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Abstract
In this work, a near-perfect broadband absorber, consisting of Fe, MgF2, Fe, TiO2 and MgF2 planar film, is proposed and investigated through simulations and experiments. The Fe material is first applied in the multilayer film structure, and it is proved to be more favorable for achieving broadband absorption. MgF2 and TiO2 are chosen as anti-reflection coatings to decrease unwanted reflections. The proposed absorber is optimized by employing a hybrid numerical method combining the transfer matrix method (TMM) and the genetic algorithm (GA). Under normal incidence conditions, the average absorption of the absorber is 97.6% in the range of 400 to 1400 nm. The finite difference time domain (FDTD) method and phase analysis reveal that the anti-reflection property and the Fabry-Perot resonance result in broadband absorption performance. Furthermore, when an additional Fe-MgF2 layer is inserted on the bottom Fe layer, an average absorption of 97.9% in the range of 400 to 2000 nm can be achieved. Our approach could be of vital significance for numerous applications involving solar energy.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Broadband absorbers have attracted extensive attention for practical applications such as infrared imaging [1,2], security detection [3,4], and solar–thermal energy harvesting [5–7]. In general, the coupling of multi-resonance effects at different wavelengths, such as surface plasmon polaritons (SPPs), guided-mode resonance (GMR) and magnetic polaritons (MPs), can be exploited to obtain broadband absorption properties [8–12]. Nevertheless, for the excitation of these resonances, micro-nano structures are required, including hyperbolic metamaterials and tapered multilayer structures. Among them, sawtooth and pyramid structures have been widely reported in the literature as broadband absorbers [13–18]. These structures can not only confine electromagnetic waves but also their ultra-sharp features induce a perfect match between the impedance of the air and the device, which may considerably reduce the surface light reflection and improve the absorption performance. However, electron beam lithography involves their fabrication process, which is costly, time-consuming, and limits their potential applications.
To address this drawback, multilayer planar absorbers consisting of metal-insulator (MI) pairs have emerged [19–21]. The Fabry-Perot resonance is excited in the metal-insulator-metal (MIM) resonator to achieve broadband absorption. Recently, several different metals and insulators, such as Cr-SiO2, W-SiO2, W-Al2O3 and Ni-SiO2 are utilized in these multilayer structures to achieve broadband light absorption [22–25]. However, the operational bandwidth for near-perfect absorption is not broad. To obtain higher absorption in a wider wavelength range, a large number of layers composed of several different materials or increasing the number of MI pairs are usually needed, which leads to a new requirement for multiple deposition steps and increases the complexity of the manufacturing processes [26]. Consequently, the aim of our research is not to broaden the absorption bandwidth by adding a large number of MI pairs. We want to design a broadband absorber using an anti-reflective film layer and a single MIM structure, which is the simplest possible configuration for absorbers.
Under this direction, in this work, a new high-efficiency broadband absorber is designed and fabricated, which consists of a five-layer planar structure based on the Fabry-Perot resonance and antireflection properties. For the first time, iron (Fe) and double dielectric film coating are combined to realize broadband absorption performance. The transfer matrix method (TMM) and genetic algorithm (GA) methods are utilized to design the structural parameters. Thus, the developed broadband absorber achieves 97.6% absorption over the full wavelength range in 400 nm – 1400 nm, while the high efficiency can be maintained well at a wide range of incident angles over 50°. Moreover, by inserting additional Fe-MgF2 layers on the bottom Fe layer, the average absorption exceeds 97.9% in the wavelength range of 400–2000nm. In addition, the physical mechanism leading to near-perfect broadband absorption performance is deeply analyzed.
2. Structural design and optimization
Figure 1(a) is the schematic illustration of the designed broadband multilayer absorber with angle-insensitive performance. The structure is simply comprised of five layers of dielectric and metallic films with a different combination. The MgF2 and TiO2 are chosen as antireflection (AR) layers with a gradient refractive index, which decreases unwanted reflections. The Fe-MgF2-Fe multilayer at the bottom forms a Fabry-Perot resonant structure. Fe is used as a resonating metal element with lower reflectivity and relatively constant, implying that it is uniformly absorbed in the optical range and near-infrared range. It is also important to note that Fe is feature abundant, has a low cost and good adhesion to numerous materials. Therefore, unique opportunities arise for practical applications. Figure 1(b) depicts the corresponding cross-section view, where ${h_1}$, ${h_2}$, ${h_3}$, ${h_4}$ and ${h_5}$ denote the thicknesses of the MgF2, TiO2, Fe, MgF2 and Fe layers, respectively. The refractive indexes of MgF2, and TiO2 are 1.37 and 2.41, respectively [27,28]. The complex permittivity for Fe is taken from Palik’ s book [29]. The reflection (R) and transmission (T) of the absorber are calculated by TMM [30]. As the thickness of the Fe substrate (${h_5}$) is thick enough to exceed the skin depth in the near-infrared region, no light is transmitted through the entire structure. Therefore, the absorption spectra can be obtained using the formula: A = 1-R, where A denotes the absorption.
To optimize the design parameters of the proposed absorber, the GA, which is a simple and efficient global optimization algorithm that can simultaneously optimize multiple parameters and objectives [31], is coupled with the TMM method. The fitness function $\eta $ is described as the integrated absorption over the considered wavelength range and can be estimated by the following expression:
Table 1. Upper and lower boundaries of structural parameters.
Table 2. The parameter values for the GA.
Figure 2(a) depicts the best fitness and the mean fitness attained from 0 to 84 generations. In the initial generations, the best fitness exhibits a significant rise as better populations are rapidly discovered. Then, the rate of increase becomes slower and finally stable. Figure 2(b) depicts the absorption spectra of the best fitness at 0, 5, 10, 20, 84, and 150 generations. Obviously, the high-quality populations are rapidly established in the initial generations (η = 86.3% at generation 0, 92.4% at generation 5, 95.6% at generation 10 and 96.8% at generation 20). In this case, the ultimate solution (η=97.6%) is obtained after 150 generations, and the corresponding optimized geometric parameters are listed in Table 3.
Fig. 2. (a) Best fitness and mean fitness attained from 0 to 80 generations. (b) The absorption spectrum at 0, 5, 10, 20, 84, and 150 generations.
Table 3. The optimized geometric parameters for the proposed absorber.
3. Sample fabrication
To observe broadband absorption performance in experiments, we fabricate the designed five-layer absorber (MgF2/TiO2/Fe/MgF2/Fe) with the evaporation method using an electron beam evaporator (Shenyang Scientific Instrument Co., Ltd., DZS-300). The evaporation materials, such as 99.99% MgF2, TiO2 and Fe pellets, are purchased from Zhongnuo Advanced Material (Beijing) Technology Co., Ltd. The Si substrates (Size: 4 cm*4 cm*0.5 mm) are washed prior to deposition. During the entire deposition process, the pressure of the vacuum chamber is maintained at 2.6*10−4 Pa. The deposition temperature is 150 °C. The substrate holder is rotated at 15 rpm to ensure film uniformity. The film growth rates are controlled at about 0.55 Å/s for MgF2, 0.45 Å/s for TiO2 and 0.6 Å/s for Fe, and a quartz crystal monitor is used to measure the thickness of the deposited film in real time. In this way, the multi-layer coating is deposited on the Si substrate.
A scanning electron microscopy (SEM) image of a cross section of the fabricated absorber is shown in Fig. 3(a-b). From top to bottom, each layer is clearly represented in the following sequence: MgF2/TiO2/Fe/MgF2/Fe. Furthermore, the chemical elemental compositions of the fabricated absorber are measured by using an energy dispersive spectroscopy (EDS) unit attached to the SEM. The EDS mappings (Fig. 3(c-h)) clearly illustrate the presence and distribution of Si, F, Fe, Mg, Ti, and O elements. Figure 3(i) is the EDS spectrum of the fabricated absorber. The corresponding element weights are approximately 26.3% for Fe, 25.3% for Si, 23.6% for F, 13.3% for Mg, 9.5% for O, and 2.0% for Ti, respectively. These results confirm the presence of MgF2 and TiO2 and demonstrate the successful fabrication of the designed absorber.
Fig. 3. (a) The SEM cross-sectional image of fabricated absorber (Singal A = HDBSD); (b) The SEM cross-sectional image of fabricated absorber (Singal A = SE2); Elemental mapping images of (c) Si, (d) F, (e) Fe, (f) Mg, (g) Ti, and (h) O, measured by SEM-EDS; (i) EDS spectrum and the corresponding element weight of the fabricated absorber.
4. Results and discussion
To ensure the accuracy and reliability of the calculated results, two numerical simulation methods, TMM and finite difference time domain (FDTD), are utilized to simulate the structure. Figure 4(a) shows the absorption spectra of the proposed structure based on optimized parameters calculated by two methods under normal incidence conditions, exhibiting strong agreement with each other. The proposed absorber has an average absorption of 97.6% in the range of 400 nm to 1400 nm, which obviously exceeds the majority of absorbers reported in the past. Notably, the absorption bandwidth could be further widened by introducing additional metal-dielectric stacks, which will be discussed later in this paper.
Fig. 4. (a) The simulated and experimental absorption spectra of the designed absorber at normal incidence; (b) Photograph of the fabricated absorber at normal incidence.
In addition, the measured absorption spectrum of the fabricated structure is also shown in Fig. 4(a). Here, the absorption is obtained from the 1 – R relation and the optical reflectance (R) is measured by using an UV-vis-NIR spectrophotometer (Cary 5000, Agilent) equipped with a 110 mm integrating sphere. The comparative results show the measured absorption spectrum exhibits good agreement with the numerical simulation (e.g., TMM calculation). The minor discrepancy is mainly due to the fact that the thickness and refractive index in the experiment may be slightly different from those used in the simulation. Figure 4(b) displays a photograph of the fabricated absorber taken at normal incidence. It exhibits a completely black appearance due to its high-efficiency broadband absorption behavior.
The effects of the metal materials on the absorption performance of the designed structure are analyzed by replacing the Fe material with high loss metal (e. g. W) or noble metal (e. g. Au), while the geometric parameters are kept unchanged. The calculated results are shown in Fig. 5(a). For noble materials, the absorption performance of the Au-based absorbent is worse than that of the Fe-based absorber, and the working wavelength of its high absorption is limited to a wavelength of 400–500 nm. The utilization of high absorption performance, non-noble metals reduce manufacturing costs, which facilitates the mass production of absorbers. On the other hand, Fe and W are both high-loss metals with broad spectra absorption properties. The average absorption values of the absorber using Fe and W materials are 97.6% and 92.1% at the wavelength of 400–1400 nm, respectively. Obviously, the Fe-based absorber exhibits higher absorption performance. To better explain the differences in absorption performance, we present detailed calculations utilizing the impedance transformation method. The relationship between S parameters and impedance Z is represented as [34–36] ${S_{21}} = {S_{12}} = \frac{1}{{\cos (nkd) - \frac{i}{2}(Z + \frac{1}{2})\sin (nkd)}}$ and ${S_{11}} = {S_{22}} = \frac{i}{2}(\frac{1}{Z} - Z)\sin (nkd)$, where S11, S22, S12, and S21 denote S parameters and n, k, and d denotes the effective refractive index, the wavevector, and the thickness of the proposed structure, respectively. Thus, the impedance Z can be expressed as $Z ={\pm} \sqrt {\frac{{{{(1 + {S_{11}})}^2} - S_{21}^2}}{{{{(1 - {S_{11}})}^2} - S_{21}^2}}} $. It is well known that, in order to achieve perfect broadband absorption, the impedance at the working wavelength should match the impedance of free-space (Z = Z0), where the real part of impedance is close to 1 and the imaginary part is close to 0. Figure 5(b-d) are the calculated impedance Z of the designed structure using the Fe, W, and Au material in the wavelength of 400–1400 nm, respectively. Comparing the calculated results, the impedance of Fe-based absorber is closest to Z0 in the considered wavelength, which agrees well the higher absorption region of the black curve shown in Fig. 5(a). Meanwhile, it can be easily inferred that the use of Fe materials enables the designed structure to better match the impedance between itself and the free space.
Fig. 5. (a) The absorption spectra of the designed absorber using Fe, W and Au metal, respectively. The calculated impedance Z for (b) Fe-based absorber; (c) W-based absorber; (d) Au-based absorber.
To investigate the impact of AR layers, the absorption performances of MIM absorbers with an AR layer and without an AR layer are compared, as shown in Fig. 6. For the MIM absorber, the absorption spectrum has a wide but low absorption peak (less than 0.85) in the considered range. This is because the MIM absorber can excite Fabry-Perot resonances within the MgF2 cavity [37]. For the MIM absorber with AR layers (e. g. TiO2/MgF2), the absorption performance is obviously increased and the structure exhibited a much broad perfect absorption bandwidth. Compared to the MIM absorber, the average absorption in the range of 400 nm – 1400 nm has increased from 70.3% to 97.6%. This is because the additional AR layers produce an effective impedance match between the absorber and the free space, which considerably lowers the incident light's surface reflection [38]. In this paper, two dielectric layers are selected as AR layers. We can also infer that the introduction of more dielectric films as an AR layer can further improve the absorption properties. However, this will lead to the complexity of the manufacturing process.
The high efficiency of broadband absorption is due to the AR effect of the top dielectric layer. It can be further verified by the admittance loci diagram [39,40], which straightforwardly illustrates the effects of thickness and refractive index of the dielectric layer on the reflectivity. The admittance of the designed structure begins with the substrate (nsub, 0) and rotates on the spiral trajectory or circular with the change of the materials or thickness. When the admittance of the structure is perfectly matched with air admittance, the admittance trajectory terminates at the air point (1, 0). Thus, the reflection is close to 0 and the near-perfect absorption is achieved. This effect also demonstrates that the distance between the termination admittance point of the multilayer structure and air admittance (1, 0) determines the reflection intensity. Figure 7 presents the admittance loci diagrams of the structure with and without the AR layers at different wavelengths, including the values of 425 nm, 572 nm and 1061 nm. It is clear that the reflection is effectively suppressed after the AR layers are added, which is described by the length of the black solid lines in the graph with AR layers compared to those without AR layers.
Fig. 7. Admittance loci diagrams of the proposed absorber at 425 nm, 572 nm, and 1061 nm wavelengths with AR layer and without AR layer.
The physical mechanism for near-perfect absorption peaks is also investigated by the phase analysis for dielectric layers (e. g. top MgF2 and TiO2 layer). In the phase analysis method, the resonances occur when the net phase shifts, including two reflection phases obtained upon reflection at both top and bottom interfaces and the propagation accumulated in the dielectric layer, are equal to a multiple of 2π [41]. Figure 8 shows the calculated net phase shifts of the top MgF2 (green curve) and TiO2 layers (blue curve), with the results divided by 2π. The red line represents the absorption spectrum of the proposed absorber. The intersection of the solid and purple dotted lines indicates the position of the resonance. Obviously, these intersection points are well-consistent with three near 100% absorption peaks (425 nm, 572 nm, and 1061 nm) in the absorption spectrum (red curve). Specifically speaking, the absorption peak at 425 nm is generated by the resonances within two dielectric layers, e.g., resonances at 406 nm and 421 nm in the top MgF2 and TiO2 layers, respectively, and the absorption peak at 572 nm results from the resonances at 569 nm and 516 nm in the top MgF2 and TiO2 layers, respectively. The near-perfect absorption peaks at longer wavelengths are generated due to the multiple resonances (e. g. resonances at 806 nm and 1261 nm in the top MgF2, and at 1109 nm in the TiO2 layer). Figure 9 depicts the electric field distribution of the designed structure calculated by the FDTD method. The results show that the electric field is concentrated in the different dielectric layers at different regions. In particular, three enhanced electric field regions in the top MgF2 layer can be found, which correspond to the absorption peak, as shown in Fig. 8 (red line). This result provides further evidence that resonance in the dielectric layer can lead to near perfect absorption.
Fig. 8. Phase analysis of top MgF2 and TiO2 and simulated absorption of the proposed absorber for the 400–2000nm range.
The angular dependence is also explored by simulation calculation. The calculated absorption spectra for both TM and TE modes are displayed in Fig. 10. The results show the broadband absorption is maintained from 0° to 50° with little change in absorption efficiency. In order to clearly understand the influence of incident angle (greater than 50°) on the absorption efficiency of our proposed absorber, we plot the average absorption efficiency of TM mode and TE mode as a function of incident angle in the range of 0 to 80, as shown in Fig. 10(c). The results show that the variations in the average absorption of the structure can be negligible before the value of the incident angle up to 50°, and then the average absorption gradually decreases as the angle further increases. The absorption of both TM and TE modes still exceeds 80% even at a very large angle of incidence of 70°. Clearly, a robust angular insensitivity property is demonstrated from the absorber, which is attributed to the broad resonances [42].
Fig. 10. The absorption spectra of the designed structure as functions of wavelength and angle of incidence for the (a) TM mode, (b) TE mode. (c) The average absorption of the absorber for both the TM and TE modes at different angles of incidence.
To further broaden the absorption band, an additional Fe-MgF2 layer is inserted on the Fe substrate, as can be observed from Fig. 11(a). With the increment of the layers, new resonances are generated at longer wavelengths, resulting in wider absorption bandwidth. The improved broadband absorber, [Fe (200 nm)/MgF2 (85.9 nm)/Fe (6.8 nm)/MgF2 (96.2 nm)/Fe (8.9 nm)/TiO2 (33.5 nm)/MgF2 (121.1 nm)], is designed to obtain the widest absorption bandwidth with high-efficiency absorption. Figure 11(b) depicts the absorption spectra of the improved structure under normal incidence, showing the average absorption reaches 97.9% in the range of 400 nm – 2000 nm, where the average absorption at the wavelength of 400-1400 nm is improved to 98.6%. Obviously, the improved absorber has excellent absorption performance, which is a significant improvement over the most advanced solar thermal absorbers currently available, as shown in Table 4.
Fig. 11. (a) Schematic illustration of the improved broadband absorber by inserting an additional Fe-MgF2 layer on the bottom Fe layer. (b) The absorption spectrum of the improved absorber at normal incidence.
Table 4. Comparison of the absorption performances of the proposed absorber and other reported absorbers. (Note: ‘Y/N’ denotes the absence of relevant research)
5. Conclusion
In conclusion, a simple design approach has been demonstrated for a broadband absorber based on the anti-reflection property and the Fabry-Perot resonance. The Fe material is first used in multilayer thin film structures, which is more advantageous than other materials for achieving broadband absorption. The AR layers composed of MgF2 and TiO2 film are proved to achieve perfect absorption. The structural parameters are optimized by combining TMM with GA methods. The optimized structure has a very high average absorption about 97.6% in the wavelength range of 400 – 1400nm at normal incidence. Furthermore, by inserting additional Fe-MgF2 layers on the Fe substrate, an absorption efficiency of over 97.9% is attained in the wavelength range of 400 – 2000nm. The developed broadband absorber will easily find applications involving solar energy.
Funding
Science Fund for Distinguished Young Scholars of Fujian Province, 2020J06025; Youth Talent Support Program of Jimei University ZR2019002; Innovation Fund for Young Scientists of Xiamen, 3502Z20206021; Xiamen Ocean and Fishery Bureau , 20CZB014HJ03; Natural Science Foundation of Fujian Province2020J01712; Youth Talent Support Program of Fujian Province.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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