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A Modular Design of Continuously Tunable Full Color Plasmonic Pixels with Broken Rotational Symmetry

Color tuning is a fascinating and indispensable property in applications such as advanced display, active camouflaging and information encryption. Thus far, a variety of reconfigurable approaches have been implemented to achieve color change. However, it is still a challenge to enable a continuous color tuning over the entire hue range in a simple, stable and rapid manner without changes in configuration and material properties. Here, we demonstrate an all-optical continuously tunable plasmonic pixel scheme via a modular design approach to realize polarization-controlled full color tuning by breaking the intrinsic symmetry of the unit cell layout. The polarization-controlled full color tunable plasmonic pixels consist of three different types of color modules oriented at an angle of 60{\deg} with respect to each other, corresponding to three subtractive primary colors. Without changing the structural properties or surrounding environment, the structural colors can be continuously and precisely tuned across all hues by illuminating linearly polarized light with different polarization directions. Meanwhile, the plasmonic pixels can be flexibly customized for various color tuning processes, such as different initial output colors and color tuning sequences, through the appropriate choice of component modules and the elaborate design of module layouts. Furthermore, we extend the color tuning to achromatic colors, white or black, with the utilization of a single module or the introduction of a black module. The proposed polarization-controlled full color tunable plasmonic pixels hold considerable potential to function as next-generation color pixels integrated with liquid-crystal polarizers.


Keywords:
Continuously tunable, Polarization-controlled full color tuning, Modular design approach, Gap surface plasmons, Achromatic color, Rotational symmetry breaking Abstract: Color tuning is a fascinating and indispensable property in applications such as advanced display, active camouflaging and information encryption. Thus far, a variety of reconfigurable approaches have been implemented to achieve color change. However, it is still a challenge to enable a continuous color tuning over the entire hue range in a simple, stable and rapid manner without changes in configuration and material properties. Here, we demonstrate an all-optical continuously tunable plasmonic pixel scheme via a modular design approach to realize polarization-controlled full color tuning by breaking the intrinsic symmetry of the unit cell layout.
The polarization-controlled full color tunable plasmonic pixels consist of three different types of color modules oriented at an angle of 60° with respect to each other, corresponding to three subtractive primary colors. Without changing the structural properties or surrounding environment, the structural colors can be continuously and precisely tuned across all hues by illuminating linearly polarized light with different polarization directions. Meanwhile, the plasmonic pixels can be flexibly customized for various color tuning processes, such as different initial output colors and color tuning sequences, through the appropriate choice of component modules and the elaborate design of module layouts. Furthermore, we extend the color tuning to achromatic colors, white or black, with the utilization of a single module or the introduction of a black module. The proposed polarization-controlled full color tunable plasmonic pixels hold considerable potential to function as next-generation color pixels integrated with liquid-crystal polarizers.
Structural colors generated from the resonant interactions between incident visible light and sophisticated artificial nanostructures have recently become one of the most interesting scientific and engineering topics in the field of optics, and have applications in high-resolution color prints, high-efficiency color filters, high-contrast color displays, anti-counterfeiting tags, and information encryption [1][2][3][4][5][6][7][8] . In contrast to conventional pigmentary colors produced by bulk absorption, structural colors provide many benefits such as high spatial resolution, good stability, material simplicity, cost effectiveness, non-toxicity, and recyclability [9][10] . An assortment of vivid and vibrant structural colors covering the entire visible spectrum can be engineered by tailoring the spectral responses, which is strongly dependent on the size and shape of the constituent nanostructures, as well as their arrangement [11][12][13][14] . However, this geometric dependence of structural colors makes it difficult to change the static colors once the nanostructures are fabricated with given sets of dimensions which severely restricts their potential applications in many areas. It is thus an outstanding problem to finely tune structural color across a full range of hues, while maintaining high spatial resolution, real-time response and high durability [15][16] .
With the development of manufacturing technologies and advanced materials, research on reconfigurable structural colors have progressed dramatically in recent years [17][18] . The most straightforward method for the realization of color tuning is to vary the geometric properties of the nanostructures, such as size, shape or period. For instance, laser-induced heating has been explored for ink-free, high-speed and sub-diffraction resolution color printing [19][20][21] . In this case, the plasmonic heating utilizes the photothermal effect of plasmonic resonance energy absorption to locally melt and reshape each nanostructure 20 . Likewise, dielectric heating arising from dipole resonance energy absorption in high-index dielectric germanium (Ge) causes a similar heating effect 21 . This laser post-processing technique will irreversibly print various new colors over nanostructured metasurfaces at an unprecedented resolution. Conversely, the reversible electrodeposition scheme was demonstrated to manipulate the colors for active artificial camouflage 22 . The bimetallic nanodot arrays were altered through electrodepositing and stripping Ag shells on top of Au nanodomes. Thus, the reversible color plasmonic display can be achieved by electrochemically controlling the deposition and stripping duration. In addition to the morphological reconfiguration of the nanostructures, the modification of the nanostructural arrangement by stretching the underlying elastomeric substrate was also shown color tuning and multiple image switching 23 . Alternatively, the color tuning can be realized by changing the dielectric properties of the constituent nanostructures or the surrounding environment [24][25][26] . In particular, through controlled hydrogenation and dehydrogenation, constituent magnesium nanoparticles in a nanostructure pixel undergo reversible transitions between metallic and dielectric states, which can be exploited for dynamic color display and information encryption [27][28] . Similarly, by applying an appropriate voltage, the dielectric properties of the surrounding environment could be changed significantly due to reversible switching between the oxidized and reduced states of the electrochromic materials 29 , changes in the molecular orientation of birefringent liquid crystal [30][31][32] , and voltage-driven hydrogenation and dehydrogenation cycles in a solid-state device 33 , which supports large color changes with potential for fast switching 34 .
Furthermore, the refractive index of the surrounding media can also be directly changed by injecting different chemical solutions into a polymeric microfluidic channel which covers the metasurfaces 35 .
Although previous methods of varying the geometric properties and changing the dielectric properties introduced above can effectively tune the colors, few solutions have achieved full color tuning, while some exhibit switching only between color states 36-37 . Moreover, most solutions require the employment of complex packaging devices, such as electrochemical cells, gas cells or microfluidic cells, which result in increased fabrication cost and complexity [27][28][29]35 . Furthermore, some techniques also suffer from a relatively long switching times, poor reliability and durability, or are limited by a one-time color shift, e.g. in the case of laser post-processing [20][21] . Recently, the modular design approach has been widely applied in photonics, which is a very practical and flexible strategy [38][39] . For effective modular design, a system is subdivided into smaller parts called modules which can be independently created, tailored or replaced between different systems to drive different functionalities. In this letter, we propose a plasmonic pixel whose color can be continuously tuned over the entire hue range by adopting the modular design approach in which independently tailored plasmonic nanoantennas serve as color modules and are combined into a composite unit cell. In contrast to the prior dual color pixels based on the polarization-dependent cross-shaped nanoantennas or nanoapertures that have limitation in terms of achieving full-color tuning and are limited to switching between a limited range of hues [40][41][42][43] , we construct an asymmetric nanostructure by combining three different types of color modules corresponding to three subtractive primary colors. Without the aid of extra active materials or external stimuli 44 , the proposed polarization-controlled full color tunable plasmonic pixels can generate a full range of hues by a continuous change in the polarization angle of the incident light. Furthermore, by taking full advantage of the modular design approach, we can flexibly customize the color tuning process to change the initial output colors and the color tuning sequences, and even to switch between two primary colors or between chromatic and achromatic colors.

RESULTS AND DISCUSSION
The perceived colors, which can be reproduced by the mixture of three primary colors, are located within a triangle with vertices corresponding to these three primary colors on the chromaticity diagram. Similarly, in order to construct the full color tunable plasmonic pixels, three different primary color modules, which are polarization dependent plasmonic nanoantennas with different lengths and orientations, are combined in a subwavelength unit cell. However, they are not excited together at the same polarization angle, as each primary color module only dominates at a specified polarization angle depending on the rotation angle of the plasmonic nanoantenna. The schematic diagram of the polarization-controlled full color tunable plasmonic pixel (FCTPP) is illustrated in Figure 1a. The rectangular aluminum and silica nanorods with three different lengths are employed to function as the color modules for yellow, magenta and cyan respectively which are determined by the absorption resonance wavelengths in the subtractive color model. Noticeably, the absorption cross-section of the nanoantenna for the yellow module is smaller than those for the magenta and cyan modules due to its relatively small size 45 . To compensate for the low absorption efficiency and the narrow bandwidth at short wavelengths for the yellow module, two identical nanoantennas that function as the yellow module are arranged along the diagonal quadrants of the unit cell. As a comparison, we also investigate the unit cell with only one nanoantenna for the yellow module, which has a smaller color gamut (Supplementary Figure S1). The lengths of the yellow, magenta, and cyan modules are 95 nm, 120 nm, and 140 nm respectively, corresponding to plasmonic resonances at different wavelengths across the visible spectrum. Most importantly, the three different types of color modules are rotated by an angle of 60° with each other to form an asymmetric nanostructure (the rotation angles of the color modules are 0° for the yellow module, 60° for the magenta module and 120° for the cyan module), making the resulting nanostructures sensitive to the linear polarization angle of the incident light. Considering that a 180° rotation of the polarization direction is divided up into three states, the modules are arranged in a 60° interval to minimize the spectral mixing that arise from the partial excitation of at least double color modules. For instance, with the polarization of incident light aligned to the long axis of one of the modules, the non-zero decomposition of this polarization along the long axis of the other two modules would still lead to partial excitation of their longitudinal resonance modes. These four plasmonic nanoantennas are densely packed at a fixed center-to-center distance of half the unitcell period. The period of the composite unit cell is set to be 360 nm, which suppresses grating effects and ensures that the print resolution is close to the diffraction limit for a high degree of  It is clearly seen that the chromaticity coordinates gradually shift from yellow towards magenta, then to cyan, and finally back to yellow again when the incident polarization angle increases from 0° to 180°, as indicated by the dashed white arrow. The polarization-controlled full color tuning is represented by the black dotted ellipse around the white point on the chromaticity diagram, which is attractive in comparison with the static color pixels or dual color pixels that generate a limited range of colors represented by a single point or a short line on the chromaticity diagram 40,47 , showing that the FCTPP can be rapidly and precisely modulated to generate a wide variety of colors over the entire hue range. We also show three stars on the chromaticity diagram that represent the chromaticity coordinates if the entire unit cell is made up of only one type of color module. The close chromaticity coordinates of the marks indicate that the partial excitations of the other two color modules caused by the non-zero decomposition of incident polarized light will not strongly influence the main resonant dips in the reflectance spectra, but only lead to low sideband reflectance. Therefore, the partial excitations of color modules in the asymmetric nanostructure will not result in a significant color change. Interestingly, the elliptical color tuning trajectory with increasing polarization angle lie outside the triangle that connect these three stars, which is caused by the mixed spectra of the resonance dips for the asymmetry structure 48 (Supplementary Figure S4). In addition, the FCTPP allows for continuous color tuning across all hues by finely controlling the polarization angle of the incident light, which is impossible for the methods of varying the geometric properties or changing the dielectric properties 22,27 , as shown in  Notably, three subtractive primary colors yellow, magenta, and cyan are obtained at the polarization angles of 0°, 60° and 120°, respectively. Figure 2c shows the corresponding chromaticity coordinates of fabricated color palettes on the chromaticity diagram, which experimentally validates that a full range of colors can be obtained at different polarization directions with a single plasmonic device. Figure 2d shows the simulated and measured reflectance spectra of the FCTPPs for different polarization angles increasing from 0° to 180°. The experimental reflectance spectra are found to be in good agreement with the simulation results. In contrast to the gradual redshift of the resonance wavelength caused by changing the structural properties or surrounding environment, the reflection dips produced by the asymmetric nanostructure drastically change among three resonance wavelengths by varying the incident polarization angle, as indicated by the red dots. The three reflection dips are most prominent at the polarization angles of 0°, 60° and 120°, respectively, which depend on the rotation angles of the color modules. Apparently, the polarization dependent reflectance spectra of the FCTPPs are   Figure S8). Thereafter the chromaticity coordinates of these three full-color tunable plasmonic pixels are tuned in clockwise order on the chromaticity diagram as the incident polarization angle increases. Nonetheless, as shown in Figure 3d-f, the color tuning sequence can also be reversed to anticlockwise on the chromaticity diagram by swapping the rotation angles of the color modules. Taking Figure 3d as an example, the color tuning trajectory evolves from yellow to cyan and then to magenta with increasing polarization angle of the incident light, which is in the opposite order to that of the plasmonic pixels in Figure3a. In general, the color tuning sequences depend on the rotation angles of each color module relative to the x-axis. In addition, the color tuning range can also be limited to a tuning between two primary colors according to the choice and combination of two distinct types of color modules from the set of yellow, magenta and cyan modules. Notably, the three different module layouts can achieve color tuning from one to another by changing the polarization angle of the incident light, similar to the dual-color pixels (Supplementary Figure S9).   Remarkably, the polarization-controlled FCTPPs afforded by the modular design approach enable color tuning not only among different color hues, but also between chromatic and achromatic colors, i.e., white or black. Following the modular design approach, we first investigate the relatively simple color switching between white and three subtractive primary colors, as shown in Figure 5a  To demonstrate the feasibility of the various processes of color change, we design a "Bagua diagram" using different polarization-controlled FCTPPs. Figure 6 presents the optical micrographs of the Bagua diagram when illuminated with different polarization directions. The outer trigram patterns consist of FCTPPs with different initial output colors of yellow, magenta and cyan, respectively. The inner Taiji patterns comprise two color switchable pixels that can switch between primary colors and achromatic colors, namely blue-black color switchable pixels for the left spiral and yellow-white color switchable pixels for the right spiral. The overall SEM image and enlarged SEM image of the border between two regions are shown in the inset of Figure   6. It is noted that the colors of the trigram patterns significantly change with increasing polarization angle of the incident light. Meanwhile the colors of the Taiji pattern would first fade to achromatic colors as the incident polarization angle increases to 90°, and then turn back to the original states when the incident polarization angle becomes 180°. Obviously, the polarization-controlled FCTPPs with different module layouts accurately reproduce various color changes.

CONCLUSION
In conclusion, we have presented polarization-controlled full color tunable plasmonic pixels based on the combination of three different types of color module in a subwavelength unit cell. By virtue of the strong confinement and polarization dependent properties of the gap-surface plasmons, the asymmetric plasmonic pixels enable polarization-controlled full color tuning by continuously varying the polarization angle of the incident light. These polarization-controlled color responses can yield an elliptical trajectory covering all hues on the chromaticity diagram. In addition, the color tuning process, such as initial output colors and color tuning sequences, can be flexibly customized through the appropriate choice of component module and the elaborate design of module layouts. Meanwhile, the color tuning between two primary colors or even switching between chromatic and achromatic colors can be realized by means of suitable functional color modules and specific module layouts. We believe that our scheme could provide a promising platform for applications in advanced display technology, optical security devices and optical data storage.

Fabrication.
A 100 nm thick film of aluminum was first evaporated onto a bare silicon substrate using an electron beam evaporator (Labline, Kurt J. Lesker Co.). The working pressure was 1.2 × 10 −6 Torr and the deposition rate was 1.5 Å/s. Then the positive-tone electron-beam resist PMMA (950K A4, MicroChem Corp.) was spin-coated onto the Al film at 5000 rpm for 60 s and then baked at 180 °C for 90 s. Electron beam lithography was performed using the eLine Plus, Raith GmbH at 30 kV acceleration voltage and 360 pA beam current with a 100 × 100 µm 2 write field.
Proximity effect correction was performed before exposure. In the next step, the exposed samples were developed in 1:3 methyl isobutyl ketone/isopropanol (MIBK/IPA) solution at 0 °C for 45 s, followed by rinsed in IPA for 5 s and blow-dried using nitrogen gas. Afterwards, the silica layer and a second Al layer were sequentially deposited with the same electron beam evaporator under the same conditions, Finally, a lift-off process was performed to remove the unexposed resist by soaking the samples in acetone at 60 °C, followed by rinsing with IPA for 10 s and dried with nitrogen.
Characterization. Scanning electron microscopy was performed with JEOL-JSM-7600F at 5 kV acceleration voltage and Raith eLine Plus systems. at 10 kV acceleration voltage. The reflectance spectra and optical micrographs were taken via a Nikon Eclipse LV100ND optical microscope equipped with a Nikon DS-Ri2 camera and a CRAIC 508 PV microspectrophotometer. A halogen lamp (LV-HL 50 W) was used to illuminate the samples in reflection mode. The reflectance spectra were normalized with an aluminum mirror. The experimental spectra, bright-field and dark-field micrographs were taken with a Nikon 20×, NA = 0.45 objective lens.

Supporting Information
Compensation for the yellow module, Spatial distributions of the fields, Comparison of color tuning trajectory, Comparison of color gamut with static color, The phenomenological expression, Incident angular tolerance, Initial color of red and green, Different color tuning ranges, Microprint under natural light, Reflectance spectra of achromatic color.

Author Contributions
Rui Feng and Hao Wang contributed equally to this research.

Notes
The authors declare no conflict of interest.    Chromaticity coordinates of the orthogonal structure and asymmetric nanostructure with increasing polarization angle. As the incident polarization angle increases from 0° to 90°, the color tuning trajectory of the orthogonal structures are represented by a straight line between yellow and magenta on the chromaticity diagram. While the asymmetric nanostructures produce a curve path with increasing polarization angle from 0° to 60°, which is caused by the mixed spectra of the resonance dips for the non-orthogonal plasmonic nanoantennas. The polarization-controlled full color tunable plasmonic pixels exhibit a wider color gamut than that of pixels that undergo static color change. The polarization dependent reflectance spectra of the FCTPPs are related to a linear combination of the polarization dependent absorption of three single color modules. As indicated by solid lines in Figure S6(a), the simulated absorptance as a function of polarization angle at three resonance wavelengths show a cosine-squared shape with maximums at the polarization angles of 0°, 60° and 120°, respectively. Moreover, the amplitude of absorptance oscillation at the wavelength of 443 nm is relatively large due to the large cross-section for the yellow module, which meets the purpose of using two antennas for the yellow module. Accordingly, a phenomenological expression can be written to estimate the polarization dependent spectra from the asymmetric nanostructures where φ is the polarization angle of the incident light, λ is the free space wavelength of light, Ay(λ), Am(λ) and Ac(λ) are the maximum resonance absorption for incident light polarized along each color module in the asymmetric nanostructure, respectively. Here, the absorption cross-sections of three single color modules are used to represent the wavelength dependent constants Ay(λ), Am(λ) and Ac(λ), which are proportional to the resonance absorption. Moreover, two nanoantennas are used to calculate the absorption cross-section of the yellow modules, as shown in Figure S6(b).
Although the absolute values are distinct, the shape of the simulated spectra (solid lines) and analytical absorption cross-sections (dash lines) are in good agreement, indicating that the polarization dependent properties of the asymmetric nanostructures can be well described by the analytical model.
The proposed phenomenological expression verifies two crucial issues. The first issue is that each nanoantenna can be deemed as independent color module due to the strong confinement property of the gap surface plasmons within the spacer, which is the fundamental of the modular design approach. The wavelength dependent constants Ay(λ), Am(λ) and Ac(λ) in the phenomenological expression are represented by the absorption cross-sections of three color modules which are obtain from total-field scattered-field (TFSF) implementation using single color module without periodicity for the incident light polarized along the nanoantenna. The shape of the simulated spectra (solid lines) and the analytical calculations (dash lines) based on absorption cross-section are in good agreement, demonstrating that there is no significant plasmonic coupling between adjacent nanoantennas. One other issue is that the absorption response of the asymmetric plasmonic pixels to polarized light obeys the Malus' law, which is the basis of the polarization-controlled color tuning. When the incident light is polarized along each color module in the asymmetric nanostructure (the polarization angles of 0°, 60° and 120°),      (d)-(f) Experimental reflectance spectra of the color switching between black and three subtractive primary colors of cyan, magenta and yellow at the specified polarization angles.