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Abstract
Nowadays, the requirement for achieving dynamic radiative cooling is more and more intense, so a cooling system is proposed and developed to meet the demand in this paper. This cooling system is composed of a filter and a periodic trapezoidal VO2-Ge multilayer absorber (VGMA). The filter on the top enables the VGMA to reflect most of the solar irradiation at daytime and the absorptance or emittance of the VGMA is very different in the spectrum band of 8-13 μm for insulating and metallic VO2 due to the phase transition characteristic of VO2. With this cooling system, close-to-zero absorptance in the range of 0.3-2.5 μm and high (low) absorptance from 8 to 13 μm are achieved for metallic (insulating) VO2. Based on changing the temperature and absorptivity or emissivity simultaneously, radiative heat can be transferred dynamically to the outer space. When VO2 is in the insulating phase, the absorption mechanism of the absorber is magnetic resonance and surface plasmon polariton resonance, and broadband high absorptivity is achieved by exciting slowlight waveguide mode at broadband wavelengths when VO2 is in metallic phase. The spectral absorptance characteristics of the absorber in the two phase states are investigated as a function of the layer number and the incident angle of the electromagnetic waves. The results show that the absorber designed is insensitive to the incident angle. Moreover, the net cooling power of the VGMA of metallic VO2 is instantly 4 times more than that of insulating VO2 once the phase change temperature is reached. This work will be beneficial to the advancement of dynamic radiative cooling.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As one of the most common ways of energy transport, radiative heat transfer can occur at finite temperature (at any temperature above 0 K) [1]. The cooling of objects on the Earth, such as buildings and engines, requires a great deal of energy every year. There are transparent windows between 3-5 and 8-13 μm in the Earth’s atmosphere for electromagnetic waves, and through these atmospheric windows, the heat of objects on the earth can be radiated into outer space to cool themselves. Passive radiative cooling offers the potential for realizing effective cooling without external energy consumption, only by the object itself, which is a kind of environmentally friendly cooling way. To date, nighttime and daytime radiative cooling have been extensively studied [2–6]. From the nighttime radiative cooling viewpoint, radiators coated with silicon monoxide (SiO), silicon nitride (Si3N4), and other films [7–9] had been studied a few decades ago. With recent progress in metamaterials, various daytime cooling radiators have been proposed and developed with high reflectivity for solar energy and strong emissivity in the atmospheric window. For instance, Kou et al. [10] showed that a polymer-coated fused silica mirror can be used to achieve daytime radiative cooling. Besides covering polymer, coated-films made of ZnS or ZnSe [11], or silver (Ag) / germanium (Ge) [12] have been used to transmit thermal radiation. Daytime cooling and energy saving can be achieved by yttria-stabilized zirconia or silica micro-grating coating and so on [6,13–15]. Tapered emitter or absorber became a good candidate in previous work of metamaterials design in radiative cooling [16,17]. For example, Hossain et al. [16] demonstrated a multilayer cone thermal emitter within the transparent window, its remarkable ability of radiative cooling led the temperature cool down 12°C below the ambient one. A pyramidal structure as a near-to-one emitter was also proposed for daytime radiative cooling [17]. Recently, a non-tapered metamaterial emitter was proposed and investigated by Liu et al. [18], which displayed a highly selective emission and its average emissivity reached 0.8 at wavelengths of 8 to 13 μm. Compared with film and bulk materials, microstructures made of nanoparticles were also employed to radiative cooling [19,20]. In a polymeric matrix, Zhai et al. [21] embedded the resonant polar dielectric microspheres as a perfect daytime radiator, because this nanoparticle structure was fully transparent to the solar spectrum while having an infrared emissivity greater than 0.93 across the atmospheric window. Structures of various radiators for radiative cooling were reviewed by Zhao et al. [22].
So far, nighttime radiative cooling technology has been quite mature while further research on the realization of radiative cooling at daytime is still needed. What’s more, most existing designed radiative cooling emitters or systems are static in the sense that the emissivity of the objects is fixed. But the temperature of external environment changes constantly in practice. For example, there is a big temperature difference between summer and winter nights, so the cooling function should be enabled in summer and disabled in winter. Obviously, static radiative cooling with fixed emissivity cannot make it happen [23]. Therefore, the peak demand for daytime dynamic cooling occurs in buildings cooling and other applications. Thus, it is of great importance to explore the possibility of dynamic radiative control. To date, active control of infrared thermal emissivity with tunable metal films and metamaterials is currently used in buildings and spacecraft cooling [24]. The vanadium dioxide (VO2) is widely used in dynamic regulation of radiative properties for its thermotropic phase transition characteristics [25]. Although the phase transition temperature of VO2 might be slightly changed due to various material composition and fabrication processes, the most common phase change temperature of pure VO2 is 68 °C [26]. When the temperature is lower than 68 °C, VO2 is in the insulating phase, and otherwise, it is in the metallic phase. Due to its obvious phase change property, VO2 has been applied for smart windows [27], infrared uncooled bolometers [28], holographic storage systems [29], optical and electrical switches [30,31], to name a few. A 77.10% tuning absorption range was achieved by VO2/tungsten (W) multilayer structure at the wavelength λ=3 μm due to the phase change of VO2 between metallic and insulating phase [32]. Taylor et al. [24] proposed a Fabry-Perot emitter made of a VO2 thin film and an opaque aluminum substrate. A generalized uniaxial transfer matrix method was adopted to calculate the radiative properties of the structure. The desired dynamic temperature-dependent emitter can be employed in building cooling and space thermal control. Based on the switch from the metallic phase to the insulating phase of VO2, researches of Van Zwol et al. [33–36] showed that VO2 plays an important role in near-field heat flux modulating and heat flow controlling numerically and experimentally. Yang et al. [37] demonstrated the near-field heat flux between two VO2 thin films as vacuum thermal switches which can turn on/off at 341 K. When the temperature was below 341 K, the near-field heat flux was enhanced due to the excitation of the surface plasmon polariton (SPP), while the near-field heat flux was significantly cut down at metallic phase of VO2. Kats et al. [28,38] theoretically and experimentally studied the perfect absorptance/emittance of the structure comprising an ultra-thin film VO2 on a sapphire substrate in the infrared region, which can be used as thermal emitters, modulators and bolometers. In addition, device capable of heating and cooling and radiative thermal transistor [39,40] made of VO2 were studied on account of the fact that VO2 exhibits an insulator to metal transition.
In brief, due to the thermal-induced phase change characteristics of VO2, dynamic radiative cooling can be realized by combining phase change and surface microstructure regulation. However, there is still plenty of room for improvement to reach a higher and broader absorptance compared with previous radiative cooling works based on VO2 [23,26,41]. In this work, we present a radiative cooling system, which consists of a filter [23] and a periodic trapezoidal VO2-Ge multilayer absorber (VGMA), that can achieve dynamic temperature-dependent radiative cooling at daytime. The filter at the top acts as a shelter to block the sunlight and transmits the wavelength of the atmospheric window, and the VGMA at the bottom strongly absorbs the electromagnetic waves of 8-13 μm and realizes the function of dynamic switching radiative cooling due to the phase transition of VO2. The theoretical and numerical analysis is also conducted to test its performance of dynamically regulating the heat emitted to outer space. The absorptance of this structure is obtained via finite difference time domain (FDTD) method. In addition, the underlying mechanisms involved in VGMA are attributed to slowlight waveguide mode which is illustrated by the electromagnetic distribution with metallic phase VO2. The relations between the absorptance or emittance and the number of layers, as well as the incident angle, are also investigated.
2. Physical model and results
The three-dimensional schematic diagram of the periodic trapezoidal VGMA designed is shown in Fig. 1(a). VO2 and Ge layers are overlapped alternately with a total pair of N=50 layers on the opaque Titanium (Ti) substrate. The period is the same in the x direction as it is in the y direction, which is Px=Py=800 nm, which is exactly the same as the bottom width of the trapezoid. The overall height of the trapezoid is t=1500 nm, the height of each VO2 and Ge layers are t1=20 nm and t2=10 nm, respectively, and the top width of the trapezoid is l=360 nm. A transverse magnetic (TM) wave of wavelength λ is incident on the slit arrays and gratings at an incidence angle θ, transverse electric (TE) waves have the same results, which will not be repeated here.
Fig. 1. (a) Schematic diagram of VGMA with Px=Py=800 nm, l=360 nm, t=1500 nm. (b) Absorptivity of the structure in different VO2 phase states in the wavelength of (b) 0.3-2.5 and (c) 3-15 μm, the blue solid line represents the absorptivity when VO2 is in metallic phase, and the red dashed curve represents that of the insulating phase of VO2.
In this work, the spectral reflectivity Rλ of the absorber is solved by the FDTD method and a commercial package (Lumerical Solutions, Inc.). Periodic and perfectly matched layer (PML) boundary conditions are set in x, y and z direction, respectively. The substrate is thick enough and the transmittance of the structure is 0. Therefore, the spectral absorptance αλ is obtained by αλ=1-Rλ and the spectral emissivity ɛλ=αλ based on Kirchhoff’s law. The complex permittivity of metallic VO2 is expressed by Drude model as [42]:
Fig. 2. The (a) real and (b) imaginary parts for the permittivity of VO2 from 0 to 30 microns, where ɛm (black dashed line) represents the metallic VO2, and ɛo (blue solid line) refers to the ordinary mode of insulating VO2 [42].
The absorptance of the structure in the spectral region of 0.3-2.5 and 3-15 μm is shown in Figs. 1(b) and 1(c), respectively, where the blue solid line represents the absorptance when VO2 is in metallic phase, and the red dashed curve refers to the absorptance of the insulating phase of VO2. Generally, the spectral distribution of AM 1.5 solar irradiation is in the short wavelength region from 0.2 to 4 μm, mostly concentrated in 0.3-2.5 μm. An ideal daytime VO2 dynamic radiative cooler should have the following characteristics: for the insulating phase of VO2, αλ=0 in the band of 0.3-2.5 and 8-13 μm, that is, the radiative cooling is turned off, while for the metallic phase of VO2, αλ should be supposed to 0 in 0.3-2.5 μm and 1 in 8-13 μm, that is, radiative cooling is turned on. However, for the structure shown in Fig. 1(a) and its absorptance in Fig. 1(b), the isolated VGMA cannot meet the requirements of radiative cooling during the day. On the other hand, its remarkable dynamic regulation in 8-13 μm is worth exploiting.
Inspired by Ref. [23], we introduce a filter composed of Ge and MgF2, which is placed on top of the VGMA to form a radiative cooling system, as shown in Fig. 3(a). The filter is almost transparent only in 8-13 μm and opaque in 0.3-2.5 μm to insulate solar energy. Thus, the solar absorptance of the system is close-to-zero. The filter here consists of 11 layers of alternating Ge and MgF2, and has two functions in the radiative cooling system, one is to block the solar irradiation from reaching the VGMA, and the other is to pass the maximum amount of infrared radiation. The thickness of each layer is presented in Table 1 [23]. This system can make up for the shortcomings of the VGMA in strongly absorbing sunlight, while retaining the dynamic control capability. The absorptance of the VGMA with the appearance of a filter on the top becomes as shown in Fig. 3(b) and Fig. 3(c) at 0.3-2.5 and 3-15 μm, respectively. In Fig. 3(b), the blue solid line and the red dashed line are the simulated absorptance of the VGMA when VO2 is in the insulating and metallic phase, respectively. Clearly, the VGMA exhibits extremely low solar absorptivity from 0.3 to 2.5 μm, note that the vertical maximum is 0.1 and the absorptance is lower than [23] in this region. It can also be observed that the VGMA has remarkably different radiative properties in the range of atmospheric window. In Fig. 3(c), when the temperature is above 68 °C, that is, after the phase transition of VO2, when it is in the metallic phase, the average absorptivity in the wavelength range of 8-13 μm is 0.8693, especially there are three close-to-unity peaks appear, namely, α=0.9859 at λ=8.423 μm, α=0.9953 at λ=9.737 μm and α=0.9623 at λ=11.790 μm. However, when the phase transition temperature of VO2 has not been reached, the red dashed line is far below the blue solid one when VO2 is in the insulating phase, and its absorptivity in the spectral of 8-13 μm is only below 0.2. Therefore, the phase transition of VO2 leads to a change on the emissivity in the wavelength range from 3 to 15 μm. The absorber can adjust the absorptivity according to the temperature dynamically. The absorptivity is low when the temperature is below the transition temperature of VO2 and when the temperature is above the transition temperature, the absorptivity is high, thereby functioning as dynamic radiative cooling.
Fig. 3. (a) The radiative cooling system, which is consisted of the VGMA on the bottom and a filter [23] on the top. The absorptance of the VGMA with the appearance of a filter on the top at (b) 0.3-2.5 and (c) 3-15 μm.
Table 1. Material composition and thicknesses for the filter [23]
3. Mechanisms and discussions
3.1 Slowlight waveguide mode analysis for metallic phase of VO2
Due to the different nature of VO2 in different phase states, the physical mechanisms of the VGMA are not the same. As shown by the blue solid curve in Fig. 3(c), when VO2 is in the metallic phase, the absorptance of the VGMA designed here is close to 1 in the wavelength range from 8 to 13 μm. Five wavelengths, including three peak wavelengths, are studied by showing the magnetic distributions in Fig. 4, which are λ=7.800 μm, λ=8.423 μm, λ=9.737 μm, λ=11.790 μm, and λ=12.720 μm. The VGMA can be regarded as a 2D trapezoidal waveguide with varying width L along the z direction, so the range of L is 360-800 nm obviously. The trapezoidal microstructure shape proposed in this work has a cross section that decreases in the z-axis, which is beneficial for electromagnetic waves of different wavelength to be absorbed at different positions of the absorber. As shown in Fig. 4, the contour indicates the magnitude of magnetic field, and the brighter the picture, the stronger locality the magnetic field is. In the first place, the magnetic field of λ=7.800 μm is concentrated on the top part of the absorber. As the wavelength redshifts at λ=8.423 μm and λ=9.737 μm, the electromagnetic wave begins accumulating at the center and bottom part of the absorber, respectively. As the wavelength continues to shift red, the positions of the magnetic field concentration also move downward. Specifically, the electromagnetic waves are absorbed corresponding to width L=530.4 nm at λ=7.800 μm and L=768 nm at λ=12.720 μm. Therefore, there is a specific matching mode between wavelength λ and width L, which can be explained by the slowlight waveguide theory [46,47].
Fig. 4. The magnetic field distributions of the VGMA at λ=7.800, 8.423, 9.737, 11.790 and 12.720 μm when VO2 is in metallic phase.
The effective medium theory (EMT) is applied to transform the VO2-Ge multilayer equivalent to a uniaxial anisotropy medium described by ${\varepsilon _ \bot }$ and ɛ|| [48]:
Fig. 5. (a) Absorptance curve of the original VGMA (blue solid) and equivalent VGMA (green dashed) without the appearance of a filter on the top; (b) Schematic diagram of air-M-air waveguide; (c) β-ωc dispersion curve for different waveguide core widths L; (d) β-vg relationship for different waveguide core widths L; (e) Relationship between L and slow-light wavelength λs; (f) Effect of metal filling ratio f change on spectral absorptance.
According to the relationship among the wavelength λ, the angular frequency ω, the group velocity vg, the propagation constant β, and the width L, the correspondence between the waveguide core width L and slowlight wavelength λs can be theoretically established, as shown in Fig. 5(e). For example, an electromagnetic wave at 7.8 μm will be absorbed at the width L = 500 nm of the absorber theoretically, and the actual width is 530.4 nm, which is consistent with the strong focus of the magnetic field in the middle of the trapezoid in Fig. 4. The theoretical calculation results are not much different from the actual ones. Based on above studies, the structure can be regarded as a set of a limited number of air-M-air waveguides with different core widths L, when L changes from 360 nm to 800 nm, it can support slowlight waveguide mode. Thus, we can adjust the absorptance curve of the absorber by gradually changing the width L of the waveguide core, and adjusting the filling ratio f of the metal layer can influence the group velocity vg, then has an impact on the spectral absorptance of the absorber. The three curves in Fig. 5(f) represent the absorptance at different f. As shown, the red dashed curve represents f = 1/3, the blue solid curve indicates f = 2/3, and the green dashed one indicates that the filling ratio of the metal is f = 3/4. When f is larger, the spectral absorptance generally increases, but when the filling ratio f reaches a certain value, the improving effect on the absorptance is not obvious.
3.2 VGMA with varying layer number and incident angle for metallic phase of VO2
Changing the layer number in Fig. 1(a) from 10 to 50, while the other dimensions are unchanged, the spectral absorptance of the VGMA is plotted in Fig. 6(a). Note that the range of each figure is between 0-1. In Fig. 6(a), each solid curve represents the spectral absorptance of the absorber at the corresponding layer number N. When the layer number N changes from 10 to 50 layers, the larger the layer number N is, the closer the absorptance of the structure is to 1 in the wavelength range of 3-15 μm.
Fig. 6. The spectral absorptance of the VGMA without a filter on the top varies with (a) the layer number N and (b) the incident angle θ when VO2 is in metallic phase.
In practical applications, the electromagnetic wave is not completely perpendicular to the surface of the absorber, but has a certain angle with the surface of the absorber, so it is of practical significance to study the influence of the incident angle of the electromagnetic wave on the absorptance performance of the absorber. The incident angle θ is used to represent the angle between the incident direction of the electromagnetic wave and the normal direction of the absorber surface. The spectral absorptance αλ of the absorber is expressed as a function of wavelength λ and incident angle θ, and a clear absorptance spectrum is obtained as shown in Fig. 6(b). As shown, the brighter the place represents the greater the absorptance αλ. Even if the incident angle is 70 degrees, the spectral absorptance of the absorber still maintains a very high value in a wide wavelength range. Therefore, it can be considered that when the VO2 is in metallic phase, the designed VGMA is insensitive to the incident angle which is useful in the applications of dynamic radiative cooling. Note that the calculated angle change contour here is the case of VGMA without a filter on the top, since the VGMA is angular insensitive, the cooling system with the top filter will also maintain high absorptance at 8-13 μm when the electromagnetic wave is incident at large angles.
3.3 Physical mechanism for insulating phase of VO2
When VO2 is in the insulating phase, there are several peak wavelengths with lower absorptance on the red dashed curve shown in Fig. 3(c), such as 3.281, 3.706, 4.576, 5.930, and 8.404 μm. We study the absorption mechanism of VGMA when VO2 is in the insulating phase by showing the electromagnetic field distribution of these peak wavelengths, which is shown in Fig. 7. The green arrows indicate the direction of the electric field vector and the rings represent the current loops. In Fig. 7, the magnetic field induced by the current loops interacts with the incident magnetic field, causing the magnetic resonance mode. In Fig. 7, the magnetic field of λ=3.281 μm is mainly localized in the upper and middle parts of the VGMA, forming two magnetic field bright spots with opposite current loops. Therefore, the dominant cause of the absorptance peak at λ=3.281 μm is magnetic resonance. However, when the wavelength shifts to λ=3.706 μm, only one current loop is formed in the middle of the VGMA with the focus of the magnetic field, corresponding to the magnetic resonance. The difference is that the excitation of SPP at λ=3.706 μm. SPP accounts for the couplings between the incident electromagnetic waves with the collective oscillation of the surface charges [48,51]. Since VO2 is in the insulating phase and the substrate is metal Ti, SPP can be excited at the interface of VO2 and Ti. The next one is at λ=4.576 μm, and the only loop is weaker compared to that of λ=3.706 μm. As the wavelength continues to redshift, the magnetic resonance effect becomes weaker while the SPP becomes stronger, until λ=5.930 μm, the SPP begins to be the dominant physical mechanism and the magnetic resonance slowly disappears completely.
Fig. 7. The electromagnetic field distributions of the VGMA at λ=3.281, 3.706, 4.576, 5.930 and 8.404 μm when VO2 is in insulating phase.
3.4 VGMA with varying layer number and further analysis for insulating phase of VO2
As with VO2 as metal, the variation of spectral absorptance is shown in Fig. 8 when the number of insulating VO2 layers N changes from 10 to 50. When N varies within a certain range, the differences among the absorptance curves are more distinct in the wavelength range of 3-5 μm, while the absorptance curves do not change much when 5 μm <λ<15 μm. Figure 6(a) and Fig. 8 indicate that the larger the layer number N, the greater the dynamic adjustment ability of the VGMA. However, when N>40, the absorptance is almost unchanged regardless of whether VO2 is in insulating or metallic phase. In addition, the five dashed lines in Fig. 8 have absorptance peaks close to 1 near λ=4.3 μm with a slight difference. The values of layer number N, λ and the absorptance α corresponding to the five dashed lines near λ=4.3 μm are listed in Table 2.
Fig. 8. The spectral absorptance of the VGMA without a filter on the top varies with the layer number N when VO2 is in insulating phase.
Table 2. The values of layer number N, λ and α in Fig. 8.
As shown in Fig. 9, this unique phenomenon can be studied by the electromagnetic field distributions of the peak wavelengths in Table 2. As the layer number N increases, the height of the trapezoid gradually increases, but other geometric parameters remain unchanged. As shown in Figs. 9(a), 9(b) and 9(c), the absorptance peak near the wavelength λ=4.3 μm is due to the effect of SPP when the layer number N is 10 and 20 respectively, the reasons are the same as those discussed above. In Fig. 9(d) and Fig. 9(e), in addition to SPP at the interface between the bottom VO2 layer and the substrate Ti, the magnetic field is also focused inside the trapezoid, and the current loop is generated accordingly, which is caused by the excitation of the magnetic resonance mode. Therefore, the reason why the absorber generates absorptance peaks near λ=4.3 μm when the layer number N is 40 and 50 is the effect of magnetic resonance and SPP, but the role of SPP is dominant. Due to the existence of the magnetic resonance mode, the localized position of the magnetic field is slightly different but roughly the same, and as the layer number N increases, the influence of the magnetic resonance mode is gradually enhanced.
Fig. 9. The electromagnetic field distributions near λ=4.3 μm as the layer number N changed: (a) N=10, λ=4.327 μm; (b) N=20, λ=4.258 μm; (c) N=30, λ=4.268 μm; (d) N=40, λ=4.283 μm; (e) N=50, λ=4.268 μm.
4. Cooling performance of the VGMA
For the VGMA designed in this study, which is exposed to the atmosphere, the net cooling power Pnet is a combination of the radiation power from the surface Prad, the absorbed atmospheric radiation power Patm and solar irradiation Psolar on the surface and the non-radiative heat transfer Pnon-radiative. Considering the temperature of a VGMA of unit area is Ts, and the ambient temperature is Tamb, the net cooling power Pnet can be expressed as [52]
Here,The net cooling power Pnet of the VGMA as function of the surface temperature Ts is shown in Fig. 10, where Pnet is represented by the blue line before the phase change, and the red one is the net cooling power after the phase change. The ambient temperature is Tamb is supposed to be 300 K in this study. In the absence of the non-radiative heat transfer as shown in Fig. 10(a), which means Pnon-radiative=0 in Eq. (8), when the temperature Ts is below 68°C, corresponding to the “off” mode of radiative cooling, the net cooling power Pnet is directly proportional to the temperature Ts, in particular, as Ts=67°C, Pnet=27.89 W/m2. If the temperature Ts continues to rise, and once the phase change temperature is exceeded, corresponding to the “on” mode, the net cooling power will increase dramatically, as Ts=69°C, Pnet=127.80 W/m2. Because of the phase change of VO2, the net cooling power of the VGMA of metallic VO2 is 4 times more than that of insulating VO2. When the non-radiative heat transfer is taken into account, as shown in Fig. 10(b), the difference of Pnet before and after the VO2 phase transition is still more than 100 W/m2, as Ts=67°C, Pnet=92.1 W/m2 and as Ts=69°C, Pnet=196.1 W/m2. The VGMA designed in this study has a remarkable dynamic radiative cooling effect.
Fig. 10. The net cooling power of the proposed VGMA: (a) without the non-radiative heat transfer; (b) with the non-radiative heat transfer.
5. Conclusion
Passive static radiative cooling with infrared selective absorbers or radiators was the main topic in previous studies. For the sake of realizing dynamic radiative cooling at daytime, a cooling system, which consists of a filter and the periodic trapezoidal multilayer absorber made of 50-pair VO2-Ge multilayer, has been designed and studied in this paper. The spectral properties indicate close-to-zero absorptance in the wavelength of 0.3-2.5 μm and high (low) absorptance in the atmospheric window 8-13 μm when VO2 is in the metallic (insulating) state. Different absorptance mechanisms and further analysis of different VO2 phase states have been investigated. Several main conclusions are presented in the following:
- (1) It is revealed that the ultra-high absorption or emission of the VGMA is due to the slowlight waveguide mode at different wavelengths, when VO2 is in the metallic phase. The EMT is employed and an air-M-air slowlight waveguide model is used to explore the relation between the slow-light wavelength and the waveguide core width.
- (2) When VO2 is in the insulating phase, the absorptance enhancement of the absorber is caused by the magnetic and SPP resonance.
- (3) The layer number of the absorber is selected appropriately, and the absorber is proved to be angle-insensitive. The net cooling power of the VGMA of metallic VO2 is up to four-fold than that of insulating VO2. In this way, the VGMA can meet the requirement of dynamic radiative cooling at the daytime. A few percent of co-doping of W, Mg or Sr to pure VO2 can significantly decrease the phase change temperature, so the proposed radiative cooling system can potentially change the dynamic temperature and this work will advance the development of radiative cooling.
Funding
National Natural Science Foundation of China (51806047, 51976044); China Postdoctoral Science Foundation (2018M630351).
Acknowledgments
A very special acknowledgment is also made to the editors and referees who make important comments to improve this paper.
Disclosures
The authors declare no conflicts of interest.
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