得的效率非常高。最近的研究表明，對於平面非磁性等離子超表面，在無損耗情況下，交叉偏振光束 40 的最大傳輸效率僅限於 25%。出現這一限制的原因是，全相位控制要求質子結構具有各向異性，並支持不止一次共振。爲了突破這一限制，40 的作者建議採用由 3 個平面元表面組成的堆疊結構。理論上，這種工作於中紅外頻率的結構具有 60% 左右的傳輸效率。這一數值與我們在可見光波段的實驗結果相當。

Another possibility discussed to get high efficiency in transmission is to employ metasurfaces with both electric- and magnetic-induced currents, which can interfere and cancel the reflection. 41 This approach for nonreflecting metasurfaces proposed in plasmonics is fundamentally similar to our case of dielectric metasurfaces where reflection is cancelled due to interference of electric- and magnetic-dipole resonances. The significant difference between plasmonic and dielectric cases is strong losses, which plasmonic structures have at optical frequencies. In 41 the authors demonstrated this concept at GHz frequencies (where metals are loss-free) with 58 stacks of structured surfaces and could achieve efficiency of ∼85% in transmission. Later demonstration of the same concept with plasmonic metasurfaces working at near-IR frequencies could achieve around 30% efficiency in theory and 20% in experiments 42. This efficiency value is more than twice lower than our experimental data in the visible spectral range.
人們討論的另一種獲得高效傳輸的方法是採用同時具有電流和磁流的元表面，它們可以相互干擾並抵消反射。41 這種在等離子體學中提出的無反射超表面方法與我們的介電超表面基本相似，在介電超表面中，由於電偶極和磁偶極共振的干擾，反射被抵消。等離子體與介電情況的顯著區別在於等離子體結構在光學頻率上具有很強的損耗。41 年，作者在 GHz 頻率（金屬無損耗）下使用 58 層結構表面堆疊演示了這一概念，並實現了 ∼85% 的傳輸效率。後來，在近紅外頻率下使用等離子體元表面演示了同樣的概念，理論效率約爲 30%，實驗效率爲 20% 42。這一效率值比我們在可見光譜範圍內的實驗數據低兩倍多。

The efficiency value of around 45% and the total transmitted power through the metasurface obtained in our experiments are lower than the maximum transmission with the single-size nanodisk arrays (around 85%). This can be explained by the variable disk size inside the metasurface and interaction between the neighboring disks of different sizes. The efficiency values can further be improved through careful optimization of the metasurface design taking into account interactions between the neighboring cells.
我們在實驗中獲得的約 45% 的效率值和通過元表面的總傳輸功率低於單尺寸納米盤陣列的最大傳輸功率（約 85%）。這可能是由於元表面內部的磁盤尺寸可變，以及不同尺寸的相鄰磁盤之間的相互作用造成的。考慮到相鄰單元之間的相互作用，通過仔細優化元表面設計，可以進一步提高效率值。

4. Conclusion  4.結論

In summary, we have introduced and experimentally demonstrated an all-dielectric metasurface consisting of a subdiffraction array of silicon nanodisks with near-unity broadband transmission at visible wavelengths. The high transmission and greatly suppressed (almost zero) reflection are due to almost complete overlap and interference of simultaneously excited electric and magnetic-dipole resonances in the nanodisks. This allows for full 2π control of phase of the incoming light. In addition, we have verified the metasurface performance by designing a gradient structure for beam deflection. A deflection efficiency of around 45% is demonstrated in the experiment. These results are particularly notable due to the deeply subwavelength periodicity of the design, which ensures that all incident light is interacting with the structure. Finally, the relative simplicity of the fabrication, which utilizes single-layer lithography and thin-film etching, as well as its compatibility with CMOS process, makes this approach promising for integrating the concept of metasurfaces to real-world applications.
總之，我們介紹並通過實驗證明了一種全介質元表面，它由硅納米盤的亞衍射陣列組成，在可見光波長下具有近乎統一的寬帶透射率。高透射率和被大大抑制（幾乎爲零）的反射是由於納米盤中同時激發的電偶極子和磁偶極子共振幾乎完全重疊和干涉造成的。這使得入射光的相位可以實現完全的 2π 控制。此外，我們還通過設計用於光束偏轉的梯度結構來驗證元表面的性能。實驗證明，偏轉效率約爲 45%。這些結果之所以特別顯著，是因爲設計具有深度亞波長週期性，從而確保所有入射光都能與該結構相互作用。最後，利用單層光刻技術和薄膜蝕刻技術進行製造的相對簡單性，以及與 CMOS 工藝的兼容性，使得這種方法有望將元表面的概念整合到現實世界的應用中。