Simultaneous Full‐Color Printing and Holography Enabled by Centimeter‐Scale Plasmonic Metasurfaces

Abstract Optical metasurfaces enable novel ways to locally manipulate light's amplitude, phase, and polarization, underpinning a newly viable technology for applications, such as high‐density optical storage, holography, and displays. Here, a high‐security‐level platform enabled by centimeter‐scale plasmonic metasurfaces with full‐color, high‐purity, and enhanced‐information‐capacity properties is proposed. Multiple types of independent information can be embedded into a single metamark using full parameters of light, including amplitude, phase, and polarization. Under incoherent white light, the metamark appears as a polarization‐ and angle‐encoded full‐color image with flexibly controlled hue, saturation, and brightness, while switching to multiwavelength holograms under coherent laser illumination. More importantly, for actual applications, the extremely shallow functional layer makes such centimeter‐scale plasmonic metamarks suitable for cost‐effective mass production processes. Considering these superior performances of the presented multifunctional plasmonic metasurfaces, this work may find wide applications in anticounterfeiting, information security, high‐density optical storage, and so forth.


The mechanism of the sharp phase difference
To explore the physical mechanism inside narrowband phonic spin-orbit interactions, the electric-field distributions of the blue PSG at different wavelengths are simulated under the illumination of the x-and y-polarizations, respectively, as shown in Figure S1a,b. The top row of Figure S1a,b show the amplitude distributions of E x and E y that are normalized to the incident magnitude (|E i |), and the bottom row displays the corresponding electric-field lines.
As depicted in Figure S1a, the electric field in obviously enhanced when under the illumination of the x-polarization incidence, but it does not occur for the y-polarization incidence. For the x-polarization incidence, the electric field is strongly coupled between the two corners of an element at the wavelength of 450 nm, as shown in Figure S1(i). In contrast, Figure S1(iii) shows that the electric field is reinforced between two adjacent elements at the wavelength of 500 nm. When at the resonant wavelength of 473 nm, those two modes are strongly coupled, as illustrated in Figure S1(ii), and their interactions result in the enhanced catenary optical field the gaps. Figure S1c,d show the magnitude profiles of |E x | and |E y | at the Ag-SiO 2 interface depicted in Figure S1(ii), respectively. The |E x | profile in the gaps can be well described by the well-known catenary curve in architecture (the fitting coefficients are greater than 0.998; the fitting catenaries are depicted in the form of black solid curves.). The generalized catenary model is given by: where a = 7.215e -3 , b = 6.934e 7 , and c = 3.733. The catenary optical field will introduce an abrupt phase shift for the x-polarization incidence while it does not happen for the y-polarization incidence. Shown in Figure S1e are the simulated reflective amplitudes of and phase difference between two orthonormal linearly polarized incidences along the x-and ydirections. The reflective amplitude of |E y | remains flat while the |E x | spectrum undergoes a dip around the resonant wavelength of 473 nm, owing to the absorption loss. Furthermore, the catenary optical field introduces an abrupt phase shift around 473 nm for the x-polarization, leading to a sharp propagation phase difference (close to 180°) between the x-and ypolarizations. As a result, narrowband photonic spin-orbit interactions will occur around this resonance wavelength.  Figure S1a(ii) and b(ii). The black solid curve in c) indicates fitting catenary curves. e) Simulated reflective amplitude spectra and phase difference for/between the x-and y-polarizations.
It is observed that the FWHM value of the red PSG is smaller than that of the blue one.
To analyze its mechanism, the |E x |/|E i | distributions of three PSGs were simulated at their peak wavelengths under the illumination of the x-polarization light. As can be seen from Figure   S2a-c, the red PSG (corresponding to the red color) can support stronger SPP compared with the blue one. Stronger the SPP is, sharper propagation phase difference is, as shown in Figure   S2d. Essentially, the narrowband cross-polarized spectrum originates from the propagation phase difference between the x-and y-polarizations. As a result, the FWHM value of the red PSG is smaller than that of the blue one. Figure S2. a-c) Simulated |E x |/|E i | distributions of three PSGs at their peak wavelengths under the illumination of the x-polarization light. d) Simulated propagation phase difference between the x-and y-polarizations. Red, green, and blue curves respond to three PSGs, respectively.  There are two resonances when obliquely illuminated for 0° and 45° azimuthal angles, and two peak wavelengths show two opposite shifts as illumination angle increases, which indicates that two SPP modes are coupled and contribute to sharp resonance for normal illumination. In contrast, the illumination angle has almost none effect on the spectrum when illuminated in the yz-plane. Figure S5. The simultated cross-polarized spectra of three PSGs with different fabrication errors for their widths. Within a fabrication tolerance of ~±15 nm, the maximum shift of the peak wavelengths is smaller than 7 nm, and the porization conversions are larger than 50% at three hologram wavelengths.    Figure S8a. The color gamut is about 49.2% of the whole color gamut of the CIE 1931 chromaticity diagram. Figure S9. Simulated holographic images for periodic and random arrangement. For simplicity, we assume that the hologram displays one colour in the print mode and each supercell contains four subpixels. a-c) The periodic amplitude distribution and two simulated holographic images. There are oblivious high-order diffraction noises that will deteriorate the quality of the holographic image and reduce the available holographic space. d-f) The random amplitude distribution and two simulated holographic images, showing that the periodic noises are suppressed well. Figure S10. a) Simulated cross the schematic illustration of the PSG with a magnesium fluoride (MgF 2 ) covering film. b) Simulated cross-polarized spectra of three PSGs with the covering film shown in (a). Corresponding periods of cerulean, yellow, and curves are 180, 340, and 420 nm, respectively, and the width w is equal to half of the period. By further optimizing the width and period, the peak wavelength can be shifted toward either higher or lower wavelength. Figure S11. An optical image of the fabricated macaw meta-mark formed by a normal smartphone camera without the decryption device under the normal illumination of the light from a xenon lamp. Figure S12. An optical image of the fabricated macaw meta-mark formed by a normal smartphone camera without the decryption device under the glance illumination of the light from a xenon lamp. The image quality is lower than the one contributed by direct reflect at normal incidence, because the 1st-order diffraction from PSGs whose grating lines are not perpendicular to the incident can be captured by the smartphone camera.

Modified Gerchberg-Saxton algorithm
Gerchberg-Saxton (GS) algorithm is widely applied to design phase-only holograms. [7] However, the far-field intensity profile obtained by the basic GS algorithm is far away from the ideal one and has a lot of white noise, which will deteriorate the quality of holographic image especially for multi-wavelength holography. To overcome this limitation, we present a modified GS algorithm that results in a near-optimum far-field intensity profile. The underlying idea of the new algorithm is to suppress the non-uniformity of the desired holographic region and to relax the noise suppression of the unused spatial-frequency space.
As a result, the designed far-field intensity profile needs to be modified. For example, the image in the black box of Figure S18a is the target far-field intensity profile. Different from the basic GS algorithm, the intensity of the region outside the the black box is not equal to Figure S18b shows the far-field intensity distribution of output beam |G 50 (u)| 2 after 50 iterations for I i = 1. In contrast to the far-field intensity profile obtained by the basic GS algorithm ( Figure S18c, also after also 50 iterations), the far-field intensity distribution in the concerned region obtained by the modified GS algorithm is very close to the ideal one with negligible noise. For the iteration process of the basic GS algorithm, the procedures of Equation S3, S4, S6 and S7 are removed.