Thermally Tunable Structural Color Based on Patterned Ultra-Thin Asymmetric Fabry–Perot Cavity with Phase-Change Material

Abstract

Tunable structural color has gained significant attention due to its dynamic characteristics. However, conventional devices are usually regulated only in their color capabilities by structural parameters, restricting real-time dynamic applications. In this study, we propose an ultra-thin asymmetric Fabry–Perot cavity patterned with phase-change materials (MPMP). The reversible phase transition of VO₂ induces changes in the MPMP’s optical performance, enabling color mode switching through temperature control and resulting in rapid color conversion and low-temperature regulation. By adjusting relevant structural parameters of the VO₂ layer and nanodiscs, the color performance range can be tailored. Through numerical investigations, we demonstrate that MPMP can produce stable transformation of dynamic structural colors by harnessing the phase-change effect. Our research unveils new possibilities for applications such as anti-counterfeiting, bio/chemical sensing, and temperature sensing.

1. Introduction

Color plays a crucial role in our lives [1]. According to the mechanisms of coloration, colors in nature can be mainly divided into pigment colors and structural colors [2,3]. The most common colors are generated by pigments, which form when chemical chromophores selectively absorb certain wavelengths of light [4]. Typically, pigment-based colors have a narrow color gamut, low resolution, and may lose their vibrancy under harsh conditions due to molecular degradation and potential environmental issues [5,6]. Structural color refers to colors produced by the interaction between light and the periodic micro- and nanoscale structures that overcome the obstacles of pigments [7]. Many methods to operate light through specific structures have been designed by researchers. Optical metasurfaces provide a new means to control light fields through resonances of their structures [8]. Metasurfaces can be composed of subwavelength structures made of metals [9,10,11,12,13] or dielectrics [14,15,16], and localized surface plasmon resonance (LSPR) and Mie resonance make it possible for metasurfaces to produce colors. Metasurfaces based on LSPR in metal nanocells can induce collective electron oscillations, making light scattering and absorption possible, and thereby achieving effective modulation of the amplitude, phase, and polarization of electromagnetic waves [9,17,18,19]. High refractive index dielectric and semiconductor structures can support Mie resonances with low optical loss, making it possible to expand the achievable color gamut and improve aspects of color quality, such as saturation and brightness [20,21,22].

Although the shape and geometric parameters of metasurface elements can have a significant control effect on color, they are difficult to change once manufactured. The fixed structure, with a determinate color space distribution, cannot adapt to changing environments, and its static working mode limits broader applications such as stealth, dynamic full-color displays, optical anti-counterfeiting, and encryption. Therefore, the structure needs to be able to transition between two or even multiple chromatic states under external stimulation, forming a controllable dynamic structural color. Many methods have been studied to achieve dynamic structural color, such as color change induced by chemical reactions [23,24], force-induced color change [25,26], electrically induced color change [27,28,29], and phase-change material color change [30,31,32,33,34]. However, the reaction time of reversible electrochemical deposition operations is relatively long, slowing the refresh rate [23,24]. Dynamic structural color achieved through mechanical control, such as compression or stretching, lacks durability and stability. The color performance will significantly weaken after a period of compression or stretching [25,26]. Additionally, the device for electrically induced color change is relatively complex, and its production is more difficult [27,28,29].

Based on the circumstances mentioned above, it is crucial to develop a structural color that can be easily transformed and has a rapid response time. Phase-change materials (PCM) are capable of switching phases under external stimuli. During this phase change, the optical dielectric constant of the PCM changes correspondingly, causing a change in the device’s reflection spectrum and resulting in a change in color. Research on structural colors based on PCM has made significant progress. The most commonly used PCMs are chalcogenide compounds, such as Ge2Sb2Te5 (GST) [35]. By utilizing the sharp change in optical properties caused by the phase transition between the crystalline and amorphous states under external stimuli, displays can be designed to exhibit significant changes in structural color before and after the phase transition [36,37]. However, chalcogenide compounds require thermal or electrical stimuli to achieve phase change at T = 150 °C. Although they can achieve a fast nanoscale phase change, the conditions required are relatively complex. In comparison, vanadium dioxide (VO₂) has a lower phase transition temperature (T = 68 °C) and a faster picosecond-level phase transition speed. VO₂ has been widely studied due to its excellent thermal stability and reversible phase transition states. It can achieve a reversible phase transition between an insulating state and a metallic state (IMT), corresponding to the monoclinic phase at low temperature and the rutile phase at high temperature. This results in a decrease in light density and a change in conductivity of three to four orders of magnitude [38]. Therefore, devices designed based on VO₂ can achieve high-speed and low-temperature control while producing certain optical property differences around the phase transition. Currently, research on VO₂ phase transition mainly covers the infrared band [39,40,41], for example, Barreda et al. propose the concept of quasi-bound states in the continuum (quasi-BIC) [42], and there is relatively little research on the visible light band [32,43]. Multilayer-based structural color is a common approach used to create color in various applications. One of the most common types of multilayer-based structural color is the Fabry–Perot (F–P) cavity, which contains the metal–insulator–metal (MIM) three-layer structure, such as the absorber Ag-VO₂-Al [32] or Ag nanoparticles-VO₂-Pt [43] three-layer MIM structure, and the VO₂-SiO₂-Ag [44] structure. This structure consists of two metallic mirrors separated by an optically transparent dielectric spacer, where the generation of structural colors is produced by the interference between multiple reflected light beams within the cavity. Research on infrared band optical solar reflectors has reported patterned VO₂ metasurface-SiO₂-Al [45] structures, which combine the advantages of thermochromism and plasmonic properties, achieving good selective reflection and absorption performance. However, currently, there are few reports on the design and application of VO₂-patterned structures in the visible light band.

In this study, we propose a patterned four-layer reflector structure (MPMP) based on PCM and an ultra-thin asymmetric Fabry–Perot cavity that can achieve stable color switching performance in the visible light spectrum through the combined effect of systematic Fabry–Perot resonance and Mie resonance. The VO₂ layer and VO₂ metasurfaces are crucial for controlling the color characteristics and color-changing properties of the system before and after the phase transition. This paper focuses on the influence of VO₂ structural parameters on the system’s color. Under the condition that all other structures remain unchanged, the system can cover most colors. By adjusting the thickness of the VO₂ layer and the radius of the VO₂ nanodisc, the hue, saturation, and brightness of the structural color can be fine-tuned. The nanodisc plays a crucial role in this fine-tuning, and the height of the VO₂ nanodisc can adjust only the brightness. Finally, by adjusting the VO₂-related parameters of the sample, we drew a reference color palette, which demonstrates the system’s potential application value.

2. Materials and Methods

2.1. Metasurface Structure

The unit cell of the proposed MPMP structure under study is illustrated in Figure 1a, which shows the conversion of structural color under temperature control. Additionally, Figure 1b,c shows the schematic of the MPMP and its geometrical parameters. This is composed of a VO₂ nanodisc positioned on top and an ultra-compact asymmetric FP nanocavity at the bottom, with a phase-change material VO₂ film sandwiched between a top Ag film and a bottom Al film seated on the substrate. We selected Al as the bottom-layer material due to its high reflectivity across all visible wavelengths and chose Ag for its low absorption loss and high reflectivity [46]. The substrate can be either a rigid substrate (such as silicon or glass) or a flexible substrate (such as aluminum foil). The thickness of each layer is defined as h₁, h₂, h₃, h₄. Furthermore, the top VO₂ nanodisc is a periodic structure, and the radius and period of the nanodisc are denoted as r and p, respectively.

The bottom Al reflecting layer with a thickness (h₄) of 200 nm is made larger than the skin depth in order to block the transmission of the incident plane wave. The Ag layer is used as the top reflective mirror with a thickness (h₂) of 5 nm, thin enough to allow a portion of the incident plane wave to pass through it. The performance of the intelligent thermal control partly relies on the middle VO₂ layer, which plays a crucial role in interference resonance as an optical cavity. When the temperature is below the phase transition temperature, the optical permittivity of VO₂ is in the insulator VO₂ state. When the temperature is above the phase transition temperature, the optical permittivity transfers to the metal VO₂ state. The difference in the dielectric constant of VO₂ before and after the phase transition results in a change of the structural reflectance, which leads to the change of the structural color. The F–P resonance dominated by the VO₂ layer plays a leading role in the phase change, while the VO₂ nanodisc on top plays an auxiliary role in the regulation, with a relatively small effect on regulation.

The MPMP structure was designed and optimized through simulations using the finite difference time domain (FDTD) solutions. This approach discretizes Maxwell’s equations into difference equations for numerical computation. The dielectric functions of Al and Ag were obtained from Palik’s handbook [47] and are available in Lumerical’s default material database. The complex refractive index data, including the refractive index n and the extinction coefficient k, of VO₂ at low (22 °C) and high temperatures (100 °C) were adopted from a previous report [47,48,49,50,51]. We also obtained data for widely used materials, GST [52] and Sb₂Se₃ [53], within the visible light range for simulations, as shown in Figure 2a,b. We focused on the data represented by dashed lines for the three materials, taking into consideration the variations in material losses. Within the visible light range, for both states, VO₂ demonstrates a lower extinction coefficient compared with GST, indicating that VO₂ experiences lower losses than GST. When comparing VO₂ with Sb₂Se₃, in the amorphous state, VO₂ exhibits lower losses than Sb₂Se₃ below approximately 670 nm, with slightly higher losses above this threshold. In the crystalline state, VO₂ displays significantly lower losses than Sb₂Se₃ below approximately 760 nm, with slightly higher losses beyond this point. Overall, VO₂ exhibits lower losses in comparison with Sb₂Se₃. Consequently, when compared with GST and Sb₂Se₃, VO₂ showcases a notable advantage in terms of lower losses.

Simulations were carried out with perpendicular illumination of plane waves on a single unit cell. In all simulations, the size of the spatial grids in all dimensions was set to 1 nm. Periodic boundary conditions were used in the x and y directions to replicate the periodic structures, while perfectly matched layer conditions were applied in the z direction to absorb the propagating waves. The reflectance and the electric and magnetic field distributions of the MPMP were recorded using frequency-domain field and power monitors.

2.2. Color Calculation

MATLAB was used to calculate color conversions from reflection spectra, based on previous color theory studies [3,52,54,55,56]. Once reflectance values were converted into color coordinates, the resulting colors could be visualized intuitively on the CIE1931 chromaticity diagram. The color coordinates were normalized XYZ tristimulus values, which are defined by a set of spectral reflectance factors. These reflectance factors, the relative energy of the illuminant, and the color-matching functions must be multiplied together at each wavelength and then summed. To obtain the tristimulus values, the simulated reflection data from the FDTD method were first interpolated to match the abridged set of color-matching functions, which were used at 5-nm intervals over the range of 380 nm to 800 nm. This range is the wavelength selection for this article and essentially covers the visible light spectrum. The tristimulus value can then be calculated using the following equations:

$$X=k{\displaystyle \sum }_{\lambda =380}^{\lambda =800}E\left(\lambda \right)\overline{x}\left(\lambda \right)P\left(\lambda \right)$$

$$Y=k{\displaystyle \sum }_{\lambda =380}^{\lambda =800}E\left(\lambda \right)\overline{y}\left(\lambda \right)P\left(\lambda \right)$$

$$Z=k{\displaystyle \sum }_{\lambda =380}^{\lambda =800}E\left(\lambda \right)\overline{z}\left(\lambda \right)P\left(\lambda \right)$$

Here, $E\left(\lambda \right)$ is the relative spectral power distribution of an illuminant, $\overline{x}\left(\lambda \right)$, $\overline{y}\left(\lambda \right)$ and $\overline{z}\left(\lambda \right)$ are the color-matching functions for the CIE1931 standard observers, $P\left(\lambda \right)$ is the spectral reflectance of the MPMP, and k is a normalized factor. The XYZ tristimulus values are normalized to a new scale ranging from 0 to 1, as follows:

$$x=\frac{X}{X+Y+Z}$$

$$y=\frac{Y}{X+Y+Z}$$

$$z=1-x-y$$

The resulting normalized values, which are the color coordinates, are denoted by x, y, and z. The resulting (x, y) plot represents the values of color on the CIE1931 chromaticity diagram. For this calculation, the light source condition used is D65, and the observation angle used is $2^{°}$.

2.3. Key Parameters of Color

Color is the sensation produced by the reflection of physical light from objects onto the optic nerve of the human eye. The perception of color by human eyes is determined by three primary characteristics: hue, chroma, and lightness. Hue is directly related to the frequency of the light wave, and refers to the different frequencies of color, with red having the lowest frequency and purple the highest. Chroma is a numerical representation of the vividness of a color, calculated according to the degree of gray in the color. Saturation is another term for chroma. Lightness describes the brightness and darkness of a color, with lighter colors having a higher value and darker colors having a lower value. Together, these three characteristics give rise to the overall perception of color.

3. Results and Discussion

3.1. The Influence of Temperature on Structural Color

After undertaking the above analysis, we obtained the reflectance of the structure through simulation, which can be converted into corresponding colors. We present partial data selected from large-scale simulations in Figure 2c. The radius (r) of the nanodisc at the top of the structure is fixed at 40 nm, with a height (h₁) of 40 nm, and the thickness (h₃) of the VO₂ layer at the bottom of the structure adjusted. To better display the data transformation characteristics, we used a step size of 5 nm for the thickness (h₃) changing from 50 nm to 100 nm, and a step size of 10 nm for the thickness (h₃) changing from 100 nm to 250 nm. With the series of data obtained, we marked the corresponding colors on the color palette, as shown in Figure 2e. The sample of data in Figure 2c is derived from the selected sample shown in Figure 2e. We show the reflectance and the corresponding transformed colors in Figure 2c, with the thickness (h₃) of the VO₂ layer at the bottom being, successively, 50 nm, 55 nm, 60 nm, 70 nm, 80 nm, 90 nm, 120 nm, 160 nm, 200 nm, and 240 nm. In the figure, the solid line represents the data at low temperature (monoclinic phase), while the dashed line represents the data at high temperature (rutile phase), corresponding to the insulator VO₂ state and metal VO₂ state, respectively. As shown in Figure 2c, the left color panel corresponds to the reflectance at the monoclinic phase, while the right color panel corresponds to the rutile phase. The colors of the lines correspond to the structural colors. Furthermore, it can be observed that, with the increase of the thickness of the bottom VO₂ layer, the reflectance spectrum in both phases shows a trend of redshift, corresponding to a color transition that initiates from the short-wavelength blue range.

For VO₂ layer thicknesses less than 60 nm, as depicted in Figure 2(ci,cii), there is minimal variation around the phase transition, resulting in a uniform medium blue structural color. This can be attributed to the insufficient difference in the optical path created by the VO₂ layer at the bottom. However, as the thickness (h₃) increases to 60 nm, distinct colors corresponding to different states of VO₂ start to emerge. As shown in Figure 2(ciii), these colors are closer to maroon and royal blue, respectively, and exhibit relatively high saturation. At the same time, significant differences can be seen in the reflectance around the phase transition. Combined with Figure 2d, these differences are mainly reflected in the longer bands of visible light, and the positions of the reflectance valley and corresponding absorption peaks are different, as shown in Figure 2(civ,cv). When the thickness is increased further, the color difference around the phase transition is still obvious, but the color saturation decreases somewhat, as shown in Figure 2(cvi,cvii). When the thickness is too large, the difference in color still exists, but the overall reflectivity is low, resulting in an actual situation where the color is not easy to distinguish. At the same time, the relative size of reflectance corresponding to reflection peaks and valleys is further reduced, so the saturation and brightness of the corresponding color are low. The above factors lead to the structural color not having a good visual effect.

Based on the calculated reflectance spectra of MPMP, Figure 2d shows the corresponding CIE 1931 chromaticity diagram with points extracted from the color palette, ordered according to the magnitude of the thickness of the VO₂ layer. The black and white marks indicate data for VO₂ in the monoclinic and rutile phases, respectively. As the thickness of the VO₂ layer increases, the corresponding reflection spectra exhibit a certain pattern of change. As the thickness of VO₂ increases, the difference between the corresponding data points around the phase transition gradually increases first and then decreases, as reflected by the distance on the CIE 1931 chromaticity diagram. When the thickness is low, the movement of points on the chromaticity diagram is noticeable, and the color saturation is high. However, as the thickness increases, the position of the points changes more slowly, and when the thickness exceeds 200 nm, the data points are densely distributed in the middle region with only slight changes, resulting in lower color saturation. The change in data starts from blue, and, except for the green with high saturation, the other colors can change to a color with higher saturation. From the edge to the center, there is a spiral change, where the change in the position of the point gradually becomes smaller, resulting in decreased saturation. This suggests that, when the thickness is large enough, the color tends to stabilize, but the visual effect is not ideal, consistent with the earlier conclusion.

$\mathit{∆}R$ is defined as the difference between the reflectance at the monoclinic phase and at the rutile phase in order to amplify the reflectance changes around the phase transition. Figure 2d demonstrates that there is little difference around the phase transition in the short-wavelength band. Where the reflection spectra are significantly different around the phase transition, there is a trend of long wavelength movement. The peak position of $\mathit{∆}R$ has a distinct redshift with the increasing thickness of VO₂, which plays a leading role in, and is the source of, the color difference between the monoclinic phase and the rutile phase.

3.2. Physical Mechanism Investigation

To elucidate the primary physical mechanism of the proposed structure, we examined the global or local distribution of the electric field intensity (${\left|E\right|}^2$) and magnetic field intensity (${\left|H\right|}^2$) for the sample consisting of 70 nm VO₂ nanodisc/10 nm Ag/70 nm VO₂/100 nm Al. As depicted in Figure 3a,b, the electric field intensity distribution diagram indicates that the energy is primarily concentrated in the VO₂ layer at the bottom of the structure, which suggests that the color filtering performance is mainly attributed to the Fabry–Perot resonance. Additionally, the electric field intensity is stronger in the monoclinic phase than in the rutile phase, which corresponds to the distinct states of VO₂.

To better visualize the energy distribution of the electric and magnetic fields within the top nanodisc, we present the magnetic field diagram in Figure 3c,d, revealing a magnetic dipole resonance with an amplified magnetic field that is primarily concentrated within the VO₂ nanodisc. In other words, the VO₂ nanodiscs act as Mie resonators, causing optical reflection at certain wavelengths through the excitation of magnetic dipole resonance, thereby modulating the reflection of the incident light in conjunction with Fabry–Perot resonance. The bar of the two magnetic field diagrams in the two phases was set to the same range; thus, it is evident that the VO₂ in the monoclinic phase has a stronger Mie resonance than that in the rutile phase, as demonstrated by the relative value of the amplified magnetic field.

We also analyzed the distribution of the horizontal electric field at the resonant wavelength before and after the phase transition, as illustrated in Figure 3e,f. It was observed that the electric field exhibits a slight concentration at the interface between Ag and SiO₂, which can be interpreted as a localized surface plasmon (LSP) associated with the silver nanodiscs [30]. Within the same range of values, the electric field intensity was found to be higher for the rutile phase than for the monoclinic phase, which is in accordance with the properties of VO₂.

3.3. The Influence of Parameters on Structural Color

As mentioned earlier, the thickness of the bottom VO₂ layer is the main factor affecting the reflectance spectrum of MPMP, and its effect and mechanism have been discussed. In addition, other structural parameters related to VO₂ also have a certain influence on the performance of MPMP, such as the radius (r) and height (h₁) of the top nanodisc of MPMP. The following will elaborate on the effects of these two structural parameters on the overall reflectance performance.

Keeping the radius of the top VO₂ nanodiscs constant (r = 40 nm), as the thickness (h₁) of the nanodiscs increases we observe a gradual decrease in the overall refractive index and a slight redshift in the peaks and valleys of the reflectance curve. As shown in Figure 4a, except for a slight change in reflectance spectra when the disk thickness increases from 0 nm to 20 nm, there is little change in the position of the peaks and valleys of the reflectance spectrum as the thickness further increases, only a decrease in overall intensity. This is mainly because the absorption loss of the top VO₂ nanodiscs also increases with their thickness.

Because the structural color of the MPMP structure mainly depends on the position of the valleys, the adjustment of the nanodiscs has a very small effect on the position of the valleys, resulting in only slight color changes. However, due to the increase in nanodisc thickness (h₁), the overall reflectance decreases, leading to a slight decrease in the lightness and saturation of the color. Figure 4b shows the parameters of the structural color produced by MPMP before and after the phase transition, with hue, lightness, and saturation being normalized values obtained by calculation. It can be seen that, as the thickness of the nanodiscs increases, there is a slight shift in hue towards different colors and a slight decrease in lightness for both structures, and that the saturation of the monoclinic phase structure decreases slightly, while that of the rutile phase structure decreases more significantly. Therefore, the thickness of the nanodiscs can be used as a tool to fine-tune the lightness and saturation of the structural color.

As the radius of the nanodisc increases, the peak and valley wavelengths of the reflection spectrum demonstrate a redshift before and after the phase transition. When the VO₂ thickness at the bottom is lower (r = 60, 70 nm), as shown in Figure 5a,b, the peak value initially decreases and then increases with increasing radius. However, as the bottom VO₂ thickness gradually increases, the trend of the peak value shifts to decreasing with increasing radius, as shown in Figure 5c,d. For structures with the same VO₂ thickness and phase state, the reflection spectra approximately intersect at a specific point. The reflectance at the wavelength corresponding to this point shows minimal variation with the radius of the nanodisc, indicating that it is independent of the structural parameters of the nanodisc. The position of this intersection point is influenced by the thickness of the bottom VO₂ layer, which acts as the Fabry–Perot resonance cavity. This suggests that, within a reasonable margin of error, its value equals the wavelength of the Fabry–Perot resonance. Figure 5a–d reveals that, as the VO₂ thickness increases, the fixed point moves towards longer wavelengths, resulting in a redshift phenomenon. This observation aligns with the conclusion regarding the resonance frequency of the Fabry–Perot resonance [31,32].

Based on the magnetic field distribution along the structure, it can be inferred that the top VO₂ nanodisc in the MPMP design acts as a Mie resonator, contributing to the structural color along with the Fabry–Perot resonance at the bottom. Additionally, due to the high extinction coefficient of VO₂, the nanodisc also plays a role in absorbing the incident light. These two effects together enable the top VO₂ nanodisc to finely tune the overall structural color. Considering the comprehensive impact of geometric parameters on MPMP, it becomes apparent that the modulation of VO₂ thickness has a more significant influence on its performance compared with the modulation of the top disk. This observation signifies the more pronounced role of Fabry–Perot resonance in the collective action of the Fabry–Perot and the Mie resonances. Furthermore, Figure 2c clearly demonstrates periodicity in the reflection curve, which aligns with the characteristic features of Fabry–Perot resonance. Hence, we can conclude that the coloration mechanism of MPMP encompasses a combination of Fabry–Perot resonance and Mie resonance, with Fabry–Perot resonance assuming a dominant role.

3.4. Practical Applications

The generation of dynamic structural colors is currently a research hotspot, as it can achieve a wide range of color patterns and can be intelligently controlled. As mentioned earlier, the color mode of MPMP can be switched by changing the heating temperature. As shown in Figure 6a,b, we demonstrate the color effects by only adjusting the VO₂ nanodiscs and the thickness of the bottom VO₂ layer. The depicted color distribution can serve as a valuable reference for practical applications in manufacturing. Each color block corresponds to the color converted from the sample data, and it can be observed that significant differences in color before and after the phase transition can be achieved within a certain size range, thereby achieving temperature-controlled dynamic structural colors. Meanwhile, we observed that, for a fixed radius, as the thickness increases, both MPMPs at two different temperatures exhibit a distinct periodicity. This finding aligns with our earlier observation that Fabry–Perot cavity resonance plays a dominant role in the phenomenon. In Figure 6c, the sample data of the color palette are marked on the CIE 1931 chromaticity diagram, and it can be seen that a large color coverage area can be achieved by controlling only VO₂, providing feasibility for practical applications.

4. Conclusions

In summary, our proposed dynamic structural color based on phase-change materials and an ultra-thin asymmetric Fabry–Perot cavity combined with a phase-change material metasurface demonstrates promising potential for a range of applications. By optimizing the VO₂-related parameters, we have shown that the thickness, radius, and height of the VO₂ layer and VO₂ nanodisc can regulate the hue, saturation, and brightness of the structural color. The combined effect of systematic Fabry–Perot resonance and Mie resonance allows for the generation of vivid and high-contrast structural colors. Furthermore, the phase-change characteristics of VO₂ enable the color of the system to be switched before and after the phase transition, enabling a wider range of applications, such as decoration, anti-counterfeiting, biosensing/chemical sensing, and temperature sensing. Overall, this study provides valuable insights into the development of dynamic structural color and its potential for practical applications.