Adaptive thermally tunable radiative cooling with angle insensitivity using phase-change-material-based metasurface

Radiative cooling is the passive cooling of a material with the help of a specific spectral response to emit thermal energy into space through atmospheric transparency windows. However, most of the proposed designs have no dynamically tunable emission response. In this paper, we present a feasible inverse pyramid structure made of a phase change material (PCM) on top of a metallic mirror to realize an adaptive radiative cooler with almost angle-independent emission response. The design uses the thermally controlled PCM called Samarium nickelate (SmNiO3) to actively tune the spectral response of the design, which, in turn, allows the design to radiatively cool itself. The emission response of the design is compatible with atmospheric transmissive windows. As the design heated up to higher temperatures, the peak of the emission spectrum red-shifts and moves toward the atmospheric transparency window.


Introduction
Every material with a finite temperature emits light with intensities governed by Planck's Law [1].This thermal light is called 'black-body' radiation, and the Stephan-Boltzmann law can be used to calculate the spectrum of the black-body object, where the emission is proportional to the fourth power of the temperature (T 4 ) and the surface emissivity (ε) [2].According to Kirchhoff radiation law, the emissivity and absorptivity of a surface are equal, which means that a black-body with has perfect absorptivity, can also be considered as a perfect emitter [3].
A black-body emitter is a non-resonant broadband emitter with no spectral selectivity.However, manipulating or controlling thermal radiation within a specific wavelength range is a crucial challenge for various applications, such as thermal camouflage, radiative cooling, and energy harvesting [4][5][6][7][8][9][10][11][12].To achieve the objective of controlling and managing thermal radiation, researchers have explored the use of metamaterials and their 2D analogs, called metasurfaces operating in the infrared spectrum.These artificially engineered materials are distinguished by their exceptional optical, and thermal properties, making them promising candidates for the development of novel devices that can manipulate thermal radiation in innovative ways.These artificial materials typically include geometrical shapes such as gratings [13], crosses [14], and hole-arrays [15] or they can be planar [16] surfaces to achieve strong light-matter interactions in terahertz [17], nearinfrared [18], and mid-infrared [19] regimes.
Although metamaterials can be used in various applications from superlenses [20] to antennas [21], their geometry-dependent spectral responses cannot be actively controlled.In recent studies, phase-change materials (PCMs) such as vanadium dioxide (VO 2 ) [22] and germanium antimony telluride (Ge 3 Sb 2 Te 6 ) [23,24] have gained significant interest among researchers because their ability to add real-time tunability to the spectral response of metamaterial structures.For example, Osgouei et al demonstrated at switchable narrowband to broadband absorption response by incorporating a VO 2 layer in a Si grating structure [25].The change in the response of PCMs arises from the change in their crystal structure with respect to their temperature, which in turn changes their optical responses.Samarium nickelate (SmNiO 3 ) is another type of PCMs that exhibits dielectric characteristics at 25 °C and metallic one at 140 °C.This feature allows researchers to design thermally tunable devices by incorporating a PCM layer into their metamaterial-based emitter structures [26,27].
In this study, we proposed an adaptive metamaterial-based absorber using SmNiO3 inverse pyramid gratings on top of a silver (Ag) reflector, which exhibits broadband perfect absorption in the mid-infrared (MIR) regime.The absorption spectrum of the design is thermally tunable because of the change in the optical properties of the used SmNiO 3 from metallic to insulator phases.Different from other common PCMs SmNiO 3 shows a gradual change in its permittivity response from cold to hot state.Therefore, utilization of this material in a Fabry-Perot-like cavity design can offer a spectrally tunable metamaterial emitter in the MIR range.This tunability changes the position of the resonance peak, while keeping the design simple making this metasurface more practical than the previous studies.The optical response of the proposed design was studied using a commercial finite-difference-time-domain software package, and the design's angle insensitivity was investigated with simulations from zero up to 60°for both transverse magnetic (TM) and transverse electric (TE) polarizations.In addition, the structural parameters of the design are optimized and the effects of the geometrical parameters are investigated.

Results and discussion
A schematic representation of the proposed design is shown in figure 1(a), in which SmNiO 3 -based inverse pyramid gratings are placed on top of an Ag bottom reflector to eliminate transmission.The optical constants of the bottom reflector layer (Ag) are extracted from the CRC Handbook of Chemistry and Physics [28], and the real and imaginary components of the permittivity of SmNiO 3 for both cold (25 °C) and hot (140 °C) states are given in figure 1(b) [29] The dimensions of the inverse pyramid gratings are denoted by t, b, h, and p, which correspond to the top and bottom width, height, and period of the grating, respectively.A commercial finitedifference time-domain (FDTD) simulation software (Lumerical FDTD Solutions) was used to compute the optical response of the proposed metasurface-based absorber and to investigate the effects of geometrical parameters on the optical responses.The simulations were carried out in a 2D geometry due to the periodicity of the structure in the z plane.A plane wave source propagating along the y-axis is used the illuminate the structure from the SmNiO 3 side.Periodic boundary conditions are utilized along the x-z direction.A reflection monitor placed behind the source to collect the reflected wave, whereas a transmission monitor is used after the Ag layer to collect any transmitted wave.Radiative cooling is a process of dumping thermal energy into outer space instead of the environment, which requires the resonance peak of the absorption spectrum of the proposed metasurface-based design to be placed in one of the transparency windows of the atmosphere (8-12 μm).Unlike the radiative cooling applications in space [4], night-time water condensation on the metasurface can impact the performance of cooling [30][31][32].For this study, the environment is assumed to be dry.In the proposed structure, the peak positions of the absorption spectrum are a function of the periodicity (p), height (h), and width (top (t) and bottom (b)) of the structure.Additionally, geometrical parameters of angle (a = -atan 2h t b ) and filling ratio = ( ) FR t p are defined in the design of the grating leading to an inverted pyramid grating when a <  90 ( < ) b t , rectangular grating when a =  90 ( = ) b t , and pyramid grating when a >  90 ( > ) b t .Therefore, three different structures are considered in the probable design of a tunable nanoantenna emitter by the variation of temperature.Variation of absorptivity of a typical design versus pyramid angle is investigated by fixing p, h, and b is at 5250 nm, 750 nm and 3000 nm, respectively, while t is varied between 500 nm and 5000 nm.The results given in figures 1(c) and 1(d) at different temperatures (cold and hot states) demonstrate that only the inverse pyramid has a tunable spectral response with respect to temperature changes.This can be visualized by presenting absorption responses at three different thicknesses ( m 1 m, m 3 m, and m 5 m) as shown in figures 1(e)-(g).It is seen that decreasing the angle broadens the absorption responses at both cold and hot states, whereas an increase in the temperature of the metasurface can cause a redshift at smaller angles.In the first case where t < b, the structure resembles a pyramid.According to the absorption spectra given in figure 1(e), it can be seen that the structure supports a narrow resonance located at 5.25 μm both at the cold and hot phases.Although the magnitude of the absorption changes between cold and hot phases, the peak location does not change which makes this design nonadaptive.In the second case, the structure with = t b corresponding to a rectangular grating is investigated.Figure 1 (f) shows the absorption spectra, where resonance occurs at 5.63 μm and 5.71 μm for the cold and hot phases, respectively.Although the grating structure has broader resonances than the pyramid structure, the resonance red-shift between the cold and hot phases is not sufficient provide an acceptable adaptive response.Finally, the case with t > b was investigated.This design is called inverse pyramid and has wide resonance peaks occurring at 8.65 μm and 9.32 μm, seen in figure 1 (g), for the cold and hot phases, respectively.
Due to the thermal tunability of the inverse pyramid design caused by the phase transition from the cold state to the hot state, the geometrical parameters are optimized for radiative cooling applications by maximizing the difference between the positions of the absorption peaks.Therefore, the optimal dimensions are t = 4.2 μm, b = 0.8 μm, h = 750 nm, and p = 5.25 μm.The optimized design has resonance peaks occurring at 8.08 μm and 9.26 μm for the cold and hot phases, respectively.The optimum design's absorption spectrum is shown in figures 2(i)-(l) while the dimensions for other spectra can be found in table 1.
For the first set of optimizations, as given in the first column of figure 2, the height of the structure, h, is varied between 650 nm and 850 nm while keeping t, b, and p constant.In this case, the resonance peaks for both cold and hot phases redshift with increasing h, because the increase in height effectively increases the length of the cavity formed by the sides of the inverse pyramid and the bottom reflector.It would be better to emphasize that the angle α is dependent on h, t, and b, while varying h and keeping t and b constant lead to a change in angle α as well.
In the second column, the simultaneous effects of t, b, and h on the absorption spectrum were investigated by keeping α constant.To conduct this study, the height of the structure was again varied between 650 nm and 850 nm.A clear redshift in the resonance can be seen with an enhancement in the width of the absorption.
As a third study, the effect of the filling ratio on the spectral response of the structure is investigated by scaling the height of the structure as in the first two studies.In the spectral responses presented in the third column of figure 2, the effect of scaling is also the same as in previous studies.It can be concluded that the resonance frequency is a strong function of height and a weak function of the angle α.To prove this claim, for the fourth study, the height of the structure was chosen as 750 nm, while t, b, and p values were swept accordingly by keeping the filling ratio and angle α constant.From the spectral responses presented in the rightmost column of figure 2, the resonances are almost identical, which shows that the governing mechanism behind this absorption is closely related to the filling ratio, a, and height of the structure, i.e., the formation of a cavity between the inverse pyramid and the bottom reflector.
Figure 3 shows the magnitude of the E and H field distributions over the optimized design at the respective resonance wavelengths of the cold and hot phases.As we can see from figure 3, the E and H fields distributions are quite similar in both hot and cold states operation.The E-field resembles a dipolar response with spots formed on the top edge of pyramid.However, the magnetic field is highly concentrated in the regions beneath of the inverse pyramid.In fact, upon light irradiation, the light diffracts from the pyramid edges and excite Fabry-Perot modes between the bottom metal reflector and top inverse SmNiO 3 pyramid.Due to the lossy nature of SmNiO 3 , the trapped light is harvested at the resonance frequency.Moreover, the resonance frequency (consequently the matching condition) can be tuned by the optical permittivity response of the SmNiO 3 in hot and cold states.Thus, in summary, in both cases, there is a strong localization of the E field on the upper corners of the design.More importantly, the H-field localizes between the design and the bottom reflector, forming a Fabry-Perot-like cavity (as also shown in the results of figure 2, rightmost column [33,34]) and this is responsible for resonant light absorption in this design.
To numerically verify and compare the emitted power density from the structure, the thermal emission model developed by Kocer et al was used [35].Using Kirchhoff's radiation law, emissivity from the surface can be written:  T , T str can be ignored; thus, the absorptivity can be written:  e l eff str str The radiation emitted from the surface of a blackbody can be written as: The optical power density is defined as the integral of the thermal emission for a given wavelength interval, which can be written: The average optical power density can be calculated: To investigate the isotropic response of the proposed structure, a set of simulations was conducted in both TM and TE polarization modes with incident angles varying from 0 to 60 degrees.As seen from the figure 4(b) location of the resonance peak is not changing with respect to the incident angle upon an incident TM polarized wave.On the other hand, because of the asymmetric nature of the grating-like structures, the structure shows no resonance when the incident wave is TE polarized.After isotropicity studies, using the extracted reflection data, the absorption spectra of the inverse pyramid design for temperatures varying from 25 °C to 140 °C were calculated and with equation (4) the emitted power for each temperature were calculated for three different wavelength windows: 5-8 μm, 8-12 μm, and 5-12 μm which are given in figures 4(f), (g), and (h) respectively.From figure 4 (d), the emitted power from the structure is almost identical to the blackbody over the 8-12 μm window which is one of the atmospheric transparency windows.

Conclusion
In this study, a thermally tunable metasurface based on a simple SmNiO 3 inverse pyramid grating as a PCM layer on top of an Ag bottom reflector was designed, and its performance was investigated for adaptive radiative cooling applications.The thermal emission capabilities of the design were studied and verified using numerical simulations.The resulting design has an almost-identical emitted power over at wavelength window 8-12 μm in which atmospheric absorption is minimal.Since the resonance element utilized in the design is a phase change material, the resonance blueshifts as the structure cools to room temperature which in turn makes the design adaptive to ambient temperature.With these features, this design can be easily implemented in satellite and, telecommunication applications without requiring any control mechanisms to modulate cooling.

Figure 2 .
Figure 2. (a)-(d) Schematic representation of the scalings with the respective rules from the optimal design.(e)-(h) Absorption spectra of the down-scaled structures.(i)-(l) Absorption spectra of the optimal design.(m)-(p) Absorption spectra of the up-scaled structures.

Figure 4 .
Figure 4. (a) Schematic representation of the radiative cooling process in the proposed metamaterial design.Upon temperature rise the emission peak moves to the middle of the atmospheric transmissive windows.(b) Absorption spectra of the structure under different incident angles at 140 °C for TM and TE polarization, showing near absolute angle independency in the emission character of the design.(c)-(d) Emitted radiative power of the structure at (i) the surface and (ii) its propagated profile considering the atmospheric transparency windows (T atm ) at 25 °C and 140 °C.(e) Absorption spectra of the inverse pyramid design for different temperatures ranging from 25 °C to 140 °C.As we go to higher temperatures, the emission peak moves to atmospheric transparency window, while the emission response at non-transmissive infrared range (5-8 μm) is gradually supressed.Emitted power from the blackbody and inverse pyramid design over the wavelength ranges of (f) 5-8 μm, (g) 8-12 μm, and (h) 5-12 μm.

Table 1 .
Parameter set for the optimizations in figure 2.
, reflectivity, and transmittivity of the structure which are functions of wavelength and the temperature, respectively.Because of the presence of an optically thick Ag bottom reflector, str are the absorptivityl ( ) c, and k B are Planck constant, the speed of light in the vacuum, and Boltzmann constant.The thermal emission of the surface can be determined by multiplying equations (2) and (3).