2.1.

Design of Radiative Cooling Device and Numerical Modeling

Figure 1(a) illustrates a typical temperature-adaptive radiative device (ATRD) based on the F–P resonator. A highly reflective metal layer is placed at the bottom, followed by a middle layer of highly IR transparent material and a continuous ${\mathrm{VO}}_2$ film covers the top. In the insulating (I) state of ${\mathrm{VO}}_2$ at $T<T_{\mathrm{MIT}}$ (metal–insulator transition temperature), ${\mathrm{VO}}_2$ allows high transmission of IR light, and incident IR light is reflected by the bottom metal layer, achieving a low IR absorption. The heat inside the object cannot radiate away, preventing the overcooling phenomenon. By contrast, the ATRD becomes highly absorptant to IR light when ${\mathrm{VO}}_2$ switches to the metal (M) state at $T>T_{\mathrm{MIT}}$. The absorption is further amplified in the atmospheric window through a design of a 1/4 wavelength cavity.³ According to Kirchhoff’s law, the IR absorptance ($A$) equals emittance ($\epsilon$) for IR opaque materials.³³ Hence, the emittance achieves a temperature-adaptive switch in the atmospheric window from low to high (or high to low) depending on the I–M phase transition of ${\mathrm{VO}}_2$, as illustrated in Fig. 1(b).

Fig. 1

(a), (c) Schematics of the ATRD and the ATMRD. (b) Working diagram of the ideal temperature-adaptive radiative cooling. (d) Surface pattern dimensions and cross-sectional diagram of designed ATMRD. (e), (f) Comparison of simulated solar absorptance and thermal emissivity between ATRD and ATMRD. The blue line represents low temperature, and the red line represents high temperature.

Here, the reflective layer uses an Ag metal with the highest reflection compared with other common metals [Figs. S1(a) and S1(b) in the Supplementary Material], which will contribute to achieving a high solar reflection [Fig. S1(c) in the Supplementary Material]. ${\mathrm{HfO}}_2$ is selected as the dielectric layer due to its high IR transparency at a broad bandwidth.³⁴ The simulated optimal emittance tunability ($\mathrm{\Delta }\epsilon =0.66$) can be achieved in ATRD by optimizing the thickness of the ${\mathrm{HfO}}_2$ and ${\mathrm{VO}}_2$ layer (Fig. S2 in the Supplementary Material), whereas the ${\alpha }_{\mathrm{sol}}$ is 33.48% at low temperature [the dotted horizontal line in Fig. 2(h)] and 43.51% at high temperature [the dotted horizontal line in Fig. 2(i)]. High solar absorptance, especially at high temperatures, will cause the object’s temperature to increase and weaken the radiation heat dissipation ability to a certain extent during daytime.

Fig. 2

(a), (b) Simulated solar absorptance spectra for ATMRD $\mathrm{L}x‐\mathrm{G}y$ samples with $x=1$, 2, 4, 6, 8, and $10\mu \mathrm{m}$ and $y=0.5$, 1, 2, and $3\mu \mathrm{m}$. Here, the dotted and solid lines represent the I and M states of ${\mathrm{VO}}_2$, respectively. The dark line represents the solar absorptance spectra of ATRD. The simulated solar absorptance as a function of feature size $L$ along with gap size $G$ at temperatures of (c) 25°C and (d) 90°C. Note that signed solid lines and dashed lines represent simulation results for square and circular patterns, respectively. The size of the symbol indicates the variation of the feature size.

Aiming at the goal of achieving low ${\alpha }_{\mathrm{sol}}$ and high $\epsilon$, we employ a periodic array pattern to replace the continuous ${\mathrm{VO}}_2$ film, as depicted in Figs. 1(c) and 1(d), namely, constructing an ATMRD. The incorporation of ${\mathrm{VO}}_2$ metasurface can obviously reduce ${\alpha }_{\mathrm{sol}}$ and enhance $\epsilon$ through rational structural design to tune the resonant frequency to the atmospheric window, as shown in Figs. 1(e) and 1(f). The resonant frequency of the metasurface strongly depends on the structure parameters of the top metallic patterns,³⁵ including geometric shape, arrangement period ($P$), feature size ($L$), and gap ($G$) with the relation $P=L+G$, as shown in Fig. 1(c). We create simple squares and circular patterns to consider the effects of $L$ and $G$ on ${\alpha }_{\mathrm{sol}}$ and $\epsilon$. For convenience, the samples with different $L$ and $G$ for squares and circular patterns are labeled as $\mathrm{L}x\text{-}\mathrm{G}y$ and $\mathrm{D}x\text{-}\mathrm{G}y$, respectively, where $x$ represents the variation of $L$ or $D$ from 1 to $10\mu \mathrm{m}$, and $y$ represents the $G$ ranging from 0.5 to $3\mu \mathrm{m}$. The simulated solar absorptance results for ATMRD with a square array structure are presented in Figs. 2(a) and 2(b) and Fig. S3 in the Supplementary Material. The amplitude of the solar absorptance curve for all samples gradually weakens as $G$ increases at a fixed $L$ or $L$ decreases at fixed $G$. The same trend is found in ATMRD with a circular array structure shown in Fig. S4 in the Supplementary Material, indicating that ${\alpha }_{\mathrm{sol}}$ significantly depends on the coverage area of ${\mathrm{VO}}_2$ in ATMRD. The integration results in Figs. 2(c) and 2(d) using Eq. (1) (see Sec. 4.2) suggest a proportional relationship between ${\alpha }_{\mathrm{sol}}$ and the coverage area of ${\mathrm{VO}}_2$: the larger the ${\mathrm{VO}}_2$ coverage area, the stronger ${\alpha }_{\mathrm{sol}}$.

Figures 3(a)–3(g) show the simulated emissivity spectra of ATMRD with the square patterns of different $L$ and $G$ in the frequency range from 2.5 to $20\mu \mathrm{m}$. Compared with the emissivity spectra of ATRD, additional peaks are induced by the periodic ${\mathrm{VO}}_2$ patterns besides the $1/4n\lambda$ resonant absorption peak. Variations in feature size $L$ and gap $G$ significantly impact the intensity and position of the emittance peak as ${\mathrm{VO}}_2$ is in the metallic phase. When $L$ is fixed, both the emissivity intensity and bandwidth increase as $G$ becomes narrower. As $L$ increases at fixed $G$, the intensity of the enhanced emissivity peak gradually decreases, whereas the long wave absorption edge shifts toward a longer wavelength, as shown in Fig. 3(g). A comparison is carried out for different $L$ or $G$ in the same period $P$ ($P=L+G$), as shown in Fig. S5 in the Supplementary Material. It is found that the emissivity intensity and bandwidth obviously increase as $L$ increases, or $G$ decreases at fixed $P$ when ${\mathrm{VO}}_2$ is in the metallic phase. The thermal emittances ($\epsilon$) at different $L$ and $G$ are calculated with Eq. (2) (presented in Sec. 4.2) by referencing the blackbody radiation spectra and exhibited in Fig. 3(h). At low temperatures, the thermal emittance (${\epsilon }_L$) of ATMRD is lower than that of ATRD, which is more beneficial in preventing the overcooling of objects at low temperatures. As the feature size $L$ increases in ATMRD, the ${\epsilon }_L$ slightly increases due to the increased area of ${\mathrm{VO}}_2$. In comparison, the emittance at high temperature (${\epsilon }_H$) is significantly enhanced. The ${\epsilon }_H$ of ATMRD increases rapidly with increasing $L$ as $L\le 4$ and reaches the maximum value at $L=4$ for the G0.5 and G1 ATMRDs, followed by a slight decline with a further increase in $L$. As $L\ge 4$, the ${\epsilon }_H$ of G1 and G0.5 surpasses that of ATRD. However, the ${\epsilon }_H$ of ATMRD with a larger gap ($G>1$) is lower than that of ATRD. The emittance tunability ($\mathrm{\Delta }\epsilon$) of ATMRD outperforms ATRD over a broader pattern range when $L>2$ and $G\le 1$, with the peak value located at $L=4$, as shown in Fig. 3(i). The results of ATMRD with a circular array structure (Fig. S6 in the Supplementary Material) also revealed consistent regularity, with slightly lower $\mathrm{\Delta }\epsilon$ than square patterns [Fig. 3(i)] because the rounded corners of circular patterns increase the gap $G$. The above results indicate that the appropriate values of feature size and gap (or period) are crucial to achieving emittance enhancement.

Fig. 3

(a)–(g) Simulated emissivity spectra at different $L$ and $G$ for ATMRD with square array structure. (h) $\epsilon$ value and (i) $\mathrm{\Delta }\epsilon$ as a function of $L$ at different $G$. Note that the dotted and solid lines in panels (a)–(g) represent the insulator and metal states of ${\mathrm{VO}}_2$, respectively. The solid lines and dashed lines in panel (i) represent the simulation results for square and circular patterns, respectively.

2.2.

Preparation and Characterization of ATMRD

Based on the above simulated results, we selected three representative feature sizes ($L=4$, 6, and $8\mu \mathrm{m}$) and three gap values ($G=1$, 2, and $3\mu \mathrm{m}$) to fabricate ATMRD using a simple mask-filling engineering. The experimental section describes the fabrication process in detail. Figure 4(a) exhibits a photograph of the ATMRD. It presents a rainbow spectrum under visible light due to the structural color induced by the micro–nanostructure.³⁶ The cross-sectional scanning electron microscopy (SEM) image and energy dispersive spectroscopy (EDS) mapping of the ATMRD in Fig. 4(b) exhibit good adhesion among different layers, providing a fundamental guarantee for the device’s performance. The thickness of the Ag, ${\mathrm{HfO}}_2$, and ${\mathrm{VO}}_2$ layers is 100, 800, and 50 nm, respectively. Figure 4(c) shows the SEM morphology of the ATMRD’s top view. All samples present well-designed geometries over the range of feature sizes $L$ from 4 to $8\mu \mathrm{m}$ and $G$ from 1 to $3\mu \mathrm{m}$, attributed to advanced photolithography and magnetron sputtering deposition technology. This method can significantly reduce manufacturing costs and achieve scale preparation compared with electron beam lithography.

Fig. 4

(a) Photograph of ATMRD L4-G1, and the middle colored area is the micro–nanostructure. (b) Cross-sectional SEM image and EDS mappings of ATMRD. (c) SEM morphology of the ATMRD’s top view with different $L$ and $G$.

Figures 5(a) and 5(b) show the X-ray diffractometer (XRD) and Raman results of ATMRD films for phase identification. The XRD pattern in Fig. 5(a) primarily exhibits the crystalline structure of ${\mathrm{HfO}}_2$, along with diffraction peaks of Ag. No other impurities are observed. The Raman results in Fig. 5(b) confirm the existence of the M1-phase ${\mathrm{VO}}_2$ film.³⁷ In addition, the ${\mathrm{VO}}_2$ film reveals an excellent IR switch from high transmittance and high reflectance at $T_{\mathrm{MIT}}=68°\mathrm{C}$, as shown in Figs. 5(c) and 5(d).

Fig. 5

(a) XRD pattern of the ATMRD. (b) Raman spectrum at room temperature for ${\mathrm{VO}}_2$ films. (c) UV-VIS-NIR transmittance spectra at 20°C and 90°C of ${\mathrm{VO}}_2$ film deposited on a sapphire substrate for reference. (d) Temperature-dependent transmittance of the ${\mathrm{VO}}_2$ film at a wavelength of 2500 nm. The inset shows the corresponding $\mathrm{d}(T\%)/\mathrm{d}T-T$ curves in the heating cycle using Lorentz function fitting.

2.3.

Radiative Cooling Performance of ATMRD

The emissivity spectra of ATMRD are detected under different temperatures, as depicted in Figs. 6(a)–6(d). The emissivity of the devices changes significantly from low to high values with the increase in temperature. The ATRD exhibits strong absorption for wavelengths larger than $4\mu \mathrm{m}$, with an emissivity peak at $\sim 8\mu \mathrm{m}$ when heated to 90°C [Fig. 6(a)], corresponding to the blackbody radiation peak. For ATMRD at 90°C, the peak intensity of L4-G1 and L6-G1 devices is significantly enhanced and almost reaches 100% [Figs. 6(b) and 6(c)], whereas L8-G1 shows a slight decrease in peak intensity [Fig. 6(d)]. The increasing $L$ causes the peak to shift toward longer wavelengths, as indicated in Figs. 6(b)–6(d) and Fig. 7(a). The temperature-dependent thermal emittances are obtained from Figs. 6(a)–6(d) using Eq. (2), intuitively evaluating the $\mathrm{\Delta }\epsilon$, as shown in Figs. 6(e)–6(h). A rapid switch from ${\epsilon }_L$ to ${\epsilon }_H$ is observed when the temperature exceeds $T_{\mathrm{MIT}}$. The ${\epsilon }_H$ values for L4-G1, L6-G1, and L8-G1 are 0.85, 0.89, and 0.84, respectively, representing a more than 13% improvement over ATRD’s value of 0.75. As the temperature gradually declines, the ${\epsilon }_H$ can maintain over a broad temperature range and then switch to ${\epsilon }_L$ at $\sim 50°\mathrm{C}$ due to a typical hysteresis effect of ${\mathrm{VO}}_2$ phase transition, contributing to more effective heat dissipation at high temperatures. However, the thermal emissivity gradually decreases as $G$ broadens from 1 to $3\mu \mathrm{m}$ at a fixed $L$, as shown in Fig. S7 in the Supplementary Material. Only $\mathrm{L}x\text{-}\mathrm{G}1$ achieves significantly improved emittance compared with ATRD, as indicated in Fig. 7(b), which is consistent with the simulated results. The $\mathrm{\Delta }\epsilon$ of ATMRD-L4-G1 ($\mathrm{\Delta }\epsilon =0.72$) is enhanced by 20% compared with the ATRD ($\mathrm{\Delta }\epsilon =0.6$).

Fig. 6

Thermal emissivity spectra at different temperatures, emittance-dependent temperature during heating and cooling, and solar absorptance at low and high temperatures for (a), (e), (i) ATRD, (b), (f), (j) ATMRD L4-G1, (c), (g), (k) ATMRD L6-G1, and (d), (h), (l) ATMRD L8-G1, respectively.

Fig. 7

(a) Comparison of the thermal emittance. (b) Comparison of emittance tunability between ATMRD $\mathrm{L}x\text{-}\mathrm{G}y$ and ATRD. (c) Comparison of solar absorptance between ATMRD $\mathrm{L}x\text{-}\mathrm{G}y$ and ATRD at different temperatures. (d) Optimal performance of ATMRD L4-G1. (e) Comparison of the emittance performance with previous reports.^{3–5,20–24,38–48}

Figures 6(i)–6(m) and Fig. S8 in the Supplementary Material present the measured solar absorptance spectra at low and high temperatures. The relationship of solar absorptance, feature size, and gap size at 20°C and 90°C is illustrated in Fig. 7(c), respectively. Solar absorptance at low temperatures shows a noticeable decline in ATMRD compared with ATRD (35.25%). When ATMRD switches to the ${\epsilon }_H$ state, solar absorptance rises slightly but remains significantly lower than ATRD’s (46.55%). Solar absorptance of the L4-G1 is 27.71% at low temperatures and rises to 35.44% at high temperatures. ATMRDs with more significant gaps achieve smaller solar absorptance but lower emissivity. Hence, the ATMRD L4-G1 achieves optimal performance with ${\alpha }_{\mathrm{sol}}=27.71\%$ at 20°C (${\alpha }_{\mathrm{sol}}=35.44\%$ at 90°C) and ${\epsilon }_H=0.85$ ($\mathrm{\Delta }\epsilon =0.72$), as shown in Fig. 7(d). Figure 7(e) compares the emittance performance of dynamic radiation cooling devices reported in recent years. The performance of the radiative cooling device designed in this work is better than most literature results, affirming the viability of the design scheme and preparation method presented in this study.

2.4.

Application Potential Assessment

We carried out verification experiments to evaluate the practical application potential of ATMRD devices. A solar simulator was employed to conduct a preliminary test of the sunlight reflection capability; the schematic diagram is shown in Fig. 8(a). The 3M tape ($\epsilon =0.96$), silicon (Si) wafer ($\epsilon =0.5$), and aluminum (Al) sheet ($\epsilon =0.1$) are selected as reference samples. The results in Fig. 8(b) show that the temperature of ATRD quickly rises and then gradually levels off to 37°C within 120 s, but the temperature is much lower than that of the 3M tape (53°C) and Si wafer (44°C). The ATMRD presents a lower temperature than the ATRD, and the temperature further declines toward that of the Al sheet with decreasing $L$. The temperature of ATMRD L4-G1 is only 33°C, slightly higher than that of the Al sheet (28°C). Such a low solar absorptance significantly reduces solar radiation interference to the cooling device.

Fig. 8

(a) Schematic of a simulated solar heating test and (c) IR thermal emittance test, and the $\theta$ represents different detection angles. (b) Temperature tracking of diverse samples under simulated solar heating. (d) Thermal IR imaging of vertical incidence under different temperatures for Al flake, commercial 3M tape, and different ATMRDs. (e) Thermal IR imaging of the ATMRD L4-G1 at different detection angles at 90°C.

The emittance switching of ATMRD, along with two reference samples, was examined by IR imaging with a thermal IR camera, as shown in Fig. 8(c). One reference sample is an Al sheet, which features a consistently low thermal emittance of 0.10, and the other is the commercial 3M tape, possessing a steady high thermal emittance of 0.96, pasted over the ${\mathrm{Al}}_2{\mathrm{O}}_3$ substrate used in ATMRD. Compared with the two references, the ATMRD shows a significant thermal radiation change over the ${\mathrm{VO}}_2$ phase transition [Fig. 8(d)]. Before the phase transition, the thermal radiation of ATMRD is consistent with that of the Al sheet and then switches to a high emittance state after the phase transition. Moreover, the emittance exhibits weak dependence on the detection angle, as displayed in Fig. 8(e). The result demonstrates that the ATMRD has excellent solar reflectance and considerable heat dissipation.

2.5.

Mechanism Analysis

To elucidate the underlying mechanism responsible for the metasurface-enhanced absorption based on the F–P resonant cavity, electromagnetic field distributions in the $x–z$ cross section of one array cell [Fig. 9(a)] were investigated for ATMRDs with different feature size $L$ with ${\mathrm{VO}}_2$ in the metal phase. Coupled with the F–P resonances in ATRD [Fig. 9(c)], the multimode polariton resonances are excited in ATMRD, as shown in Figs. 9(d)–9(k) and Figs. S9–S11 in the Supplementary Material, producing the corresponding sharp peaks in the emissivity spectra in Fig. 3. The results show that the polariton resonance strongly depends on the structural parameters of feature size and gap size or period of the metasurface.

Fig. 9

(a) Schematic diagram of simulated ATMRD using FDTD, the $x–z$ plane at $y=0\mu \mathrm{m}$. (b) Equivalent LC circuit model for MP excitation when ${\mathrm{VO}}_2$ is in the metallic phase. Electromagnetic field distribution of the $x–z$ cross section of one array cell at different wavelengths in the ${\mathrm{VO}}_2$ metallic phase. (c) ATRD. (d)–(h) ATMRD L4-G1. (i) ATMRD L8-G1. (j), (k) ATMRD L10-G1. Note that the contour color indicates the magnetic field strength, expressed as $|H{|}^2$, and the black arrows represent the electric field vectors. The white arrow indicates the current loop of the equivalent LC circuit.

The surface plasmon polariton (SPP) resonance emerges on the surface of the ${\mathrm{VO}}_2$ units when the feature size $L$ (or period $P$) matches the wavelength of the incident wave. For ATMRD L4-G1, the SPP resonance occurs at $\sim 5\mu \mathrm{m}$ due to the strong electric polarization above the ${\mathrm{VO}}_2$ units in Fig. 9(d). For L6-G1, L8-G1, and L10-G1, the SPP resonance appears at 7, 9, and $11\mu \mathrm{m}$, respectively, as shown in Figs. S10C and S11E in the Supplementary Material and Fig. 9(k).

As the incident wavelength $\lambda >P$, the electric polarization in the ${\mathrm{HfO}}_2$ medium between the metallic ${\mathrm{VO}}_2$ and the Ag substrate gradually increases, as characterized by the polarized electric field vectors, which indicate electric current loops in Figs. 9(e)–9(g). The alternatively polarized electric field induces strong localized magnetic polaritons (MPs).⁴⁷ The electromagnetic polariton resonances can be understood by employing an equivalent inductor–capacitor (LC) circuit model.⁴⁸ The sandwiched ${\mathrm{HfO}}_2$ spacer serves as a capacitor ($C$), whereas the top metallic ${\mathrm{VO}}_2$ microstructure and the bottom Ag substrate function as inductors ($L_k+L_m$), as illustrated in Fig. 9(b), forming a resonant LC circuit. The LC circuit induces the magnetic field and develops magnetic dipoles according to Lenz’s law.⁴⁹ Eventually, the localized strong magnetic field is induced at the resonance frequency of the magnetic and electric dipoles, where the total impedance equals zero.³⁵ In other words, the MP resonance is excited at the resonance frequency, resulting in an enhanced absorption effect. At $6.8\mu \mathrm{m}$, an intense MP resonance centers below the gaps of ${\mathrm{VO}}_2$ units of L4-G1 in Fig. 9(e). As the wavelength of incident light becomes longer, the induced electric polarization period also changes for a longer period of time. The strong polariton resonances occur at $\sim 9.2$ and $\sim 12.5\mu \mathrm{m}$, with the enhanced magnetic response centering below the ${\mathrm{VO}}_2$ units, as shown in Figs. 9(f) and 9(g). Further increasing the incident wavelength, the polarization becomes weak. Hence, the emissivity spectrum experiences gradual suppression at a longer wavelength.

For $\lambda <P$, the polarized electric field period is smaller than the feature size $L$. Figures 9(i) and 9(j) indicate two localized SPP resonances on one ${\mathrm{VO}}_2$ unit for L8-G1 and L10-G1. This is because two periodic polarization electric fields are formed on the surface of each metallic ${\mathrm{VO}}_2$ unit when $\lambda$ is half of $P$, thus exciting two localized SPP resonances. Meanwhile, the multiple MP resonances can also be excited between ${\mathrm{VO}}_2$ layers and Ag layers at resonant frequencies. However, the polarization strength gradually weakens as the $\lambda$ becomes much smaller than $P$. Therefore, the metastructure loses its effects, as $\lambda$ is much smaller than $P$.

4.1.

Fabrication of Radiative Cooling Device

Radiative cooling devices featuring a triple-layer film structure of $\mathrm{Ag}/{\mathrm{HfO}}_2/{\mathrm{VO}}_2$ were fabricated on a $c\text{-}{\mathrm{Al}}_2{\mathrm{O}}_3$ substrate using magnetron sputtering. Initially, a reflective layer of Ag was deposited on the substrate using a high-purity Ag target. Subsequently, an 800-nm ${\mathrm{HfO}}_2$ layer was deposited utilizing a ceramic target. For ATRD, a 50-nm-thick layer of vanadium is directly deposited on the top of the ${\mathrm{HfO}}_2$ layer using a high-purity metal vanadium target at room temperature. The vanadium film underwent thermal treatment to transform into the ${\mathrm{VO}}_2$ M1 phase using a rapid annealing furnace (RTP-500, Beijing East-star Research Office of Applied Physics, Beijing, China). For ATMRD, the ${\mathrm{VO}}_2$ microstructure was fabricated through mask-filling engineering, as illustrated in Fig. S12 in the Supplementary Material.

The pre-prepared $\mathrm{Ag}/{\mathrm{HfO}}_2$ device underwent plasma cleaning initially to remove surface contaminants. Photoresist (L300, Seoul, Republic of Korea) was spin-coated on the ${\mathrm{HfO}}_2$ layer at a speed of 4000 r/min, and the patterned potholes on the ${\mathrm{HfO}}_2$ layer were achieved through exposure in a photolithography machine. Subsequently, pure vanadium was deposited into the patterned potholes, and the photoresist mask, along with excess vanadium, was eliminated through immersion and ultrasonic delamination in an acetone solution. Following this step, the patterned vanadium microstructure underwent additional thermal treatment to transform the ${\mathrm{VO}}_2$ (M) phase, thereby producing the final ATMRD.

4.2.

Characterization

The morphology was observed by field emission scanning electron microscopy (FE-SEM, Hitachi S-4800, Tokyo, Japan). The phase structure of the films was measured utilizing an XRD (Rigaku SmartLab SE, Tokyo, Japan) and a Raman spectrometer (Horiba LabRAM HR Evolution, Paris, France) equipped with a 532-nm laser. An ultraviolet–visible–near-IR spectrophotometer (UV-VIS-NIR, Agilent UV3600, Santa Clara, California, United States) fitted with an integrating sphere measured the transmittance and reflectivity from 300 to 2500 nm at different temperatures using a homemade heating table. Thermal spectral reflectance was characterized by a Fourier transform IR spectrometer (Nicolet iS50, Madison, Wisconsin, United States) equipped with mid-IR IntegratIR spheres (PIKE Technologies, Inc., Madison, Wisconsin, United States) and mercury cadmium telluride (MCT) detectors over the $\sim 2$ to $18\mu \mathrm{m}$ wavelength range at 12-deg angle of incidence. According to Kirchhoff’s law of radiation, in a state of thermodynamic equilibrium, the spectral emittance $\epsilon (\lambda ,T)$ equals the spectral absorptance $A(\lambda ,T)$.³³ As a radiative cooling device comprises a thick Ag layer, the transmittance ($T$) in the solar and thermal IR wavelength ranges was considered zero. Thus, its thermal spectral emittance in this range was computed as $\epsilon (\lambda ,T)=A(\lambda ,T)=1-R(\lambda ,T)$.

The solar absorptance (${\alpha }_{\mathrm{sol}}$) and thermal emittance ($\epsilon$) can be calculated from the corresponding spectral data using the following equations:

The solar heating simulation test was carried out using a solar simulator (PLS-SXE300, Beijing Perfectlight Technology Co., Ltd., Beijing, China), and a temperature recorder fitted with a Pt temperature sensor recorded the temperatures. Before measuring each type of material surface, the shutter of the solar simulator remained closed, and the sample was first stabilized at room temperature. Then, the shutter was opened, and the surface temperature was recorded as a function of time. Thermal IR images were captured by an FLIR A310 infrared camera (IR camera) working at a 7.5- to $14\text{-}\mu \mathrm{m}$ wavelength. To minimize reflections in the surrounding environment, the experiments were conducted in an open, outdoor environment. Before testing, the IR camera was calibrated using a thermocouple and 3M tape (a commercial product with a constant emittance of 0.96) as a reference to ensure that the displayed surface temperature matches the reference sample’s actual temperature. The sample was heated using a heating stage, and the IR camera recorded video images at a fixed detection angle.

4.3.

Simulation Design

We used finite-difference time-domain (FDTD, Ansys Lumerical, Canonsburg, Pennsylvania, United States) modeling for numerical simulations of the radiative cooling device. A three-dimensional unit cell model was established, including the ${\mathrm{VO}}_2$ submicrometer square or circle, ${\mathrm{HfO}}_2$ layer, and Ag substrate. The materials’ optical properties were obtained from Ref. 24 for ${\mathrm{VO}}_2$ and Ref. 34 for ${\mathrm{HfO}}_2$. The optical properties of Ag employed in the simulation were calculated from Palik’s handbook.⁵⁰ The simulation region had a size of $x\times y\times z$ referring to the period of the $P$ micrometer disks. The perfect matching layer boundary conditions were applied along the propagation of electromagnetic waves ($z$ direction), and periodic boundary conditions were applied along the $x$ direction and $y$ direction. A broadband linearly polarized plane wave was directed toward the unit cell from above the structure at normal incidence. Positioned above the plane wave source was a frequency–domain power monitor designed to capture the reflected waves. The simulation exclusively focuses on the transverse magnetic (TM) wave, where metamaterial particles are excited by the $y$ component of the magnetic field. Due to the symmetry of the considered patterns, the reflectance remains consistent for both transverse electric and TM waves. All simulations detailed in this paper are conducted within a three-dimensional computational domain, employing a nonuniform structured mesh with a minimum mesh size of 1 nm.³⁵