Introduction

Environmental cooling is a high-energy consumption operation embarked upon by society [1]. In certain countries, space cooling accounts for 70% of peak residential electrical demand on extremely hot days and 20% of electricity utilized in buildings [2]. Heating ventilation and air conditioning (HVAC) systems were used as a method to reduce problems raised with space cooling. However, it is another challenge since it requires energy supply, resulting in excessive consumption of fossil fuels and large greenhouse gas emissions, such as \({\text{CO}}_{2}\) [3]. These factors create environmental instability [4, 5], minimizes device functionality [6,7,8] and global warming [9]. Therefore, a variety of techniques were developed for lowering nonrenewable energy consumption and environmental protection. Due to the non-emissions of any dangerous gas, environmental-friendly ship, decreasing energy waste, and qualifying as a source of renewable energy, the passive radiative cooling (PRC) technique has gotten attention [10]. Passive radiative cooling is a method of pumping heat from the earth surface into cold outer space (3 K) via transparence /atmospheric window without energy input [11, 12].

For infrared region, the Earth’s atmosphere has three transparency windows, which are classified as near-infrared (NIR) (2.5–5 µm) mid-infrared (MIR) (8–14 µm), and far-infrared (FIR) (16–27 µm) respectively [13, 14]. By radiating heat from the earth surface into outer space (3 K) through these atmospheric windows and reflecting solar irradiation (0.3–2.5 µm), the temperature of environments/materials can be minimized below ambient temperature without using any energy input [15]. Solar radiation divides the cooling system into two main parts, namely, nighttime cooling [16, 17] and daytime cooling [18]. The passive radiative cooling effect was mostly achieved at night in several of the earlier studies. However, the cooling effect during the day was not realized due to the considerable effect of solar radiation. For instance, Hossain et al. [19] developed highly efficient cooling based on a selective emitter made of an Al/Ge structure, and Chen et al. [20] studied both experimental and theoretical methods using polymer coating, but they were only effective at night and required a solar reflector.

Actually, creating the perfect solar reflector and thermal emitter simultaneously has been tried in various ways. As a result, implementing solar reflectors like ZnS, ZnSe, and polymer broadband emitters is the conventional method of achieving the daytime cooling effect [21] Since these reflectors achieve less than 85% solar reflectance [22], they can’t cool below ambient temperature during the daytime. Therefore, minimizing solar absorption and maximizing the thermal emitter are crucial factors in the design of a daytime radiative cooler. Accordingly, different scholars have followed this method and achieved a daytime cooling system. Accordingly, Rephaeli et al. [22] conducted the first numerical demonstration on photonic materials that highly reflect solar radiation (0.3–2.5 µm), and Raman et al. [22] conducted the first experimental demonstration on a single planar device which reflects 0.97% of ordinarily incoming solar power. Their result was successful solar reflection while reducing thermal emittance and having a complex design that reduced cooling power. Recently, Chen et al. [23] proposed mesoporous photonic structures and random dielectric microsphere coatings [24], which have excellent solar reflectiveness and high mid-infrared emittance, while the reported net cooling power is less \(80\text{ W}{\text{m}}^{-2}\) for both studies.

Today, varieties of material structures like photonic [23, 25], porous and coating polymer [20, 26], nanoparticles [27], plasmonic and microsphere coating [24, 28], and Metal-dielectric –metal (MDM) metamaterials [19, 29] have become popular experimental and numerical areas to improve cooling power both at night and daytime. Particularly, thin-film optical filters (MDM) are receiving the most attention recently [30]. For example, Lee et al. [8] in 2017 and Liu et al. [29] in 2021 conducted research on a one-window and narrow band absorber/emitter MDM for nighttime. On the other hand, Zu et al. [31] in 2022 joined experimental work using zeolite material, which has high solar reflectivity and Yan et al. [32] in 2023 develop two 10-layer \({\text{SiO}}_{2}\) metamaterial radiative coolers with complicated structures that are doped with cylindrical \({\text{MgF}}_{2}\). Nonetheless, achieving unity emissivity in the infrared atmospheric windows and solar reflection requires a significant amount of effort to be put into the previous work. MDM is a type of man-made (artificial) structure that is occasionally created with peculiar properties not present in conventional materials [33] and gets attention for enhancing cooling performance. Veselago carried out the initial theoretical investigations on electromagnetic MDM in 1968 [34], and Pendry et al. [35] presented the first experimental investigation later, in 2000.

Achieving a high-performance radiative cooler that has high solar reflection and nearly-ideal strictly selective unity infrared emissivity is still a significant and challenging issue, especially for the radiative cooler at day time. Additionally, most of the previous works did not consider \({\text{P}}_{\text{cond}+\text{conv}}\) (loss of power due to conduction and convection) for net power calculation, which minimizes the net cooling. Accordingly, the aim of this study is to get maximum net cooling power and a cool environment below ambient temperature based on high solar reflective and near-unit thermal emittance in three windows by using MDM structure. To improve the mentioned issue, we present a new design that is based on the three layers MDM micro honeycomb structure, which can cool below ambient temperature even considering the \({\text{P}}_{\text{cond}+\text{conv}}\). In the same vein, we found significant net cooling power of 138.2 W⁄m2 and 198 W⁄m2 during the day and nighttime receptivity. Over all, as compared this study with previous work; high infrared absorber/emitter in all three windows simultaneously, high solar reflection, high net cooling power, low cost materials and easily fabrication are the improved goal in this study.

Materials and methods

An electromagnetic wave may be absorbed, reflected, or transmitted in the material system [36]. Energy conservation is used to determine the absorbance/emittance indirectly using \(\text{A}+\text{T}+\text{R}=1\) and Kirchhoff’s law, which states that under thermodynamic equilibrium conditions, materials emissivity and absorptivity are equal, is used to determine the absorbance indirectly using scattering parameters (S parameters) during the simulation process [37]. Therefore, a wave that is absorbed, reflected, or transmitted is evaluated by the Kirchhoff rule using Eq. (1).

$${\text{A}}\left(\upomega \right) = 1 - \left| {{\text{S}}_{11} } \right|^{2} - \left| {{\text{S}}_{12} } \right|^{2} .$$
(1)

Where; \(\text{A}\left(\upomega \right)\), \({\text{S}}_{12}\) and (\({\text{S}}_{11}\)) are absorptivity, transmisivity, and reflectivity, respectively. Since the ground layer is nickel (metal) and the opaque materials do not transmit sunlight through themselves [38], the sum of Kirchhoff’s law on Eq. (1) has improved as follows:

$${\text{A}}\left(\upomega \right) = 1 - \left| {{\text{S}}_{11} } \right|^{2}$$
(2)

The impedance matching degree between the micro/nano structure and free space can be determined by the real part ((\(\text{Re}(\text{Z})\))) and imaginary part ((\(\text{Im}(\text{Z})\))). The micro/nano structure’s emission properties is given by \(\text{Z}=\sqrt{\frac{{(1+{\text{S}}_{11})}^{2}-{{\text{S}}_{21}}^{2}}{({1-{\text{S}}_{11})}^{2}-{{\text{S}}_{21}}^{2}}}\). Therefore, the “S” parameters provide the effective impedance (Z) of the micro/nano structure.

As shown in Fig. 1a, we designed a three-dimensional (3D) cylinder-centered honeycomb MDM absorber/emitter using nickel (Ni) film and a titanium dioxide (TiO2) spacer. TiO2 is selected as a dielectric material due to its wide band gap, high refractive index, stable chemical characteristics, and transparency to the majority of infrared radiation [39]. On the other hand, Ni is selected for metal layers due to its high extinction coefficient. It absorbs infrared depending on the Ni thickness, non-easy oxidizes and less light energy to enter [40]. The TiO2 and Ni optical constants used in this study are taken from Kischkat’s [41] and Rakic’s [42] research respectively. The designed emitter experiences a plane wave incident along the z-axis with a power of 1W and a periodic boundary condition set up in both the x and y directions for the unit cell. The differential version of Maxwell’s equations was numerically investigated using the finite element method (FEM), and structural design, calculations, and analysis of parameters were performed using the COMSOL-MULTI PHYSICS package software. The perfect-matched layer was assigned to the top and bottom of computational domains during numerical analysis in order to reduce reflection [37]. In a designed emitter, both magnetic polarization (MP) and surface plasma polariton (SSP) are created [43]. The high absorptivity/emissivity in the cut wavelength range result from TM and TE. Kirchhoff’s rule was applied to evaluate the absorptivity/emissivity, and solar reflectivity. The fabrication of the designed structure can be done layer-by-layer with e-beam patterning [44] or inductively coupled plasma reactive-ion etching [45, 46].

Fig. 1
figure 1

a Three dimensions (3D) honeycomb MDM for passive radiative cooling model. b Schematic of unit cell of MDM

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The overall working wavelength for this study is 0.3–27 µm, and the unit cell period \({\text{P }} = { }16\;\upmu {\text{m}}\) is used to ensure the designed microstructure. The mean thermal emitance for three different atmospheric windows \(\left( {\overline{\upvarepsilon }_{{{\text{ther}}}} = 2.5 - 5\;\upmu {\text{m,}}\;8 - { }14\;\upmu {\text{m }}\;{\text{and }}\;16 - 27\;\upmu {\text{m}}} \right)\) at an optimized structure was calculated to evaluate the designed emitter performance using Eq. (4). Additionally, the mean solar reflective (\(\left( {{\overline{\text{R}}}_{{{\text{solar}}}} = 0.3{ } - 2.5\;\upmu {\text{m }}} \right)\)) was evaluated as a ratio of the reflected solar intensity over the whole solar spectrum to the integral solar intensity within the same range, which was calculated as Eq. (3).

$${{{\overline{\text{R}}}_{{{\text{solar}}}} = \mathop \smallint \limits_{{\uplambda _{1} }}^{{\uplambda _{2} }} {\text{d}}\uplambda {\text{I}}_{{{\text{AM}}1.5}} \left( {\uplambda ,0} \right){\text{R}}\left( {\uplambda ,0} \right)} \mathord{\left/ {\vphantom {{{\overline{\text{R}}}_{{{\text{solar}}}} = \mathop \smallint \limits_{{\uplambda _{1} }}^{{\uplambda _{2} }} {\text{d}}\uplambda {\text{I}}_{{{\text{AM}}1.5}} \left( {\uplambda ,0} \right){\text{R}}\left( {\uplambda ,0} \right)} {\mathop \smallint \limits_{{\uplambda _{1} }}^{{\uplambda _{2} }} {\text{d}}\uplambda {\text{I}}_{{{\text{AM}}1.5}} \left( {\uplambda ,0} \right)}}} \right. \kern-0pt} {\mathop \smallint \limits_{{\uplambda _{1} }}^{{\uplambda _{2} }} {\text{d}}\uplambda {\text{I}}_{{{\text{AM}}1.5}} \left( {\uplambda ,0} \right)}}$$
(3)

And thermal emittance calculated using Eq. (4)

$${{\overline{\upvarepsilon }_{{{\text{ther}}}} = \mathop \smallint \limits_{{\uplambda _{1} }}^{{\uplambda _{2} }} {\text{d}}\uplambda {\text{I}}_{{{\text{BB}}}} \left( {{\text{T}}_{{{\text{sur}}}} ,\uplambda } \right)\upvarepsilon _{{{\text{sur}}}} \left( {\uplambda ,\uptheta } \right)} \mathord{\left/ {\vphantom {{\overline{\upvarepsilon }_{{{\text{ther}}}} = \mathop \smallint \limits_{{\uplambda _{1} }}^{{\uplambda _{2} }} {\text{d}}\uplambda {\text{I}}_{{{\text{BB}}}} \left( {{\text{T}}_{{{\text{sur}}}} ,\uplambda } \right)\upvarepsilon _{{{\text{sur}}}} \left( {\uplambda ,\uptheta } \right)} {\mathop \smallint \limits_{{\uplambda _{1} }}^{{\uplambda _{2} }} {\text{d}}\uplambda {\text{I}}_{{{\text{BB}}}} \left( {{\text{T}}_{{{\text{sur}}}} ,\uplambda } \right)}}} \right. \kern-0pt} {\mathop \smallint \limits_{{\uplambda _{1} }}^{{\uplambda _{2} }} {\text{d}}\uplambda {\text{I}}_{{{\text{BB}}}} \left( {{\text{T}}_{{{\text{sur}}}} ,\uplambda } \right)}}$$
(4)

The abbreviations of Eq. (3) and Eq. (4) are defined under Eq. (9). The transmissivity cooler is zero throughout the full wavelength range due to opaque structure has non-transmittance.

Cooling power analysis

The models and computation analysis are the main aspects of determining passive radiative cooling performances. There are two key parameters that are indicative of cooling capability. The first key is maximizing cooling output power (\({\text{P}}_{\text{net}}\)). To attain \({\text{P}}_{\text{net}}> 0\) for a given surface temperature (\({\text{T}}_{\text{sur}}\)) and ambient temperature (\({\text{T}}_{\text{amb}}\)), the emissivity must be high inside the atmospheric transparency windows \(\left( {2.5 - 5\;\upmu {\text{m}},{ }8 - 14\;\upmu {\text{m}},{ }\;{\text{and}}\;{ }16 - 27\;\upmu {\text{m}}} \right)\) and high solar reflectivity \(\left( {0.3 - 2.5{ }\upmu {\text{m}}} \right)\). The emitter surface temperature (\({\text{T}}_{\text{sur}}\)), the surrounding air temperature (\({\text{T}}_{\text{atm}}\)), the emissivity of the emitter (\({\upvarepsilon }_{\text{sur}}(\uplambda ,\uptheta )\)) and atmospheric emissivity (\({\upvarepsilon }_{\text{atm}}(\uplambda ,\uptheta )\)) are identified to determine net cooling power. \({\text{T}}_{\text{sur}}\) is strongly connected to the designed emitter [47]. The second key is ambient temperature, which is the condition for making the surface temperature below ambient temperature. A surface’s net cooling power (\({\text{P}}_{\text{net}}\left( {\text{T}}_{\text{sur}} ,{\text{T}}_{\text{atm}}\right)\) is calculated by comparing the power flowing into and away from it [48] at a given structure of area (A) and calculated by Eq. (5).

$${\text{P}}_{{{\text{net}}}} \left( { {\text{T}}_{{{\text{sur}}}} ,{\text{T}}_{{{\text{atm}}}} } \right) = {\text{P}}_{{{\text{rad}}}} \left( {{\text{T}}_{{{\text{sur}}}} } \right) - {\text{P}}_{{{\text{atm}}}} \left( {{\text{T}}_{{{\text{atm}}}} } \right) - {\text{P}}_{{{\text{sun}}}} \left( {{\text{T}}_{{{\text{sun}}}} } \right) - {\text{P}}_{{{\text{cc}}}}$$
(5)

where, \({\text{P}}_{\text{rad}}\left({\text{T}}_{\text{sur}}\right)\), is the power emitted by the proposed radiative coolers, \({\text{P}}_{\text{atm}}\left({\text{T}}_{\text{atm}}\right)\) is the amount of heat received by the thermal radiation of the atmosphere, \({\text{P}}_{\text{sun}}\left({\text{T}}_{\text{sun}}\right)\) is the structure’s absorption of incident solar energy and \({\text{P}}_{\text{cond}+\text{conv}}\) is the loss of power due conduction and convection [22, 48]. They can be calculated by Eq. (6), Eq. (7), Eq. (8) and Eq. (9) respectively.

$${\text{P}}_{{{\text{rad}}}} \left( {{\text{T}}_{{{\text{sur}}}} } \right) = 2\uppi {\text{A}}\mathop \smallint \limits_{0}^{{{\raise0.7ex\hbox{$\uppi $} \!\mathord{\left/ {\vphantom {\uppi 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} {\text{d}}\uptheta \sin\uptheta \cos\uptheta \mathop \smallint \limits_{0}^{\infty } {\text{d}}\uplambda {\text{I}}_{{{\text{BB}}}} \left( {{\text{T}}_{{{\text{sur}}}} ,\uplambda } \right)\upvarepsilon _{{{\text{sur}}}} \left( {\uplambda ,\uptheta } \right)$$
(6)
$${\text{P}}_{{{\text{atm}}}} \left( {{\text{T}}_{{{\text{atm}}}} } \right) = 2\uppi {\text{A}}\mathop \smallint \limits_{0}^{{{\raise0.7ex\hbox{$\uppi $} \!\mathord{\left/ {\vphantom {\uppi 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} {\text{d}}\uptheta \sin\uptheta \cos\uptheta \mathop \smallint \limits_{0}^{\infty } {\text{d}}\uplambda {\text{I}}_{{{\text{BB}}}} \left( {{\text{T}}_{{{\text{atm}}}} ,\uplambda } \right)\upvarepsilon \left( {\uplambda ,\uptheta } \right)\upvarepsilon _{{{\text{atm}}}} \left( {\uplambda ,\uptheta } \right)$$
(7)
$${\text{P}}_{{{\text{sun}}}} \left( {{\text{T}}_{{{\text{sun}}}} } \right) = {\text{A}}\mathop \smallint \limits_{0}^{\infty } {\text{d}}\uplambda {\text{I}}_{{{\text{AM}}1.5}} \left( {\uplambda ,0} \right)\varepsilon_{{{\text{sur}}}} \left( {\uplambda ,0} \right)$$
(8)
$${\text{P}}_{{{\text{cond}} + {\text{conv}}}} \left( {{\text{T}}_{{{\text{sur}}}} , {\text{T}}_{{{\text{atm}}}} } \right) = {\text{Ah}}_{{\text{c}}} \left( {{\text{T}}_{{{\text{atm}}}} - {\text{T}}_{{{\text{sur}}}} } \right)$$
(9)

Here, \({\text{I}}_{{{\text{BB}}}} \left( {{\text{T}},{\uplambda }} \right) = 2{\text{ch}}/{\uplambda }^{5} \left( {{\text{e}}^{{\frac{{{\text{hc}}}}{{{\lambda K}_{{\text{B}}} {\text{T}}}} - 1}} } \right)\) is spectral distribution intensity of a black body according planks law at operations temperature T, λ is the wavelength, c is the speed of light, K is the Boltzmann constant, and h is the Planck constant. Where; \({\upvarepsilon }_{\text{sur}}(\uplambda ,\uptheta )\) directional surface emissivity of emitter at wavelength\(\uplambda\), \({\upvarepsilon }_{\text{atm}}(\uplambda ,\uptheta )\) is emissivity of the atmosphere and \({\text{h}}_{\text{c}}\) is the sum of the conduction and convection heat transfer coefficients. The spectral emissivity of the atmosphere is given by the formula \({\upvarepsilon }_{\text{atm}}\left(\uplambda ,\uptheta \right)=1-\text{t}{(\uplambda )}^{1/\text{cos}\theta }\), where \(\text{t}(\uplambda )\) is the spectral transmittance at the zenith that we acquired using MODTRAN (V 6.0, Spectral Sciences Inc., USA and Gemini Telescopes, Science and Technologies). The air mass AM1.5 and water vapor column 1.0 mm are assumed to generate data. We suppose the MDM structure faces the sun, IAM1.5 (λ) is the spectrum, which is the direct normal irradiance from the sun at the wavelength \(\uplambda\) and Global Tilt spectrum with irradiance of \(994{ }{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} }}} \right. \kern-0pt} {{\text{m}}^{2} }}\).

Model verification

The authenticity of the data was cross-checked in different ways to verify the model. Firstly, the simulated result is compared with work previously reported experimentally by Lee et al. [49] and Kim et al. [50], as shown in Fig. 2a, b, respectively. Figure 2 a illustrates the emissivity of a cylindrically designed metal-dielectric-metal (MDM) emitter we obtained by simulation (black line) and the emissivity obtained experimentally by Kim et al. (red line) with a 1.8  µm diameter cylinder, 3 µm unit cells, and a \(0.{2}\;\upmu {\text{m}}\) dielectric thickness. Similarly, Fig. 2b illustrates the emissivity of a cylindrically designed metal-dielectric-metal emitter by simulation (red line) and experimentally (black line) reported by Lee et al. with a 1.57 µm diameter cylinder, 3 µm unit cells, and a 0.1 µm dielectric thickness. The numerical way that we regenerated the data using the FEM method and COMSOL software agreed with the result reported earlier experimentally. This shows that the FEM is a valid tool to generate accurate data.

Fig. 2
figure 2

verification of simulated model. a Experimental (red lene) [50] and simulated absorptivity/ emissivity cylinder MDM emitter with \({\text{d}} = 1.8{ }\upmu {\text{m}}.\) b the experimental (red lene) [49] and simulation absorptivity/ emissivity cylinder MDM desighn with \({\text{d}} = 1.57\;\upmu {\text{m}}\) (color figure online)

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Correspondingly, we have considered the effect of the number of unit cells on the emitance and reflectance capacity to validate the data. As shown in Fig. 3, the number of unit cells was taken from 1 to 4, and the variance of mean reflectance and mean emittance with the number of unit cells is significantly unchanged. These results indicate that the FEM method is a valid tool to generate accurate data.

Fig. 3
figure 3

Simulation absorptivity/emissivity and reflectivity of honey ben MDM emitter with different number of unit cell

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Considering the mesh size, it should balance computation accuracy with valid results. Since the solar reflection and thermal emissivity simulated spectrum at small mesh sizes is steady state, the maximum mesh size is selected at 0.3 μm to ensure the accuracy of the simulation results. Lastly, in 2021, Chen et al. [24] conducted research using FEM and FDTD on microsphere coatings for passive cooling and proved that the FEM tool is valid.

Results and discussions

Figure 4a (red area) and Fig. 4b (blue area) indicate a global AM1.5 solar irradiance spectrum below 2.5 µm and normalize three atmospheric transparency windows in the zenith direction, respectively. Due to the fact that the reflectance of solar irradiation wavelengths beyond 2.5 µm has a significantly small influence on net cooling [2], we assumed a 0.3–2.5 µm wavelength range to calculate the structure’s refelection of incident solar energy \({\text{P}}_{\text{sun}}\), as observed in Fig. 4a (red area). The three atmospheric windows \(\left( {2.5{-}5\; \upmu {\text{m}}, \;8{-}14 \;\upmu {\text{m}},\;{\text{ and}}\; 16 {-}27\; \upmu {\text{m}}} \right)\) were considered, and especially the last two of them fall in the blackbody’s greater thermal radiation regions at a temperature of around 300 K, as shown on Fig. 5b. The direct normal solar irradiation (\({\text{P}}_{\text{sun}}\)) calculation is \({\text{I}}_{{{\text{AM}}1.5}} \left( {\uplambda } \right) = { }994{ }{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} }}} \right. \kern-0pt} {{\text{m}}^{2} }}\).

Fig. 4
figure 4

a A reference of AM 1.5 global solar spectra (red area) and emissivity of designed MDM cooler (green line). b A modeled normalization of infrared atmospheric transmittance (blue area) and simulated emissivity/absorptivity of cooler (black line) at optimization of \({\text{h}}_{1} = 3\;\upmu {\text{m}},{\text{ h}}_{2} = 2.5\;\upmu {\text{m}},{\text{ h}}_{3} = 0.3\;\upmu {\text{m}},{\text{ b}} = 0.7\;\upmu {\text{m}},{\text{ D}} = 3\;\upmu {\text{m}},{\text{ P}} = 16\;\upmu {\text{m}}\) (color figure online)

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Fig. 5
figure 5

a Desighned of three different MDM cooler strucure. b Blackbody irradiance spectra transmittance at 300 K temperature

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Increasing mean emissivity in the target windows and mean increasing reflectivity in the solar irradiation are the main issues in improving the overall net cooling power. The maximum solar irradiation intensity occurring in the 0.3–1.5 µm wavelength range and at optimized and normal incidence, the designed cooler achieved 0.98% mean solar reflectance in the \(0.3{-}1.5 \;\upmu {\text{m}}\) wavelength range. However, the designed cooler can successfully reflect 0.95% in the overall wavelength range \(\left( {0.3{-}2.5 \;\upmu {\text{m}}} \right)\) at optimized parameters of \({\text{h}}_{1} = 3\;\upmu {\text{m}}, {\text{h}}_{2} = 2.5\; \upmu {\text{m}}, {\text{h}}_{3} = 0.3 \;\upmu {\text{m}}, {\text{b}} = 0.7\; \upmu {\text{m}}, {\text{D}} = 3\;\upmu {\text{m}}, \; {\text{and}} \;{\text{P}} = 16\; \upmu {\text{m}}\) as observed in Fig. 4a (green line). Therefore, the 0.95% total solar reflectance achieved in this article is the major factor that increased the net cooling (\({\text{P}}_{\text{net}})\) performance during the daytime. On the other hand, the cooler has high selective and ultra-broadband emissivity in transparent windows. Figure 4b (black line) shows the emissivity/absorptivity spectrum of the designed cooler in the \(2.5{-}5 \;\upmu {\text{m}}, 8{-}14 \;\upmu {\text{m}}, \;{\text{and}}\; 16{-}27 \;\upmu {\text{m}}\) wavelength ranges and normalized atmospheric transmittance (blue area).

In this study, cooler achieved 0.84 emissivity in the first windows \(\left( {2.5 {-}5 \;\upmu {\text{m}}} \right)\)\(,\) 0.98 emissivity in the middle windows \(\left( {8{-}14 \;\upmu {\text{m}}} \right)\), and 0.73 emissivity in the last window \(\left( {16{-}27\;\upmu {\text{m}}} \right).\) Effective coupling between different resonant modes, including surface plasmon polariton, magnetic polariton, and the tungsten interband transition, is crucial to achieving virtually high emittance in the studied range from ultraviolet to far-infrared. The high percentage of absorptivity/emissivity achieved in mid-infrared \(\left( {8{-}13\;\upmu {\text{m}}} \right)\) is due to magnetic polariton (MP). Since the blackbody radiation approaches high in MIR region, as shown in Fig. 5b, it has high contribution to enhance net cooling power. The final two windows are situated in the blackbody’s greater thermal radiation zone at an ambient temperature of around 300 K. Furthermore, we compared the absorbance/emittance performance of three different cooler structures, namely, full-designed (black line), without-cylinder-designed (red line), and without honeycomb (blue line), as shown in Fig. 5a. As seen from the comparison, a broad band emittance was obtained when the cooler was designed as a cylindrical-centered honeycomb structure (full design).

The designed absorber/emitter has impedance-matched to free space [51, 52] by matching the intended structure’s impedance to the incoming signal’s impedance through optimization and preventing absorption/transmission of solar irradiation. During simulation, the effect of parameters on absorber/emitter performance is analyzed. However, the values of \("{\text{h}}_{4}", "\text{a}"\) and \("\text{L}"\) are unchanged throughout all simulations and fixed at \({\text{h}}_{4} = 0.5 \;\upmu {\text{m}}, {\text{a}} = 0.15\;\upmu {\text{m}}\; {\text{and}}\;{\text{ L}} = 13\;\upmu {\text{m}}\).

Effect of cylinder height (\({\mathbf{h}}_{1}\)) and dielectric thickness (\({\mathbf{h}}_{3}\)) on radiation properties

Optimization is one of the ways to improve impedance matching to increase surface absorbance efficiency in atmospheric transparency windows. The energy density of electromagnetic waves propagating in materials is affected by both electric and magnetic fields. As a result, the height of the cylinder and the dielectric thickness greatly influence the resonance frequency of an MDM absorber/emitter. The effect of cylinder height (h1) on a selective emitter’s spectrum emissivity is investigated. In all target atmospheric windows, the designed cooler emissivity slightly increased as the value of h1 increased from \(1 \mu \text{m to }3 \mu \text{m}\) and gradually decreased as the value of h1 increased from \(3 \mu \text{m to }7 \mu \text{m}\). On the other hand, the emitter loses ultra-selective emittance and becomes a narrow emitter as h1 exceeds 7 μm. If the emissivity of the emitter is in a narrow band, the average emissivity at the target wavelength decreases, which reduces the cooling performance. The emitter reached maximum selective and ultra-broadband emissivity across all atmospheric windows at \({\text{h}}_{1} = 3\;\upmu {\text{m}},{\text{ h}}_{2} = 2.5\;\upmu {\text{m}},{\text{ h}}_{3} = 0.3\;\upmu {\text{m}},{\text{ b}} = 0.7\;\upmu {\text{m}},{\text{ D}} = 3\;\upmu {\text{m}},{\text{ and }}\;{\text{P}} = 16\;\upmu {\text{m}}\) as shown in Fig. 6a (blue line). This finding suggests that the cylinder height absorber or emitter has an impact on spectra efficiency.

Fig. 6
figure 6

Emissivity/absorptivity of MDM cooler with different parameter variations. a Height of cylinder (h1). b Dielectric tackiness (h3) (color figure online)

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Usually, the resource-frequency junction between metal and dielectric produces an electric and magnetic field. Therefore, as the metal gap (spacer) width changed, the resonance frequency also changed, which determined the absorbance/emitance of the cooler. In this study, the impact of dielectric thickness (\({\text{h}}_{3}\)) on absorbance/emitance is investigated by varying (\({\text{h}}_{3}\)), as shown in Fig. 6b. The average emissivity in target windows increases as the dielectric thickness (\({\text{h}}_{3}\)) increases from \(0.1{ }\upmu {\text{m }}\;{\text{to}}\;{ }0.7{ }\upmu {\text{m}}\). On the other hand, as values of (\({\text{h}}_{3}\)) are increased from 0.3 µm to longer wavelengths, the emissivity of the emitter or cooler in the second and third windows gradually shifts to longer wavelengths, and the selective ultra-broad band approach to broadband in the \(2.5{-}30\; \upmu {\text{m}}\) wavelength range. Due to the fact that non-selective absorbance of absorber in the target wavelength range can reduce cooling performance, the absorbance of coolers at \({\text{h}}3{ } > { }0.3\;\upmu {\text{m}}\) slowly become unimportant. According to the simulation result, the designed emitter/absorber reached the highest average selectively and ultra-broadband emissivity across the target wavelength range at \({\text{h}}_{3} = 0.3\;\upmu {\text{m}}\). This result briefly indicates that the absorbance/emittance of absorber/emitter performance in required windows is influenced by variations in dielectric thickness (\({\text{h}}_{3}\)).

Effect of honey been height (\({\mathbf{h}}_{2})\) and honey been width (b) on radiation properties

In order to fully investigate how geometry parameters influence the spectral absorbance/emittance, the effect of honeycomb height (h2) and honeycomb width (b) on cooler was evaluated. As the value of h2 increases from \(1 \;{\text{to }}\;2.5 \;\upmu {\text{m}}\), the absorptivity/emissivity of the designed structure increase gradually in the second window and create another peak in the third window due to the magnetic polarization effect. However, as the value of h2 increases from 2.5 µm to 4 µm, the absorptivity/emissivity of the designed structure slowly decrease in the second window. On the other hand, the absorptivity/emissivity of the designed emitter shift to a longer wavelength and broadband in the third window as the value of h2 increases from \(2.5 \;\upmu {\text{m}} \;{\text{to}}\; 4\; \upmu {\text{m}}\), as shown in Fig. 7a. Although the absorptivity/emissivity increased with the value of h2 in the third window, they gradually move out of the target wavelength range. Obviously, the absorption of sunlight in an unwanted wavelength range reduces the cooling efficiency. Therefore, in the target wavelengths, nearly perfect selective ultra-broadband absorbance/emittance was achieved at \({\text{h}}_{1} = 3\;\upmu {\text{m}}, {\text{h}}_{2} = 2.5\; \upmu {\text{m}}, {\text{h}}_{3} = 0.3 \;\upmu {\text{m}}, \;{\text{b}} = 0.7\;\upmu {\text{m}}, {\text{D}} = 3\;\upmu {\text{m}}, \;{\text{and}}\; {\text{P}} = 16\;\upmu {\text{m}}\) geometry optimized as illustrated on Fig. 7a (green line).

Fig. 7
figure 7

Emissivity/absorptivity of MDM cooler Change with; a height of honeycomb width. b Base of honeycomb (color figure online)

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Additionally, the impact of honeycomb width (b) was taken into consideration. Changing the value b shows the effect only in the second window. As shown in Fig. 7b, as the value of b increases from \(0.7\; {\text{to}} \;2.7\; \upmu {\text{m}}\), the cooler absorptivity/emissivity in the first and third windows do not change significantly. However, as the value of “b” increase from \(0.7\;{\text{ to}}\; 2.7\;\upmu {\text{m}}\), the absorptivity/emissivity of the designed cooler decreases gradually in the second window. Through optimizations, at \({\text{h}}_{1} = 3\;\upmu {\text{m}}, {\text{h}}_{2} = 2.5\; \upmu {\text{m}}, {\text{h}}_{3} = 0.3 \;\upmu {\text{m}}, \;{\text{b}} = 0.7\;\upmu {\text{m}}, {\text{D}} = 3\;\upmu {\text{m}},\; {\text{and}}\; {\text{P}} = 16\;\upmu {\text{m}}\), the high average and ultra-broadband emissivity were obtained in the target wavelength range. This result shows that honeycomb width clearly influences the performance emissivity of the emitter.

Effect of diameter of cylinder (\(\mathbf{D}\)) and width of periodic unit (\(\mathbf{P}\))

In MDM electromagnetic properties, the periodic unit cell arrangement is crucial. As a result, we took into account the honeycomb unit cell impact when analyzing the emitter’s spectrum emittance performance. Figure 8b shows that, as the value of “P” increases from \(14{ }\upmu {\text{m }}\;{\text{to}}\;{ }16{ }\upmu {\text{m }}\), the absorptivity/emissivity of the designed structure decreases gradually in the second window and increases as the value of “P” increases from \(16{ }\upmu {\text{m }}\;{\text{to}}\;{ }19{ }\upmu {\text{m}}\). However, the average emissivity in the third window was mostly the same, while the emissivity range shifted to a longer wavelength as the value of “P” increased from \(14{ }\upmu {\text{m }}\;{\text{to }}\;19{ }\upmu {\text{m }}\). This finding is in agreement with [53], which reported that the emission shifted to longer wavelengths as particle size increased. In the fit wavelength range, the emitter obtained broadband emissivity at optimized structure (blue line). On the other hand, the emitter becomes narrow and ultra-selective as the periodic unit cell increases in wavelength.

Fig. 8
figure 8

Emissivity/absorptivity of MDM cooler with different parameters. a Diameter of cylinder (D). b Period of MDM unit cell (P)

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Further, the cylinder diameter effect on absorbance performance is analyzed. Figure 8a shows that as the cylinder diameter (D) increased from \(1.5{ }\upmu {\text{m }}\;{\text{to}}\;{ }3{ }\upmu {\text{m}}\), the ultra-broadband selective emitter lost and became a simple broadband emitter. However, at \({\text{D }} = { }3{ }\upmu {\text{m}}\), the emitter or absorber becomes an ultra-broadband selective emitter. But the minimum average of emitance/absorbance achieved at \(\text{D }= 1.5 \mu \text{m}\) as compared to emitance/absorbance at D = 0.7 μm. This difference implies that the value of the parameters affects the emissivity. Thus, maximum emissivity, selective emission, and ultra-broadband emission in the identified wavelength range is obtained through optimizing geometry at \({\text{h}}_{1} = 3\; \upmu {\text{m}}, {\text{h}}_{2} = 2.5 \upmu {\text{m}}, {\text{h}}_{3} = 0.3 \upmu {\text{m}}, \;{\text{b}} = 0.7\;\upmu {\text{m}}, {\text{D}} = 3\; \upmu {\text{m}}, \;{\text{and}} \;{\text{P}} = 16 \;\upmu {\text{m}}\) (green line). Overall, the findings demonstrate that the variation of “D” has a more discernible impact on second windows \(\left( {8{-}13\; \upmu {\text{m}}} \right)\).

Angular emissivity and polarization independent

The influence of incidence angles on the spectrum emissivity of MDM emitters is considered, as shown in Fig. 9a. The absorbance/emittance curve did not change much when the incidence angle increased from 0° to 60°, which explains that the designed emitter has the ability to emit infrared over a wide angle. The ability of the cooler to maintain a uniform effect at a wide angle plays an important role in the stability of its net cooling performance. The emittance curve significantly dropped, but it still had a respectable emittance when the incident angle was 75°. But the MDM’s emittance stability was lost as the incidence angle exceeded 75°, which perfectly matches the radiative properties of the majority of non-conductor surfaces [54] and a cooling power performance towards zero. Based on this finding, it can be concluded that the emitter is appropriate for plane waves with incident angles ranging from 0° to 75°.

Fig. 9
figure 9

The angle-dependent emissivity of MDM cooler drawn: a by line. b by counter fill

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We investigated the emitter’s polarization independency. Using an electric field vector revolving around the z-axis on the \(\text{xy}\) plane, the spectrum emittance of the MDM emitter was simulated. As shown in Fig. 10a, both transverse magnetic field (TM) and transverse electric field (TE) values are simulated at an angle of incidence of 0°, which is approximate overlap. On the other hand, Fig. 10b indicates that the designed emitter is equal as the azimuthal (ψ) angle increases from 0° to 75°. This result indicates that the designed absorber/emitter is polarization-independent because of the rotational asymmetry. Even if the set incidence angle is 0°, this clarifies that the designed emitter has symmetry.

Fig. 10
figure 10

a computed spectral emittance/absorbance of cooler for TM (black line) and TE (red line) polarization at optimized. b The optimized MDM cooler spectral absorptivity/emissivity as a function of polarization angle (ψ) (color figure online)

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Performance of passive radiative cooling

Calculating the performance of passive radiative cooling is the basic goal of this article. To find the total radiative cooling efficiency, Kirchhoff’s rule facilitates the average absorbance of the designed cooler, which is used to calculate the overall net cooling performance as stated early in Eq. 5–9. The radiative cooling efficiency of a cooler strongly impacted by different factors, like the power emitted from the cooler’s surface, the amount of heat received from the atmosphere, and the non-radiative heat received from the surrounding area, in addition to the cooler’s solar reflectance profile. Based on solar irradiation, net cooling efficiency is divided into two main categories, namely daytime and nighttime efficiency. The net cooling power as a function of surface temperature \(({\text{T}}_{\text{sur}})\) without including convection and conduction heat transfer is calculated. Although it is difficult to obtain high cooling efficiency during the day, in this research, the MDM cooler achieved a net cooling power of 138.2 W⁄m2 at ambient temperature when exposed to direct solar irradiation. This result has made it possible for the cooler to achieve a thermal equilibrium temperature of 264 K, which means our cooler can reduce the ambient temperature by 36 K without taking into account the effects of parasitic convection and conduction, as shown in Fig. 11(black line). The obtained result is high efficiency when compared with previously studied reported, such as Raman et al. [22] and Lin et al. [14].

Fig. 11
figure 11

Total cooling power (\({\text{P}}_{\text{net}}\)) versus surface temperature structure at daytime (\({\text{T}}_{\text{amb}}\) = 300 K); a at zero conduction and convection coefficients (\(\text{hc}=0\)). b At different conduction and convection coefficients (color figure online)

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Additionally, the cooler efficiency is further examined by considering the conduction and convection effects, as seen in Fig. 11(red, blue and green lines). Even considering non-radiative heat exchange a cooler can reduce temperature below ambient temperature. To properly assess non-radiative heat exchange impact, three different combined conduction and convection coefficients, such as \({\text{hc}} = 3,{ }6{\text{ and }}12{ }\left( {{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {\left( {{\text{m}}^{2} {\text{ K}}} \right)}}} \right. \kern-0pt} {\left( {{\text{m}}^{2} {\text{ K}}} \right)}}} \right)\), are taken into consideration. When \({\text{T}}_{\text{amb}} = 300 \text{K}\), the calculated steady-state temperature at \({\text{hc }} = { }3,{ }6{\text{ and }}12{ }\left( {{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} {\text{ K}}}}} \right. \kern-0pt} {{\text{m}}^{2} {\text{ K}}}}} \right)\) becomes 278.5 K, 283.7 K, and 289.8 K, respectively. Since the optimum surface temperature is 300 K, the designed cooler achieved temperatures below the ambient temperature of 21.5 K, 16.3 K, and 10.2 K at \({\text{hc }} = 3,{ }6{\text{ and }}12{ }\left( {{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} {\text{ K}}}}} \right. \kern-0pt} {{\text{m}}^{2} {\text{ K}}}}} \right)\), respectively. This result shows that, even if taking high conduction and convection coefficients \({\text{hc }} = { }12{ }\left( {{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {\left( {{\text{m}}^{2} {\text{ K}}} \right)}}} \right. \kern-0pt} {\left( {{\text{m}}^{2} {\text{ K}}} \right)}}} \right)\) for net cooling power calculation, the cooler can cool down below the ambient temperature at daytime.

Furthermore, within and without considering non-radiative heat exchange, the net cooling efficiency at night was evaluated, as shown in Fig. 12. Due to the fact that the sunlight is blocked at night, the cooling efficiency gets better as the surface emissivity rises until the surface temperature and atmosphere temperatures are equal (\({\text{T}}_{\text{sur}}\hspace{0.17em}-\hspace{0.17em}{\text{T}}_{\text{amb}}\) = 0). This effect is due to the surface’s constant emissivity, and energy from the environment is only selectively received to balance the energy released. Therefore, the cooler achieved a net cooling power of 198 W⁄m2 at ambient temperature with a steady-state temperature of 244 K, which could reduce 56 K below the assumed ambient temperature as indicated in Fig. 12 (black line). Although many researchers have found good net cooling in different ways during the night, the results obtained in this study are high and impressive.

Fig. 12
figure 12

Total cooling power (\({\text{P}}_{\text{net}}\)) versus surface temperature structure at nighttime (\({\text{T}}_{\text{amb}}\) = 300 K); a at zero conduction and convection coefficients (\(\text{hc}=0\)). b At different \(\text{hc}\) (color figure online)

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Additionally, conduction and convection heat exchange are taken into account to determine the cooler performance during the night. The cooling power is decreased when the conduction and convection coefficients increase and the surface temperature is lower than the assumed ambient temperature. The steady-state temperature at night was calculated by taking \({\text{hc }} = { }3,{ }6{\text{ and }}12{ }\left( {{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {\left( {{\text{m}}^{2} {\text{ K}}} \right)}}} \right. \kern-0pt} {\left( {{\text{m}}^{2} {\text{ K}}} \right)}}} \right)\) as described in Fig. 12 (red, blue and green), and the designed cooler achieved temperatures below the ambient temperature of 27.7 K, 19.2 K, and 12 K, respectively. This result briefly indicates that the designed MDM emitter has high net cooling performance at night due to the high average emissivity in target atmospheric windows, and sunlight is blocked at night.

To evaluate the statistics of this research, the relation between emissivity and wavelength at different parameters (\({\text{h}}_{1}, {\text{h}}_{2}, {\text{h}}_{3} ,\text{ b},\text{ D},\text{ P}\)) is fitted with a correlation coefficient (\({\text{R}}^{2}\)). The correlation coefficient describes the quality of the sketched graph, and based on the polynomial function, the correlation coefficient (\({\text{R}}^{2}\)). for all graphs was calculated. Thus, the calculated correlation coefficient of all graphs for this study is\(0.9< {\text{R}}^{2}<0.977\), except for the graph of net cooling power versus surface temperature for day and night. However, high net cooling power is the main finding of our study. The correlation coefficients of surface temperature and net cooling were calculated separately using a linear function for daytime and nighttime, as shown in Table 1. As we can see from Table 1, the observed correlation coefficients during day and night are \(0.987< {\text{R}}^{2}<0.999\) and \(0.988< {\text{R}}^{2}<0.977\) , respectively. This result briefly indicates that the sketched graphs are correlated properly.

Table 1 Correlation coefficient of surface temperature versus net cooling power at different conduction or convection coefficients during daytime and nighttime
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On the other hand, we calculated the emittance performance of each MDM structure in Fig. 5a, which clarifies that the MDM structure plays an important factor in ultra-broadband selective emitters. Different spectra efficiency is obtained for different structures, and the cooler achieved \(138.2{ }{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} }}} \right. \kern-0pt} {{\text{m}}^{2} }}\), \(93.4{ }{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} }}} \right. \kern-0pt} {{\text{m}}^{2} }}\) and \(37.3{ }{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} }}} \right. \kern-0pt} {{\text{m}}^{2} }}\) for full design, without cylinder design, and with only cylinder (without honeycomb) design, respectively. To verify the cooling performance of these structures, non-radiative heat exchange is taken into account. For example, considering \(\left( {12{ }{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {\left( {{\text{m}}^{2} {\text{ K}}} \right)}}} \right. \kern-0pt} {\left( {{\text{m}}^{2} {\text{ K}}} \right)}}} \right)\) conduction and convection coefficients, the designed cooler achieved below the ambient temperature of 10.2 K, 8 K, and 3.4 K for full design, only honeycomb (without cylinder design), and only cylinder (without honeycomb, respectively). Generally, Table 2 analyzes the net cooling power for; full design, without cylinder design, and metal-dielectric-metal with only cylinder design.

Table 2 Comparation of three designed cooler structures at daytime
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Moreover, we referred the previously numerically and experimentally reported with different prospective on metamaterial and photonic structures to compare and demonstrates with our result. For example, the work of Zhai, Y. et al. [15] and Kecebas et al. [30] studied hybrid MDM as shown in Fig. 13a (black dot line) and MDM with 7 layers as shown in Fig. 13a (red line), respectively. In addition, Raman [22] Scholar developed a photonic thin film with 10 layers and achieved a net cooling power of \({4}0.{1}\;{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} }}} \right. \kern-0pt} {{\text{m}}^{2} }}\), which can cool 32 K (5°C) below ambient temperature, as shown in Fig. 13b (red line). Table 3 clearly summarizes the current work, with previous reports focused on: structure, numbers of layers, kinds of materials, AM1.5 solar irradiation, cooling performance below ambient temperature, and net cooling power. This is listed clearly in Table 3. Our cooler minimizes the complexity of structure and fabrication difficulties compared to the multi-layer photonic structures of Raman et al. [22] and Kecebas et al. [30] and maximize cooling performance compared to Lin et al. [14] and Zhai et al. [15].

Fig. 13
figure 13

a Emissivity of MDM reported by Kacebas et al. (red line) and Zhias et al. (blue line). b Emissivity of photonic materials reported by Raman et al. (red line) and Lin et al. (blue line) (color figure online)

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Table 3 Comparation of cooler performance current study with privous studies
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Conclusion

Utilizing spectrum emissive structures that are particularly created in the optical properties of materials has different applications. A spectrum ultra-broadband and selective emitter through the infrared atmosphere transparency window can increase the performance of radiative cooling. In this study, a MDM resonator for radiative cooling was designed. The measurement of absorptivity showed a wide-angle absorption/emission that spectrally matched the primary infrared atmospheric transparency window. The designed cooler achieved emissivity 0.84 in the first windows \(\left( {2.5{-}5 \;\upmu {\text{m}}} \right)\)\(,\) 0.98 in the middle windows \(\left( {8{-}14\; \upmu {\text{m}}} \right)\), and 0.73 in the in the last window \(\left( {16 {-}27\; \upmu {\text{m}}} \right).\) The deigned emitter achieved high-performance radiative cooling with a net cooling power of \(138.2\;{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} }}} \right. \kern-0pt} {{\text{m}}^{2} }}\) and \({198}\;{{\text{W}} \mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} }}} \right. \kern-0pt} {{\text{m}}^{2} }}\) at day and night, respectively. The obtained net cooling power has the ability to cool down to 36 K and 56 K below the ambient temperature during daytime and nighttime, respectively. Overall, the designed cooler/emitter structure will be encouraged to be used for passive radiative cooling since it will lower the peak demand for atmospheric cooling, have a high net cooling power, low coast material consideration, easy to fabricate, and lower non-greenhouse gas emissions.