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Abstract
We propose a lithography-free wide-angle polarization-insensitive ultra-broadband absorber by using three pairs of tungsten (W) and calcium fluoride (CaF2) films. The simulation results show that the absorptivity is larger than 0.9 with normal incidence in the wavelength range from 400 nm to 1529 nm. By adding a pair of CaF2-W films, we can get a broader absorption bandwidth with absorptivity larger than 0.9 over the wavelength of 400–1639 nm. In addition, the absorption performance is insensitive to the polarization and angle of incidence. The electric field distributions at the absorption peaks show that the absorption is originated from the destructive interference between the reflection waves from the top and bottom interfaces of the multilayer CaF2-W films. Furthermore, the ultra-broad bandwidth is attributed to the anti-reflection effect from the increased effective refractive index from top to down of the proposed absorber. Such physical mechanism of broadening bandwidth based on anti-reflection effect provides a new idea for the design of broadband absorber. Meanwhile, this broadband absorber is a good candidate for potential applications such as detection and energy harvesting.
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1. Introduction
Bandwidth manipulation with near-perfect absorption is an important topic in the field of optical applications. Absorbers with different bandwidths have different applications. Narrowband absorbers can be applied in the sensing [1], thermal emission source [2], and filter [3]. On the other hand, broadband absorbers have many applications such as radiative cooling [4], solar cell [5], and photo-detection [6]. Many broadband absorbers based on microstructures have been proposed with various schemes such as multiple resonances in metasurfaces [7,8], interferences in metal-dielectric stacks [9], hyperbolic metamaterials [10,11], and impedance match [12,13]. However, the fabrication of these microstructures is complicated and expensive. Due to the advantages of simple structures and lithography-free fabrication processes, metamaterials with multilayer films have been developed to manipulate the electromagnetic wave [14–19]. To date, the ultra-broadband absorbers in the visible and near-infrared ranges have been reported based on optical topological transition with dozens of layers [20,21]. On the other hand, to reduce cost, the lithography-free broadband absorbers with several layers are proposed with different design strategies [22–26]. However, how to achieve a broader absorption bandwidth with several layers is still a challenge.
In this paper, we propose a lithography-free wide-angle polarization-insensitive ultra-broadband absorber by using three pairs of W-CaF2 films in the visible and near-infrared ranges. The perfect absorption is originated from the destructive interference from the top and bottom interfaces of the multilayer CaF2-W films. Furthermore, the ultra-broad absorption bandwidth is attributed to the anti-reflection effect from the increased effective refractive index from top to down of the proposed absorber. This broadband absorber is a good candidate for potential applications such as detection and energy harvesting.
2. Ultra-broadband absorber
Figure 1(a) shows the schematic diagram of the proposed broadband absorber, which is composed of three pairs of CaF2 and W films. Au is used as the substrate material in order to prevent the transmission. The thicknesses of calcium fluoride films are identical and equal to d = 100 nm. From top to bottom, the thicknesses of tungsten films are l1 = 5 nm, l2 = 12 nm and l3 = 30 nm, respectively. The absorption performance is evaluated by the rigorous coupled-wave analysis (RCWA) in this paper [27]. The absorptivity is defined as A = 1-R-T where R and T are the reflectivity and transmissivity, respectively. The refractive indices of W determined by Lorentz-Drude model are used from Ref. [28]. In addition, the refractive indices of CaF2 and Au are taken from Ref. [29,30]. Figure 1(b) shows the simulation spectrum of the proposed structure under TE-polarization (electric field perpendicular to the incidence plane) normal incidence. From Fig. 1(b), we can see a broadband absorption bandwidth jointed by three absorption peaks of ${\lambda _1}\textrm{ = }472$nm, ${\lambda _2}\textrm{ = 764}$nm and ${\lambda _3}\textrm{ = 1081}$nm. Furthermore, Fig. 1(b) shows that the absorptivity is larger than 0.9 in the wavelength range from 400 nm to 1529 nm. We make a comparison between the similar previous broadband absorbers with several layers and our work in Table 1. As shown in Table 1, the proposed absorber has a broader bandwidth with absorptivity larger than 0.9 than those reported in Ref. [22–25]. Although the bandwidth in Ref. [26] is larger than that in our work, too many film materials in Ref. [26] increase the fabrication complexity. Thus, considering the reduction of fabrication complexity, the absorption bandwidth of our absorber has obvious advantages.
Fig. 1. (a) Schematic diagram of the proposed broadband absorber. (b) Absorption spectrum of the multilayer films.
Table 1. Comparison between references and our work.
Now, we investigate the angle-dependence absorption characteristics of the proposed structure with simulations. The structure parameters used in Fig. 2 are d = 100 nm, l1 = 5 nm, l2 = 12 nm and l3 = 30 nm. Figures 2(a) and 2(b) show the absorption spectra with different incident angles for TE and TM polarizations (magnetic field perpendicular to the incidence plane), respectively. From Fig. 2, we can see that the absorptivity of the proposed structure for both polarizations is above 0.9 in the wavelength range from 400 nm to 1452 nm for angles up to 40°, and the absorptivity is larger than 0.78 in the same wavelength range for angles up to 60°. Thus, the absorption of our proposed absorber is insensitive to both the polarizations and incident angles in the visible and near-infrared ranges. Such characteristics make the proposed absorber suitable for the practical applications, such as solar cells and photo-detectors.
In the reported broadband absorbers based on multilayer films, the identical thicknesses of metal layers are used, while the different thicknesses of metal layers are employed in our design strategy. To compare the effects from the different settings, we calculate the absorption spectra of metal films with the identical thicknesses of W layers in Fig. 3(a). In the simulation process of the next part of this paper, a TE-polarization light with normal incidence is employed. The thickness of CaF2 film is set as 100 nm. For comparation, the absorption spectrum in Fig. 1(b) is re-plotted with red curve. Compared with the red curve, the others in Fig. 3(a) show that the absorption bandwidth with absorptivity larger than 0.9 is greatly reduced. Thus, compared with other absorbers which have the same thicknesses of metal films, our absorber, which adopts the increased W thickness from top to bottom, has broader absorption bandwidth. The thickness of CaF2 film is another important parameter of the proposed absorber. The influence of d on the absorption performance is investigated in Fig. 3(b). Other structure parameters used in Fig. 3(b) are l1 = 5 nm, l2 = 12 nm and l3 = 30 nm. From Fig. 3(b), we can see that ultra-broadband absorption peaks shift towards longer wavelengths as d increases. Furthermore, the absorption bandwidth can be remained with different values of d. Thus, we can tune the absorption peaks by changing the thickness of CaF2 films.
Fig. 3. (a) Absorption spectra with different configurations of W films. (b) Absorption spectra with different thickness configurations of CaF2 films.
Next, we study the influence of the number of CaF2-W film pairs on the absorption spectrum. In the simulation process, we add or reduce the CaF2-W pairs on the base of structure with 3 pairs of CaF2-W films used in Fig. 1(b). The black curve in Fig. 4 is the spectrum without the top CaF2-W pair. For comparison, we replot the spectrum in Fig. 1(b) with the red curve. As shown from the black curve in Fig. 4, the bandwidth with the absorptivity more than 0.9 is much narrower than that in Fig. 1(b). On the other hand, a CaF2-W pair is added to the top of the structure in Fig. 1(b). The film thickness of the added CaF2 film is unchanged with 100 nm, while the thickness of W film is reduced to 3 nm in order to meet the design strategy that the thickness of W film is reduced from the substrate upward. The blue curve shows the absorption spectrum with the adding CaF2-W pair. As shown from the blue curve, the bandwidth with absorptivity more than 0.9 ranges from 400 nm to 1639 nm, which is larger than that with 3 CaF2-W pairs in Fig. 1(b). From the above discussion, we can manipulate the absorption bandwidth by adding or reducing CaF2-W pairs. On the other hand, if the required absorption bandwidth is not very wide, the total thickness of the proposed structure can be reduced by reducing the CaF2-W pairs to decrease fabrication cost.
3. Mechanism of ultra-broadband absorption
To reveal the physical origin of perfect absorption, we plot the Ey distributions at ${\lambda _1}\textrm{ = }472$nm, ${\lambda _2}\textrm{ = 764}$nm and ${\lambda _3}\textrm{ = 1081}$nm in Figs. 5(a), 5(b) and 5(c), respectively. Y-axis is perpendicular to the incidence plane. For comparison, we plot the electric field distribution along Z-axis direction at the resonance wavelengths in Fig. 5(d). The structure parameters used in Fig. 5 are d = 100 nm, l1 = 5 nm, l2 = 12 nm and l3 = 30 nm. As seen in Fig. 5, these curves show that Ey periodically oscillates with attenuated amplitudes from top to bottom. Such Ey distributions indicate that the multilayer films can be treated as a layer of equivalent lossy film, and the optical thickness of this lossy film is equal to the odd times the quarter resonance absorption wavelength where the destructive interference effect occurs from the top and bottom interfaces of the multilayer CaF2-W films. The relation between the resonance absorption peaks and the thickness of the multilayer films is nearly satisfied with
where ${\lambda _0}$ is resonance absorption wavelength, h is the thicknesses of the whole CaF2-W pairs, and ${n_{{\lambda _0}}}$ is the effective refractive index of multilayer films at the resonance wavelength. As seen in Fig. 5, the corresponding m values of the absorption peaks at ${\lambda _1}\textrm{ = }472$nm, ${\lambda _2}\textrm{ = 764}$nm and ${\lambda _3}\textrm{ = 1081}$nm are 3, 2 and 1, respectively. Due to the destructive interference at these resonance wavelengths, the air-film interface has the high transmittance from air into the lossy material and the high reflection from the opposite direction. Thus, we can conclude that, perfect absorption can be achieved from the resonance between air-film interface and gold substrate.Fig. 5. Electric field distributions at the absorption peaks of (a) ${\lambda _1}\textrm{ = 472}$nm, (b) ${\lambda _2}\textrm{ = 764}$nm, (c) ${\lambda _3}\textrm{ = 1081}$nm. (d) Electric field distributions along Z-axis at three resonance wavelengths.
On the other hand, as shown in Fig. 5, the intensity of Ey in the gold substrate is nearly zero at three absorption peaks. Thus, the absorption contribution of gold substrate will be small. To verify this effect, the absorption spectra of the silica substrate and gold substrate are calculated in Fig. 6. The structure parameters used in Fig. 6 are d = 100 nm, l1 = 5 nm, l2 = 12 nm and l3 = 30 nm. The refractive index of silica in the visible and near-infrared ranges is set as 1.44. As seen in Fig. 6, the two curves have similar trends. Furthermore, the absorptivity with silica substrate is slightly smaller than that with gold substrate. Therefore, the gold substrate has little effect on the absorption efficiency. In the occasion that the requirements of the absorptivity are not very high, silica can be used to replace gold to reduce the cost in the fabrication process.
In order to explore the physical mechanism of broad bandwidth, we equate one pair of CaF2-W films to a layer of absorbing film in Fig. 7. Figure 7(a) shows that the thicknesses of CaF2 and W are d and l, respectively. Figure 7(b) shows the equivalent film with thickness of D = d + l. A plane wave with wavelength $\lambda $ for TE-polarization is incident upon the CaF2-W films with normal incidence. We define ${\delta _1}$ and ${\delta _2}$ as $\frac{{2\pi }}{\lambda }{n_{Ca{F_2}}}d$ and $\frac{{2\pi }}{\lambda }{n_w}l$, respectively. By employing the recursive method, the reflection and transmission coefficients of the CaF2-W films can be written as [31]
Fig. 7. (a) Schematic diagram of a pair of CaF2 and W films. (b) Equivalent film with thickness of D = d + l.
We can evaluate neff with different thickness of W film by using Eqs. (4) and (5). In the calculation process, d is set as 100 nm. The real part and imaginary part of effective refractive indices with different W thicknesses have been shown in Figs. 8(a) and 8(b), respectively. As seen in Figs. 8(a) and 8(b), the larger the thickness of W film, the larger both the real part and imaginary part of effective refractive index. According to the results in Figs. 8(a) and 8(b), the structure in Fig. 1(a) is equivalent to a three-layer films shown in Fig. 8(c) with D1 = d + l1 = 105 nm, D2 = d + l2 = 112 nm and D3 = d + l3 = 130 nm. Furthermore, the real parts of the refractive indices in Fig. 8(c) increase from top to bottom. If neglecting the contribution of the imaginary part of neff to reflection and transmission, such film configuration with increased refractive indices can efficiently extend the anti-reflection bandwidth [33]. At the same time, because the equivalent film layer is lossy, the ultra-broadband absorption can be achieved with the anti-reflection effect. Such physical mechanism of bandwidth expansion based on anti-reflection effect provides a new idea for the design of broadband absorber.
Fig. 8. Effective refractive indices as a function of wavelength: (a) real part, (b) imaginary part. (c) Three-layer equivalent film of the proposed absorber.
In order to verify the reliability of effective medium theory on the interpretation of the broadband absorption, we calculate the absorption spectrum with blue curve based on the effective refractive index in Fig. 9(a). The structure parameters are set as D1 = d + l1 = 105 nm, D2 = d + l2 = 112 nm and D3 = d + l3 = 130 nm. As seen in Fig. 9(a), the absorptivity is larger than 0.88 in the wavelength range from 400 nm to 1529 nm. For comparation, the absorption spectrum of the CaF2 and W multilayer films in Fig. 1(b) is re-plotted with red curve. As shown in Fig. 9(a), the red and blue curves agree well. In addition, to further demonstrate the contribution of the increased W thicknesses from top to down on the broadband absorption, we reverse the W film thickness used in Fig. 1(b). Figure 9(b) shows the absorption spectrum with d = 100 nm, l1 = 30 nm, l2 = 12 nm and l3 = 5 nm. From Fig. 9(b), we can see that the maximum absorptivity is less than 0.76 which indicates that the anti-reflection effect plays a positive role in our design strategy.
Fig. 9. (a) Absorption spectra for equivalent film structure and the CaF2-W pairs structure. (b) Absorption spectrum with d = 100 nm, l1 = 30 nm, l2 = 12 nm and l3 = 5 nm.
The above discussion shows that the proposed absorber has good performance based on the anti-reflection effect. We believe that the proposed structure with 3 pairs of CaF2-W films can be experimentally realized based on the existing coating technology [16,17,23]. The films of CaF2 and W can be deposited with electron beam evaporation or magnetron sputtering. The film thickness can be controlled with quartz crystal oscillation method.
4. Conclusion
A lithography-free wide-angle polarization-insensitive ultra-broadband absorber is proposed by using three pairs of W-CaF2 films. The absorptivity is larger than 0.9 with normal incidence in the wavelength range from 400 nm to 1529 nm. In addition, the absorptivity for both polarizations is above 0.9 in the wavelength range from 400 nm and 1452 nm for angles up to 40°. The absorption bandwidth can be manipulated by adding or reducing CaF2-W pairs. Furthermore, the ultra-broadband absorption is achieved with the anti-reflection effect from the increased effective refractive index from top to down of the proposed absorber. This broadband absorber is a good candidate for potential applications such as energy harvesting and detection.
Funding
National Natural Science Foundation of China (51901001); Natural Science Foundation of Anhui Province (1908085MF198, 2008085MA28, 2008085MF221).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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