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Color camouflage, solar absorption, and infrared camouflage based on phase-change material in the visible-infrared band

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Abstract

In this paper, we design a sandwich multilayer film structure based on phase-change material Ge2Sb2Te5 (GST). In the visible band, based on the amorphous and crystalline state of GST, visible light absorption and color camouflage can be achieved. The transition between the amorphous and crystalline state of GST by temperature modulation can achieve dynamic color tuning without affecting the absorption. In the infrared band, the structure can realize the infrared camouflage function in the amorphous and crystalline states, which means that it has a higher reflection function in the infrared band. Therefore, the multilayer film based on the phase-change material GST has a simple structure and mature preparation process, which can be effectively compatible with the visible-infrared band to realize the multi-functions of color camouflage, visible light absorption and infrared camouflage.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

The problem of energy crisis has gradually become prominent, and new energy sources have become a hot spot for researches. The solar energy, as a representative of new resource, can effectively alleviate the energy problem. Therefore, how to effectively use solar energy has become the focus of current research. At present, solar energy research includes solar cells [14], photocatalytic [58], photothermal generators [9,10]and so on. Solar absorbers are key devices for solar thermal conversion. The solar absorber absorbs the light of the effective working wavelength and converts the light energy into heat energy, electric energy or other forms of energy, which directly affects the efficiency of the light-to-heat conversion system and the thermal photovoltaic system. At present, the solar absorber still needs further research, mainly because the absorber has many problems such as narrow absorption bandwidth, low absorption rate, and poor spectral selectivity. To solve the above problems, designing high-efficiency solar absorbers is the research focus of solar energy utilization [1115]. However, it is relatively limited to only study solar energy absorption for visible light. Therefore, adding visible light camouflage can broaden the application of visible light absorbers.

Among optical camouflage, visible light camouflage occupies a pivotal position [16,17]. In the visible band, the anti-camouflage detection capability of the target detection system directly depends on the discrepancy of three visual characteristics between the detected target and the background environment: brightness, chromaticity and relative motion. In order to achieve the purpose of reducing the above-mentioned discrepancy, which means reducing the probability of detection by relevant detectors. The ways to achieve visible light camouflage can be divided into the following four aspects: (1) controlling the visible light signal of the equipment shape and special components, (2) controlling the relative motion characteristics of the target, (3) adjusting the light scattering and propagation path characteristics of the equipment surface, (4) regulate the brightness [18] and chromaticity display [19] characteristics of the equipment surface. Since the first two paths will inevitably change the shape and structure of the equipment, it is obvious that they cannot be the optimal design solution for visible light camouflage. Therefore, the current research is mainly focused on the latter two points. In particular, plasma color has been extensively studied in recent years due to the development of computational simulation and manufacturing process technology. Plasma is produced by the resonance of free electrons between a metal and a dielectric. Plasma resonance can produce rich color variations. Currently, color display is achieved by various plasma microstructures, including nanopore array [20], metal thin film [21], metal-insulator-metal [22], stacked dielectric structure [23] and grating [24]. The color and spectrum displayed by plasma are inextricably linked to the structure, such as the period and size of the MIM structure and the thickness of the metal film. In other words, once the structure is fabricated, the color displayed and the function achieved are already determined. Therefore, it is essential to achieve dynamic and flexible tunable color changes. Phase-change materials (PCM) are capable of switching between different states under thermal, electrical or laser stimulation and thus have great potential for dynamic displays [25]. During the phase transition, physical properties such as structural resistance, refractive index, and dielectric constant change. It has remarkable characteristics such as good switching characteristics, flexible switching speed, and low energy consumption [25,26]. VO2, as a typical representative of phase-change materials, has been widely studied. However, the properties can exist stably only in a specific temperature range, which also makes its application limited. In contrast, Ge2Sb2Te5 (GST) is very stable in both the amorphous and crystalline state before and after the phase transition. The optical property can be tuned by the phase transition, and it is easy to be compounded with other materials to form micro-nano structures. Currently, nano-grating including GST layer has been proposed [27].In hypersurface research, GST film can be intercalated with ITO, and color change can be achieved by modulating the thickness of the ITO layer [28].

The application of military target detection systems and precision guidance systems puts military target survival to a great trial and can be extremely destructive to military targets. One of the important wavelengths for military application is the infrared band. Infrared camouflage is the use of camouflage techniques to reduce the infrared radiant energy of a target so that the radiant property of the target and the background are consistent and avoid detection by infrared detector. Infrared camouflage is achieved by reducing the surface absorption. Current researches have achieved infrared camouflage function by microcavity resonance effect [29], surface plasmon polarization [30], surface phonon polarization [31], F-P cavity resonance [32] and photonic forbidden band effect [33]. Typical spectral control microstructures are photonic crystal, grating and slot hole structures, among which photonic crystal and grating structure have excellent spectral property control effect. With the development of modern detection technology, a single camouflage is no longer sufficient to protect the target, and multi-band compatible camouflage technology has become a research hotspot in the military field. The current multi-band camouflage compatible technology has involved visible light, infrared light and microwave. There is also research on compatible laser camouflage. Currently, the stacking of structures that achieve different functions is able to achieve multi-band camouflage compatibility. Among them, Taehwan Kim et al. achieved infrared-microwave band camouflage compatibility by stacking structures [34]. While achieving infrared camouflage, broadband absorption in the GHz band is achieved. Based on this, Huanzheng Zhu et al. designed a structure which can achieve visible, infrared, microwave and laser compatible camouflage by algorithm, and greatly enabled multifunctional applications of the devices [35]. The color changes implemented in this article are not tunable. Once the structure is fixed, the color is definitely immutable. Meanwhile, M. Said Ergoktas et al. used graphene material as an intercalation material to achieve camouflage in the visible-microwave band by controlling the concentration of inserted ions [36]. However, there is a shortcoming that the spectral characteristics of a single band cannot be regulated by controlling the ion concentration. Currently, there is a lack of research to achieve dynamic and flexible tunability in the visible band as the multi-band compatible camouflage is achieved. Based on the above two points, we consider realizing the broadband absorption of visible light while being compatible with dynamic color camouflage and infrared camouflage applications.

In this paper, a SiO2/GST/SiO2/Al sandwich multilayer film structure is proposed based on the phase-change material GST. By controlling the temperature, the GST can be made to switch between amorphous and crystalline state, which can make the multilayer film structure realize different functions. In visible light, the multilayer film structure has good absorption performance for sunlight, and switching the GST state will not change the absorption performance of the overall multilayer film structure. Changing the GST state causes a peak wavelength shift, and this brings about the color change. Switching between the amorphous and crystalline state of GST enables a shift from cool to warm tone. Regardless of whether the structure is under the amorphous state or a crystalline state, the metal substrate can effectively reflect infrared light and realize the infrared camouflage function in the infrared band. Therefore, the designed structure is effectively compatible with the visible-infrared band to achieve solar absorption, color camouflage and infrared camouflage function, and has good practical value.

2. Material and structure

Figure 1(a) and (b) represent the three-dimensional and two-dimensional figure of the structure, respectively. The multilayer film structure is sandwich structure with SiO2, GST, and SiO2 from bottom to top, and its structure parameters are t3 = 250nm, t2 = 10nm, and t1 = 40nm, respectively. The transmittance is 0 because the thickness of the substrate is thick enough that the evanescent wave cannot pass through. In the simulation, We use the time domain finite difference method to simulate the structure. The x-axis and y-axis are set to periodic boundary condition, the z-axis is set to perfect matching boundary condition, and the plane light source is set to incident vertically on the surface. The substrate and the SiO2 film are obtained by magnetron sputtering deposition, and the GST film can be obtained by magnetron sputtering three-target co-sputtering. The GST obtained by magnetron sputtering is the amorphous state. After annealing the GST obtained by magnetron sputtering above 160°C (433.15 K), the amorphous GST (aGST) will change into the crystalline GST (cGST), and the crystalline GST can return to the amorphous state after rapid annealing at 640°C (913.15 K). Since SiO2 has a high melting and boiling point, the GST annealing process does not affect it [37].

 figure: Fig. 1.

Fig. 1. 3D figure (a) and 2D figure (b) of multilayer film structure.

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3. Results and discussion

Figure 2(a) indicates the transmittance in the infrared band and the position of the atmospheric window. In the atmospheric window band (3–5 µm and 8–14 µm), the energy is radiated directly to the outside due to the high transmittance in the atmosphere, on which the principle of infrared detection is based. According to Kirchhoff's law of thermal equilibrium, the radiation is equal to the absorption in thermal equilibrium. In order to achieve infrared camouflage, the structure must be made to have a high reflectivity effect (low emissivity) in the atmospheric window so as to avoid be detected. Figure 2(b) shows the refractive index parameters of aGST and cGST in the visible band, and Fig. 2(c) shows the dielectric constants of aGST and cGST in the infrared band. In the visible band, we observe that the refractive index parameters of aGST and cGST increase with wavelength increasing, the extinction coefficient of aGST decreases with wavelength increasing, and the extinction coefficient of cGST increases gradually with wavelength increasing. In the infrared band, aGST has no electromagnetic losses due to the imaginary part of the dielectric constant is nearly zero, and cGST has some electromagnetic losses due to the imaginary part of the dielectric constant is not zero. In this paper, simulation is carried out based on this aGST and cGST material data [37,38], the material parameters used for SiO2 and Al are derived from Palik [39].

 figure: Fig. 2.

Fig. 2. (a) Atmospheric transmittance in the infrared band and the position of the atmospheric window. (b) Refractive index parameters of aGST and cGST in the visible band. (c) Dielectric constants of aGST and cGST in the infrared band.

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The substrate Al metal acts as a metal mirror to reflect light efficiently and therefore the absorption of the structure is A = 1 - R. Figure 3(a) represents the absorption and reflection spectra of aGST and cGST in visible light, respectively. We observe that the overall absorption of the multilayer film structure under the aGST state is slightly higher than that under the cGST state. The average absorption of the multilayer film structure is calculated to be 70.1% under the aGST state and 65.1% under the cGST state. This indicates that the structure is able to absorb effectively the energy of visible light. Meanwhile, we observe that the peak absorption of the structure is 455 nm under the cGST state and 630 nm under the aGST state. Therefore, changing the GST state can achieve the shift of peak wavelength, which is beneficial for our subsequent researches on color modulation.

 figure: Fig. 3.

Fig. 3. (a) Absorption and reflection spectra of aGST and cGST in the visible band. (b) Absorption and reflection spectra of aGST and cGST in the infrared band.

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Figure 3(b) represents the absorption and reflection spectra of aGST and cGST in the infrared band, respectively. We observe that the multilayer film structure under both aGST and cGST state show high reflection phenomenon. According to Kirchhoff's law of thermal equilibrium, the emissivity is equal to the absorption. In order to meet the requirement of infrared camouflage to achieve high reflection in the infrared band. We observe that under the aGST state, the multilayer film structure achieves high reflection in the infrared band. By calculation, we obtain 97.23% average reflection of the multilayer film structure in 3–14 µm. A minimum value of reflection exists in 8–14 µm, but its minimum value stays above 90%. Similarly, under the cGST state, the multilayer film structure achieves high reflection with 96.41% average reflection of the multilayer film structure, which is basically the same as that under the aGST state. At the same time, we observe that the lowest value of reflection under the cGST state is around 3 µm. However, its lowest reflection value still remains above 80%, which is also able to achieve a good reflection effect and is in accordance with the requirement of infrared camouflage. By changing the GST state, the structure absorption and peak position can be modulated in the visible light. In the infrared band, effective infrared camouflage can be achieved, thus effectively realizing the dynamic tunable function.

In order to achieve a better infrared camouflage function, the temperature should not be too high according to the Stirpan-Boltzmann law. Therefore, the multilayer film structure will inevitably absorb visible energy leading to an increase in the temperature, but the infrared camouflage function of GST under conventional conditions [40] is basically not affected. Moreover, the energy absorbed during the transition from aGST to cGST is required, so the energy absorbed in visible light can be used for the energy required for the transition from aGST to cGST.

In order to further investigate the absorption principle of the structure, the electric field distribution of the structure is investigated. When light is incident from a low-refractive index material to a high-refractive index material, the reflected light will have a half-wave loss, resulting in thin-film interference. It is observed from Fig. 4(a) and (b) that visible light penetrates the top SiO2 and GST and enters the bottom SiO2. Since the refractive index of SiO2 is smaller than that of Al, the thin-film interference condition is satisfied. Therefore, visible light achieves multiple reflections within the bottom SiO2 to enhance absorption. When debugging the structural parameters, we also found that changing the thickness of the underlying SiO2 has a great influence on the absorption spectrum of visible light. Figure 4(c) and (d) represent the electric field distribution of aGST and cGST in the infrared band, respectively. We observe that high reflection is achieved under both aGST and cGST state. The little energy absorbed in the infrared band is caused by the structural material itself. Therefore, the metal mirror is able to reflect infrared light efficiently, so that the structure remains high reflection.

 figure: Fig. 4.

Fig. 4. Electric field distribution of aGST (a) and cGST (b) in the visible band, electric field distribution of aGST (c) and cGST (d) in the infrared band.

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In the visible band, the wavelength shift is able to be achieved by changing the state of GST. Figure 5(a) represents the solar absorption spectra under standard AM1.5, aGST and cGST. By comparing the spectra under the three cases, the aGST and cGST state are able to absorb the most of sunlight. By comparing with the absorption spectra Fig. 3, the absorption under the aGST state is higher than that under cGST, so the absorbed solar energy under the aGST state is slightly higher than that under cGST. To characterize the infrared camouflage performance of the multilayer film structure, Fig. 5(b) represents the radiation intensity of the blackbody and multilayer film structure spectra at 300 K. The peak wavelength of blackbody radiation is obtained at 9.65 µm by Planck's blackbody radiation Eq. (1) [38], where h is the Planck constant, c0 is the speed of light in a vacuum and k is Boltzmann constant.

$${E_\textrm{b}}(\lambda ,T) = \frac{{2\pi h{c_0}^2{\lambda ^{ - 5}}}}{{{e^{\frac{{h{c_0}}}{{k\lambda T}}}} - 1}}$$
$${E_e}(\lambda ,T) = A(\lambda ) \times {E_b}(\lambda ,T)$$

 figure: Fig. 5.

Fig. 5. (a) Solar absorption spectra in the visible band. (b) The spectral radiation intensity of blackbody and emitter (aGST and cGST) at 300 K. (c) Coordinates on the chromaticity diagram under aGST and cGST state. (d) Different colors under the aGST and cGST state.

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The peak wavelength of blackbody radiation is 9.65 µm at 300K is also corroborated by Wien's displacement law Eq. (3), where b is the Wien constant. The spectral radiation intensity of the multilayer film structure under the aGST and cGST state is calculated by Eq. (2) [38], where A(λ) is absorption rate. We observe that the structure exhibits low radiation throughout the infrared band. In Table 1, we divide the infrared band into three bands (3–5 µm, 5–8 µm, 8–14 µm) and calculate the emissivity (α) by Eq. (4) [35], respectively. The λ1 and λ2 are the lower and upper limit of the band, respectively.

$${\lambda _{\max }} = \frac{b}{T}$$
$$\alpha = \frac{{\int\limits_{{\lambda _1}}^{{\lambda _2}} {A(\lambda ) \times {E_b}(\lambda ,T)d\lambda } }}{{\int\limits_{{\lambda _1}}^{{\lambda _2}} {{E_b}(\lambda ,T)d\lambda } }}$$

Tables Icon

Table 1. Emissivity of Different Infrared Bands

Figure 5(c) represents the chromaticity coordinates of aGST and cGST on the CIE chromaticity diagram. The chromaticity diagram coordinate of aGST is (0.2379, 0.2241) and that of cGST is (0.4466, 0.3827). Through Fig. 5(d), we observe that switching between the crystalline and amorphous state of GST can cause the multilayer film structure to present a color shift from blue to red, which is a shift from cool to warm tone. In this way, automatic color switching can be achieved. The parametric scanning method is adopted in this study. In order to consider broadband absorption and color camouflage, the two SiO2 layers with the highest structural absorption are finally chosen as the structural parameters to achieve a significant color camouflage. If the goal is to achieve a specific color, then the parametric scanning approach is no longer applicable and the algorithm needs to be considered to determine the thickness parameters of the two SiO2 layers.

The transition from aGST to cGST is an intermediate process, so to further illustrate the property of GST. The crystalline fraction of GST is controlled by controlling the annealing time of the external heat source during the transition from amorphous to crystalline state. We investigate the intermediate state of GST (GST with different crystalline fractions). The dielectric constants ɛeff (λ) of GST in different crystalline states can be calculated by Eq. (5) [4143], where ɛc (λ) and ɛa (λ) are the permittivities of GST in the crystalline and amorphous, respectively.

$$\frac{{{\varepsilon _{eff}}(\lambda ) - 1}}{{{\varepsilon _{eff}}(\lambda ) + 2}} = m \times \frac{{{\varepsilon _c}(\lambda ) - 1}}{{{\varepsilon _c}(\lambda ) + 2}} + (1 - m) \times \frac{{{\varepsilon _a}(\lambda ) - 1}}{{{\varepsilon _a}(\lambda ) + 2}}$$

Through Fig. 6(a), we observe that the peak wavelength appears blueshifted with crystallization fraction increasing. Figure 6(b) shows the coordinate positions on the chromaticity diagram for different crystallization fractions. We can observe that as the crystallization fraction of GST increases, the coordinates of GST on the chromaticity diagram show a linear change. Through Fig. 6(c), we clearly observe the colors displayed at different crystallization fractions. This makes the color artifacts more intuitive.

 figure: Fig. 6.

Fig. 6. (a) Absorption spectra of multilayer film structure of GST crystallization fraction from 0%−100%. (b) Coordinates of GST crystallization fraction from 0%−100% on the chromaticity diagram. (c) Different colors of GST crystallization fraction from 0%−100%.

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In order to further investigate the applicability of the multilayer film structure, we investigate the incident angle of the multilayer film structure. Figure 7(a) and (b) show the variation of reflection with incident angle for aGST and cGST in visible light, respectively. We find that the reflection of the multilayer film structure decreases with the incident angle increasing under both aGST and cGST state. Since the transmittance of the structure is zero, the reflection decreases, and then the absorption increases. Figure 7(c) and (d) represent the variation of reflection with incident angle for aGST and cGST in the infrared band, respectively. We observe that the incident angle has almost the same effect on aGST and cGST. In the range of small angle variation, aGST and cGST are unaffected. As the incident angle increases, a reflection trough appears near 8 µm at the incident angle of 40° with 75% reflection. Similarly, we observe that the reflection trough of 8–14 µm is not affected and the reflection remains above 90%. Therefore, multilayer film structure is suitable for small angle infrared camouflage. The opposite concept to infrared camouflage is infrared detection (i.e., the ability to effectively absorb infrared light). Therefore, we can consider the possibility of transfer from infrared camouflage to infrared detection with the significant change of incident angle.

 figure: Fig. 7.

Fig. 7. Reflection spectra of the incident angle of aGST (a) and cGST (b) in the visible band and the incident angle of aGST (c) and cGST (d) in the infrared band.

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It is known from Fig. 7(a) and (b) that the absorption gradually increases with the increase of the incident angle. As shown in Fig. 8(a), we calculate the average absorption with angular variations from 0°−40° as 70.10%, 70.15%, 72.90%, 76.90%, 81.14%, and 84.99%, respectively. Meanwhile, we observe that the position of the peak wavelength is essentially constant. As shown in Fig. 9(a), we calculate the average absorption with angular variations from 0°−40° as 65.10%, 65.12%, 68.31%, 72.91%, 77.87%, and 82.39%, respectively. We find that the absorption of aGST and cGST can basically remain the same when the incident angle increases.

 figure: Fig. 8.

Fig. 8. Absorption spectra for different incident angles under the aGST state (a), coordinates of different incident angles on the chromaticity diagram (b) and the presentation of different colors (c).

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 figure: Fig. 9.

Fig. 9. Absorption spectra for different incident angles under the cGST state (a), coordinates of different incident angles on the chromaticity diagram (b) and the presentation of different colors (c).

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To further illustrate the color change due to the change of incident angle, we investigate the color change. Figure 8(b) represents the coordinate positions on the chromaticity diagram corresponding to the change of the incidence angle of aGST. The coordinates of the incident angle from 0°−40° are (0.2379,0.2241), (0.2352,0.2222), (0.2278,0.2151), (0.2165,0.2046), (0.2035,0.1926), and (0.1917,0.1822), respectively. Through Fig. 8(c), we can clearly observe that the color gradually deepens as the incident angle increases. Figure 9(b) represents the coordinate positions on the chromaticity diagram corresponding to the change of the incidence angle of cGST. Under the cGST state, the coordinates of the incident angle from 0°−40° are (0.4466,0.3827), (0.4417,0.3820), (0.4325,0.3816), (0.4173,0.3807), (0.3970,0.3790), and (0.3734,0.3762), respectively. Through Fig. 9(c), we can clearly observe that the color gradually diminishes with the increase of the incident angle. Therefore, the multilayer film structure is capable of dynamic color tunability.

Figure 10 shows the effect of polarization angle on the multilayer film structure. Since, the designed structure is a multilayer film structure with a highly symmetrical structure, the multilayer film structure is theoretically insensitive to polarization angle. Through simulation calculation, we verify the result that the multilayer film structure is indeed insensitive to polarization. Therefore, this is beneficial to the practical application of multilayer film structure.

 figure: Fig. 10.

Fig. 10. Reflection spectra of aGST (a) and cGST (b) polarization angle in the visible band, and aGST (c) and cGST (d) polarization angle in the infrared band.

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4. Conclusion

In this paper, we propose a simple multilayer film sandwich structure based on the phase-change material GST, which is compatible with the visible-infrared band to achieve various functions such as solar energy absorption, color camouflage, and infrared camouflage. Realizing the function of solar energy absorption, both aGST and cGST realize better absorption and can effectively absorb the energy of sunlight. Realizing the color camouflage function, the shift from cool to warm tone can be dynamically tunable by shifting from aGST to cGST. Due to the effect of the metal mirror, the structure can achieve high reflection of infrared light under both aGST and cGST. Therefore, the designed multilayer film structure can effectively realize various functions such as solar absorption, color camouflage and infrared camouflage, and has practical application prospects.

Funding

the Postgraduate Scientific Research Innovation Project of Hunan Province (CX20210078); Program for New Century Excellent Talents in University (NCET-12-0142); Natural Science Foundation of Hunan Province (13JJ3001); the Foundation of NUDT (JC13-02-13, ZK17-03-01); China Postdoctoral Science Foundation (2018M633704); National Natural Science Foundation of China (60907003, 61805278).

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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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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Figures (10)

Fig. 1.
Fig. 1. 3D figure (a) and 2D figure (b) of multilayer film structure.
Fig. 2.
Fig. 2. (a) Atmospheric transmittance in the infrared band and the position of the atmospheric window. (b) Refractive index parameters of aGST and cGST in the visible band. (c) Dielectric constants of aGST and cGST in the infrared band.
Fig. 3.
Fig. 3. (a) Absorption and reflection spectra of aGST and cGST in the visible band. (b) Absorption and reflection spectra of aGST and cGST in the infrared band.
Fig. 4.
Fig. 4. Electric field distribution of aGST (a) and cGST (b) in the visible band, electric field distribution of aGST (c) and cGST (d) in the infrared band.
Fig. 5.
Fig. 5. (a) Solar absorption spectra in the visible band. (b) The spectral radiation intensity of blackbody and emitter (aGST and cGST) at 300 K. (c) Coordinates on the chromaticity diagram under aGST and cGST state. (d) Different colors under the aGST and cGST state.
Fig. 6.
Fig. 6. (a) Absorption spectra of multilayer film structure of GST crystallization fraction from 0%−100%. (b) Coordinates of GST crystallization fraction from 0%−100% on the chromaticity diagram. (c) Different colors of GST crystallization fraction from 0%−100%.
Fig. 7.
Fig. 7. Reflection spectra of the incident angle of aGST (a) and cGST (b) in the visible band and the incident angle of aGST (c) and cGST (d) in the infrared band.
Fig. 8.
Fig. 8. Absorption spectra for different incident angles under the aGST state (a), coordinates of different incident angles on the chromaticity diagram (b) and the presentation of different colors (c).
Fig. 9.
Fig. 9. Absorption spectra for different incident angles under the cGST state (a), coordinates of different incident angles on the chromaticity diagram (b) and the presentation of different colors (c).
Fig. 10.
Fig. 10. Reflection spectra of aGST (a) and cGST (b) polarization angle in the visible band, and aGST (c) and cGST (d) polarization angle in the infrared band.

Tables (1)

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Table 1. Emissivity of Different Infrared Bands

Equations (5)

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E b ( λ , T ) = 2 π h c 0 2 λ 5 e h c 0 k λ T 1
E e ( λ , T ) = A ( λ ) × E b ( λ , T )
λ max = b T
α = λ 1 λ 2 A ( λ ) × E b ( λ , T ) d λ λ 1 λ 2 E b ( λ , T ) d λ
ε e f f ( λ ) 1 ε e f f ( λ ) + 2 = m × ε c ( λ ) 1 ε c ( λ ) + 2 + ( 1 m ) × ε a ( λ ) 1 ε a ( λ ) + 2
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