1. Introduction

Color, as an important carrier of visual information, has been deeply studied since ancient times. In recent years, inspired by the interaction between micro and nanostructures in nature and light, the structural colors generated by light scattering from micro and nano devices have gained significant attention [1–3]. With the advancement of microfabrication technology, two-dimensional artificial metasurfaces, as subwavelength-scale tools, have been widely used for full-color modulation of structural colors [4,5]. The design of metasurfaces is incredibly flexible, allowing for the precise control of electromagnetic waves according to human desires. As a result, they have been extensively applied in fields such as light modulators [6], photodetectors [7], solar energy photovoltaics [8], surface-enhanced Raman spectroscopy [9], and optical holography [10], with promising prospects. Dielectric metasurfaces possess high-quality factor resonances, leading to vibrant colors and a wide gamut [11,12]. The colors produced by dielectric metasurfaces result from the combined interactions of electric and magnetic resonances, enabling functionalities that plasmonic metasurfaces cannot achieve.

By extending spectral tunability to asymmetrical nanostructures, it becomes possible to customize resonance effects based on the polarization of incident light, such as linear [13] or circular polarization [14]. Nanoarrays composed of gratings [15] and cross-shaped antennas [16] have been designed to produce a range of colors under orthogonal polarization. This polarization-dependent spectral control is particularly attractive for high-density optical data storage and has been demonstrated across single or multiple data layers where each layer resonates at specific wavelengths or polarizations of light [17,18]. There is a significant advantage to independently controlling elements while reaching the limit of optical diffraction to increase information density and achieve easy target reading [19]. This requires different mechanisms for color generation that exhibit significant color changes under orthogonal polarization. Despite rapid progress in the study of structural colors, most nanostructures’ optical properties are static, which strongly limits their application. To achieve colors that vary with polarization angle over a broad spectral range, different geometric forms must be considered. Existing methods still have significant limitations on the dynamic tuning range, and the development of a pixel that can easily and freely adjust across the entire visible spectrum remains an unresolved technical challenge. Recently, several techniques have been developed to improve tunability. Phase change materials, in combination with microfluidics and active materials, have been employed to construct metasurfaces that exhibit dynamic and reversible optical responses [12,20,21].

In recent years, the use of flexible polymers, such as polydimethylsiloxane (PDMS), as a stretchable substrate for tunable nanophotonic devices has gained significant attention [22,23]. PDMS is highly promising due to its elasticity, inertness, non-toxicity, and non-flammability [22]. By fabricating photonic nanostructures on flexible PDMS substrates, it becomes possible to tune photonic devices through mechanical deformation in a simple and repeatable manner. Some studies show that the tensile rate of PDMS can reach 12.5 m/min during the crosslinking process [24]. The combination of molecularly-thin solid-state materials and flexible substrates gives rise to a hybrid material known as flexible metasurfaces [25]. These flexible metasurfaces have found applications in various fields, including stretchable, flexible, and tunable photonic devices. Examples of such devices include solar cells [26], iLEDs [27], tunable filters [28], and structural color displays [21]. In the field of photonics, lithium niobate (LiNbO$_3$) is considered one of the most important materials and is often referred to as the "silicon of photonics". LiNbO$_3$ possesses several advantages, including a high refractive index, a wide transparent wavelength range, and a large second-order electro-optic coefficient of up to 30 pm/V, and good compatibility with integrated photonics circuits [29,30]. As a result, it has been extensively studied and applied in the fields of optics and photonics. Specifically, LiNbO$_3$ exhibits broad transparency, spanning from ultraviolet to infrared wavelengths (transparent range: 350 nm to 5.2 $\mu$m) [30,31]. Additionally, the optical anisotropy of LiNbO$_3$ enhances its sensitivity to polarization [30]. By implementing specific structural designs, biaxial pixels can be engineered to exhibit heightened polarization sensitivity. Despite the individual advantages of PDMS and LiNbO$_3$, the research combining these two excellent materials in metasurfaces is currently relatively limited. However, the potential benefits of integrating PDMS and LiNbO$_3$ in tunable metasurfaces hold promise for the development of new and advanced photonics devices. Further research in this area could lead to exciting advancements and novel applications in the field of photonics.

Therefore, in this study, we utilized a structure composed of nanodimer LiNbO$_3$ placed on a PDMS substrate to investigate the phenomenon of polarization-sensitive structural colors. By meticulously optimizing the geometric configuration, we were able to induce strong magnetic dipole (MD) resonances while effectively suppressing other multipolar resonances through surface lattice resonances. As a result, this structure exhibited a single reflection peak with an exceptional efficiency of up to 99% and a narrow full width at half maximum (FWHM) of less than 9 nm. Furthermore, the stretchable properties of the PDMS substrate offer the possibility of achieving active tuning by mechanically adjusting the period of the unit structure, allowing for changes in the reflected color. Moreover, this metasurface demonstrates remarkable sensitivity to linear polarization, making it highly valuable for applications such as color displays, data storage, and anti-counterfeiting technologies.

2. Structural design and theoretical analysis

Using the wave optics module of COMSOL Multiphysics, we performed full-wave simulations to calculate the total electric (E) field. Perfectly Matched Layers (PML) were applied along the $z$-axis, while periodic boundary conditions were used in the $x$- and $y$-directions. The reflectance spectra and multipole decomposition were computed using COMSOL Multiphysics. The spectral optimization of the geometry was solved using Lumerical finite-difference time-domain (FDTD) method, as PML was also applied along the $z$-axis and periodic boundary conditions were imposed in the $x$- and $y$-directions. Taking into account the optical anisotropy of the LiNbO$_3$ crystal [30], we assumed a constant refractive index of $n_y$ = $n_e$ = 2.18 and $n_x$ = $n_z$ = $n_o$ = 2.26. LiNbO$_3$ is a type of uniaxial birefringent crystal, and it is precisely due to this crystal structure that it exhibits exceptional electro-optic properties. Based on the different crystal cutting directions, it can be further divided into $x$-cut, $y$-cut, and $z$-cut LiNbO$_3$. The gaps between the LiNbO$_3$ nanodimers are $y$-cut to align with the polarization properties of the designed metasurface. The optical anisotropy of LiNbO$_3$ strengthens the polarization characteristics, facilitating the design of biaxial pixels and minimizing crosstalk. In addition to its geometric shape, the birefringent properties of LiNbO$_3$ largely determine the performance of the device. Therefore, compared to isotropic materials, LiNbO$_3$ possesses superior material properties. The metasurface was fabricated on a PDMS substrate, which offers high optical transparency and mechanical flexibility in the visible wavelength range of interest for this study. The refractive index of the flexible PDMS substrate was set to 1.41 [32]. The refractive index difference between LiNbO$_3$ and PDMS is small, and a single nanostructure’s magnetic (electric) dipole resonance is too weak to produce perfect reflection. Interestingly, by arranging the nanostructures in an array, the interaction between the magnetic (electric) dipole resonance and the periodic structure reflection can significantly enhance the reflection intensity. In the design of LiNbO$_3$ metasurfaces, sharp reflection peaks can be achieved by adjusting the shape, size, and layout of the unit structures. In terms of suppressing backscattering and enhancing forward scattering directivity, the design and optimization of metasurfaces can effectively suppress backscattered light and enhance forward-scattered light with specific directionality by controlling the phase and interference effects of reflected light. Therefore, the design and optimization of the reflection spectra are closely related to the design and optimization of metasurface structures, and the desired reflection characteristics and directional scattering effects can be achieved by optimizing the optical performance of the metasurface.

We proceeded to investigate the "biaxial" pixels composed of coupled nanodimers (as shown in Fig. 1), which enable independent variation of colors in the vertical direction, resulting in a wide color spectrum while minimizing crosstalk. As depicted in Fig. 1, the proposed schematic of the LiNbO$_3$ metasurface consists of an overlaid layer of nanodimer arrays on a PDMS substrate. The LiNbO$_3$ dimensions are W$_x$ = 100 nm, W$_y$ = 140 nm, g = 20 nm, P$_x$ = P$_y$ = 300 nm, h = 300 nm. (The optimization process for parameters other than periodic effects can be found in Supplementary Material Fig. 6).

 

Fig. 1. The schematic diagram of the all-dielectric color filter with periodic LiNbO$_3$ dimer nano-pixels on a PDMS substrate

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Compared to isolated or randomly structured nano-resonators, periodic nano-resonator arrays can provide stronger optical response with the help of Surface Lattice Resonance (SLR), which is the coupling between Mie resonances or plasmon resonances and specific diffraction orders. According to Babicheva $et$ $al.$, strong resonance appears around the wavelength of Rayleigh Anomaly (RA) [33], where the normal incident RA to ($i$, $j$) diffraction order can be represented by a critical point of appearance or disappearance at each diffraction order [34,35],

Here, $n_d$ is the refractive index of the dielectric, and $k_x$ and $k_y$ are the $x$ and $y$ components of the wave vector. Additionally, when the refractive index of the substrate and the surrounding medium are different, the RA mode in the homogeneous medium is split into two RA modes. To identify the resonant modes involved and more clearly describe the metasurface, we employ a multipolar decomposition method applicable to periodic structures based on the induced currents inside the resonant cavity. The multipole decomposition of the electromagnetic source is an important method for studying the interaction between electromagnetic waves and matter, which has wide application in classical and quantum electrodynamics. The multipole moments can comprehensively characterize the radiation field distribution of the electromagnetic source and its coupling with the external field, and are important tools for studying the properties of electromagnetic sources. Under the assumption of harmonic excitation exp($i\omega t$), higher-order multipole terms have little effect on the far-field scattering and can be neglected. Therefore, the far-field scattering can be characterized by the contributions of the aforementioned multipoles, and the expression for the total far-field scattered intensity is as follows [12,36,37],

In dielectric metasurfaces, efficient reflection of incident waves is achieved by the destructive interference between forward-propagating and scattered waves when the electric or magnetic dipole modes are excited. However, practical implementation can be hindered by the substrate’s reflective background and broad resonance modes, resulting in lower quality (Q) factor of the reflection peak and affecting the overall reflection efficiency and monochromaticity. The specific goal of optimizing this study is to reduce the reflection of light at wavelengths other than the resonance peak and enhance the Q factor of the resonance peak. To address this issue, we propose a solution by introducing a gap, denoted as "g", in the middle of the LiNbO$_3$ nanoblock to selectively modulate the shorter-wavelength higher-order resonance modes, thereby reducing the reflective background and narrowing the broad resonance modes. To demonstrate the effectiveness of the LiNbO$_3$ nanodimer design, we compare the performance of the LiNbO$_3$ nanoblock with that of the LiNbO$_3$ nanodimer in Figs. 2(a and d). It is observed that the nanodimer exhibits significantly narrower reflection peaks compared to the nanoblock. Moreover, at relatively shorter wavelengths, RAs can suppress higher-order Mie resonances [38]. The LiNbO$_3$ nanoblock exhibits a small peak at 423 nm due to the reflective background and broad resonance modes of the substrate, severely compromising the monochromaticity in the visible spectrum and resulting in a lower Q factor of the reflection peak, as shown in Fig. 2(a). By introducing a gap in the rectangular LiNbO$_3$ structure, deep modulation of the shorter-wavelength higher-order resonance modes occurs, leading to a reduced reflective background and narrower resonance modes across the entire spectral range, as shown in Fig. 2(d). Compared to the LiNbO$_3$ nanoblock, the LiNbO$_3$ nanodimer significantly suppresses the reflection peak at 423 nm in the visible spectrum, thereby improving the overall reflection efficiency and monochromaticity across the entire spectral range. Overall, the LiNbO$_3$ nanodimer exhibits improved reflection efficiency and spectral monochromaticity.

 

Fig. 2. (a, d, h) Simulated reflection spectra of the nanoblock and nanodimer under $x$-polarization, and the nanodimer under $y$-polarization, respectively. (b, e, i) Multipole decomposition of the scattering cross-section for the ED, MD, EQ, MQ, and TD. The insets illustrate the phase distribution of each multipole moment. (c, f, g) Magnetic and electric field distributions of the metasurface at the resonant peaks.

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Nanograting assists in efficiently exciting additional nanostructure resonances, also known as lattice resonances, which occur at wavelengths close to the RA. Due to the interaction of the RA, wave propagation in the nano-resonator array on a PDMS substrate ($n$ = 1.41) reaches the diffraction limit; the shaded region in Fig. 2(a and d) represents the RA wavelength at $\lambda$ = P $\times$ $n$ = 300 $\times$ 1.41 = 423 nm, where P is the period of the array and $n$ is the refractive index of the substrate. In metasurface display designs, the coupling effect of the lattice structure, known as Mie lattice resonances, needs to be considered. At relatively shorter wavelengths, RAs can suppress higher-order Mie resonances. The dimer design enhances lattice coupling and can dominate the reflection spectrum, leading to sharper and more singular resonances. Combining fundamental magnetic dipole resonances with Mie lattice resonances is a feasible and reasonable approach, as there are no other Mie resonances occurring at longer wavelengths. Simultaneously, the contribution of toroidal dipoles to reflection can be suppressed. To excite magnetic dipole resonances, the corresponding magnetic dipole resonance must occur near the longer wavelength of RA. The optical response of the dielectric nanostructure array can be approximated as a periodic multipolar coupling system [38].

To further investigate the modulation depth of dielectric metasurface designs, we decompose the scattering cross-section into multipole modes, including ED, MD, TD, EQ, and MQ, as shown in Figs. 2(b and e). The multipole decomposition calculations indicate that in the LiNbO$_3$ rectangular nanostructures, small resonance peaks are collectively excited by multipole modes, especially the TD mode. However, the LiNbO$_3$ nanodimer effectively eliminate the influence of short-wavelength multipole excitations. The design of the nanodimer allows for overlapping resonance peaks of each multipole. Consequently, the nanodimer design enhances the displacement current and strengthens the magnetic resonance, resulting in a strong coupling phenomenon. This phenomenon can dominate the reflection spectrum, leading to a single sharp resonance. The suppression of background reflection can be considered as the realization of the generalized Kerker effect [39], provided by destructive interference between the ED, MD, EQ, MQ, and TD scattered waves. By examining the phase distribution shown in the illustration in Figs. 2(b and e), we observe phase oscillations occurring at the reflection peak. In particular, when the structure is designed as a nanodimer, all multipole moments demonstrate phase oscillations at nearly the same wavelength, resulting in sharp peaks. Figures 2(c and f) respectively show the electric field distribution |E| in the $xoz$ plane and the magnetic field distribution |H| in the $yoz$ plane for $x$-polarized incident light at 488 and 497 nm wavelengths. The |H| distribution shown in Figs. 2(c and f) is calculated at the $x$ = 0 nm position, which is at the center of the gap between the LiNbO$_3$ nanodimers. Clearly, the magnetic field distribution of both structures is strongest at the center of the nanopixel and weakest near the nanopixel. This indicates that the magnetic field is strongly confined within the LiNbO$_3$ nanoblocks. However, after opening a gap in the middle of the nanoblock, a strong electric field enhancement is formed within this air gap, resulting in a sharp and singular reflection peak. In particular, the electric field distribution shown in Fig. 2(f) reveals the formation of circulating flow in the $xoz$ plane at the resonance peak, justifying the multipole expansion based on displacement currents. The suppression of backscattering is provided by the destructive interference between the ED, MD, EQ, MQ, and TD scattered waves. The proposed structure can simultaneously support MD, EQ, MQ, TD, and other resonance modes, which not only suppresses backscattering but also enhances the directionality of forward scattering, enabling the designed resonant structures to achieve far-field unidirectional scattering at the same wavelength position [39].

Under the design of LiNbO$_3$ nanodimers, the $x$- and $y$-polarized reflection spectra for each Mie resonance mode are plotted in Figs. 2(d and h). Figure 2(d) shows that for $x$-polarized incident light, the peak at $\lambda$ = 497 nm corresponds to the MD$_y$ oriented in the $y$-direction. For $y$-polarized incident light, as shown in Fig. 2(h), the reflection peak broadens as the electric field moves along the resonator’s long axis, and the magnetic dipole mode MD$_x$ is excited at a shorter wavelength of $\lambda$ = 442 nm. For $y$-polarized light, the toroidal dipole mode can also be excited in the scatterer at the shorter wavelength of $\lambda$ = 420 nm (Fig. 2(i)); however, it does not contribute to a single reflection peak, so we do not further discuss it. Similarly, Fig. 2(g) shows the electric field distribution |E| in the $yoz$ plane and the magnetic field distribution |H| in the $xoz$ plane for $y$-polarized incident light at a wavelength of 442 nm. Clearly, the resonance mechanism is the same for both polarization states. It primarily relies on the intrinsic properties of LiNbO$_3$, as the significant refractive index difference between LiNbO$_3$ and PDMS enables LiNbO$_3$ to support dipole resonances and form a photonic bandgap. In addition, white light incident on the periodic structure excites guided modes through the light-matter interaction on the surface. These modes leak into the surrounding environment and interact with the directly reflected light. The interference between the directly reflected light and the radiated light generates high-quality Fano resonances, and the pronounced Fano resonance peaks and the presence of the photonic bandgap result in improved reflection spectra, which can be utilized to create better color impressions.

The aim of this study is to explore the active tuning of the metasurface by mechanically adjusting the periodic structure of the unit through the stretchable properties of the PDMS substrate. To cover the entire color palette, we changed the period of the nanometer pixels along the $x$- and $y$-directions using different strains of the PDMS substrate within the range of 400 to 650 nm. It is worth noting that the results shown in Fig. 3 are a result of both the substrate strain and the gap "g" changing simultaneously. To analyze the reflection properties of the nanometer pixels under different polarizations, we simulated the reflection spectra of the eight nanometer pixels in $x$- and $y$-polarizations separately, as shown in Figs. 3(a and c). For $x$-polarization, the reflection spectrum shows a red shift as the substrate strain increases. Center wavelengths of the reflection spectra were 459, 486, 500, 511, 533, 554, 577, and 590 nm when the substrate strain of the nanostructure was varied from −15% to 40%. For these eight nanostructures, the efficiency can also be maintained at approximately 100%. Of course, there will be slight differences in the bandwidth and Q value of the reflection spectra. However, for the same eight nanostructures, there will be no obvious shift in the center wavelength of the reflection spectra for $y$-polarization, with center wavelengths of 417, 435, 443, and 453 nm, followed by a significant decrease in reflection, with almost no resonance. Figures 3(b and d) show the CIE 1931 chromaticity coordinates, including eight colors generated by $x$- and $y$-polarizations under strain from −15% to 40%. The chromaticity diagram for $x$-polarization in Fig. 3(b) has significant differences in tone from blue to red due to the presence of different center wavelengths throughout the visible region, but with lower saturation in the blue area. In contrast, the colors in Fig. 3(d) are mainly concentrated in the blue area. Therefore, the entire color gamut can be covered using two orthogonal polarized incident lights. Figure 3(e) supplements the 16 geometric parameters and their corresponding color blocks under different polarizations with different PDMS substrate deformations. The comprehensive color gamut can reach 90% of the standard Red Green Blue (sRGB) indicated by the white dashed line in Figs. 3(b and d). It can be seen that the color blocks generated under different polarizations are significantly different, except for slight overlap in the blue area, with significant differences in all other colors, which will significantly reduce the cross-talk of the "biaxial" pixel. Therefore, we have achieved tunable structural colors with two orthogonal polarizations, which is ideal for practical applications such as 3D displays and data storage.

 

Fig. 3. (a) Reflectance of metasurface under varying substrate strains, $x$-polarization. (c) Reflectance of metasurface under varying substrate strains, $y$-polarization. (b) and (d) Chromatic diagrams showing simulated colors in CIE 1931 color space for panels (a) and (c) respectively. (e) Changes in structural parameters under different substrate strains and corresponding calculated colors for different polarizations.

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When applying strain to a PDMS substrate, not only does the period change, but the gap between the dimers also undergoes changes. This adds complexity to the analysis of theoretical models. In response to this issue, we conducted a separate study focusing on the influence of the nanopatterned period on color functionality, as illustrated in Fig. 4. Figure 4(a) shows the reflection spectra obtained by simultaneously varying the period parameter P in different directions of the dimer nanostructure under $x$-polarized light. In the case of unit cell arrangement, the period size P ranges from 250 nm to 450 nm with a step size of 20 nm. As the period parameter increases, a redshift in the resonance phenomenon is observed. Due to the significant influence of periodicity on the position of mode spectra, it is possible to design LiNbO$_3$ dimer arrays at multiple positions in the visible light range to achieve perfect reflection. However, considering the results from both Fig. 3(a) and Fig. 4(a), the periodicity change has a dominant effect on the generated colors of the metasurface compared to the variation in the nanodimer gaps. Therefore, adjusting the color range can be achieved solely by changing the periodic parameters of the nanodimers. This provides great convenience for theoretical analysis. In addition, we also investigated the effect of separate changes in the $x$- and $y$-directions of the period induced by strain under $x$-polarized light on the reflection peak. Simulation results demonstrated that the change in lattice period is mainly caused by the variation in the $x$-directional period (P$_x$). When the $y$-directional period (P$_y$) changes, a slight blueshift of the reflection peak is observed, but the impact on the peak value is not significant, as shown in Figs. 4(b and c). This is because under $x$-polarized light, the LiNbO$_3$ dimer metasurface supports MD resonance in the $x$-direction, where the period change direction aligns with the magnetic field direction. For MD resonance, the electric field is mainly concentrated inside each nanodimer, resulting in weak near-field interactions. Therefore, the peak wavelength of the MD resonance can be shifted to longer or shorter wavelengths by increasing or decreasing the $x$-directional lattice size, consistent with the results reported in [32]. The inset in Fig. 4(c) demonstrates the color gamut range generated under $x$-polarized light when the period size changes along different directions. Significant color gamut changes are observed when only the $x$-directional period (P$_x$) is modified. In contrast, the color gamut range generated by changes in the $y$-directional period (P$_y$) is relatively small. Therefore, under $x$-polarized light, the strain applied to the PDMS flexible substrate has a predominant effect in the $x$-direction. This is because the resonance peak shifts in opposite directions under different stretching directions. When stretching is applied along the $x$-direction, the magnetic field aligns with the incident light, enhancing the coupling effect. However, when stretching is applied along the $y$-direction, the coupling magnetic field weakens, resulting in some energy loss. When stretching is applied simultaneously in the $x$- and $y$-directions, the coupling effect in the $x$-direction is significantly stronger than in the $y$-direction, as evident from the extent of peak shifting. Therefore, the energy loss incurred is minimal, as shown in Fig. 4(a). The redshift and blueshift of the dipole resonance indicate the different dominant roles of lateral and longitudinal coupling between the dielectric resonators. By applying strain, it can be inferred that the lateral magnetic coupling and longitudinal electric coupling are mainly altered, with lateral magnetic coupling being significantly stronger than longitudinal magnetic coupling.

 

Fig. 4. The reflection spectra of the designed metasurface under $x$-polarization are obtained by changing (a) P (simultaneously changing P$_x$ and P$_y$, i.e., P = P$_x$ = P$_y$), (b) P$_x$, and (c) P$_y$ values. Similarly, the reflection spectra under $y$-polarization are obtained by changing (d) P (simultaneously changing P$_x$ and P$_y$, i.e., P = P$_x$ = P$_y$), (e) P$_x$, and (f) P$_y$ values. The insets in (c and e) illustrate the color-changing tendencies of the spectra in the CIE1931 color space under different polarizations.

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Conversely, under $y$-polarization, the primary strain that affects the PDMS substrate is the strain in the $y$-direction. Therefore, when both the $x$- and $y$- directions experience strain simultaneously, the coupling effect in the $y$-direction is stronger than in the $x$-direction, as depicted in Fig. 4(d). On the other hand, when strain occurs in the $x$-direction, the coupling magnetic field weakens, resulting in a smaller magnitude of blue shift in the reflection spectrum, as shown in Fig. 4(e). However, when strain happens in the $y$-direction, the coupling magnetic field strengthens, leading to a larger magnitude of blue shift in the reflection spectrum, as demonstrated in Fig. 4(f). Similarly, this is because the incident magnetic field H aligns with the direction of stretch along the unit cell when strain is applied in the $y$-direction, and aligns with the direction of contraction along the unit cell when strain is applied in the $x$-direction. Therefore, when stretching is applied in the $y$-direction, the coupling magnetic field is enhanced, while stretching in the $x$-direction weakens the coupling magnetic field. When stretching is applied simultaneously in the $x$ and $y$ directions, the $y$-directional coupling is stronger than the $x$-directional coupling. The inset in Fig. 4(e) illustrates the color gamut range generated under $y$-polarized light at different strains. Through these findings, we elucidate the primary coupling mechanisms of the dielectric resonator array, providing insights for further optimization of tunability.

Due to the distinct color contrast of $x$-polarized and $y$-polarized light under different periodic variations, we can also achieve multicolor switching of two orthogonal polarized incident lights, which is of great significance for data storage and display technologies. Figure 5 presents the reflection spectra of the PDMS substrate at four different stretching levels: 0% (Fig. 5(a)), 20% (Fig. 5(b)), 30% (Fig. 5(c)), and 40% (Fig. 5(d)), respectively. Only when the substrate is close to the free state, $y$-polarized light exhibits resonance with its peak at 440 nm, while resonance is weak in other states. Under $x$-polarized incident light, the peak shifts to 500, 540, 570, and 590 nm respectively as the stretching increases, and the reflection peak has a narrow bandwidth with an efficiency of over 99%. In addition, we present the reflection spectra for a polarization angle of 45$^\circ$, which helps us study how reflectance changes with polarization tuning. When the substrate is in a free state, we observe that at a 45$^\circ$ polarization angle, the reflection peak splits and its intensity decreases by half. Likewise, when the substrate is strained at 20%, 30%, and 40%, the reflection peak intensity also decreases by half as the incident polarization angle varies. Figure 5(e) depicts the virtual colors generated by the nanostructures at these four different stretching levels under varying polarization angles from 0$^\circ$ to 90$^\circ$. It is evident that the nanostructures can achieve color switching from green to purple, from green to pink, from yellow to light blue, and from red to blue, only by changing the polarization angle in these four different stretching states. The CIE 1931 chromaticity coordinates corresponding to the reflection spectra in the four stretching states are shown in Fig. 5(f). As the polarization angle varies, the color gradually changes, which is a result of the reflection response of the polarized light. According to Malus’ law, we have [40],

 

Fig. 5. (a-d) Simulated reflectance spectra of pixels under different substrate strains for $x$-polarization, 45$^\circ$-polarization, and $y$-polarization, for 0%, 20%, 30%, and 40% strain. (e) Reflection mode color responses for the four different strains when the incident polarization angle is incrementally stepped by 15$^\circ$. (f) Corresponding to CIE 1931 color trends.

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As for the equation, $\phi$ represents the polarization angle of the incident light, and $R_v/R_h$ represents the reflectivity of the electric field perpendicular/parallel to the $x$-axis. As $\phi$ changes from 0$^\circ$ to 90$^\circ$, the resonance peak of the reflection spectrum in the four stretching states shifts nearly 100 nm. This means that we can dynamically adjust the structural color by changing the polarization angle of the incident light, thereby obtaining dual-color or multiple mixed colors. Flexible color switching allows signal nanoscale pixels to encode dual or multiple information states in display technologies. In this context, our proposed nanostructure can be used to create microimage displays containing high-density storage, digital displays, and 3D displays.

This study presents a polarization-sensitive LiNbO$_3$ metasurface, constructed using LiNbO$_3$ material with birefringence effect and a flexible PDMS substrate. This metasurface not only exhibits active tunability but also takes advantage of the birefringent properties of LiNbO$_3$ to design biaxial pixels that are more sensitive to polarization. We compared the performance and characteristics of our proposed biaxial color pixels with similar structures or methods reported previously, as shown in Table 1.

Table 1. Comparison of dual-axis color pixel modulation performance

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The main focus of this study lies in the simulation and theoretical analysis of the entire metasurface design, assuming that the strain induced by substrate deformation is uniformly distributed across the entire device. When PDMS undergoes deformation, its surface experiences strain. By utilizing specific stretching techniques, this strain can be evenly distributed throughout the entire device, as highlighted in the Ref. [43,44]. Due to the chemical inertness of LiNbO$_3$, it cannot be etched chemically. Mechanical engraving is also challenging due to the material’s hardness. However, innovative techniques like thermal diffusion or proton exchange, laser writing, focused ion beam milling, and plasma dry etching have been successfully employed [45]. The manufacturing process of PDMS-based LiNbO$_3$ devices relies on a transfer technique detailed in Ref. [46]. The technique involves casting PDMS onto a LiNbO$_3$ layer, followed by thermal compression curing and peeling off to create the desired pattern.

3. Conclusion

In this study, we showcase the potential of all-dielectric metasurfaces in presenting different colors through polarization-dependent scattering of incident light. Specifically, we propose independently tunable biaxial color pixels composed of isolated nanodimers, capable of displaying the full spectrum of colors through linearly polarized-dependent reflection. By arranging LiNbO$_3$ nanodimers on a PDMS substrate, we achieve a single reflection peak with a narrow FWHM of less than 9 nm and an impressive reflection efficiency of up to 99%. This is achieved by exciting the strong MD resonance and suppressing other multipole resonances through lattice resonance. Additionally, the scalable nature of the PDMS substrate allows for active and continuous tuning within a strain range of 40%, covering nearly 150 nm of the visible light spectrum, enabling seamless variation of reflected colors. We also have contemplated the significance and future development directions of this work. Firstly, the utilization of polarization-dependent coloring with sensitivity to strain enables highly sensitive parameter detection and visual feedback, advancing next-generation visual sensor technology. Secondly, strain-tunable coloring holds applications in sectors such as anti-counterfeiting technology and unique apparel design. Lastly, the independent control capability of these biaxial color pixels offers new possibilities for applications in high-density optical storage and other domains. Overall, this type of metasurface finds extensive use in areas like color displays, data storage, visual sensing, and anti-counterfeiting technology.

Appendix

Structure optimization

The geometrical configuration parameters have a significant influence on the optical properties of metasurfaces. In this supplementary material, we focus on analyzing the effects of each geometrical parameter, except for the period P, on the performance of the metasurface. We take the default configuration with W$_x$ = 100 nm, W$_y$ = 140 nm, g = 20 nm, P = P$_x$ = P$_y$ = 300 nm, and h = 300 nm as an example. Figure 6(a) illustrates that as the gap parameter "g" increases from 0 nm to 40 nm, the FWHM of the reflection peak rapidly decreases from 21 nm to 0.5 nm. Simultaneously, the Q factor increases from 23 to 1004, and the reflectance remains consistently above 90%. Moreover, the resonant wavelength shifts from 489 nm to 502 nm. By referring to the CIE 1931 color space diagram, it is evident that there is a significant change in color as the gap "g" varies. When the gap between the LiNbO$_3$ nanodimers is 0 nm, the reflection spectrum shows a wider peak covering a significant portion of the blue range. On the other hand, with a nanodimer gap of 40 nm, the reflection spectrum becomes narrower with a higher Q value. However, there is still some reflection at wavelengths other than the peak, resulting in broader reflection spectra in either the blue or red regions. As a result, despite the peak being in the green wavelength, the overall color coordinates tend to be closer to the white spectrum region. As for the other three structural parameters, h, W$_x$, and W$_y$, we observe a slight redshift in the reflection peak when these parameters increase. However, there is minimal impact on the Q factor and the color gamut, as shown in Figs. 6(b-d). To summarize, the geometrical configuration parameters play a crucial role in determining the optical characteristics of metasurfaces. By adjusting these parameters, precise control over the optical performance and color response of metasurfaces can be achieved.

 

Fig. 6. (a-d) The influence of gap "g", height "h", W$_x$ and W$_y$ on the reflection spectra, and the insets are the chromaticity diagram of their color gamut variation.

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In the default configuration of the LiNbO$_3$ metasurface, we further investigated the influence of angles on the structural color. Figure 7(a) illustrates the reflection spectra of the designed metasurface at different polarization angles. When the incident light’s polarization direction is parallel to the $x$-axis (termed $x$-polarized, $\phi =0^\circ$), a high Q factor reflection peak is generated due to the enhanced electric field interaction between the dimers. As the polarization angle gradually increases, the reflection peak undergoes a gradual splitting. Upon reaching a polarization angle of $90^\circ$ (i.e., $y$-polarized light incidence), a lower Q factor reflection peak is observed, exhibiting color range variations, as shown in Fig. 7(d). Additionally, the LiNbO$_3$ metasurface exhibits varying responses to incident angles depending on the polarization state. Under $x$-polarization, the LiNbO$_3$ metasurface demonstrates strong sensitivity to the incident angle of light, resulting in a rapid redshift of the resonance peak as the incident angle increases. The redshift ranges from 497 nm to 600.0 nm for a single MD resonance (Fig. 7(b)), thus enabling a relatively wide color range (Fig. 7(e)), with a reflectance exceeding 75% even within a $30^\circ$ range. In contrast, under $y$-polarization, the LiNbO$_3$ metasurface exhibits a slower response to the incident angle of light, resulting in a slight blueshift of the reflection peak, as shown in Fig. 7(c). At larger incident angles, the background reflectance increases, and the reflection peak broadens further. The corresponding color range remains within the blue color regime (Fig. 7(f)).

 

Fig. 7. (a-c) Effect of polarization angle and $x$- and $y$-polarization incidence angle on reflection spectra. (d-f) the chromaticity diagram of their color gamut variation.

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Funding

National Natural Science Foundation of China (62174040, 62364004); the Guizhou Provincial Science and Technology Projects (ZK[2022]211); the Scientific Research Funded Project of Guizhou Minzu University (2024007); Natural Science Research Project of Department of Education of Guizhou Province (QJJ2022015); the 13th batch of outstanding young scientific and Technological Talents Project in Guizhou Province ([2021]5618); the Young scientific and technological talents growth project of the Department of Education in Guizhou Province (KY[2022]184); Nature Science Foundation of Guizhou Minzu University (GZMUZK[2021]YB07).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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