Supporting Materials Visible-frequency dielectric metasurfaces for multi-wavelength 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,,* 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 1
Sample fabrication. We fabricated the devices on a quartz substrate. The process began with the deposition of a 320nm-thick amorphous silicon film using an Inductively Coupled Plasma Enhanced Chemical Vapor Deposition System (ICPECVD, Sentech SI 500D). A 50-nm thick aluminum film was then deposited via electron beam evaporation, used as a charge-dissipation layer and hard mask. The 300nm thick positive electron beam resist (ZEP-520A) was coated and patterned using electron beam lithography (EBL, Vistec EBPG 5000+). The patterns were transferred into the aluminum and Si layer by subsequent etching using an Inductively Coupled Plasma (ICP, Sentech PTSA SI 500) etcher. Finally, the aluminum layer was removed at room temperature using aluminum etchant. The refractive index of the Si thin film is presented in Figure S1. Figure S1. The real (n) and imaginary (k) parts of the refractive index of the deposited 320nm thickness silicon film. Simulations. We performed the simulations in frequency domain by commercial software COMSOL Multiphysics. Using ports along z-axis we characterize the phase delay and the amplitude of transmission electromagnetic fields, as well as the scattering coefficients of the nano-structures. Both a normally incident plane wave and periodic conditions were assumed to save the computation time. 2
Design of meta-molecule. Figure S2 illustrates one meta-molecule. Each meta-molecule is consisted of 2 2 sub-pixels where the S R, S G and S B stand in their centers. Therefore, the distance between the centers of the neighboring nano-blocks is P/2, with P being the dimension of the meta-molecule. The 22.5º rotation produces 8 phase levels for each kind of nano-block. For better performance finer steps are needed. Note that two S B s occupy two diagonal sub-pixels in order to enhance the efficiency at wavelength B (473nm). The dashed circles represent the area the nano-blocks will occupy in case of different orientations. The dimension of the metamolecule thus must be large enough to avoid the overlapping between different circles. It should be pointed out that for both holograms the meta-molecule is set as 420nm 420nm due to fabrication difficulties under the present conditions, which is however larger than the propagation wavelength of G in the substrate (532nm/ 365nm). As a result, the dim second-order images may arise to reduce the efficiency. This can be resolved by decreasing the dimension, say, smaller than 365nm (for B, the effective period is less than 473 2/ ). Figure S2. Top view of the distribution of the three types of Si nano-blocks in one meta-molecule. The S R, S G and S B with false colors represent nano-blocks of different sizes that corresponding to the wavelengths at R (633nm), G (532nm) and B (473nm), respectively. The dot-dashed lines separate this meta-molecule into 2 2 subpixels. 3
Interaction between nano-blocks. We calculated the scattering coefficients of one metamolecule that consisted of S R, S G and S B s (the solid line in Figure S3), which is compared with the numerical result that neglects the interactions between S R, S G and S B s (The dashed line in Figure S3). The two approximate curves indicate weak interactions between different nanoblocks, which is a result of the strong confinement of light field within Si nano-blocks, as shown in Figure S4. Figure S3. Numerical calculation of scattering coefficients. The scattering coefficient of one meta-molecule where the interactions between different sized nano-blocks have been considered (solid). The dot-dashed curve present the result without considering the interactions between nano-blocks of different sizes. 4
Figure S4. Optical energy distributions of one meta-molecule under different views. For simplicity, we neglect the substrate during the calculation, which slightly affect the scattering properties of nano-structures. The plane wave is circularly polarized and incident from the Z 5
direction and the wavelength is selected as R, G and B in sequence. Side views of the optical energy distributions at different observation planes that go through the centers of (a) S G and S B and (b) S R and S B, respectively. (c) Top views of the optical energy distributions at plane Z = 0.6h. It is clearly shown that energy is strongly confined in the nano-blocks. Design of achromatic and highly-dispersive holograms. The phase distributions of both holograms are designed using the Gerchberg-Saxton (GS) algorithm. In the case of achromatic hologram, the target images at R, G and B are the same flower that ranges from 15 < < 30,0< <14 and centers at 22.5, 7, in order to avoid the overlapping between the target image and the background (the and are defined in Figure S5). The identical locations and sizes at R, G and B are achieved by independently retrieving the phase distributions at the three wavelengths. Therefore, different phase distributions are required at R, G and B which have compensated the chromatic aberrations. In the case of highly-dispersive holograms, we have used a target image including three different parts. Each part is designed for a specific wavelength: The flower is designed for R, the peduncle is designed for G, and the pot is designed for B. Their ranges are as follows: 15 < <30,0 < <14 for the red flower; 15 < <30, 7 < <3 for the green peduncle; 15 < <30, 12 < < 7 for the blue pot. Note that for conventional diffraction optics, gratings diffract light of different wavelengths into adjacent directions due to dispersion. The longer the wavelength, the larger the diffraction angle. Holograms that work for a broadband range also reconstruct images with larger sizes at longer wavelengths. On the contrary, the designed meta-holograms here can be either achromatic or highly-dispersive because the diffraction properties for the three wavelengths can be tuned independently. In the case of achromatic holograms, the flower keeps its direction while illuminated by R, G and B, which is non-dispersive. In the case of highlydispersive holograms, the red flower is diffracted into the positive y direction, the blue pot is diffracted into the negative y direction, and the green peduncle is diffracted near the x = 0 axis. 6
Figure S5. Illustration of the angular distributions of reconstructed images. The angular distribution of the far field reconstructed image of the achromatic hologram (left) and the highlydispersive hologram (right). The full far field images generated by the highly-dispersive color hologram. The monochromatic lasers at R, G and B are combined and pass through the Glan-prism to generate linear polarized lights. When they pass through an achromatic quarter-wave plate (Thorlabs AQWP05M-600, 400nm-800nm), they are circularly or linearly polarized beams (Figure 3c). Figure S6a present the result for left-circular polarized incident beams, where only the 0th order and the order on the right side exists, while for right-circular polarized incident beams, only the 0th order and the order on the left side exists (Figure S6b). For linear polarized incident beams, three orders appear (Figure S6c). The second diffraction orders also exist, but their intensities are too weak to be captured by the camera. 7
Figure S6. The full far field images generated by the highly-dispersive meta-hologram. Images generated for incident beams of (a) left-circular polarization, (b) right-circular polarization and (c) linear polarization. 8