Design and analysis of Salisbury screens and Jaumann absorbers for solar radiation absorption

Abstract

Two types of resonance absorbers, i.e., Salisbury screens and Jaumann absorbers are systematically investigated in solar radiation absorption. Salisbury screen is a metal-dielectric-metal structure which overcomes the drawback of bulky thickness for solar spectrum. Such structures have a good spectral selective absorption property, which is also insensitive to incident angles and polarizations. To further broaden absorption bandwidth, more metal and dielectric films are taken in the structure to form Jaumann absorbers. To design optimized structural parameters, the admittance matching equations have been derived in this paper to give good initial structures, which are valuable for the following optimization. Moreover, the analysis of admittance loci has been conducted to directly show the effect of each layer on the spectral absorptivity, and then the effect of thin films is well understood. Since the fabrication of these layered absorbers is much easier than that of other nanostructured absorbers, Salisbury screen and Jaumann absorbers have a great potential in large-area applications.

Keywords

thin films / admittance loci / solar absorber

Introduction

Solar absorbers are important energy conversion components, which are widely used in various forms of solar utilizations, such as solar thermal, thermophotovoltaic and photo-thermoelectric systems. The thermal radiative properties of good solar absorbers should be spectral selective. They should have a broadband strong absorption in visible and near-infrared regime to maximize the solar absorption, and a small emittance in mid-infrared spectral range to minimize thermal emission. In addition, these properties should not be sensitive to incident directions and polarizations. Although it is theoretically possible to tune the optical constants at the material level, the tunability is quite limited [¹]. To achieve the desired spectral property, it is hard to rely on intrinsic optical properties of individual material. Nanostructured materials open up a new avenue for achievement of spectral selectivity by various types of structures. Numerous nanostructures have been proposed to achieve perfect solar absorption, in which plasmonic nanostructures and metamaterials are regarded as strong candidates for perfect absorbers [²–⁹]. These nanostructures offer a great flexibility to control absorption features by tailoring the geometry and collective arrangements. Nevertheless, to obtain such structures, complex nanofabrication processes are usually required, and the scalability problem and the formidable costs make it difficult for large-area applications.

For resonance absorbers, layered film structures, such as Salisbury screens and Jaumann absorbers have a special advantage considering the balance between the high absorption ability and simple structures. Actually, layered structures, especially metal dielectric layered structures, have been widely applied. In 1947, Hadley and Dennison proposed the metal-dielectric-metal layered structures, and took them as transmission narrowband filters [¹⁰,¹¹]. Metal-dielectric multiple films have large color shifts with angle, high chroma, a large color gamut, and light fastness, which have been used in world currencies as anti-counterfeiting inks [¹²]. Salisbury screen, one of the first nearly perfect absorber, is a structure composed of metal-dielectric-metal tri-layers. It was invented in 1952 with a bulky thickness in radar waves. However, the thickness will largely decrease in solar spectrum, and it is inspired to extend such a structure to a selective solar absorber. In Salisbury screens, metal films are taken as resisting screens. They are generally regarded as ideal reflectors in mid-infrared regime, and perfect metal films will totally reflect incident waves, which make the emittance extremely low. Considering the optical loss in the visible and near-infrared regime, metal films are also taken as absorption components. To keep the transmission of radiation energy, top resisting screens for solar energy should be ultrathin. Theoretically, Berning and Turner have found that induced transmittance can be considerable if the ratio of extinction coefficient to refractive index of the metal is high [¹³]. Recently, Kats et al. have demonstrated a new type of optical coatings by investiga- ting strong interference of ultrathin absorbing dielectric on metallic substrates [¹⁴]. Similarly, Wang et al. have investigated the photon tunneling effect caused by ultrathin metals, which can achieve a good absorption property [¹⁵].

Many theories focusing on ultrathin metal films have been developed to further enrich mechanisms and applications of such layered absorbers [¹⁶–¹⁹]. Kats et al. have developed the method for phasor diagrams considering phase shifts of partially reflected waves in lossy dielectric layers, and observed other routes for perfect absorption [²⁰]. Shu et al. have studied the asymmetric Fabry-Perot (FP) absorber with the ultrathin film, and found that the electric field located in middle dielectrics enhances the absorption of adjacent metals [²¹]. Similar works have been done by some other researchers, and resonances occurring in middle dielectrics have been investigated to control absorption peaks [²²–²⁴]. Yan has pointed out that the top ultrathin metal film regulates not only the FP cavity’s quality factor, but also the coupling strength between cavity mode and the external light of incidence [²⁵]. The top ultrathin layer mainly causes absorptive and radiative losses, which eventually forms the equilibrium to satisfy critical coupling of perfect absorption [²⁶]. For aforementioned theories, it usually needs to repeatedly iterate reflection coefficients or calculate fields, and these intermediate variables hardly reflect absorption properties directly.

In this work, Salisbury screens have been employed to achieve the desired spectral property and the method of admittance loci [²⁷–²⁹] has been developed to analyze the effect of ultrathin metal and dielectric films on the performance. The diagram method can better understand the absorption property of each layer. To the best of the authors’ knowledge, no such analyses have been conducted for layered absorbers with ultrathin films before. Furthermore, to broaden the absorption bandwidth, more metal and dielectric film are taken in Jaumann absorbers. In the design process, initial structural parameters of these layered absorbers can be calculated by the admittance matching equations, followed by optimization for applications of selective solar absorbers.

Design of Salisbury screens and Jaumann absorbers

The Schematic of the Salisbury screen and the plot of admittance loci diagram are depicted in Fig. 1. Salisbury screens containing top ultrathin metals, middle dielectrics, and metallic substrates are shown in Fig. 1(a). Jaumann absorbers, which are considered as modified structures of Salisbury screens, have more alternative metal and dielectric films. In this work, since tungsten (W) has a good resistance to corrosion and high temperature, W is taken as the metallic material in both top and bottom layers. Silica (SiO₂) is taken as dielectrics in middle layers, and it is lossless in visible and near-infrared regime [³⁰]. Optical constants of the materials refer to the material database in FDTD solutions. Therefore, the simulation results can be validated by this commercial photonics software.

To quickly find structural parameters of Sablisbury screens and Jaumann absorbers at a given wavelength, the admittance matching equations are used. The admittance y = H/(s× E) is the ratio of magnetic field to electric field, where s is a unit vector in wave propagation direction, and H and E are vectors of magnetic field and electric field, respectively. The admittance loci diagram has a great value in visualizing characteristics of multilayer films. As shown in Fig. 1(b), a plot of admittance loci diagram simulates the layer-by-layer growth of multilayer films on the substrate. As each layer in turn increases from a thickness of zero to its final value, the admittance at that point is calculated and the locus is recorded. The admittance calculation of films having q layers can be realized by the characteristic matrix expressed as [³¹]

(1)\left[\begin{array}{l}B\hfill \\ C\hfill \end{array}\right]=\{\left[\begin{array}{ll}\cos {\delta }_R\hfill & \mathrm{i}\sin {\delta }_R/{\eta }_R\hfill \\ \mathrm{i}{\eta }_R\sin {\delta }_R\hfill & \cos {\delta }_R\hfill \end{array}\right]{\displaystyle \prod _{r=R+\mathrm{1}}^q\left[\begin{array}{ll}\cos {\delta }_r\hfill & \mathrm{i}\sin {\delta }_r/{\eta }_r\hfill \\ \mathrm{i}{\eta }_r\sin {\delta }_r\hfill & \cos {\delta }_r\hfill \end{array}\right]}\}\left[\begin{array}{l}\mathrm{1}\hfill \\ {\eta }_m\hfill \end{array}\right],

where B and C are electric and magnetic components in the matrix, subscripts R and r indicate the growing layer R and the deposited layers r, and m indicates the substrate. The phase shift of layers is expressed as

{\delta }_R=\mathrm{2}\mathrm{\pi }{N}_R\left(d-{\displaystyle {\sum }_{r=R+\mathrm{1}}^q{d}_r}\right)\cos {\theta }_R/\lambda ,

(2){\delta }_r=\mathrm{2}\mathrm{\pi }{N}_r{d}_r\cos {\theta }_r/\lambda ,

where d is the thickness and l is incident wavelength. The tilted admittances h in TE and TM polarizations are respectively calculated by

(3){\eta }_r=\mathit{\gamma }{N}_r\cos {\theta }_r,{\eta }_r=\mathit{\gamma }{N}_r/\cos {\theta }_r,

where g is the vacuum optical admittance and q is the refraction angle of each layer, which accords with the Snell law. Gaussian units are applied to the admittance expression so that g is unity, and the admittance Y numerically equals the complex refractive index N at normal incidence. The admittance calculated by characte-ristic matrix can be expressed as

(4)Y={\displaystyle \frac{C}{B\mathit{\gamma }}}.

The admittance matching condition of tri-layered absorbers as Salisbury screens is directly deduced by admittance matching with the incident media based on Eq. (1), i.e.,

(5){\eta }_{\mathrm{0}}={\displaystyle \frac{\mathrm{i}{\eta }_{\mathrm{1}}\sin {\delta }_{\mathrm{1}}\cos {\delta }_{\mathrm{2}}+\mathrm{i}{\eta }_{\mathrm{2}}\cos {\delta }_{\mathrm{1}}\sin {\delta }_{\mathrm{2}}-{\eta }_{\mathrm{1}}{\eta }_m\sin {\delta }_{\mathrm{1}}\sin {\delta }_{\mathrm{2}}/{\eta }_{\mathrm{2}}+{\eta }_m\cos {\delta }_{\mathrm{1}}\cos {\delta }_{\mathrm{2}}}{\mathrm{i}{\eta }_m\sin {\delta }_{\mathrm{1}}\cos {\delta }_{\mathrm{2}}/{\eta }_{\mathrm{1}}+\mathrm{i}{\eta }_m\cos {\delta }_{\mathrm{1}}\sin {\delta }_{\mathrm{2}}/{\eta }_{\mathrm{2}}-{\eta }_{\mathrm{2}}\sin {\delta }_{\mathrm{1}}\sin {\delta }_{\mathrm{2}}/{\eta }_{\mathrm{1}}+\cos {\delta }_{\mathrm{1}}\cos {\delta }_{\mathrm{2}}}}.

At normal incidence, a largely simplified expression is obtained as

(6)\mathrm{i}{\displaystyle \frac{N_{\mathrm{0}}{N}_m-N_{\mathrm{1}}^{\mathrm{2}}}{N_{\mathrm{1}}}}\tan {\delta }_{\mathrm{1}}+\mathrm{i}{\displaystyle \frac{N_{\mathrm{0}}{N}_m-N_{\mathrm{2}}^{\mathrm{2}}}{N_{\mathrm{2}}}}\tan {\delta }_{\mathrm{2}}+{\displaystyle \frac{N_m{N}_{\mathrm{1}}^{\mathrm{2}}-N_{\mathrm{0}}{N}_{\mathrm{2}}^{\mathrm{2}}}{N_{\mathrm{1}}{N}_{\mathrm{2}}}}\tan {\delta }_{\mathrm{1}}\tan {\delta }_{\mathrm{2}}=N_m-N_{\mathrm{0}}.

After complex refractive indices of materials are given, the optimal thicknesses of films from phase shift terms (d₁, d₂) in Eq. (6) can be obtained.

Similarly, admittance matching equations of multi-layered absorbers as Jaumann absorbers at normal incidence are derived as

(7)

(8)

(9)

Equations (7)–(9) are applicable in calculating structural parameters of Jaumann absorbers with three, four, and five films, respectively. A general admittance matching equation and design process can be referred to in Ref. [³²].

Because ideal solar absorbers are frequency-selective, the following optimization is necessary. To evaluate the performance of absorbers over the entire solar spectrum, the total absorptivity and emissivity are defined as

(10){\alpha }_{\mathrm{total}}={\displaystyle \frac{{\displaystyle {\int }_{\mathrm{0.28}\mathrm{\mu m}}^{\mathrm{4\; \backslash hskip\; -3pt\mu m}}\alpha \left(\lambda \right)I_{\mathrm{AM1}\mathrm{.5}}\left(\lambda \right)}\mathrm{d}\lambda }{{\displaystyle {\int }_{\mathrm{0.28}\mathrm{\mu m}}^{\mathrm{4\; \backslash hskip\; -3pt\mu m}}{I}_{\mathrm{AM1}\mathrm{.5}}\left(\lambda \right)}\mathrm{d}\lambda }},

(11){\epsilon }_{\mathrm{total}}={\displaystyle \frac{{\displaystyle {\int }_{\mathrm{0.28}\mathrm{\mu m}}^{\mathrm{20}\mathrm{\mu m}}\epsilon \left(\lambda \right)I_{\mathrm{BB}}\left(\lambda \right)\mathrm{d}\lambda }}{{\displaystyle {\int }_{\mathrm{0.28}\mathrm{\mu m}}^{\mathrm{20}\mathrm{\mu m}}{I}_{\mathrm{BB}}\left(\lambda \right)\mathrm{d}\lambda }}},

where I_AM1.5(l) is the spectral irradiance of AM 1.5 direct and circumsolar spectrum, I_BB(l) is the spectral intensity of blackbody at temperature T_A = 373.15 K, and α(l) and ε(l) are the spectral absorptivity and emissivity respectively. When heat convection and conduction are neglected, the absorption efficiency is expressed as

(12)\eta ={\displaystyle \frac{{\alpha }_{\mathrm{total}}G-{\epsilon }_{\mathrm{total}}\left(\sigma T_{\mathrm{A}}^{\mathrm{4}}-\sigma T_{\mathrm{sky}}^{\mathrm{4}}\right)}{G}},

where G is the incidence heat flux of solar irradiation, s is Stefan-Boltzmann constant, and T_sky = 273.15 K is the atmosphere temperature.

To optimize the design of the selective solar absorber, the enumeration method and an optimization algorithm can be used. The enumeration method needs to simulate all possible structural parameters, which results in futile simulations. A narrower range of structural parameters will notably reduce the amount of simulations. Similarly, most optimization algorithms need to simulate a large number of structures, and then screen out optimized structural parameters. For both design approaches, a good initial structure will significantly accelerate the optimization process.

Results and analysis

Performance of Salisbury screens

Figure 2 demonstrates the optimized Salisbury screens and their absorptivity spectra. As shown in Fig. 2(a), the optimal thicknesses of Salisbury screens achieving perfect absorption at a particular wavelength are directly calculated based on Eq. (6). The optimal thickness of silica layer increases with wavelength. If the metals that sandwich the dielectric films are perfect reflectors, the optimal thickness should theoretically be linearly dependent on the wavelength. However, the dispersion of lossy materials that generates phase shifts at the interfaces varies with incident wavelengths, which results in the fact that optimal thicknesses of silica are no longer proportional to wavelengths. The top metal film is not only a part of mirror but also absorption components in absorbers; therefore, the optimal thickness of the top tungsten film changes with wavelengths in a more complicated manner. The absorptivity spectra of thin film absorbers achieving a perfect absorption at wavelengths of 400, 500, 600, 1000, and 1500 nm shown in Fig. 2(b) are simulated by using the transfer matrix method (TMM). These absorbers refer to the structural parameters in Fig. 2(a) indicated by the vertical lines. It is found that absorptivity spectra have peaks at particular wavelengths, which is consistent with the prediction.

Figure 3 exhibits the total conversion efficiency and absorptivity spectrum of the absorber. Figure 3(a) shows the conversion efficiency of the absorber when the thicknesses of top W vary from 1 nm to 11 nm with an interval of 0.1 nm and the thicknesses of middle silica change from 50 nm to 250 nm with an interval of 2 nm. The efficiencies have also been calculated, employing structural parameters that achieve perfect absorption (as shown in Fig. 2(a)), which are shown as the blue line in Fig. 3(a). The black dot indicates the maximum efficiency of 78.64% and the thicknesses of upper films are 3.8 nm and 84.9 nm, which are calculated by the method combining admittance matching equation and the genetic algorithm, one of the optimization algorithms. The absorptivity spectrum of the maximal efficiency is shown in Fig. 3(b), and the absorptivity of the peak is 0.9954, occurring at a wavelength of 626 nm. It means that the weights of absorptivity peaks and widths are carefully balanced for broadband absorbers. On the other hand, the efficiencies of optimal thicknesses given by admittance matching conditions slightly deviate from the maximum because the extreme absorptivity peak is their unique goal. However, it is proved that the admittance matching analysis has a great value in designing narrowband absorbers and is also helpful for broadband absorbers. The emissivity of layered absorbers in the mid-infrared spectrum is less than 4% as shown in Fig. 3(b), which minimizes the thermal radiation loss at the same time.

To further check the sensitivity of the solar absorber with a maximum efficiency to incident angles and polarizations, the absorption spectra at different incident angles have been calculated and the results are shown in Fig. 4. It can be seen that the broadband spectral absorption maintains in a broad angular range for the TE polarization, as shown in Fig. 4(a). The broad range, however, shrinks rapidly when incident angles are larger than 60°. In contrast, the spectral range of high absorptivity extends to an incident angle of 80° at TM polarization, as shown in Fig. 4(b). Considering the fact that solar incident is unpolarized, the solar absorber can maintain a high absorption over a large incident angle range from the normal to 60°, which is proved to be effective in practical applications.

Effects of top metal and dielectric films

Next, an attempt has been made to further analyze the significance of each layer on the overall performance of the absorber. Admittance loci diagram records admittances of films, which vividly illustrates the effects of complex refractive indices and thicknesses of films on reflectance. Because the main concern here is the influence of ultrathin thickness and material loss of top metals on the absorptivity as well as the influence of thickness of dielectrics, admittance loci diagram is suitable to perform such an analysis.

In admittance loci diagrams, the real and imaginary parts of admittance numerically equal the refractive index and extinction coefficient, respectively. The admittance of incident media is vacuum, which is point (1, 0) in the diagrams. When the end of an admittance locus is at point (1, 0), the admittance matching is satisfied and no reflection occurs. To display the effect of admittance on reflectance, isoreflectance contours are added to the admittance loci diagrams. They are circles with centers (h₀(1 – R)/(1+ R),0) on the real axis, and the radii are given by 2h₀R^0.5/(1−R), where R is the reflectance.

Figure 5 displays the spectral absorptivity and admittance loci diagrams of double layered structures. The spectral absorptivity with various thicknesses when top metallic film is deleted is given in Fig. 5(a). These structures of double layers cannot achieve a perfect absorption at any wavelength, which can be easily understood by their admittance loci diagrams. In Fig. 5(b), the admittance loci at different wavelengths are arcs of complete circles on account of lossless silica used in the growing layer. Arcs start from complex refractive indices of substrate W, and curvature radii of arcs depend on refractive indices of silica. There are no arcs going through point (1, 0), which corresponds to the admittance of incident media to satisfy admittance matching. Therefore, none of them can achieve a perfect absorption. The spectral absorptivity at the same wavelength in Fig. 8(a) has repeated absorptivity peaks with the increase of the thickness while the values of peaks are the same, which is corresponding to circulating circles in Fig. 8(b).

After top ultrathin metallic films being added, a perfect absorption can be achieved by properly choosing the thicknesses of the top metal and middle dielectric films. Figure 6 presents the absorptivity spectra and admittance loci diagrams of Salisbury screens. The absorptivity spectra of Salisbury screens with different thicknesses of top W and fixed thickness of silica 100 nm are shown in Fig. 6(a). It is seen that absorbers with ultrathin metal films of 3 nm have almost a perfect absorption at a certain wavelength. As the thicknesses of top W increase, the amplitudes of absorptivity peaks decline dramatically, and peak locations shift to longer wavelengths. Figure 6(a) shows three admittance loci at a wavelength of 700 nm, 1000 nm, and 1500 nm, respectively. The admittance loci with middle silica are circle arcs, and the admittance loci with top W are helical lines. This means that there are other routes combining circle arcs with helixes to pass through point (1, 0), which makes it possible to achieve a perfect absorption. In Fig. 6(b), the admittance locus at a wavelength of 700 nm is closest to point (1, 0) of the three admittance loci. Therefore, it has a higher absorp-tivity peak than others as in Fig. 6(a). The dots depict the admittances changing by the interval of 1 nm, and their distribution is from sparse to dense. Isoreflectance contours are eccentric circles. Therefore, the admittance variations with the same value on the left of admittance loci diagrams have a greater influence on reflectance. The admittance loci of top ultrathin metal films start from the left zone which is very sensitive to the admittance variation, and dots in the initial segment of top ultrathin metal films are sparse that have larger admittance variations, which results in a great potential in controlling absorptivity amplitudes.

Figure 7 gives the absorptivity spectra and admittance loci diagrams of Salisbury screens. The absorptivity spectra of Salisbury screens with different thicknesses of silica and fixed thickness of top W 3 nm are shown in Fig. 7(a). It is found that the absorptivity peaks shift to longer wavelengths with the increase of silica thickness. The amplitudes of absorptivity peaks slightly drop as silica thickness increases. Based on Figs. 6(a) and 7(a), an empirical conclusion may be reached that the amplitudes of absorptivity peaks mainly depend on the top W film while the locations of absorptivity peaks are mainly determined by the middle silica layer. The admittance loci of the four structures in Fig. 7(a) at the wavelengths of the absorptivity peaks are shown in Fig. 7(b). All ending points are located inside the isoreflectance circle of R = 0.05, which means that their absorptivity is higher than 0.95. Strictly speaking, the absorptivity peaks are the nearest points of admittance loci to point (1, 0), which require reasonable lengths of arcs and helixes as well as origins of the admittance loci. The main role of the segments in the admittance loci of silica is to make their ends (i.e., the origins of the segments in the admittance loci of top W) approach the admittance matching point (1, 0). On the other hand, distances between admittances of substrates and point (1, 0) prolong as wavelength increases. Considering the fact that refractive indices of silica are almost invariant with the wavelength, the thicknesses of silica determine the lengths of arcs. As such, longer lengths of arcs mean thicker thicknesses of silica, which is the reason why thicker silica makes absorptivity peaks red shift.

Experiments with samples of Salisbury screens

The Salisbury screens investigated here are fabricated by using the Denton multi-target magnetic control sputtering system. W substrates with thicknesses of about 500 nm are first coated on polished silicon wafers. Then silica films are deposited on W substrates, and the thicknesses of silica layers are tested by using the Ocean Optics film thickness measurement system before the deposition of top W films. Because it is difficult to control the exact thicknesses of top ultrathin films, different sputtering times are taken to fabricate different thicknesses, which are later measured by the Zeiss Ultra Plus filed emission scanning electron microscope.

After fabricating absorber samples, the hemisphere reflectivity spectra of samples are obtained by using the PerkinElmer Lambda 750 s spectrometer with a spectralon coated integrating sphere. The absorptivity spectra are then obtained by (1 – R) and shown in Fig. 8(a). Four different configurations of structures are listed in the legend of Fig. 8(a). For both thicknesses of top W films (1 and 10 nm), the amplitudes of absorptivity are larger than 0.8. The locations of peaks have obvious red shift as predictions when the silica becomes thicker. The simulation results with the same structural parameters are shown in Fig. 8(b). The absorptivity spectra in the simulations have similar variations. The locations of absorption peaks are generally consistent between the simulations and the experiments, while the absorptivity values in the simulations have some deviations from the experimental results. The emissivity spectra of absorber samples are measured by the Frontier Fourier-transfer infrared spectrometer with a Pike Integra-ting sphere at room temperature. Compared to the simulation results as shown in Fig. 8(c), a higher emissivity occurs in the wavelength range of 4–6 mm.

Because the wavelength is much longer than the characteristic scale of films, the distinction is more likely to come from intrinsic optical constants rather than structures. Actually, optical constants of tungsten thin films with a b-W phase and a g-W phase are different from the α-W phase (bulk tungsten) in the wavelength range longer than 2.5 mm [³³]. To find explanations for the errors between the experiments and the simulations in the visible and near-infrared range, scanning electron microscope images of a sample are taken to observe morphology features in Fig. 9. The surface of the sample is a non-uniform plane with islands divided by cracks as shown in Fig. 9(a). In the cross section of the sample in Fig. 9(b), the interfaces between the three layers are clear, and the top film has a significant roughness. It is found that non-uniform surfaces in the experiments are the main characteristic different from homogeneous and smooth films employed in the simulations.

Performance of Jaumann absorbers

To demonstrate the effectiveness of Jaumann absorbers for solar absorption purpose, the optimization method has also been employed to design such multilayer absorbers, and the results are shown in Fig. 10. The optimized thicknesses and their efficiencies are listed in Table 1. The initial thicknesses in the optimization algorithm are obtained by solving Eqs. (7)–(9). As layers increase, more absorptivity peaks occur to broaden the absorption platform of spectra, while emissivity grows due to the larger thickness. Six layered absorbers have broadband and high absorptions, which even maintain an absorptivity higher than 0.95 in the wavelength range of 0.4–1.5 mm.

As the number of layers increases, broadband absorption is attributed to the stronger interference in multilayer systems. However, it is found that the most significant growth (17.53%) in efficiency occurs when ultrathin W film is deposited on tri-layered absorbers. Moreover, the contribution of top ultrathin film to the efficiency declines dramatically in multilayer absorbers as shown in No. 4 absorber. It means that surface ultrathin metal films have little effect on complex layered absorbers.

Conclusions

Salisbury screens and Jaumann absorbers are investigated and proved to have a good performance. Physical mechanism of perfect absorption is attributed to the admittance matching between absorbers and incident media. Based on admittance analyses, admittance matching equations are deduced to choose the thickness of each film. The method is fast and direct, which is suitable for designing narrowband absorbers. Moreover, it is helpful to provide a set of preferable initial values for optimization algorithms. Furthermore, the effects of top metals and dielectrics on Salisbury screens are understood by admittance loci diagrams. The loci of top ultrathin metals start from the left zone which is very sensitive to the admittance variation, and the dots of loci are sparse which have larger admittance variations in admittance loci diagrams. Therefore, top ultrathin metal films have a great potential in adjusting the absorptivity. The reason why thicker middle silica makes absorptivity peaks red shift is that the distances between admittances of substrates and the admittance matching point increase at longer wavelengths in admittance loci diagrams. It is also demonstrated that Jaumann absorbers can achieve an even better performance.

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