Letter pubs.acs.org/NanoLett
Visible-Frequency Dielectric Metasurfaces for Multiwavelength Achromatic and Highly Dispersive Holograms Bo Wang,† Fengliang Dong,‡ Qi-Tong Li,† Dong Yang,† Chengwei Sun,† Jianjun Chen,†,§ Zhiwei Song,‡ Lihua Xu,‡ Weiguo Chu,*,‡ Yun-Feng Xiao,†,§ Qihuang Gong,†,§ and Yan Li*,†,§ †
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State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University and Collaborative Innovation Center of Quantum Matter, Beijing 100871, China ‡ CAS Center for Excellence in Nanoscience, National Center for Nanoscience and Technology, Beijing 100190, China § Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China S Supporting Information *
ABSTRACT: Dielectric metasurfaces built up with nanostructures of high refractive index represent a powerful platform for highly efficient flat optical devices due to their easy-tuning electromagnetic scattering properties and relatively high transmission efficiencies. Here we show visible-frequency silicon metasurfaces formed by three kinds of nanoblocks multiplexed in a subwavelength unit to constitute a metamolecule, which are capable of wavefront manipulation for red, green, and blue light simultaneously. Full phase control is achieved for each wavelength by independently changing the in-plane orientations of the corresponding nanoblocks to induce the required geometric phases. Achromatic and highly dispersive meta-holograms are fabricated to demonstrate the wavefront manipulation with high resolution. This technique could be viable for various practical holographic applications and flat achromatic devices. KEYWORDS: Dielectric metasurface, color hologram, visible, multiwavelength, achromatic hologram, highly dispersive hologram
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nanoposts for two infrared wavelengths.11 The M-level phase control at N discrete wavelengths normally requires M × N types of resonators. When M increases, the resonator dimension differences decrease, which increases the fabrication difficulty, especially for shorter wavelengths. However, the resonator types can be sharply reduced to N when the phase is manipulated via the Pancharatnam−Berry (PB) phase by varying the in-plane orientations instead of the sizes of nanostructures.12,15,20,30−36 A three-color meta-hologram was theoretically studied9 but the Si nanostructures were separated in four microscale segmented areas according to three colors, making it hard to extend to the fabrication of achromatic lenses. Here, we proposed and realized dielectric metasurfaces built up of Si nanoblocks with only three sizes multiplexed with subwavelength spacing to manipulate the phases for red, green, and blue wavelengths. Full phase control is easily achieved for each wavelength by changing the in-plane orientations of the corresponding nanoblocks to serve as narrow-band half-wave plates for nonoverlapping discrete wavelengths with high conversion efficiencies in the transmission mode for the
ecently, much attention has been paid to shaping light spectrally with metasurfaces, which is vital for various practical applications.1−11 Operation of metasurfaces at multiwavelengths without dispersion normally requires a metamolecule comprising multiple or geometrically complex metaatoms. Manipulating the phases at dual wavelengths6 and three primary colors3 was realized by plasmonic metasurfaces consisting of nanostructures with different surface plasmon resonances. Several works generated independent wavefronts at two wavelengths with different polarizations by utilizing the polarization and wavelength selectivities of metal nanostructures.5,7,8 To date, all the metal metasurfaces operating at two or three wavelengths show the low diffraction efficiency and inevitable twin diffraction in the transmission mode because of only two-level phase or amplitude distributions across the surface. Alternatively, dielectric metasurfaces built up of highrefractive-index nanostructures can achieve relatively high transmission efficiency with full phase range (0−2π) control.10−29 To realize achromatic devices, two or more Si nanoresonators are coupled to control the phases by changing the dimensions and/or spacing of resonators. Achromatic lenses were realized by aperiodic array of coupled Si nanoresonators for three discrete telecommunication wavelengths1,2 or by metamolecules constructed with four Si © 2016 American Chemical Society
Received: June 8, 2016 Revised: July 6, 2016 Published: July 11, 2016 5235
DOI: 10.1021/acs.nanolett.6b02326 Nano Lett. 2016, 16, 5235−5240
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Figure 1. Illustration of one unit of the rotational Si nanoblock structure and its scattering and PB phase manipulation. (a) One-pixel unit structure. Two sets of coordinate systems and their correlations are shown. The X−Y is associated with the lattice periods and the x−y is imbedded with the length and the width of the nanoblocks in the plane of substrate surface. Their common axis Z is perpendicular to the plane of surface and pointing from the side of silica to air. The angle between x and X axis is defined as ϕ. The pixels are arranged with period P = 370 nm. The height of nanoblock is h = 320 nm, length is lx = 145 nm, and width is ly = 105 nm. The refractive of silica nSiO2 is 1.46. (b) Phase delays as a function of ϕ, the handedness impacts the plus−minus sign of the phase. (c) The numerical result of Qsca’s of the nanoblock for ϕ = 0. (d) The relative phase delay of the transmitted light in the far field, for x- and y-polarizations, respectively. (e) The calculated transmittance (dashed line) and the conversion efficiency (solid line).
Figure 2. Illustration of the meta-molecule. (a) Three Si nanoblocks with distinct x- and y-dimensions (lx and ly) marked as SR, SG, and SB, but with the same height h = 320 nm. (b) Simulated spectra of diffraction efficiency of an array composed of the individual nanoblock with period of 420 nm in the wavelength range of 400−800 nm. The blue dashed curve presents the diffraction efficiency of SB for a denser distribution with period 420/ √2 nm. The red circles, green cubes, and blue triangles present the diffraction efficiencies of SR, SG, and SB at R, G, and B, respectively, when all the four nanoblocks exist in one meta-molecule. (c) One meta-molecule consisting of multiplexed Si nanoblocks to form the metasurface. The dimension of the pixel is 420 nm × 420 nm.
substrate with the in-plane orientation ϕ as illustrated in Figure 1a. Note that the nanoblock has different dimensions along xand y-directions and thus the phase can be locally changed by choosing different in-plane orientations of the nanoblock. When a circularly polarized light beam is normally incident from the side of silica, the transmitted light is generally composed of two parts: one with the same handedness as the incident light with no phase delay, and the other with the opposite handedness with a phase delay of ±2ϕ with ± depending on the handedness of the incident beam, as shown in Figure 1b. This geometrically induced PB phase is wavelength independent, but the conversion efficiency (defined as percentage of the transmitted light that converted its polarization) strongly relies on the resonant properties of the unit structures, which can be tuned by their shapes and dimensions. The scattering efficiencies Qsca (defined as the ratio of the scattering cross-section to the geometrical cross-section of the nanoblock) of one example unit for both polarizations along x- and y-directions are calculated in the wavelength range
circularly polarized incident beam. The strong confinement of light within these Si nanoblocks basically avoids their interactions in each unit so that the phase for each color can be manipulated almost independently, as demonstrated by two kinds of specially designed color holograms, the achromatic meta-hologram generating identical images for all three wavelengths, and the highly dispersive meta-hologram projecting distinct images at specific wavelengths. Both holograms verified the successful quasi-continual control of the phases for three visible wavelengths across the surface with a subwavelength resolution. This technique has the potential for applications that require the independent wavefront manipulation at different wavelengths by simply changing the orientation distributions of nanoblocks in each unit. Furthermore, it can be scalable to other frequencies with similar fabrication processes. The metasurface proposed here is composed of subwavelength units arranged in square pixels. We begin with the local phase change based on a single Si nanoblock on the fused silica 5236
DOI: 10.1021/acs.nanolett.6b02326 Nano Lett. 2016, 16, 5235−5240
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Figure 3. Achromatic and highly dispersive meta-holograms and experimental setup for characterization. (a) The achromatic meta-hologram generates the same image (a “flower”) for all R (633 nm), G (532 nm), and B (473 nm) colors in the far field. (b) The highly dispersive metahologram independently projects distinct R, G, and B images: a “flower”, a “peduncle” and a “pot”, respectively. Insets: Partial SEM of the fabricated metasurfaces. Scale bar, 1 μm. (c) Experimental setup for the meta-hologram characterization. A’s are attenuators. After combination of three lasers, the beam passes through a Glan-Prism (P), an achromatic quarter-wave plate working from 400 to 800 nm (λ/4), generating a circularly polarized beam to focus onto the hologram (H) by a lens (L). The off-axis setup is adopted here to avoid overlapping between the target image and the background. The far-field image is projected to a screen inclined by an angle of 22.5° to reduce the distortion of image that is captured by a visible camera.
of resonant peaks, while particles of larger sizes would undergo a red shift.27,38 Therefore, simply changing the dimensions of Si nanoblocks can tune the resonances as well as the efficiency peaks. We selected three Si nanoblocks with different dimensions along x and y and the same thickness along z, which are marked as SR, SG and SB, respectively. Top views of three nanoblocks, along with their dimensions are presented in Figure 2a, with false colors in red, green, and blue. The calculated diffraction efficiency spectra for individual SR, SG, and SB in the range from 400 to 800 nm are displayed in Figure 2b. Their resonance peaks are near three wavelengths available in our experiment, 633 nm (R), 532 nm (G), and 473 nm (B). Therefore, only one kind of nanoblock is predominantly activated to induce the geometric PB phase for one wavelength upon being illuminated by three wavelengths simultaneously. Consequently, we multiplex SR, SG, and SB into a subwavelength unit to construct a meta-molecule that provides multichannel full phase manipulations at R, G, and B. In each unit, the inplane orientations of SR, SG, and SB control the phase at R, G, and B, respectively. Because the absorption of silicon increases with the decrease of the visible wavelength as shown in Figure S1, the efficiency of SB at B is smaller than that of SG at G and much smaller than that of SR at R. Therefore, two SB’s are arranged in each meta-molecule in order to enhance the efficiency for B (the corresponding diffraction efficiency
between 400 and 800 nm.While calculating the scattering efficiencies of one pixel of a metasurface, we adopt infinite periodic array of such identical pixels as a good approximation.22,25 As illustrated in Figure 1c, Qsca spectra are strongly polarization dependent: The peak of Qsca for x-polarization is around 670 nm while that for y-polarization is around 600 nm. Near the resonant wavelengths, the strong light-matter interaction usually gives rise to an abrupt phase change. Calculations indicated that the relative phase for x- and ypolarization for the transmitted light, (ϕx − ϕy), is approximate to π within the wavelength region between two Qsca peaks but rapidly drops to nearly zero beyond this region. Therefore, one Si nanoblock unit can work effectively as a narrow band halfwave plate with the fast-axis changing with its in-plane orientation. Figure 1e gives the conversion efficiency of nearly 100% in this half-wave plate condition region for a circularly polarized incident beam. The diffraction efficiency of this structure, the percentage of energy transferred by the geometric phase with respect to the incident beam, depend not only on the conversion efficiency but also on the transmittance. As shown in Figure 1e, the transmittance of the designed structure between 570 and 670 nm are around 50%. The energy losses are due to the back scattering and the absorption. The efficiency spectra change with the Si block dimensions. Intuitively, particles of smaller sizes would undergo a blue shift 5237
DOI: 10.1021/acs.nanolett.6b02326 Nano Lett. 2016, 16, 5235−5240
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Figure 4. Experimental results of the achromatic color hologram. (a) The target image, a flower. (b−h) Reconstructed images of the meta-hologram illuminated by (b) R only, (c) G only, and (d) B only. The combination of R, G, and B enables to generate flower of (e) white (R, G and B), as well as (f) yellow (R and G), (g) cyan (G and B), and (h) purple (R and B).
Figure 5. Experimental results of the highly dispersive color hologram. The reconstructed images of the meta-hologram illuminated with (a) R, G, and B, (b) only R, (c) only G, and (d) only B.
rotation step of 22.5°. Finer steps can also be used for better performance. Partial SEM images of the holograms are presented in the insets of Figure 3a,b. Experimental setup for hologram characterization is shown in Figure 3c. Three lasers are combined and circularly polarized before they illuminate the sample. To avoid overlapping between the target image and the background, the off-axis setup is adopted here, and the screen is inclined accordingly to project an undistorted picture to be captured by a visible camera. The reconstructed images by the achromatic meta-hologram illuminated by three available lasers (R at 633 nm, G at 532 nm, and B at 473 nm) are shown in Figure 4 with panel a being the target image as a reference. Figure 4b−d presents reconstructed images of the first kind of the holograms illuminated by only R, G, and B, respectively. Unlike the holograms designed for a single wavelength in which images of different sizes and positions are obtained for different wavelengths due to chromatic aberration,10,30−32,37 this hologram generates images with identical size and position for the three wavelengths as expected. In addition, full color image can be created by balancing the relative input powers of R, G and B. For instance, the combination of R, G and B enables to generate flower of white (Figure 4e), as well as yellow (R and G, Figure 4 f), cyan (G and B, Figure 4g) and purple (R and B, Figure 4h). The reconstructed images of the highly dispersive color hologram are given in Figure 5. When three lasers are combined to illuminate the meta-hologram, a colorful image containing three independent monochromic parts is reconstructed as shown in Figure 5a: a red “flower”, a green
increases from the blue solid curve to the blue dashed curve in Figure 2b).3 Figure 2b also presents the calculated diffraction efficiencies of SR, SG, and SB at the three wavelengths of interest, while all four nanoblocks simultaneously exist in the metamolecules. It is clearly verified that cross-talks between different channels are weak at the three wavelengths because the light energy is highly confined within the silicon nanoblocks. The diffraction efficiencies of SR at R, SG at G, and SB at B are 19%, 5.7%, and 6.4%, respectively. The decrease of the efficiencies from those of the individual nanoblocks are mainly caused by the increased absorption and reflection with the number of nanoblocks in one meta-molecule. The multivisible wavelength phase manipulation using this metasurface is manifested by two kinds of specially designed holograms. The achromatic meta-hologram is to generate identical target images at the R, G, and B, like the achromatic lens focusing light of different wavelengths to the same focal plane, and the highly dispersive meta-hologram is to project distinct images at R, G, and B. The basic ideas are illustrated in Figure 3a,b. The light phases after the metasurface for different wavelengths are manipulated independently. Using the Gerchberg-Saxton (GS) algorithm, the required phase distributions are retrieved and then converted into the in-plane orientations of the corresponding nanoblocks. The metasurfaces are composed of 452 × 452 meta-molecules whose dimension is 420 nm × 420 nm. Note that the scattering property of the structure is insensitive to the lattice period, and pixels of other dimensions can also be applied. For each kind of nanoblock, the number of discrete phase level is 8 with a 5238
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Nano Letters “peduncle”, and a blue “pot”. The individual part with distinct color appears at different locations if only one laser is used, as shown in Figure 5b−d. The results clearly demonstrate the three almost independent channels formed by the three nanoblocks. The phase of each designed wavelength after the metasurface is determined only by the in-plane orientation of the corresponding nanoblocks. The design of quasi-continual phase manipulation across the surface at each wavelength effectively avoids the dual-images that inevitably occur when using two-level phase encoding metasurfaces. However, conjugate images will appear if the incident beams are not circularly polarized. For the linear polarization, the conjugate images have the same intensity as the main images. Weak undesired images for both holograms appear sometimes. For instance, the dim undesired orders around the green flower in Figure 4c and the blue peduncle in Figure 5c are observed. One possible reason is the fabrication error. Because SG and SB are around 100 nm, small size fluctuations would possibly cause the sharp change of efficiency spectra. The measured efficiencies of the reconstructed images for the highly dispersive color hologram are 18% at R, 5.2% at G, and 3.6% at B, which agree well with the simulated diffraction efficiencies shown in Figure 2b. The results are an order of magnitude higher than those of the previously demonstrated color holograms3 and further improvement is expected by using other dielectric materials with smaller absorptivity.39 In summary, we have proposed and implemented dielectric metasurfaces capable of manipulating the phases at red, green, and blue wavelengths. The meta-molecule consists of three kinds of Si nanoblocks, each providing a channel for a specific wavelength to independently manipulate the corresponding phase by setting the in-plane orientations of each nanoblock with fine phase step achievable within fabrication latitude. The experimental results of two kinds of meta-holograms agree well with the designs. This type of metasurface can find numerous applications where spectral wavefront manipulation is required such as achromatic lenses and holograms. Although the metasurfaces demonstrated here are fabricated with silicon for the visible light, this technique can be extended to other frequencies using high index materials with smaller absorptivity.39
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advised on the optical setup and the interpretation of the data; W.C. and Y.L. supervised the analysis, experiments, and edited the manuscript. All authors discussed the results and implications and commented on the manuscript at all stages. B.W. and F.D. contributed equally to this work. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Basic Research Program of China under Grant 2013CB921904, the National Natural Science Foundation of China under Grant 11474010 and 61590933, the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry under Grant Y5691I11GJ, and Youth Innovation Promotion Association CAS under Grant Y5442912ZX.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b02326. Process of sample fabrication, numerical methods of simulations, design of meta-molecule and interactions between nanoblocks, and full far-field images generated by the color hologram(PDF)
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REFERENCES
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. Author Contributions
B.W., F.D., and Y.L. conceived the idea; B.W. performed the designs, simulations, and measurements; F.D., Z.S., L.X., and W.C. fabricated the metasurfaces and assisted in design; Q.L. performed the measurements and analysis; D.Y. assisted in design; C.S. assisted in measurements; J.C., Y.X., and Q.G. 5239
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