Abstract

Spectrally selective solar absorbers are widely employed in solar thermal energy systems. This work theoretically investigates thermal radiative properties of metamaterials consisting of 1-D and 2-D grating-Mie-metamaterials (tungsten nanoparticles embedded in alumina) on top of multilayered refractory materials (tungsten-silicon nitride-tungsten) as a promising selective solar absorber. The proposed metamaterial shows high absorptance from the ultraviolet to near-infrared lights, while exhibiting low emittance in the mid-infrared regime owing to Mie-resonances, surface plasmon polaritons, and metal-dielectric-metal resonance. The optical properties of designed metamaterial solar absorbers are angular independence of up to 75° and polarization insensitive. The total absorptance of 1-D and 2-D grating-Mie-metamaterials are 90.59% and 94.11%, respectively, while the total emittance are 2.89% and 3.2%, respectively. The photon-to-heat conversion efficiency is theoretically investigated under various operational temperatures and concentration factors. Thermal performance of grating-Mie-metamaterials is greatly enhanced within a one-day cycle, and the stagnation temperature under different concentration factors manifests the potential feasibility in mid and high-temperature solar thermal engineering.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Solar energy as the most abundant and clean renewable energy resource is one of the most promising pathways to solve the energy crisis for past decades, while reduces the environmental impact of fossil fuels. Solar thermal technology converts striking photon into heat which can be used for domestic or industrial heating and air conditioning systems [14]. It can be employed for electricity generation through concentrated solar power (CSP) via Rankine cycle [5], solar thermoelectric generators (STEGs) [2], and solar thermophotovoltaics (STPVs) [68]. In the abovementioned approaches, a solar absorber, as a consequential component, that converts striking sunlight to thermal energy substantially affects the overall performance of solar thermal systems. Since solar absorbers re-emit thermal energy when it is heated up [9]. Therefore, it is significant to develop an ideal spectrally selective solar absorber that enhances the photon-to-heat conversion efficiency. An ideal selective solar absorber should exhibit an unity absorptance over the UV, visible, and near-infrared regimes, where solar radiation energy distributes, to convert most radiation into heat, accompanying with zero emittance in the mid-infrared region to minimize thermal leakage from spontaneous blackbody radiation. This spectral selectivity is highly demanded for further improvement of conversion efficiency for solar thermal systems. In addition, a selective solar absorber is required to be omnidirectional diffuse and polarization insensitive, since the solar radiation is randomly distributed and angular time-dependent [10]. Furthermore, the optimized cut-off wavelength, at which it absorptance spectrum changes steeply, of a selective absorber, shifts according to its operational temperature because of the shifting nature of blackbody radiation as stated by Wien’s displacement law [11]. Consequently, it is worthwhile to design a perfectly selective solar absorber according to the operational temperature and concentration factor (CF) to maximize the absorption of solar energy.

Selective absorptance or emittance exists in natural materials, such as black carbon paint, black chrome [1214], and Pyromark [15], however, their high emittance in mid-infrared regime as well as limited tunability of their cut-off wavelengths confine their practicability in various solar thermal applications. Recently, metamaterial absorbers have attracted great attention because of their high selective absorption due to exciting plasmonic resonance at particular wavelengths inside the structures [16,17], which provides alternative methods to modify the wavelength selective properties for sunlight trapping. Advances in micro/nanofabrications have promoted enormous metamaterials based on sub-wavelength metallic patterns on a metal film separated by a dielectric spacer and make the manipulation of sunlight absorption more feasibly. Excitation of plasmonic resonance at different wavelengths can be achieved by one dimensional (1-D) or two dimensional (2-D) surface gratings [1826]. Liu et al. experimentally demonstrated the absorption of 97% at the wavelength of 6 $\mu$m in a sub-wavelength perfect absorber consisting of a film-coupled crossbar structure [27]. An absorption peak of 88% at the wavelength of 1.58 $\mu$m is obtained in a plasmonic absorber made of a layer of 200 nm gold patch array on a thin Al$_2$O$_3$ layer and a gold film [28]. By depositing a 2-D Ag grating with a period of 300 nm on a 60 nm SiO$_2$ and a Ag film, Aydin et al. reveal an ultra-thin plasmonic absorber in the visible spectrum [29]. Strong visible light absorption has also been achieved by film-coupled colloidal nanoantennas [30], circular plasmonic resonators [31] by exciting magnetic resonance inside the metamaterial absorbers. Mie-resonance metamaterials are another class of artificial materials which utilize Mie-resonance of inclusions for the shaping of absorptance spectra. Ghanekar et al. theoretically and experimentally demonstrated a selective absorber/emitter that consists of nanoparticles embedded thin film to shape the thermal emission spectrum due to Mie-resonance [7,8,32,33]. Dai et al. systematically investigated a type of plasmonic light absorber based on a monolayer of gold nano-spheres with less than 30 nm in diameters deposited on top of a gold substrate and obtained an absorptance of approximately 90% around 810 nm [34]. However, it is still a challenge to design a perfect broadband solar absorber that is angular, polarization-independent with unity absorptance from UV to near-infrared lights and zero emittance in the mid-infrared region. In addition, literature is rare pertaining to nanoparticles embedded surface gratings based broadband selective absorbers.

In present study, we theoretically propose metamaterial structures made of 1-D and 2-D tungsten (W) nanoparticles embedded alumina (Al$_2$O$_3$) surface gratings on top of W-silicon nitride (Si$_3$N$_4$)-W multilayer stacks as perfect selective solar absorbers. The thermal radiative properties of proposed metamaterials are illustrated in a broad region from UV to mid-infrared regime. The influence of geometric parameters, such as the volume fraction of W nanoparticles and grating configurations, on the spectral selectivity of grating-Mie-metamaterials are studied. The effects of oblique incidence and polarization states on the spectral absorptance are explored and it is proved the proposed structures are angular independence of up to 75$^{\circ }$ and polarization insensitive for transverse electric (TE) and transverse magnetic (TM) polarizations. The photon-to-heat conversion efficiency of proposed structures is theoretically investigated under various operational temperature and concentration factors. Thermal performance of grating-Mie-metamaterials is greatly enhanced within a one-day cycle and the stagnation temperature under different concentration factors is simulated to manifest the potential practicability in mid and high -temperature solar thermal engineering.

2. Theoretical fundamentals

2.1 Photon-to-heat conversion efficiency analysis of the solar absorber

A schematic of a typical solar thermal engineering system is shown in Fig. 1A. In such solar thermal to electrical techniques, the sunlight incident on the absorber (Q$_{abs}$) is converted into a heat flux (Q$_{h}$) and delivered to the thermal system, where it generates desired work (heating, cooling, electricity, etc.). Waste heat (Q$_{c}$) is transported to a heat sink. The spontaneous blackbody thermal radiation (Q$_{re-emit}$) leaks at the surface as radiative (Q$_{rad}$) and convective (Q$_{conv}$) thermal losses. Therefore, the solar absorber must be dark to sun and be ideally reflective to the mid-infrared light so as to depress the thermal leakage by convection and radiation.

 figure: Fig. 1.

Fig. 1. (A) A typical solar thermal energy conversion system. (B) Solar spectral irradiance (AM1.5, global tilt), radiative heat flux of blackbody thermal radiation at 200 $^{\circ }C$ and 500 $^{\circ }C$, and reflectivity spectrum of ideal selective solar absorber and black surface.

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To quantitatively evaluate the performance of solar absorbers, the photon-to-heat conversion efficiency, $\eta _{abs}$, is given by:

$$\eta_{\mathrm{abs}}=\alpha_{\mathrm{abs}}-\epsilon_{\mathrm{abs}} \frac{\sigma\left(T_{\mathrm{abs}}^{4}-T_{\mathrm{amb}}^{4}\right)}{C F \cdot Q_{\mathrm{abs}}}$$
where CF is the concentration factors, and Q$_{abs}$ is the solar radiative heat flux at AM 1.5 (global tilt) [35]. $\sigma$ is the Stefan-Boltzmann constant. $T_{abs}$ and $T_{amb}$ are the operational temperature of solar absorber and the environment, respectively. The solar absorptance, $\alpha _{abs}$, is expressed as the following:
$$\alpha_{abs}=\frac{\int_{0.3 \mu m}^{4.0 \mu m} I_{sun}(\lambda,\theta,\phi) \alpha(\lambda,\theta, \phi) d \lambda}{\int_{0.3 \mu m}^{4.0 \mu m} I_{sun}(\lambda,\theta, \phi) d \lambda}=\frac{\int_{0.3 \mu m}^{4.0 \mu m} I_{sun}(\lambda,\theta, \phi)[1-R(\lambda,\theta, \phi)] d \lambda}{\int_{0.3 \mu m}^{4.0 \mu m} I_{sun}(\lambda,\theta, \phi) d \lambda}$$
where $\lambda$ is the wavelength of solar radiation, $\phi$ is the azimuthal angle, and $\theta$ is the polar angle. $\alpha (\lambda ,\theta , \phi )$ and $R(\lambda ,\theta , \phi )$ are the spectral directional absorptance and reflectance at a certain operational temperature. $I_{sun}$ is the incident solar intensity at AM 1.5 (global tilt) [35]. The numerator of this equation is the total absorbed solar energy, the denominator is the incident solar heat flux, $Q_{abs}$. Since the available data of AM 1.5 is confined from 0.3 $\mu$m to 4.0 $\mu$m [35], which includes 95% of solar radiation, the integration interval is limited from 0.3 $\mu$m to 4.0 $\mu$m.

The total thermal emittance, $\epsilon _{abs}$, is given by:

$$\epsilon_{\textrm{abs}}=\frac{\int_{2.5 \mu m}^{20 \mu m} I_{bb}(\lambda,\theta, \phi) \epsilon(\lambda,\theta, \phi) d \lambda}{\int_{2.5 \mu m}^{20 \mu m} I_{bb}(\lambda,\theta, \phi) d \lambda}=\frac{\int_{2.5 \mu m}^{20 \mu m} I_{bb}(\lambda,\theta, \phi)[1-R(\lambda,\theta, \phi)] d \lambda}{\int_{2.5 \mu m}^{20 \mu m} I_{bb}(\lambda,\theta, \phi) d \lambda}$$
where $I_{bb}(\lambda ,\theta , \phi )$ is the blackbody radiation intensity given by Plank’s law. $\epsilon (\lambda ,\theta ,\phi )$ is the spectral directional absorptance at a certain operational temperature. Since our proposed structure are opaque within the wavelengths of interest (0.3 $\mu$m to 20 $\mu$m), we take $\alpha (\lambda ,\theta , \phi )$ = $\epsilon (\lambda ,\theta , \phi )$ = 1 – $R(\lambda ,\theta , \phi )$ according to Kirchhoff’s law of thermal radiation. It can be discovered from Fig. 1B that most of the solar radiation is distributed over the UV, visible, and near-infrared region, while most of the blackbody thermal radiation expands within the mid-infrared regime according to Wien’s displacement law. The spectral radiant emittance of a 500$^{\circ }C$, at which most of mid-temperature solar applications works, blackbody is double as the peak spectral irradiance intensity of AM 1.5. Consequently, it is required to design spectrally selective solar absorbers. An ideal spectral selective absorber has an unity absorptance over the solar radiation regime and zero emittance within the mid-infrared thermal region, along with a very sharp transition between these two regions (as expressed by the dashed black line in Fig. 1B). The cut-off wavelength, $\lambda _{cut-off}$, at which the transition happens, should be where the total blackbody intensity begins to surpass the total solar radiation intensity. The $\lambda _{cut-off}$ will shift left to shorter wavelengths, called blue-shift, when the operational temperature goes up, as well as the peak of the blackbody thermal radiation moves to the left. The $\lambda _{cut-off}$ will shift to longer wavelengths, called red-shift, when the absorber is under higher concentration factors, since the solar energy accounts for a larger proportion in the enhancement of conversion efficiency. Note that, the optical properties of solar absorbers are dependent of operational temperature. It will shift a little according to various temperatures at difference thermal loads of diverse working conditions, so the photon-to-heat efficiency of solar absorbers varies as a function of $\lambda _{cut-off}$, CF, and $T_{abs}$. Consequently, it is a trade off to design a perfectly selective solar absorber for diverse solar thermal engineering.

2.2 Theoretical method of radiative property calculations

As our proposed structures involve 1-D grating structure of Al$_2$O$_3$, we employ the second order approximation of effective medium theory to obtain the dielectric properties given by the expressions [3638]:

$$\varepsilon_{TE,2}\!=\!\varepsilon_{TE,0}\!\left[\! 1\!+\!\frac{\pi^2}{3}\!\left(\frac{\Lambda}{\lambda}\right)^2\!\phi^2(1-\phi)^2\frac{(\!\varepsilon_{A}\!-\!\varepsilon_{B}\!)^2}{\varepsilon_{TE,0}}\right]$$
$$\!\varepsilon_{TM,2}\!=\!\varepsilon_{TM,0}\!\left[\!1\!+\!\frac{\!\pi^2}{\!3}\!\left(\!\frac{\!\Lambda}{\!\lambda}\! \right)^2\!\phi^2(\!1\!-\!\phi)^2 (\!\varepsilon_{\!A}\!-\!\varepsilon_{\!B}\!)^2\varepsilon_{TE,0}\!\left(\!\frac{\varepsilon_{TM,0}}{\varepsilon_{\!A}\varepsilon_{\!B}}\!\right)^2\right]$$
where $\varepsilon _{A}$ and $\varepsilon _{B}$ are dielectric functions of two media (Al$_2$O$_3$ and vacuum) in surface gratings, $\Lambda$ is grating period and filling ratio $\phi =w/\Lambda$ where $w$ is width of Al$_2$O$_3$ segment. The expressions for zeroth order effective dielectric functions $\varepsilon _{TE,0}$ and $\varepsilon _{TM,0}$ are given by [36,39]:
$$\varepsilon_{TE,0}\!=\phi\varepsilon_{A}+(1-\phi)\varepsilon_{B}$$
$$\varepsilon_{TM,0}\!=\left(\frac{\phi}{\varepsilon_{A}}+\frac{1-\phi}{\varepsilon_{B}}\right)^{{-}1}$$

For symmetric 2-D grating consisting two media having dielectric functions $\varepsilon _A$ and $\varepsilon _B$ (refractive indices $n_A$ and $n_B$, respectively) and filling ratio $f$ of medium B in medium A, the effective refractive index of the medium is given by [40]:

$$n_{2-D}=[\bar{n}+2\hat{n}_{2-D}+2\check{n}_{2-D}]/5$$
where $\bar {n}$, $\hat {n}_{2-D}$ and $\check {n}_{2-D}$ can be obtained using
$$\bar{n}=(1-f^2)n_A+f^2n_B$$
and,
$$\hat{\varepsilon}_{2-D}=(1-f)\varepsilon_{A}+f\varepsilon_{\bot}$$
$$1/\check{\varepsilon}_{2-D}=(1-f)/\varepsilon_{A}+f/\varepsilon_{\|}$$
where $\varepsilon _{\bot }$ and $\varepsilon _{\|}$ are given by:
$$\varepsilon_{\|}=(1-f)\varepsilon_{A}+f\varepsilon_{B}$$
$$1/\varepsilon_{\bot}=(1-f)/\varepsilon_{A}+f/\varepsilon_{B}$$

For 1-D and 2-D triangular gratings as shown in Fig. 2, gratings can be treated as a composition of multiple layers of rectangular gratings that each has decreasing filling ratio and period equal to that of parent grating [39]. Slicing the triangular structure into 100 layers is sufficient to achieve converging values of near-field radiative heat flux. As the effective medium approximation is valid for grating periods smaller than the wavelength of interest, $\Lambda / \lambda <1 /\left (n +\sin \theta \right )$, where $\theta$ is the incident angle, $n$ is the refractive index of layer underneath the surface grating structure [38], so we limit ourselves the period of $\Lambda =$ 100 nm and $\Lambda =$ 200 nm for 1-D and 2-D gratings, respectively, and keep this parameter fixed during optimization.

 figure: Fig. 2.

Fig. 2. Schematics of 1-D and 2-D grating-Mie-metamaterial based solar absorbers. (A) 1-D triangular Al$_2$O$_3$ surface gratings of height, $h$ = 150 nm, period, $\Lambda$ = 100 nm, on top of W-Si$_3$N$_4$-W stacks with the thickness of $t_1$ = 12 nm, $t_2$ = 35 nm, and $t_3$ = 500 nm, respectively. The Al$_2$O$_3$ triangular grating is doped with 5 nm in radius W nanoparticles with a volume fraction, $f$, of 25%. (B) 2-D pyramid encapsulated with W nanoparticles ($r$ = 5 nm in radius with a volume fraction, $f$, of 25%) sits on stockpiles of W-Al$_2$O$_3$-W. The thickness of W, Al$_2$O$_3$, and W is 10 nm, 40 nm, and 500 nm, respectively. The height of the surface grating layer is 200 nm and the period $\Lambda$ = 200 nm in both $x$ and $y$ direction.

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In order to calculate the effective dielectric function the Mie-metamaterial, we apply the Clausius-Mossotti equation [41,42]:

$$\varepsilon_{eff}=\varepsilon_{m}\left(\frac{r^{3}+2\alpha_{r} f}{r^{3}-\alpha_r f}\right)$$
where $\varepsilon _{m}$ is the dielectric function of the matrix, $\alpha _r$ is the electric dipole polarizability, $r$ and $f$ are the radius and volume fraction of nanoparticles respectively. To consider the size effects of nanoparticle inclusions, the Maxwell Garnett formula is employed with the expression for electric dipole polarizability using Mie theory [43], $\alpha _r=3jc^{3}a_{1,r}/2\omega ^{3}\varepsilon _{m}^{3/2}$, where $a_{1,r}$ is the first electric Mie coefficient given by:
$$a_{1,r}\!=\!\frac{\sqrt{\varepsilon_{np}}\psi_{1}(x_{np})\psi_{1}^{'}(x_{m})\!-\!\sqrt{\varepsilon_{m}}\psi_{1}(x_{m})\psi_{1}^{'}(x_{np}) }{\sqrt{\varepsilon_{np}}\psi_{1}(x_{np})\xi_{1}^{'}(x_{m})\!-\!\sqrt{\varepsilon_{m}}\xi_{1}(x_{m})\psi_{1}^{'}(x_{np})}$$
where $\psi _{1}$ and $\xi _{1}$ are Riccati-Bessel functions of the first order given by $\psi _{1}(x)=xj_{1}(x)$ and $\xi _{1}(x)=xh_{1}^{(1)}(x)$ where $j_{1}$ and $h_{1}^{(1)}$ are first order spherical Bessel functions and spherical Hankel functions of the first kind, respectively. Here, ‘$'$’ indicates the first derivative. $x_{m}=\omega r\sqrt {\varepsilon _{m}}/c$ and $x_{np}=\omega r\sqrt {\varepsilon _{np}}/c$ are the size parameters of the matrix and the nanoparticles, respectively; $\varepsilon _{np}$ is the dielectric function of nanoparticles.

It is worth to mention that Maxwell-Garnett-Mie theory is trustworthy when the average distance between inclusions is much smaller than the wavelength of interest [44]. Additionally, nanoparticle diameter (5 nm) considered in this work is much smaller than the thickness of thin films (100 nm and 200 nm). Thus, the effective medium theory holds true for the calculations presented here.

The hemispherical emissivity of the thermal emitter can be expressed as [45]

$$\epsilon(\omega)=\frac{c^{2}}{\omega^{2}}\int_0^{\omega/c}dk_{\rho}k_{\rho}\sum_{\mu=s,p}(1-|\widetilde{R}_{h}^{(\mu)}|^{2}-|\widetilde{T}_{h}^{(\mu)}|^{2})$$
where c is the speed of light in vacuum, $\omega$ is the angular frequency and $k_{\rho }$ is the magnitude of inplane wave vector. $\widetilde {R}_{h}^{(\mu )}$ and $\widetilde {T}_{h}^{(\mu )}$ are the polarization dependent effective reflection and transmission coefficients which can be calculated using the recursive relations of Fresnel coefficients of each interface [46]. The dielectric functions can be related to real $(n)$ and imaginary $(\kappa )$ parts of refractive index as $\sqrt {\varepsilon }=n+j\kappa$. Dielectric functions of the materials (Al$_2$O$_3$, W and Si$_3$N$_4$) utilized in this work are taken from literature [4749]. The melting temperatures of Al$_2$O$_3$, W and Si$_3$N$_4$ are 2027 $^{\circ }$C, 3422 $^{\circ }$C, and 1900 $^{\circ }$C, and the thermal expansion coefficients of Al$_2$O$_3$, W and Si$_3$N$_4$ of 5.4 $\times$ 10 $^{-6}$ m/(m$\cdot$K), 4.2 $\times$ 10 $^{-6}$ m/(m$\cdot$K), and 3.3 $\times$ 10 $^{-6}$ m/(m$\cdot$K), respectively. The melting temperatures of the selected materials are higher than the operating temperature of high-temperature solar thermal engineering application (800 – 1000 $^{\circ }$C) and the thermal expansion coefficient of these materials are all the same order of magnitude, which proves that these materials have very low temperature coefficients under a relatively operating temperature and avoid the internal thermal stress from different materials , and room temperature values of dielectric functions are used for Al$_2$O$_3$, W and Si$_3$N$_4$. W nanoparticles are absorptive at visible and near-infrared region (from 0.3 $\mu$m to 1.5 $\mu$m) and the inclusion of W nanoparticles enhances the spectral emissivity of interest, which has investigated in authors’ previous work [50,51]. Other metal nanoparticles, such as nickel, platinum, rhenium, and tantalum and dielectric materials like silica can also be selected as alternatives for Mie-metamaterials. The top layer of solar absorbers considered in our design is either a 1-D or 2-D grating structure with nanoparticles embedded inside and can be approximated as a homogeneous layer using effective dielectric property.

2.3 Thermal performance calculations of solar absorbers for a one-day cycle

In order to demonstrate the thermal performance of the designed solar absorber under direct solar irradiation, we can solve the thermal balance equation as expressed by the following to obtain its temperature variations for a one-day cycle [52,53]:

$$Q_{total} (T_{abs},T_{amb}) = Q_{sun}(T_{abs})+Q_{amb} (T_{amb})-Q_{re-emit}(T_{abs})$$
It is supposed that the backside of the solar absorber is thermally insulated (i.e., no thermal load is connected to absorber), we only consider the heat transfer between solar absorber and air on the upper hemisphere. Here, Q$_{sun}$ is the heat flux of solar radiation incident on solar absorbers. Q$_{amb}$ is incident thermal radiation from ambient, and Q$_{re-emit}$ stands for the heat flux through thermal re-emission from upper side of the solar absorber to the ambient. Q$_{total}$ is the net heating power of the solar absorber.

Solar radiation absorbed by the absorber, Q$_{sun}$, is given by $Q_{sun}(T_{abs})$ as following:

$$Q_{sun}(T_{abs}) = A\cdot{CF}\int_0^\infty \textrm{d}\lambda I_{AM 1.5} (\lambda) \alpha (\lambda, \theta_{sun}, T_{abs})$$
Here, $A$ is the area of the solar absorber. $\alpha (\lambda , \theta _{sun}, T_{abs})$ is the temperature, wavelength and angular dependent absorptance of solar absorber, however, the absorptance of designed solar absorber is angular independent up to 80$^{\circ }$ and the materials of proposed solar absorbers are refractory and with low thermal expansion coefficients. Hence, it is reasonable to use the absorptance that obtained with dielectric function at the room-temperature.

The absorbed power of incident thermal radiation from atmosphere $Q_{amb} (T_{amb})$ can be expressed as follows:

$$Q_{amb}(T_{amb}) = A\int_0^\infty \textrm{d}\lambda I_{BB} (T_{amb},\lambda) \alpha (\lambda, \theta, \phi, T_{abs}) \epsilon (\lambda, \theta, \phi)$$
$I_{BB} (T_{amb}, \lambda )$ = $2hc^{5}{\lambda^{-5}}$ $\exp ( hc/\lambda k_{B}T-1)^{-1}$ defines the spectral radiance of a blackbody at a certain temperature, where h is the Planck’s constant and $k_{B}$ is the Boltzmann constant. $\alpha (\lambda , \theta , \phi , T_{abs})$ = $\frac {1}{\pi }\int _0^{2\pi }\textrm {d}\phi \int _0^{\pi /2} \varepsilon _{\lambda }\cos \theta \sin \theta \textrm {d}\theta$ is the temperature-dependent absorptance of solar absorber [9]. $t (\lambda , \theta , \phi )$ is the transmittance value of atmosphere obtained from MODTRAN 4 [54].

The heat flux of thermal re-emission from the solar absorber upper surface is defined as follows:

$$Q_{re-emit}(T_{abs}) = A\int_0^\infty \textrm{d}\lambda I_{BB} (T_{abs},\lambda) \epsilon (\lambda, \theta, \phi, T_{abs})$$
where $\epsilon (\lambda , \theta , \phi , T_{abs})$ = $\alpha (\lambda , \theta , \phi , T_{abs})$ is the emissivity of the solar absorber according to Kirchhoff’s law of thermal radiation [55].

The time-dependent temperature variations of the solar absorber can be obtained by solving the following equation:

$$C_{abs} \frac{dT}{dt} = Q_{total}(T_{abs}, T_{amb})$$
Since the multilayer structures of sputtering solar absorber is only 350 nm thick, it is rational to neglect its thermal resistance. Therefore, the heat capacitance of the absorber, C$_{abs}$, consider here equal to the heat capacitance of 300 $\mu$m silicon wafer.

The transient temperature fluctuations of the solar absorber under different 5 suns (CF = 5) are simulated by solving Eq. 17, which is integrated to obtain the temperature evolution of solar absorber as a function of time. For each simulation, the initial temperature of the solar absorber is assumed to be the same as the ambient temperature.

3. Results and discussions

3.1 Design structure and effect of geometric parameters

Schematics of 1-D and 2-D grating-Mie-metamaterials are depicted in Fig. 2. It comprises 1-D (Fig. 2A) and 2-D (Fig. 2B) W nanoparticles embedded Al$_2$O$_3$ gratings on top of the metal-dielectric-metal stacks. For Fig. 2A, the top surface grating layer is 150 nm thick W nanoparticles embedded Al$_2$O$_3$ with a period $\Lambda$ = 100 nm on top of W-Si$_3$N$_4$-W stacks with the thickness of $t_1$ = 12 nm, $t_2$ = 35 nm, and $t_3$ = 500 nm, respectively. While, for the 2-D surface grating structure, the period $\lambda$ = 200 nm is in both $x$ and $y$ direction, and the thickness of the top 2-D surface gratings layer is 200 nm. The 2-D gratings layer are Al$_2$O$_3$ encapsulated with W nanoparticles. The metal-dielectric-metal stockpiles layer is W ($t_1$ = 10 nm), Al$_2$O$_3$ ($t_2$ = 40 nm), and W ($t_3$ = 500 nm). Volume fraction of W nanoparticles is adjusted for both 1-D and 2-D surface grating structures to be 25% with a radius of 5 nm to achieve the best result. The bottom W layer of both cases are set to be 500 nm to block all the incident light, so the proposed structures can be considered as opaque and the reflectivity, $R$, of designed solar absorbers equals to 1 – $\epsilon$.

From Eq. 7 to Eq. 12, reflectivity spectrum of proposed structure can be obtained as shown in Fig. 3A. The normalized solar spectral intensity and normalized 500 $^{\circ }C$ blackbody thermal radiation irradiance are also shown in Fig. 3A. It is observed that both the 1-D and 2-D grating structures have very low reflectivity (< 0.1) with the solar radiation regime (from 0.3 $\mu$m to 1.2 $\mu$m), while show a high reflectivity (> 0.95) within the mid-infrared region (from 4.0 $\mu$m to 20 $\mu$m). Table 1 lists total absorptance and emittance of the proposed 1-D and 2-D grating based solar absorbers. The integration interval of total absorptance is from 0.3 $\mu$m to 4.0 $\mu$m, which covers 99.9% of the solar radiation energy at AM 1.5. While the total emittance calculations takes from 0.3 $\mu$m to 20 $\mu$m, where 98.5% of a 500 $^{\circ }C$ and 93.2% of a 200 $^{\circ }C$ blackbody thermal radiation irradiance are spread over. Since the designed is highly diffuse, which will be investigated in section 3.2 later, it is reasonable to consider the total normal absorptance and emittance approximately to be the total hemispherical absorptance and emittance. It exhibits that the designed structure has a high absorptance (> 0.9) at solar radiation distributed regime and a quite low emittance (< 0.06) in the mid-infrared wavelength region, which demonstrates a high selectivity of the proposed grating-Mie-metamaterials.

 figure: Fig. 3.

Fig. 3. (A) Normalized spectral distribution of solar heat flux (AM 1.5) and normalized thermal radiation of a 500 $^{\circ }C$ blackbody, as well as the calculated reflectivity spectra of proposed 1-D and 2-D surface grating-Mie-metamaterials. Normal reflectivity spectra as a function of the thickness of 1-D (B) and 2-D (C) surface gratings layer, $h_1$ and $h_2$ are the height of the 1-D and 2-D triangular surface gratings, respectively.

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Tables Icon

Table 1. Total normal absorptance and emittance of the designed 1-D and 2-D grating-Mie-metamaterials at $T_{abs}$ = 200 $^{\circ }C$ and 500 $^{\circ }C$.

In order to get the optimized geometric parameters for a final design, we investigate the geometric effects on the proposed grating-Mie-metamaterial based solar absorbers. The effects of the thickness of top grating layer, $h$, volume fraction, $f$, and the size of W nanoparticles, $r$. The thickness of each layer in the metal-dielectric-metal stack ($t_1$, $t_2$, and $t_3$) and the period , $\lambda$ are set to be invariable geometric parameters, as shown in Fig. 2. Other geometric parameters are fixed as in Fig. 2 when one of the investigated parameters varies in our calculations. The incident angle is fixed as 0$^{\circ }$. Figures 3B and 3C exhibit how the reflectivity spectra vary with the thickness of the top grating layer in the wavelength region from 0.3 $\mu$m to 3.0 $\mu$m, where 98.9% of the solar radiation energy is distributed.

As shown in Fig. 3, the normal reflectivity over visible and near-infrared regime drops and its coverage over solar radiation region becomes larger, when the thickness of the top grating layer increases. It follows the similar rules with both 1-D and 2-D surface grating structures. As a result, a lower and broader reflectivity band from 0.3 $\mu$m to 1.6 $\mu$m can be achieved with a thickness of 150 nm and 200 nm for 1-D and 2-D surface grating structures. It gives hints that if a solar absorber works at a low temperature and high solar concentration factors, we can increase the thickness of the top grating layer to obtain a higher photon-to-heat conversion efficiency. Meanwhile, the reflectivity goes beyond 0.95 when the wavelength is larger than 3 $\mu$m, which keeps the minimization of thermal leakage from blackbody radiation.

Figures 4A and 4B illustrate the effects of volume fraction, $f$, on the reflectivity spectra of solar absorbers at normal incidence. For the 1-D surface grating structure (Fig. 4A), it can be seen that there are two peaks (as marked by solid red circle) appears at around 0.5 $\mu$m and 1.2 $\mu$m. When the volume fraction of W nanoparticles increases from 10% to 30%, the two peaks both shift to longer wavelengths, while it makes the reflectivity band broader. Since the W supports surface plasmon polaritons (SPPs), the right-shifts of these two peaks presented here can be attributed to the excitation of SPPs. Ghanekar et al. [7,45] investigated explicitly the behavior of SPPs of metal nanoparticles embedded in dielectric thin film. For the 2-D surface grating structure, there is no evident to show reflectivity peaks shifting, which makes it more suitable for a high absorptance with solar radiation regime.

 figure: Fig. 4.

Fig. 4. Normal reflectivity spectra as a function of W nanoparticles volume fraction, $f$ = 10%, 20% or 30%, for 1-D (A) and 2-D (B) surface grating-Mie-metamaterials, $f_1$ and $f_2$ defines the volume fractions of W nanoparticles embedded in the 1-D and 2-D Al$_2$O$_3$ host, respectively. 1-D (C) and 2-D (D), reflectivity spectra vary as the size of W nanoparticles increases ($r$ = 1, 3, and 5 nm), $r_1$ and $r_2$ denotes the size of the W nanoparticles in the 1-D and 2-D triangular surface grating structures, respectively. Refractive indices of W, SiO2 and SiO2 doped with W nanoparticles of volume fraction 20% and 10 nm radius. (E) Real part of refractive index. (F) Imaginary part of refractive index.

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Figure 4C and 4D elucidate how the size, $r$ of W nanoparticles affects the radiative properties of both 1-D and 2-D grating structures. The reflectivity spectra of both structures barely change when the radii of W nanoparticles change from 1 nm to 5 nm, because the maximum diameter of W nanoparticles is 10 nm which is quite smaller compared to the minimum wavelength investigated here (300 nm). The two reflectivity peaks of 1-D grating structure show a small red-shift. For the 2-D surface grating structure, no apparent shifts and reflectivity peaks are discovered. Consequently, the size of W nanoparticles exhibits little effect on the radiative properties when its radius is less than 5 nm. Consequently, we can obtain the desirable conversion efficiency through optimizing the geometric parameters of 1-D and 2-D grating-Mie-metamaterials. Fig. 4E and 4F illustrate the effect of W nanoparticle inclusions on the refractive indices of Al$_2$O$_3$ host. The pure Al$_2$O$_3$ has a near constant refractive index (n) $\sim$ 1.73 and a negligible extinction coefficient ($\kappa$). Nano-sized W nanoparticles ($d$ $\leq$ 10 nm) much smaller than the operating wavelength are introduced into the Al$_2$O$_3$ matrix, which brings about the increased refractive index and extinction coefficient as a result of the addition of new materials as well as the Mie-scattering of electromagnetic waves by spherical nanoparticles [7,50].

3.2 Diffuse and polarization-independent behaviors of solar absorbers

In traditional CSP solar thermal systems, the solar tracker system is incorporated to make solar absorbers face the sun all the time, since the sunlight is randomly distributed and not always normalized to the surface of solar absorber. Nevertheless, the solar tracker consumes extra electricity and reduces the system efficiency, so it is consequential to make the absorptance of the proposed solar absorber angular-independent. In addition, the polarization insensitivity is also highly required to maximum the solar absorption since the sunlight is unpolarized.

Figure 5 illustrates the contour plot of reflectivity spectra for the designed solar absorbers as functions of incident angle, $\theta$, and wavelength, $\lambda$, at TE and TM waves, where, the redder color represents higher reflectivity, while the bluer color indicates lower reflectivity. It is shown that the reflectivity of both 1-D and 2-D grating structures maintains lower within visible and near-infrared regions (0.3 $\mu$m to 1.7 $\mu$m) in Figs. 5A and 5C, while remains at a high reflectivity in the mid-infrared region (3 $\mu$m to 20 $\mu$m). The reflectivity of these two structures at 0.55 $\mu$m, where the irradiance peak of solar radiation lies, with various incident angles, are listed in Table 2. It is manifested that, for both TE and TM polarized waves, the reflectivity of designed solar absorbers is very low from an incidence angle of 0$^{\circ }$ to 75$^{\circ }$. The dips for TM waves that appear at around 12 $\mu$m are due to the surface plasmon resonance of top Al$_2$O$_3$ gratings. However, the thermal radiation of blackbody of 500 $^{\circ }C$ and 200 $^{\circ }C$ is mainly distributed over the interval of 2 $\mu$m to 8 $\mu$m and 4 $\mu$m to 11 $\mu$m, respectively, which exhibits little overlap between blackbody radiation and two dips. Consequently, these two dips in reflectivity spectra affect lightly the selectivity performance of proposed solar absorbers in low- and mid-temperature solar thermal systems. For the high-temperature solar thermal engineering (e.g. 800 – 1000$^{\circ }C$), the corresponding blackbody thermal radiation has even little relation with these two dips. Above all, the proposed solar absorbers are direction-insensitive and polarization-independent.

 figure: Fig. 5.

Fig. 5. Angle dependent reflectivity of TE polarization and TM polarization for proposed 1-D (A) and 2-D (B) selective solar absorbers contour plotted against wavelength, $\lambda$ and angle of incidence, $\theta$.

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Tables Icon

Table 2. Reflectivity of the designed 1-D and 2-D grating-Mie-metamaterials at solar irradiance peak of 0.55 $\mu$m, with various incident angles and for both TE and TM polarizations.

3.3 Photon-to-heat conversion efficiency analysis of spectrally selective solar absorber

Photon-to-heat conversion efficiency is the ultimate target for any solar thermal engineering, so the thermal performance of the designed solar absorbers have been quantitatively investigated by analysing Eq. 1. As designed above, the melting point of selected materials are higher (1900 $^{\circ }C$) than the operational temperature (the highest is around 1200 $^{\circ }C$) of solar thermal systems and the thermal expansion coefficient for these materials are ultra-low, so the optical properties of the designed grating-Mie-metamaterials are considered to be temperature-independent and we are able to employ the reflectivity data evaluated by the optical properties at room temperature. Additionally, the designed structures of solar absorbers are demonstrated to be angular-insensitive as well as polarization-independent, the normal reflectivity calculated in section 3.1 are used to determine the photon-to-heat conversion efficiency. The spectral integration for $\alpha _{abs}$ and $\epsilon _{abs}$ is executed over wavelength from 0.3 $\mu$m to 20 $\mu$m, which covers most of the solar radiation and the blackbody radiation (above 200 $^{\circ }C$).

Figure 6A shows the photon-to-heat conversion efficiency, $\eta _{abs}$, as a function of operational temperature, $T_{abs}$ under one sun (no concentrated optical system included) for an ideal absorber surface, the 1-D and 2-D grating-Mie-metamaterial based solar absorbers, and a black surface from 100 $^{\circ }C$ to 500 $^{\circ }C$. Note that the ambient temperature is fixed to be 25 $^{\circ }C$ and the cut-off wavelength, $\lambda _{cut-off}$ is adjusted to various operational temperature to keep an ideal performance of selective solar absorbers. The reflectivity of the black surface is unity over all wavelength investigated and shows no spectral selectivity (the black dotdash line in Fig. 1B). It is clearly illustrated that the energy conversion efficiencies of solar absorbers are 88.74% and 92.02% for 1-D and 2-D surface grating structures at $T_{abs}$ = 100 $^{\circ }C$, respectively. These two curves intersect at 338.1 $^{\circ }C$. The stagnation temperatures, at which $\eta _{abs}$ = 0 (i.e., no solar energy is harvested), of 1-D and 2-D surface grating structures are 483.2 $^{\circ }C$ and 469.5 $^{\circ }C$, respectively. This difference results from that the 1-D grating structure has a lower absorptance in visible and near-infrared spectral region, while has an lower emittance in the mid-infrared regime, as shown in Fig. 3A. The black surface that is considered to be a reference only converts 34.82% solar energy to heat at $T_{abs}$ = 100 $^{\circ }C$, and its efficiency goes down to zero at 126 $^{\circ }C$ very quickly, which further demonstrates the significance of wavelength selectivity in enhancing the solar to heat energy conversion efficiency. The mismatch between the proposed solar absorbers and the ideal solar absorber becomes even larger when the operational temperature goes up from 100 $^{\circ }C$ to 500 $^{\circ }C$. It can be explained from two points: (1) the thermal emittance of both 1-D and 2-D grating structures (e.g. 5.2% and 6.0% at 500 $^{\circ }C$, listed in Tab. 1) are higher than the ideal one; and (2) the reflectivity spectrum of the ideal surface changes more sharply at the cut-off point than those proposed structures. Therefore, the geometric parameters still has room to be optimized approaching the ideal one.

 figure: Fig. 6.

Fig. 6. (A) Calculated photon-to-heat conversion efficiency of an ideal selective absorber, the multilayer solar absorber with measured/simulated radiative properties, and a black surface as a function of absorber operational temperature, T$_{abs}$, under unconcentrated solar light; (B) Photon-to-heat conversion efficiency for abovementioned four absorber surfaces as a function of concentration factors, CF, at an absorber operational temperature of T$_{abs}$ = 500 $^{\circ }C$.

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 figure: Fig. 7.

Fig. 7. (A) Thermal performance of the 1-D (orange solid curve), 2-D (yellow solid curve) grating-Mie-metamaterials, and the black surface (purple solid curve) over a one-day cycle from sunrise (5:00 a.m.) to one hour after sunset (8:00 p.m.) at a varying ambient temperature (blue solid curve) under 10 suns (CF = 10). (B) The stagnation temperature of 1-D, 2-D surface gratings selective absorbers, and black surface at various concentration factors from 1 sun to 500 suns.

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As shown in Fig. 6B, the conversion efficiency increases as the concentration factor, CF, changes 1 to 1000 when the operational temperature, $T_{abs}$, is 500 $^{\circ }C$. The conversion efficiency of 1-D surface grating structure is higher than the 2-D one, since the operation temperature is higher than the intersection temperature of 338.1 $^{\circ }C$, as shown in Fig. 6A. The conversion efficiency of 2-D grating structure goes beyond the 1-D one at CF = 5, this is because the concentration factor becomes even higher and the solar radiation is much larger than the thermal radiation of a 500 $^{\circ }C$ blackbody. The conversion efficiency of the black surface exceeds that of 1-D and 2-D surface gratings at CF =201 and 311, respectively. It is reasonable since the quantity of solar radiation absorption dominates the photon-to-heat conversion efficiency. Consequently, the advantage of the selective solar absorber loses when the concentration factor becomes higher than 311 in this work.

3.4 Thermal performance investigation of solar absorbers in a one-day cycle

In order to evaluate the thermal performance of proposed solar absorbers, we set the concentration factor to be 10 over a one-day sunlight cycle on July 10, 2018 in Boston, Massachusetts [56]. The input data of the ambient temperature [56] and the solar illumination [57] for Eq. 17, the temperature variations of the 1-D (solid orange curve), 2-D (solid yellow curve) surface grating structure, and the black surface (solid purple curve) are simulated from sunrise (5:00 a.m.) to one hour after sunset (8:00 p.m.). It is exhibited that the highest stagnation temperatures of the proposed structures are 667 $^{\circ }C$ (1-D gratings) and 684 $^{\circ }C$ (2-D gratings) under 10 suns, while, for the black surface, the stagnation temperature has a maximization of 266 $^{\circ }C$. It is clearly shown that the heating rate of the selective solar absorber is much higher than that of the black surface, which is significant to the solar thermal power plant when a quick response is required according to electricity load (Fig. 7). It is clear that the thermal performance of proposed selective solar absorber is better than that of the black surface at the highest stagnation temperature and heating rate that reveals the significance of selective solar absorbers in the CSP systems.

Furthermore, we simulate the stagnation temperature of 1-D, 2-D surface grating structures, and black surface as a function of incident concentration factors. It is shown that the stagnation temperature of the 1-D and 2-D grating structures increases from 362.8 $^{\circ }C$ to 1460 $^{\circ }C$ (1-D) and 373.3 $^{\circ }C$ to 1481 $^{\circ }C$ (2-D) when the concentration factor increases from 1 to 500. The stagnation temperature of proposed selective absorbers is always higher than that of the black surface, which further demonstrates the importance of applications to CSP system. Moreover, the fabrication of the proposed Grating-Mie-Metamaterials based absorbers is feasible. The metal-dielectric-metal resonator of both 1-D and 2-D proposed nanostructure involves Al$_2$O$_3$, W, and Si$_3$N$_4$, which are general materials used in nanofabrication. W can be deposited using the DC magnetron sputtering method [8,58,59]. RF, DC, and pulsed reactive magnetron sputtering are well established approaches to deposit the Al$_2$O$_3$ thin film [60,61]. LPCVD and PECVD are both feasible candidates for depositing Si$_3$N$_4$ thin film [6265]. The W nanoparticles embedded thin film can be manufactured through co-sputtering method as described in these literature [8,59,66]. Following by the fabrication of 1-D [6769] and 2-D [10] triangular grating nanostructures described in these articles, the 1-D and 2-D surface grating structures can be fabricated.

4. Conclusion

In this work, we theoretically propose the grating-Mie-metamaterial based selective solar absorbers consisting of 1-D and 2-D W nanoparticles embedded Al$_2$O$_3$ gratings on top of W-Si$_3$N$_4$/Al$_2$O$_3$-W stacks. High absorptance in the visible and near-infrared region and low emittance in the mid-infrared region can be achieved at normal incidence in both 1-D and 2-D surface grating structures. The physical mechanisms responsible for the high absorption include the excitations of SPPs, Mie-resonance, and metal-dielectric-metal resonance. The affects of all the key geometric parameters have been investigated such as the grating height, the volume fraction and the size of W nanoparticles. The 2-D surface grating has a higher absorptance than the 1-D grating one in visible and near-infrared regime, while the 1-D grating structure has a lower spectral emittance than the 2-D grating one. The total absorptance of both designed solar absorbers are higher 0.9 at normal incidence, while the total normal emittance is lower than 0.06 even at a high operation temperature of 500 $^{\circ }C$, which promises an excellent thermal performance of spectrally selective solar absorbers with a high photon-to-heat conversion efficiency. Furthermore, the effects of incidence angle and light polarization are investigated to prove the features of angular insensitivity and polarization independence. The solar to heat conversion efficiency under a one-day cycle is also performed to illustrate the advantage over a black surface, which further demonstrates the significance of the incorporation of spectral selectivity technology into solar thermal engineering.

Funding

National Aeronautics and Space Administration (NNX15AK52A); National Science Foundation (1836967).

Acknowledgements

This project was supported in part by National Science Foundation through grant numbers CBET-1836967, and National Aeronautics and Space Administration through grant number NNX15AK52A.

Disclosures

The authors declare no conflict of interest.

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References

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  1. X. Lim, “How heat from the sun can keep us all cool,” Nat. News 542(7639), 23–24 (2017).
    [Crossref]
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2019 (1)

2018 (4)

Y. Tian, A. Ghanekar, X. Liu, J. Sheng, and Y. Zheng, “Tunable wavelength selectivity of photonic metamaterials-based thermal devices,” J. Photonics Energy 9(03), 1 (2018).
[Crossref]

A. Ghanekar, M. Sun, Z. Zhang, and Y. Zheng, “Optimal design of wavelength selective thermal emitter for thermophotovoltaic applications,” J. Therm. Sci. Eng. Appl. 10(1), 011004 (2018).
[Crossref]

M. Ono, K. Chen, W. Li, and S. Fan, “Self-adaptive radiative cooling based on phase change materials,” Opt. Express 26(18), A777–A787 (2018).
[Crossref]

P. Yang, C. Chen, and Z. M. Zhang, “A dual-layer structure with record-high solar reflectance for daytime radiative cooling,” Sol. Energy 169, 316–324 (2018).
[Crossref]

2017 (3)

F. Cao, L. Tang, Y. Li, A. P. Litvinchuk, J. Bao, and Z. Ren, “A high-temperature stable spectrally-selective solar absorber based on cermet of titanium nitride in sio 2 deposited on lanthanum aluminate,” Sol. Energy Mater. Sol. Cells 160, 12–17 (2017).
[Crossref]

X. Lim, “How heat from the sun can keep us all cool,” Nat. News 542(7639), 23–24 (2017).
[Crossref]

A. Ghanekar, Y. Tian, S. Zhang, Y. Cui, and Y. Zheng, “Mie-metamaterials-based thermal emitter for near-field thermophotovoltaic systems,” Materials 10(8), 885 (2017).
[Crossref]

2016 (5)

A. Ghanekar, L. Lin, and Y. Zheng, “Novel and efficient mie-metamaterial thermal emitter for thermophotovoltaic systems,” Opt. Express 24(10), A868–A877 (2016).
[Crossref]

S. Han, J.-H. Shin, P.-H. Jung, H. Lee, and B. J. Lee, “Broadband solar thermal absorber based on optical metamaterials for high-temperature applications,” Adv. Opt. Mater. 4(8), 1265–1273 (2016).
[Crossref]

D. Kraemer, Q. Jie, K. McEnaney, F. Cao, W. Liu, L. A. Weinstein, J. Loomis, Z. Ren, and G. Chen, “Concentrating solar thermoelectric generators with a peak efficiency of 7.4%,” Nat. Energy 1(11), 16153 (2016).
[Crossref]

S. Ferré, A. Peinado, E. Garcia-Caurel, V. Trinité, M. Carras, and R. Ferreira, “Comparative study of sio 2, si 3 n 4 and tio 2 thin films as passivation layers for quantum cascade lasers,” Opt. Express 24(21), 24032–24044 (2016).
[Crossref]

A. Ghanekar, L. Lin, and Y. Zheng, “Novel and efficient mie-metamaterial thermal emitter for thermophotovoltaic systems,” Opt. Express 24(10), A868–A877 (2016).
[Crossref]

2015 (4)

A. Ghanekar, L. Lin, J. Su, H. Sun, and Y. Zheng, “Role of nanoparticles in wavelength selectivity of multilayered structures in the far-field and near-field regimes,” Opt. Express 23(19), A1129–A1139 (2015).
[Crossref]

F. Cao, D. Kraemer, L. Tang, Y. Li, A. P. Litvinchuk, J. Bao, G. Chen, and Z. Ren, “A high-performance spectrally-selective solar absorber based on a yttria-stabilized zirconia cermet with high-temperature stability,” Energy Environ. Sci. 8(10), 3040–3048 (2015).
[Crossref]

A. Ghanekar, L. Lin, J. Su, H. Sun, and Y. Zheng, “Role of nanoparticles in wavelength selectivity of multilayered structures in the far-field and near-field regimes,” Opt. Express 23(19), A1129–A1139 (2015).
[Crossref]

H. Wang, V. P. Sivan, A. Mitchell, G. Rosengarten, P. Phelan, and L. Wang, “Highly efficient selective metamaterial absorber for high-temperature solar thermal energy harvesting,” Sol. Energy Mater. Sol. Cells 137, 235–242 (2015).
[Crossref]

2014 (2)

C. K. Ho, A. R. Mahoney, A. Ambrosini, M. Bencomo, A. Hall, and T. N. Lambert, “Characterization of pyromark 2500 paint for high-temperature solar receivers,” J. Sol. Energy Eng. 136(1), 014502 (2014).
[Crossref]

B. J. Lee, Y.-B. Chen, S. Han, F.-C. Chiu, and H. J. Lee, “Wavelength-selective solar thermal absorber with two-dimensional nickel gratings,” J. Heat Transfer 136(7), 072702 (2014).
[Crossref]

2013 (6)

J. Dai, F. Ye, Y. Chen, M. Muhammed, M. Qiu, and M. Yan, “Light absorber based on nano-spheres on a substrate reflector,” Opt. Express 21(6), 6697–6706 (2013).
[Crossref]

H. Wang and L. Wang, “Perfect selective metamaterial solar absorbers,” Opt. Express 21(S6), A1078–A1093 (2013).
[Crossref]

A. Isenstadt and J. Xu, “Subwavelength metal optics and antireflection,” Electron. Mater. Lett. 9(2), 125–132 (2013).
[Crossref]

L. Gao, F. Lemarchand, and M. Lequime, “Refractive index determination of sio2 layer in the uv/vis/nir range: spectrophotometric reverse engineering on single and bi-layer designs,” J. Eur. Opt. Soc. publications 8, 13010 (2013).
[Crossref]

J. Wu, C. Zhou, H. Cao, and A. Hu, “Polarization-dependent and-independent spectrum selective absorption based on a metallic grating structure,” Opt. Commun. 309, 57–63 (2013).
[Crossref]

L. Wang and Z. Zhang, “Measurement of coherent thermal emission due to magnetic polaritons in subwavelength microstructures,” J. Heat Transfer 135(9), 091505 (2013).
[Crossref]

2012 (4)

L. Wang and Z. Zhang, “Wavelength-selective and diffuse emitter enhanced by magnetic polaritons for thermophotovoltaics,” Appl. Phys. Lett. 100(6), 063902 (2012).
[Crossref]

C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers (adv. mater. 23/2012),” Adv. Mater. 24(23), OP181 (2012).
[Crossref]

A. Moreau, C. Ciraci, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492(7427), 86–89 (2012).
[Crossref]

M. G. Nielsen, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Efficient absorption of visible radiation by gap plasmon resonators,” Opt. Express 20(12), 13311–13319 (2012).
[Crossref]

2011 (3)

K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2(1), 517 (2011).
[Crossref]

N. Wang, L. Han, H. He, N.-H. Park, and K. Koumoto, “A novel high-performance photovoltaic–thermoelectric hybrid device,” Energy Environ. Sci. 4(9), 3676–3679 (2011).
[Crossref]

D. Kraemer, B. Poudel, H.-P. Feng, J. C. Caylor, B. Yu, X. Yan, Y. Ma, X. Wang, D. Wang, A. Muto, K. McEnaney, M. Chiesa, Z. Ren, and G. Chen, “High-performance flat-panel solar thermoelectric generators with high thermal concentration,” Nat. Mater. 10(7), 532–538 (2011).
[Crossref]

2010 (3)

D. Y. Shchegolkov, A. Azad, J. O’Hara, and E. Simakov, “Perfect subwavelength fishnetlike metamaterial-based film terahertz absorbers,” Phys. Rev. B 82(20), 205117 (2010).
[Crossref]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96(25), 251104 (2010).
[Crossref]

2008 (4)

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: design, fabrication and characterization,” Opt. Express 16(10), 7181–7188 (2008).
[Crossref]

H. M. Qiblawey and F. Banat, “Solar thermal desalination technologies,” Desalination 220(1-3), 633–644 (2008).
[Crossref]

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. G. de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref]

A. Gorin, A. Jaouad, E. Grondin, V. Aimez, and P. Charette, “Fabrication of silicon nitride waveguides for visible-light using pecvd: a study of the effect of plasma frequency on optical properties,” Opt. Express 16(18), 13509–13516 (2008).
[Crossref]

2007 (3)

Y.-B. Chen, Z. Zhang, and P. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129(1), 79–90 (2007).
[Crossref]

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19(21), 3628–3632 (2007).
[Crossref]

K. Aydin and E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial components,” J. Appl. Phys. 101(2), 024911 (2007).
[Crossref]

2004 (1)

D. Mills, “Advances in solar thermal electricity technology,” Sol. Energy 76(1-3), 19–31 (2004).
[Crossref]

2002 (1)

R. Marques, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of em waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89(18), 183901 (2002).
[Crossref]

1999 (1)

R. Cremer, M. Witthaut, D. Neuschütz, G. Erkens, T. Leyendecker, and M. Feldhege, “Comparative characterization of alumina coatings deposited by rf, dc and pulsed reactive magnetron sputtering,” Surf. Coat. Technol. 120-121, 213–218 (1999).
[Crossref]

1996 (2)

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43(10), 2063–2085 (1996).
[Crossref]

Y. Zhao, Y. Qian, W. Yu, and Z. Chen, “Surface roughness of alumina films deposited by reactive rf sputtering,” Thin Solid Films 286(1-2), 45–48 (1996).
[Crossref]

1994 (2)

R. Bräuer and O. Bryngdahl, “Design of antireflection gratings with approximate and rigorous methods,” Appl. Opt. 33(34), 7875–7882 (1994).
[Crossref]

M. Ino, N. Inoue, and M. Yoshimaru, “Silicon nitride thin-film deposition by lpcvd with in situ hf vapor cleaning and its application to stacked dram capacitor fabrication,” IEEE Trans. Electron Devices 41(5), 703–708 (1994).
[Crossref]

1993 (2)

T. Vink, W. Walrave, J. Daams, A. Dirks, M. Somers, and K. Van den Aker, “Stress, strain, and microstructure in thin tungsten films deposited by dc magnetron sputtering,” J. Appl. Phys. 74(2), 988–995 (1993).
[Crossref]

D. H. Raguin and G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32(7), 1154–1167 (1993).
[Crossref]

1992 (1)

1990 (1)

H. Kanoh, O. Sugiura, P. Breddels, and M. Matsumura, “Amorphous-silicon/silicon-nitride thin-film transistors fabricated by plasma-free (chemical vapor deposition) method,” IEEE Electron Device Lett. 11(6), 258–260 (1990).
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1989 (1)

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Figures (7)

Fig. 1.
Fig. 1. (A) A typical solar thermal energy conversion system. (B) Solar spectral irradiance (AM1.5, global tilt), radiative heat flux of blackbody thermal radiation at 200 $^{\circ }C$ and 500 $^{\circ }C$ , and reflectivity spectrum of ideal selective solar absorber and black surface.
Fig. 2.
Fig. 2. Schematics of 1-D and 2-D grating-Mie-metamaterial based solar absorbers. (A) 1-D triangular Al $_2$ O $_3$ surface gratings of height, $h$ = 150 nm, period, $\Lambda$ = 100 nm, on top of W-Si $_3$ N $_4$ -W stacks with the thickness of $t_1$ = 12 nm, $t_2$ = 35 nm, and $t_3$ = 500 nm, respectively. The Al $_2$ O $_3$ triangular grating is doped with 5 nm in radius W nanoparticles with a volume fraction, $f$ , of 25%. (B) 2-D pyramid encapsulated with W nanoparticles ( $r$ = 5 nm in radius with a volume fraction, $f$ , of 25%) sits on stockpiles of W-Al $_2$ O $_3$ -W. The thickness of W, Al $_2$ O $_3$ , and W is 10 nm, 40 nm, and 500 nm, respectively. The height of the surface grating layer is 200 nm and the period $\Lambda$ = 200 nm in both $x$ and $y$ direction.
Fig. 3.
Fig. 3. (A) Normalized spectral distribution of solar heat flux (AM 1.5) and normalized thermal radiation of a 500 $^{\circ }C$ blackbody, as well as the calculated reflectivity spectra of proposed 1-D and 2-D surface grating-Mie-metamaterials. Normal reflectivity spectra as a function of the thickness of 1-D (B) and 2-D (C) surface gratings layer, $h_1$ and $h_2$ are the height of the 1-D and 2-D triangular surface gratings, respectively.
Fig. 4.
Fig. 4. Normal reflectivity spectra as a function of W nanoparticles volume fraction, $f$ = 10%, 20% or 30%, for 1-D (A) and 2-D (B) surface grating-Mie-metamaterials, $f_1$ and $f_2$ defines the volume fractions of W nanoparticles embedded in the 1-D and 2-D Al $_2$ O $_3$ host, respectively. 1-D (C) and 2-D (D), reflectivity spectra vary as the size of W nanoparticles increases ( $r$ = 1, 3, and 5 nm), $r_1$ and $r_2$ denotes the size of the W nanoparticles in the 1-D and 2-D triangular surface grating structures, respectively. Refractive indices of W, SiO2 and SiO2 doped with W nanoparticles of volume fraction 20% and 10 nm radius. (E) Real part of refractive index. (F) Imaginary part of refractive index.
Fig. 5.
Fig. 5. Angle dependent reflectivity of TE polarization and TM polarization for proposed 1-D (A) and 2-D (B) selective solar absorbers contour plotted against wavelength, $\lambda$ and angle of incidence, $\theta$ .
Fig. 6.
Fig. 6. (A) Calculated photon-to-heat conversion efficiency of an ideal selective absorber, the multilayer solar absorber with measured/simulated radiative properties, and a black surface as a function of absorber operational temperature, T $_{abs}$ , under unconcentrated solar light; (B) Photon-to-heat conversion efficiency for abovementioned four absorber surfaces as a function of concentration factors, CF, at an absorber operational temperature of T $_{abs}$ = 500 $^{\circ }C$ .
Fig. 7.
Fig. 7. (A) Thermal performance of the 1-D (orange solid curve), 2-D (yellow solid curve) grating-Mie-metamaterials, and the black surface (purple solid curve) over a one-day cycle from sunrise (5:00 a.m.) to one hour after sunset (8:00 p.m.) at a varying ambient temperature (blue solid curve) under 10 suns (CF = 10). (B) The stagnation temperature of 1-D, 2-D surface gratings selective absorbers, and black surface at various concentration factors from 1 sun to 500 suns.

Tables (2)

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Table 1. Total normal absorptance and emittance of the designed 1-D and 2-D grating-Mie-metamaterials at T a b s = 200 C and 500 C .

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Table 2. Reflectivity of the designed 1-D and 2-D grating-Mie-metamaterials at solar irradiance peak of 0.55 μ m, with various incident angles and for both TE and TM polarizations.

Equations (21)

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η a b s = α a b s ϵ a b s σ ( T a b s 4 T a m b 4 ) C F Q a b s
α a b s = 0.3 μ m 4.0 μ m I s u n ( λ , θ , ϕ ) α ( λ , θ , ϕ ) d λ 0.3 μ m 4.0 μ m I s u n ( λ , θ , ϕ ) d λ = 0.3 μ m 4.0 μ m I s u n ( λ , θ , ϕ ) [ 1 R ( λ , θ , ϕ ) ] d λ 0.3 μ m 4.0 μ m I s u n ( λ , θ , ϕ ) d λ
ϵ abs = 2.5 μ m 20 μ m I b b ( λ , θ , ϕ ) ϵ ( λ , θ , ϕ ) d λ 2.5 μ m 20 μ m I b b ( λ , θ , ϕ ) d λ = 2.5 μ m 20 μ m I b b ( λ , θ , ϕ ) [ 1 R ( λ , θ , ϕ ) ] d λ 2.5 μ m 20 μ m I b b ( λ , θ , ϕ ) d λ
ε T E , 2 = ε T E , 0 [ 1 + π 2 3 ( Λ λ ) 2 ϕ 2 ( 1 ϕ ) 2 ( ε A ε B ) 2 ε T E , 0 ]
ε T M , 2 = ε T M , 0 [ 1 + π 2 3 ( Λ λ ) 2 ϕ 2 ( 1 ϕ ) 2 ( ε A ε B ) 2 ε T E , 0 ( ε T M , 0 ε A ε B ) 2 ]
ε T E , 0 = ϕ ε A + ( 1 ϕ ) ε B
ε T M , 0 = ( ϕ ε A + 1 ϕ ε B ) 1
n 2 D = [ n ¯ + 2 n ^ 2 D + 2 n ˇ 2 D ] / 5
n ¯ = ( 1 f 2 ) n A + f 2 n B
ε ^ 2 D = ( 1 f ) ε A + f ε
1 / ε ˇ 2 D = ( 1 f ) / ε A + f / ε
ε = ( 1 f ) ε A + f ε B
1 / ε = ( 1 f ) / ε A + f / ε B
ε e f f = ε m ( r 3 + 2 α r f r 3 α r f )
a 1 , r = ε n p ψ 1 ( x n p ) ψ 1 ( x m ) ε m ψ 1 ( x m ) ψ 1 ( x n p ) ε n p ψ 1 ( x n p ) ξ 1 ( x m ) ε m ξ 1 ( x m ) ψ 1 ( x n p )
ϵ ( ω ) = c 2 ω 2 0 ω / c d k ρ k ρ μ = s , p ( 1 | R ~ h ( μ ) | 2 | T ~ h ( μ ) | 2 )
Q t o t a l ( T a b s , T a m b ) = Q s u n ( T a b s ) + Q a m b ( T a m b ) Q r e e m i t ( T a b s )
Q s u n ( T a b s ) = A C F 0 d λ I A M 1.5 ( λ ) α ( λ , θ s u n , T a b s )
Q a m b ( T a m b ) = A 0 d λ I B B ( T a m b , λ ) α ( λ , θ , ϕ , T a b s ) ϵ ( λ , θ , ϕ )
Q r e e m i t ( T a b s ) = A 0 d λ I B B ( T a b s , λ ) ϵ ( λ , θ , ϕ , T a b s )
C a b s d T d t = Q t o t a l ( T a b s , T a m b )