Near-perfect spectrally-selective metasurface solar absorber based on tungsten octagonal prism array

Abstract

Solar selective absorbers influence the photothermal efficiency of high-temperature solar thermal applications directly and significantly. In present work, a metasurface absorber consisting of an octagonal prism array is proposed, optimized and analyzed. Firstly, the structure parameters of the absorber are optimized, finding the optimal absorber achieves near-perfect spectrally-selectivity compared with the perfect solar absorber. The high solar absorptivity of 0.9591, low emissivity of 0.1594–0.3694, and high photothermal efficiency of 94.72–83.10% are achieved at 1073–1573 K and 1000 suns. Then, the mechanisms leading to the excellent spectral selectivity are investigated, suggesting that the coupling effects of multi-plasmon resonance modes and the impedance matching lead to the high solar absorptivity. Meanwhile, the impedance mismatching is the mechanism to minimize the emissivity in the mid-IR region. Moreover, whether the spectral absorptivity can be changed by structural parameters is investigated, suggesting that the excircle diameter of the first tungsten octagonal prism and the height of SiO₂ under the octagonal prism can influence the spectral absorptivity obviously. Finally, the metasurface absorber is demonstrated to be highly insensitive to both polarization and incident angles. These results suggest that the proposed metasurface absorber should be suitable for high-temperature solar thermal devices.

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1. Introduction

Solar energy, as an abundant, clean, and sustainable renewable energy, has gained much attention in recent years because of its ability to alleviate energy shortage and reduce environmental pollution from fossil fuels.^1–3 Concentrated solar power is a promising technology that generates electricity through solar-thermal conversion and thermal-driven power cycle.⁴ To improve the power cycle efficiency, the temperature of the solar–thermal conversion has been increased continuously during the last two decades.⁵⁵ Recently, a solar power tower system with graphite-based receiver has even been proposed to operate at above 1300 °C.^5,54 However, the radiative thermal loss from the solar absorber increases with the fourth power of temperature, reducing the photothermal efficiency of the absorber significantly.^56,57 To ensure that the solar-electric efficiency, which is the product of the photothermal efficiency and the power cycle efficiency, can be improved effectively under high temperature, the photothermal efficiency is necessary to be as high as possible.

To enhance the photothermal efficiency, the absorber should exhibit high absorptivity in the solar spectrum and low emissivity in the mid-IR region (i.e. good spectral selectivity).⁶ However, there are two problems with present state-of-the-art commercial Pyromark absorber when the temperature rises to 1300 °C. Firstly, the solar absorptivity of this commercial absorber is as high as 0.965 within the solar spectrum, but its spectral emissivity also can be as high as ∼0.85 within the mid-IR region.⁵³ Meanwhile, this absorber cannot withstand the high temperature of above 1100 °C.

To solve the two problems, many absorbers have been proposed in the literature, which can be roughly divided into multilayered absorbers and metasurface absorbers (MAs).

The multilayered absorbers were usually designed to utilize the interference effects among different layers to achieve good spectral selectivity.⁷ For example, He et al. designed a SiO₂/AlCrTaTiZrN absorber, obtaining the high solar absorptance (α_sol) of 0.928 and high photothermal efficiency (η) of 87.7% at 873 K, when the solar concentration ratio is 100.⁸ Qiu et al. fabricated a HfB₂/TiB₂ absorber, which could achieve a high α_sol of 0.932 and a high η of 68.6% at 1073 K, when the solar concentration ratio is 100.⁹ Atasi et al. reported a W/WAlN/WAlON/Al₂O₃ absorber with the α_sol of 0.90, and its ε_tot is as low as 0.15 at 773 K.¹⁰ Nuru et al. fabricated an AlxOy/Pt/AlxOy multilayer absorber, obtaining the α_sol of 0.951, and the ε_tot is as low as 0.08 at 773 K.¹¹ Tian et al. investigated a multilayered stack consisting of SiO₂/Al₂O₃/W/Al₂O₃/W, founding that the α_sol and the photothermal efficiency (η) of it are 0.881 and 82.3% at 673 K, respectively, when the solar concentration ratio is 100.¹² Wang et al. demonstrated a SiO₂–Si₃N₄ multilayer, which could obtain the spectral absorptivity (α_λ) of 0.95 in the solar spectrum and the spectral emissivity of 0.1 in the mid-IR region.¹³ AL-Rjoub et al. deposited a WSiAlN_x/WSiAlO_yN_x multilayer absorber with the α_sol as high as 0.96 and the ε_tot as low as 0.11 at 673 K.¹⁴ Wang et al. developed a Cr/AlCrN/AlCrNO/AlCrO multilayer absorber, and the results showed that the α_sol of 0.94 and the ε_tot of 0.25 at 773 K are obtained.¹⁵

The metasurface absorbers (MAs) were designed to obtain good spectral selectivity through exciting different resonance modes. The geometries of these MAs were designed to possess the sizes equivalent to incident wavelengths to obtain good spectral selectivity through the excitation of multi-plasmon resonance modes. For example, Zhao et al. designed a MA based on C–Si trapezoidal pyramids and Al pyramids, and the results indicated that the average α_λ of 0.9316 within 0.3–1.4 μm was obtained owing to the excitation of Surface Plasmon Polaritons (SPPs).¹⁶ Zhou et al. proposed a MA consisting of SiO₂/Si₃N₄/Ti substrate and Ti rings, which could achieve the average α_λ of 0.9 within 0.3–4 μm and the α_sol of 0.97 by enhancing the synergistic effects of the plasmon resonances.¹⁷ Liu et al. reported a MA based on a TiN disk array, achieving the α_λ higher than 0.90 within 0.316–1.426 μm due to the excitation of plasmonic resonances and their hybrid coupling effects.¹⁸ Chen et al. investigated a MA consisting of Ni disks, obtaining the α_sol of above 0.90 and the η of as high as 89.01% at 800 K by coupling the SPPs, Magnetic Polaritons (MPs), and the intrinsic absorption of Ni.¹⁹ Wu et al. proposed a MA based on nanoporous W/SiO₂ film, and the results indicated that the η of 90.32% at 800 K is obtained owing to the impedance matching with the free space.²⁰ Jiang et al. designed a MA by combining a planar multilayer system and a nanowire array, obtaining the average α_λ of above 0.9 within the wavelength of 0.3–1.909 μm due to the coupling effects of multiple resonance modes.²¹ Hassan et al. designed a MA based on nanowire array, which could achieve the average α_λ of 0.97 at the wavelength of 0.3–1.3 μm.²²

To sum up, even though many solar selective absorbers have been proposed and investigated, however, there are still many problems with these absorbers. Firstly, the photothermal conversion performance of the absorbers has not reached the ideal value. Then, the thermal stability of the absorbers under high temperatures remains relatively low. Finally, the complex structures of some absorbers are difficult to manufacture. Therefore, designing a simple solar absorber that can be easily manufactured and can obtain excellent photothermal conversion performance, eminent thermal stability, incident and polarization angle insensitivity is still a challenging task.

In this article, a spectrally-selective metasurface absorber (MA) based on tungsten octagonal prisms was proposed and investigated. Firstly, structure parameters of the proposed MA were optimized to achieve good spectral selectivity and high photothermal efficiency. Next, a three-dimensional simulation of the electromagnetic fields revealed the physical absorption mechanisms of the MA. In addition, the influences of the structure parameters on the absorption performance were investigated. Finally, the influences of changes in polarization and incident angles were explored. The novelty of this work is that an absorber with simple structure was proposed, and it was proved to be able to achieve higher photothermal efficiency than ten new absorbers proposed within the last five years at various operating conditions. It is well known that 1% improved photothermal efficiency can improve the output of the plant by 0.9–1.4% while keeping investment constant.²³ Thus, the proposed absorber is promising to improve the performance of the plant.

2. Design of the metasurface absorber

The metasurface absorber (MA) proposed for high-temperature solar applications is composed of many structural units which are arranged in a periodic way (see Fig. 1a and b). As illustrated in Fig. 1c, the components of the structural unit (see Fig. 1c) are the first and the second tungsten films, the first and the second SiO₂ films, the first and the second tungsten octagonal prisms, and the SiO₂ octagonal prism. Moreover, considerations for designing different components of the MA are detailed as follows.

Fig. 1 (a) Sketch of a concentrated solar collector; (b) 3D structure of the designed MA; (c) a structural unit.

Firstly, the first SiO₂ film between the first and the second tungsten films was designed to produce magnetic polaritons.²⁴ Then, the tungsten octagonal prism array, the second SiO₂ film, and the second tungsten film were constructed to excite magnetic polaritons as well. Then, localized surface plasmon resonances (LSPRs) will be excited at the vertex of the tungsten octagonal prism.²⁵ Furthermore, at the upper surface of the first and the second tungsten octagonal prisms, surface plasmon polaritons were excited.²⁵ In addition, the SiO₂ octagonal prisms that wrap the tungsten octagonal prisms were constructed to prevent the tungsten from being oxidized and grain growth.²⁶ Moreover, the melting points of the tungsten and SiO₂ are 3673 K and 1996 K, respectively, which are much higher than 1573 K. Hence, the proposed absorber will possess excellent thermal stability. Finally, the designed structure can be fabricated by some mature techniques such as ICP etching, magnetic sputterings, atomic layer deposition, and electron-beam lithography.²⁷

Besides, the structure parameters of the proposed MA are also shown in Fig. 1. Where h₁, h₂, h₃, h₄, h₅, h₆, and h₇ are the heights of different components, and d₁, d₂, and d₃ are the excircle diameters of the SiO₂ octagonal prism, the first and the second tungsten octagonal prisms, respectively. p is the periodicity of the structural unit. In the following sections, firstly, the finite element method is used to calculate the spectral absorptivity of the MA under different structure parameters. Then, the structure parameters would be optimized based on orthogonal experiments to make the spectral selectivity reach the best at high temperature.

3. Simulation methods

A finite element model was developed by solving Maxwell's equations that can describe the solar radiation transport in the proposed MA.²⁸ Owing to the symmetric structure of the MA, only a unit (seen in Fig. 1c) is simulated in the model. In the model, the effects of wavelength on the refractive indexes of the tungsten and SiO₂ are considered,^29,30 as shown in Fig. S1 in the ESI.†^24,25 The transport process of the light in the MA can be described by the Maxwell's equations, which was solved by finite element method using a commercially available software package COMSOL Multiphysics 5.6.³¹

The boundary conditions on the boundaries perpendicular to the x-axis and y-axis are Floquet periodicity boundary conditions. In addition, the boundary conditions on the top surface and bottom surface are port conditions. The port condition on the top surface is used to emit solar radiation into the MA, and the incident angle (θ) and polarization angle (φ) are shown in Fig. 1b and c. The port condition on the bottom surface is used to calculate the transmitted radiation. The height of the first tungsten film (h₁) is set to be 150 nm, which exceeds the penetration depth of incident radiation. Therefore, solar radiation cannot penetrate the MA, which has the spectral transmittance (τ_λ) of zero. The spectral absorptivity (α_λ) and spectral reflectance (ρ_λ) of the MA can be calculated by eqn (1) and (2).^32,33

ρ_λ = |S₁₁|² (1)

α_λ = 1 − ρ_λ (2)

where S₁₁ is the scattering matrix coefficient of the reflection.

Some parameters are defined for evaluating the performance of the MA. The solar absorptivity (α_sol) equals the proportion of the absorbed solar radiation in the incident solar radiation, as shown in eqn (3).³⁴ The total emissivity (ε_tot) equals to the ratio of the radiative power values radiated by the MA and blackbody, as illustrated in eqn (4).²³ The photothermal efficiency (η) equals the ratio of solar radiation transformed into thermal energy and the incident solar radiation, as shown in eqn (5).³⁵

where T_abs, T_amb, C and I_s are the temperature of MA, temperature of ambient, solar concentration ratio and solar flux intensity at AM1.5, respectively; I_AM1.5(λ) is the spectral solar irradiance at AM1.5;³⁶ I_B(λ, T_abs) is the spectral irradiance of blackbody at T_abs, which is calculated by Planck's radiation law, as shown in eqn (6).³⁷

To make sure that the simulation results are insensitive to the mesh number, grid independence tests have been performed as illustrated in Table S1 in the ESI.† To validate the current model, the model have been verified through comparing the results calculated by the present model and Han et al.'s model, as shown in Fig. S2 in the ESI.† The results indicate that the present model can be considered reliable.

4. Results and discussion

In the following paragraphs, firstly, a near-perfect metasurface absorber (MA) is designed by optimizing its structure parameters. Next, the underlying absorption mechanisms giving rise to the near-perfect spectrally-selectivity of the MA were revealed and analyzed. Then, the influences of structure parameters on the performance were illustrated. Finally, sensitivities of the MA to incident angle and polarization angle were studied. In addition, it is worth noting that the incident light defaults to be normally incident TM polarized wave.

4.1 Near-perfect spectrally-selective metasurface absorber

The structures of the metasurface absorber (MA) were optimized by orthogonal tests to obtain good spectral selectivity and solar-thermal conversion performance. In the optimization, the photothermal efficiency (η) under 1573 K and 1000 suns was selected as the object function. After the optimization, a optimal MA with the structure parameters of p = 155 nm, h₁ = 150 nm, h₂ = 10 nm, h₃ = 20 nm, h₄ = 10 nm, d₁ = 150 nm, h₅ = 240 nm, d₂ = 130 nm, h₆ = 70 nm, d₃ = 80 nm and h₇ = 70 nm was obtained.

The AM1.5 solar spectrum and spectral absorptivity of the optimal MA are demonstrated in Fig. 2. It can be found that the α_λ is above 0.9 at the wavelength of 0.285–1.8 μm. Specifically, the α_λ even exceeds 0.98 at the wavelength of 0.373–1.656 μm. According to eqn (3), the optimal MA achieves an excellent solar absorptivity (α_sol) of 0.9591. In addition, the α_λ of a 150 nm tungsten film was also simulated and compared with the optimal MA. As shown in Fig. 2, the α_λ of tungsten is 0.3773–0.7885 lower than that of the optimal MA within 0.285–1.8 μm. Meanwhile, the α_sol of tungsten is 0.5189 lower than that of the optimal MA, indicating that the reasonable design of the optimal MA has improved the optical performance of tungsten greatly. It also can be found in Fig. 2 that the α_λ drops sharply with increasing λ when λ > 1.8 μm, and therefore the α_λ even becomes below 0.06 when λ > 3.616 μm. To sum up, the optimal MA exhibits high absorptivity in the solar spectrum and low emissivity in the mid-IR region.

Fig. 2 AM1.5 solar spectrum and spectral absorptivity of the optimal MA.

In addition, the total emissivity (ε_tot) and photothermal efficiency (η) under different MA temperatures (T_abs) when T_amb = 300 K and C = 1000 suns were calculated through eqn (4) and (5) to further demonstrate the spectral selectivity of the optimal MA. It can be observed from Table 1 that the ε_tot increases with increasing T_abs, and ε_tot is within 0.1594–0.3694 when T_abs = 1073–1573 K. Besides, η decreases with increasing T_abs, and η is within 83.10–94.72% when T_abs = 1073–1573 K.

Table 1 Performance of the optimal MA under different temperatures

C/suns	Tabs/K	Tamb/K	Current optimal MA		Perfect absorber
			εtot	η	εtot	η
1000	1073	300	0.1594	94.72%	0.3487	96.39%
1000	1173	300	0.1990	93.78%	0.3753	94.72%
1000	1273	300	0.2410	92.32%	0.1813	92.85%
1000	1373	300	0.2841	90.20%	0.2214	91.07%
1000	1473	300	0.3272	87.19%	0.2564	88.54%
1000	1573	300	0.3694	83.10%	0.2907	85.08%

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For a perfect solar absorber, it should achieve the highest η under the corresponding working conditions.³⁸ When the wavelength is smaller than a truncation wavelength, its α_λ should be 1. When the wavelength is larger than the truncation wavelength, the its α_λ should be 0.³⁹ The ε_tot and η of the perfect absorber under different T_abs are also calculated when T_amb = 300 K and C = 1000 suns, and the results are shown in Table 1. As illustrated in Table 1, the ε_tot of the optimal MA is just 0.0597–0.0787 larger than that of the perfect absorber when T_abs = 1273–1573 K. Moreover, the η of the optimal MA is just 0.53–0.1.98% lower than that of the perfect absorber when T_abs = 1073–1573 K. Thus, it is concluded that the optimal MA can convert solar energy to thermal energy efficiently at high temperatures, and the spectral selectivity is almost the same as that of the perfect absorber. Hence, the optimal MA can be considered as a near-perfect spectrally-selective absorber.

Furthermore, the performance of the near-perfect MA was compared with that of some previously developed absorbers in Table 2. As can be seen in Table 2, Wu et al. designed a MA based on nanoporous W/SiO₂ film, which can obtain the η of 90.32% that is 2.52% lower than the 92.84% of the near-perfect MA when C = 1 and T_abs = 373 K.²⁰ Wang et al. reported an absorber using manganese-iron oxide nanoparticles, achieving the η of 89.30% that is 5.74% lower than the 95.04% of the present near-perfect MA under C = 1000 and T_abs = 1023 K.⁴⁰ Niranjan et al. studied a W/WAlSiN/SiON/SiO₂ multilayer, which can obtain the η of 89.50% that is 5.01% lower than the 94.51% of the near-perfect MA when C = 100 and T_abs = 773 K.⁴¹ He et al. studied an absorber based on alloy nitride MoTaTiCrN nanofilms, obtaining the η of 86.90% that is 6.92% lower than the 93.82% of the near-perfect MA under C = 100 and T_abs = 823 K.⁴² Ye et al. reported an absorber based on a tungsten sphere and cuboid array, which can achieve the η of 87.56% that is 0.81% lower than the 88.37% of the near-perfect MA when C = 100 and T_abs = 1000 K.⁴³ Zhang et al. designed a chimney-like absorber, which can obtain the η of 91.62% that is 1.83% lower than the 93.45% of the near-perfect MA when C = 1000 and T_abs = 1200 K.⁴⁴ Li et al. reported an absorber based on TiN particles, obtaining the η of 93.00% that is 1.12% lower than the 94.12% of the near-perfect MA when C = 1 and T_abs = 373 K.⁴⁵ Zhao et al. proposed a Al_0.4Hf_0.6NbTaTiZrN MA, which can achieve the η of 74.90% that is 20.45% lower than the 95.35% of the near-perfect MA under C = 100 and T_abs = 673 K.⁴⁶ Raza et al. designed an absorber using SiC–W nanoparticles, achieving the η of 82.68% that is 3.13% lower than the 85.81% of the near-perfect MA under C = 100 and T_abs = 1050 K.⁴⁷ Qiu et al. studied an absorber based on TiB₂–ZrB₂ composite ceramic, which can obtain the η of 83.90% that is 10.61% lower than the 94.51% of the near-perfect MA when C = 100 and T_abs = 773 K.⁴⁸ He et al. reported a double-layer alloy nitride HfNbTaTiZrN absorber, obtaining the η of 90.10% that is 3.75% lower than the 93.85% of the near-perfect MA under C = 100 and T_abs = 823 K.⁴⁹ The above mentioned results demonstrate that the photothermal conversion performance of the present near-perfect MA is better than some previously absorbers.

Table 2 Performance comparisons of the near-perfect MA and some existing absorbers

Absorber	C	Tabs/K	Tamb/K	αsol	εtot	η
Present	1	373 K	0	0.9591	0.2800	92.84%
Ref. 20	1	373 K	0	—	—	90.32%
Present	1000	1023	300	0.9591	0.1410	95.04%
Ref. 40	1000	1023	300	0.9270	0.5500	89.30%
Present	100	773	0	0.9591	0.0693	94.51%
Ref. 41	100	773	0	0.9550	0.1570	89.50%
Present	100	823	300	0.9591	0.0805	93.82%
Ref. 42	100	823	300	0.9230	0.0650	86.90%
Present	100	1000	0	0.9591	0.1329	88.37%
Ref. 43	100	1000	0	0.9535	0.1375	87.56%
Present	1000	1273	300	0.9591	0.2102	93.45%
Ref. 44	1000	1273	300	0.9457	0.2056	91.62%
Present	1	373	300	0.9591	0.0280	94.12%
Ref. 45	1	373	300	0.9500	0.0300	93.00%
Present	100	673	300	0.9591	0.0503	95.35%
Ref. 46	100	673	300	0.8600	0.1950	74.90%
Present	100	1050	300	0.9591	0.1475	85.81%
Ref. 47	100	1050	300	0.9545	0.2000	82.68%
Present	100	773	0	0.9591	0.0693	94.51%
Ref. 48	100	773	0	0.9340	0.2320	83.90%
Present	100	823	300	0.9591	0.0805	93.85%
Ref. 49	100	823	300	0.9600	0.2250	90.10%

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4.2 Mechanisms for the spectrally-selective characteristics

To reveal the mechanisms of the excellent spectral selectivity and the good photothermal performance of the near-perfect MA, the transmission and absorption of solar radiation in the near-perfect MA is simulated. The distributions of the magnitudes of electromagnetic fields and Poynting vectors, the impedance matching between the MA and the free space, and the spectral absorptivity of different components were studied, and the results are as follows.

Firstly, to reveal the dissipation mechanisms of electromagnetic waves within the MA, the Poynting vectors and the distributions of the magnitudes of the electric field (|E|) and magnetic field (|H|) were illustrated in Fig. 3.

Fig. 3 Distributions of the |E|, |H| and Poynting vectors (white arrows) at various wavelengths. (a) |E| in the xz plane at y = 0 nm; (b) |H| in the xz plane at y = 0 nm; (c) |E| in the xy plane at z = 225 nm; (d) |E| in the xy plane at z = 295 nm.

Fig. 3a and b describe the |E| and |H| distributions in the xz plane at y = 0, respectively. As shown in Fig. 3a and b, there are four regions with strong |E| at both sides of the first and second tungsten octagonal prisms, and three regions with strong |H| appear at the upper surface of the first and second tungsten octagonal prisms. These results suggest the excitation of surface plasmon polaritons (SPPs) at the top of the first and the second tungsten octagonal prisms. In addition, two regions with strong |E| arise at the edges of the bottom of the second tungsten octagonal prism, and two regions with strong |H| arise at the first and second SiO₂ films. The |E| and |H| at these regions increase with rising wavelength. These results implicate that magnetic polaritons (MPs) are excited at the first and second SiO₂ films, and the intensity of MPs increases with rising wavelength.

Then, because the xy planes at z = 255 nm and z = 295 nm are at the middle of the first and second tungsten octagonal prisms, they are suitable to be selected as the typical planes to illustrate the dissipation mechanisms of electromagnetic waves within the tungsten octagonal prisms. The |E| distributions in these two planes are shown in Fig. 3c and d, respectively. It can be seen in Fig. 3c and d that regions with strong |E| are strongly concentrated at the vertexes of the first and the second tungsten octagonal prisms, which suggests that the local surface plasmon resonances (LSPRs) are excited. In addition, the |E| increases with rising wavelength, indicating that the intensity of LSPRs increases with rising wavelength.

Finally, the energy transport and absorption of the electromagnetic waves are also visually presented in Fig. 3. As can be seen from Fig. 3, most of the Poynting vectors (white arrows) point to four components, including the two tungsten octagonal prisms, and the two tungsten films. This is because there are multiple plasmonic modes in these parts, efficiently converting solar radiation to thermal energy due to ohmic loss.

As discussed above, it can be concluded that the coupling of SPPs, MPs and the LSPRs leads to the good absorption of the radiation within the solar spectrum.

Then, to better explore the absorption mechanisms of the near-perfect MA, the impedance matching of the MA and the free space was studied. The relation between effective impedance (z_λ) and S parameters can be described by eqn (7).^50,51

where the S₁₁ and S₂₁ are the scattering matrix coefficients of the reflection.

Furthermore, the relation between the z_λ and the α_λ can be expressed by eqn (8).⁴⁴ According to eqn (8), perfect spectral absorptivity (α_λ) can be achieved when the effective impedance z_λ is matched to the impedance of the free space (z₀), as shown in eqn (9). In addition, near-zero absorptivity will be achieved when eqn (10) is met.

Re(z_λ) = Re(z₀) = 1, Im(z_λ) = Im(z₀) = 0 (9)

Re(z_λ) = 0, Im(z_λ) = 1 (10)

where Im(z_λ) and Re(z_λ) are the imaginary and real parts of z_λ of the MA, respectively; Im(z₀) and Re(z₀) are the imaginary and real parts of z₀ of the free space, respectively.

The imaginary part Im(z_λ) and real part Re(z_λ) of the effective impedance z_λ of the near-perfect MA are calculated and illustrated in Fig. 4. It is manifest from the Fig. 4 that Im(z_λ) and Re(z_λ) are nearly 0 and 1 within λ = 0.373–1.656 μm, which agrees with the near-perfect α_λ (>0.98) within this region in Fig. 4. Furthermore, the Im(z_λ) and Re(z_λ) appear dramatic changes within λ = 2–3.5 μm, which causes a rapid decrease in the α_λ. Meanwhile, Im(z_λ) and Re(z_λ) are close to 1 and 0, respectively, when λ > 3.5 μm, which leads to almost 0 of the α_λ. The above results indicate that the impedance of the near-perfect MA highly matches that of the free space within λ = 0.373–1.656 μm, but they doesn't match with each other at all when λ > 3.5 μm.

Fig. 4 The imaginary part Im(z_λ) and real part Re(z_λ) of the z_λ of the near-perfect MA.

Then, to investigate the energy absorption capacities of different components in the near-perfect MA, the spectral absorptivity of the five components was studied. It can be observed from Fig. 5a that the prisms play significant roles in enhancing the absorption performance, and the first and the second tungsten films also contribute some α_λ. This is because the prisms introduce multiple resonance modes which enhance the transports of the electromagnetic waves in the tungsten, where the electromagnetic waves are dissipated quickly due to ohmic loss. Meanwhile, the α_λ curves of the first and the second SiO₂ films are close to zero within the whole solar spectrum. However, the two films are still necessary for improving the α_λ, because they can be combined with adjacent tungsten components to build a metal–dielectric–metal structure for exciting MPs, and also can protect the MA from being oxidized.

Fig. 5 Spectral absorptivity (α_λ) of different parts of the near-perfect MA. (a) α_λ of different components; (b) α_λ of different layers of the prims.

In addition, to analyze the influences of the prisms in the near-perfect MA, the prisms are divided into three layers in Fig. 5b. It is manifest from the Fig. 5b that the α_λ of the layer 1, layer 2 and layer 3 are approximately 0.9–47.1%, 0.3–60.7%, and ∼0 when λ = 0.28–4.0 μm, respectively. As the wavelength increases, the α_λ of layer 2 decreases gradually, resulting in the decrease in the α_λ of the prisms. However, the α_λ values of the first and the second tungsten films are increased at the same time (see Fig. 5a), so the α_λ of the MA is near perfect within λ = 0.373–1.656 μm. Meanwhile, the α_λ of layer 3 is nearly zero, which suggests that this layer barely absorbs the electromagnetic waves. Nevertheless, layer 3 is also essential for the MA, because it can protect the MA from oxidation.

4.3 Influences of structure parameters on the spectral absorptivity

According to the analysis in the previous section, the excellent spectral selectivity of the near-perfect MA is due to the coupling effects of multi-plasmon resonance modes and the impedance matching with the free space at octagonal prisms and underneath films. However, the influences of their structure parameters on the absorption performance of the MA are still unclear. Therefore, geometric influences on the spectral absorptivity were analyzed in this section. Meanwhile, it should be noted that the other parameters remained identical to the optimal parameter values when one parameter was analyzed.

4.3.1 Influences of the structure parameters of tungsten octagonal prisms. The parameters related to the octagonal prisms are the excircle diameters of the first (d₂) and the second (d₃) tungsten octagonal prisms, and the heights of the first (h₆) and the second (h₇) tungsten octagonal prisms. According to the above discussion, the octagonal prisms have important influences on the spectral absorptivity (α_λ) of the MA. Hence, the influences of the four parameters were studied, and the results are presented in Fig. 6.

Fig. 6 Spectral absorptivity (α_λ) of the MA at different structure parameters of tungsten octagonal prisms. (a) Influences of d₂; (b) influences of h₆; (c) influences of d₃; (d) influences of h₇.

It is manifest from the Fig. 6a that the α_λ ascends obviously with increasing d₂ in the whole solar spectrum region. This is because the first tungsten octagonal prism can not only excite SPPs and LSPRs, but also can excite MPs together with the second SiO₂ film and the second tungsten film. Therefore, d₂ has a great influence on the α_λ of the MA. As shown in Fig. 6b, when h₆ = 0.06–0.10 μm, the α_λ varies irregularly and slightly within λ = 0.28–1.8 μm, however it increases slightly with increasing h₆ when λ > 1.8 μm. In addition, when the h₆ increases from 0.1 μm to 0.30 μm, the α_λ declines sharply within λ = 1.0–2.2 μm but increases obviously within λ = 2.2–4.0 μm. As shown in Fig. 6c, when d₃ = 0.06–0.10 μm, the α_λ increases slightly when λ is around 0.4 μm but decreases appreciably within λ = 0.28–2.0 μm with increasing d₃. Moreover, α_λ increases significantly within λ = 2.2–4.0 μm when d₃ increases from 0.10 μm to 0.30 μm. As is presented in Fig. 6d, the increase in h₇ has a little influence on the α_λ within λ = 0.28–4 μm when h₆ = 0.05–0.09 μm. However, the α_λ declines dramatically within λ = 0.8–2.2 μm and increases obviously within λ = 2.2–4.0 μm when the h₇ increases to 0.30 μm.

To sum up, all the parameters related to the octagonal prisms will affect α_λ of the MA. It is known that the fabrication uncertainties of the absorber are smaller than 0.01 μm.⁵² When the variations of these parameters are within the fabrication uncertainties, only the d₂ has obvious influences on the α_λ, indicating that d₂ should be controlled carefully in the fabrication. However, h₆, d₃, and h₇ influence α_λ slightly, indicating that these geometries are able to sustain relatively large fabrication uncertainties.

4.3.2 Influences of the structure parameters of underneath films. The parameters that are relevant to the underneath films are the height of the first SiO₂ film (h₂), the height of the second tungsten film (h₃), the height of the second SiO₂ film (h₄). The influences of the three parameters on the spectral absorptivity (α_λ) are shown in Fig. 7.

Fig. 7 Spectral absorptivity (α_λ) of the MA at different structure parameters of underneath films (a) influences of h₂; (b) influences of h₃; (c) influences of h₄.

It can be found from Fig. 8a that the α_λ remains virtually unchanged within λ = 0.28–1.8 μm when h₂ increases from 0.01 μm to 0.05 μm, but α_λ declines obviously when h₂ increases from 0.05 μm to 0.20 μm. In addition, the α_λ exhibits an upward trend with the increase in h₂ when λ is larger than 1.8 μm within h₂ = 0.01–0.05 μm. Moreover, the increase in α_λ is significant when the h₂ increases to 0.20 μm within λ > 1.8 μm. As shown in Fig. 8b, the α_λ varies slightly when h₃ = 0.01–0.20 μm within λ = 0.28–4 μm, suggesting that this parameter has little influences on the absorption performance. It is manifest from the Fig. 8c that the α_λ declines gradually with increasing h₄ within 0.3–2 μm, but the α_λ hardly changes as h₄ changes when λ = 2–4 μm.

Fig. 8 Spectral absorptivity (α_λ) under various incident angles (θ). (a) α_λ of TE wave. (b) α_λ of TM wave.

To sum up, the h₄ has obviously influences on the α_λ of the MA when λ = 0.35–2 μm, but the h₂ has slight influences on the α_λ within the fabrication uncertainty. And the h₃ influences little on the α_λ when h₃ = 0.01–0.20 μm.

4.4 Influences of incident angle and polarization angle

The incident and polarization angles of realistic solar radiation are variational in practical applications, and the MA should be insensitive to these angles for converting radiation into heat effectively. Therefore, the sensitivities of the near-perfect MA to the incident angle θ and polarization angle φ (seen Fig. 1c) were studied within λ = 0.28–4.0 μm in this section.

The influences of the θ of TE and TM polarized waves on the α_λ of the near-perfect MA were evaluated, as shown in Fig. 8. It can be observed from Fig. 8a that the α_λ of the near-perfect MA changes 5% or less when the θ of the TE polarized wave increases from 0° to 50° within λ = 0.33–1.92 μm. Moreover, as seen in Fig. 8b, the α_λ changes 5% or less when the θ of the TM polarized wave increases from 0° to 50° within 0.28–1.27 μm and 2.44–3.00 μm.

Meanwhile, the solar absorptivity (α_sol) of the near-perfect MA under TE and TM polarized waves with various incident angles are shown in Fig. 9. As can be seen in Fig. 9, when the θ is within 0–50°, the solar absorptivity (α_sol) of 0.9591–0.9572 and 0.9591–0.9471 were achieved by the TE and TM polarized waves, respectively. These results suggest that the near-perfect MA presents excellent insensitivity when the incident angle is within 0–50°.

Fig. 9 Solar absorptivity (α_sol) of the MA under TE and TM polarized waves with various incident angles.

In addition, it can be found from Fig. 10 that the α_λ of the near-perfect MA is almost unchanged when the φ of the normally incident wave increases from 0° to 90°. The results indicate that the near-perfect MA is completely insensitive to the φ in Fig. 1c when λ = 0.28–4.0 μm. Moreover, because the near-perfect MA is rotationally symmetric, its α_λ under normally incident TE polarized wave (i.e. the electric field is in the y direction) and TM polarized wave are the same. Additionally, the symmetric structure of the near-perfect MA is also the main reason to obtain excellent polarization insensitivity.¹⁷

Fig. 10 Spectral absorptivity (α_λ) under normally incident wave with various polarization angles (φ).

5. Conclusions

In this article, a near-perfect spectrally-selective metasurface solar absorber consisting of an octagonal prism array is designed and investigated for solar energy harvesting at high temperatures, and the following conclusions are obtained.

(1) A near-perfect spectrally-selective absorber with p = 155 nm, h₁ = 150 nm, h₂ = 10 nm, h₃ = 20 nm, h₄ = 10 nm, d₁ = 150 nm, h₅ = 240 nm, d₂ = 130 nm, h₆ = 70 nm, d₃ = 80 nm, and h₇ = 70 nm was obtained after optimizing the metasurface structure. The high solar absorptivity of 0.9591 and a low emissivity of 0.1594–0.3694 were achieved by the near-perfect absorber, leading to high photothermal efficiency of 94.72–83.10% under 1000 suns and 1073–1573 K.

(2) The underlying absorption mechanisms leading to the spectral selective absorption of this near-perfect absorber were revealed. It is found that coupling effects of multi-plasmon resonance modes combined with the impedance matching with the free space lead to the high solar absorptivity. Moreover, the impedance mismatching is the mechanism to minimize the emissivity in the mid-IR region.

(3) Influences of the structure parameters of the absorber are studied. The results suggest that the excircle diameter of the first tungsten octagonal prism and the height of the SiO₂ under the octagonal prism have stronger influences on the spectral absorptivity than other parameters within the fabrication uncertainty.

(4) Sensitivities of the near-perfect absorber to the incident angle (θ) and polarization angle (φ) are investigated. The solar absorptivity of 0.9591–0.9572 and 0.9591–0.9471 are achieved under TE and TM polarized waves within θ = 0–50°, respectively. And the α_λ of the near-perfect MA is almost unchanged within φ = 0–90°. These results demonstrate that the near-perfect absorber is insensitive to the incident angle within θ = 0–50° and polarization angle within φ = 0–90°.

Abbreviations

C	Solar concentration ratio
d1	Excircle diameter of the SiO2 octagonal prism (nm)
d2	Excircle diameter of the first tungsten octagonal prism (nm)
d3	Excircle diameter of the second tungsten octagonal prism (nm)
E	Electric field (V m^−1)
h1	Height of the first tungsten film (nm)
h2	Height of the first SiO2 film (nm)
h3	Height of the second tungsten film (nm)
h4	Height of the second SiO2 film (nm)
h5	Height of the SiO2 octagonal prism (nm)
h6	Height of the first tungsten octagonal prism (nm)
h7	Height of the second tungsten octagonal prism (nm)
H	Magnetic field (A m^−1)
Is	Solar flux intensity at AM1.5, 1000 W m^−2
IAM1.5(λ)	Spectral solar irradiance at AM1.5 (W m^−2 m^−1)
IB(λ, Tabs)	Spectral irradiance of blackbody (W m^−2 m^−1)
LSPRs	Local Surface Plasmon Resonances
MPs	Magnetic Polaritons
rdst	Destination origin
rsrc	Source origin
SPPs	Surface Plasmon Polaritons
S11, S21	Scattering matrix coefficients
Tabs	Temperature of metasurface (K)
Tamb	Temperature of ambient (K)
zλ	Effective impedance of metasurface
xyz	Cartesian coordinates (nm)
αsol	Solar absorptivity
αλ	Spectral absorptivity
εtot	Total emissivity
η	Photothermal efficiency (%)
θ	Incident angle (°)
λ	Wavelength (μm)
ρλ	Spectral reflectance
φ	Polarization angle (°)

Author contributions

Mingpan Xu: conceptualization, methodology, validation, investigation, visualization, writing – original draft; Lin Guo: methodology, validation, investigation, visualization, writing – original draft; Pengfei Zhang: methodology, validation, investigation, visualization, writing – original draft; Yu Qiu: conceptualization, methodology, investigation, writing – original draft, writing – review & editing, supervision; Qing Li: methodology, formal analysis, writing – review & editing, supervision; Jikang Wang: formal analysis, visualization.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No.52006247, No.52176093). The authors will also like to thank the Natural Science Foundation of Hunan Province (2021JJ40753), the Natural Science Foundation of Shandong Province (No. ZR2021QE078), and the Collaborative Innovation Project of Colleges in Jinan (No. 2021GXRC059).

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Footnote

† Electronic supplementary information (ESI) available. See https://doi.org/10.1039/d2ra02802f

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