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Abstract
In this paper, a metal-dielectric metamaterial absorber is proposed to achieve ultrabroadband absorption at frequencies from ultraviolet to near-infrared. Based on finite element method solutions, the average absorption of the absorber is 97.75% from 382 nm to 1100 nm, with a maximum of 99.92%, resulting from multiple resonance coupling. The influences of geometric parameters and incident conditions on absorption are investigated. Broadband and narrowband absorption changes are realized by changing incident light polarization. Polarization-independent properties can be realized by changing the dielectric structure to centrosymmetric. The average absorption of the polarization-independent structure is 97.11% from 250 nm to 1115 nm, with a maximum of 99.98%. The proposed absorber structure has wide optical applications including solar energy harvesting and light-emitting devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials have opened up many new approaches to manipulating electromagnetic (EM) waves, and they have many unique optical properties at the subwavelength scale [1,2]. Metamaterials have been demonstrated for changing amplitude [3,4], polarization states [5,6], transmission [7,8], and phase [9] of EM waves. Absorption, in particular, is an approach to control amplitude, which is important in many applications. Therefore, metamaterial absorbers (MMAs), as a branch of metamaterials, have been highly anticipated as they are becoming an essential component of many optical devices [10]. In 2008, Landy et al. demonstrated the first metamaterial absorber, which consisted of two distinct metallic resonators [11]. This absorber realized perfect absorption in a narrow gigahertz band. Follow-up studies quickly occurred in other bands. Several methods can be applied for realizing narrow perfect absorption with MMA, such as surface plasmon polaritons (SPPs) [12–14], dipole resonance [15,16], and Fabry–Pérot resonance [17,18]. To address limitations of single-band absorbers in applications, multiband narrow band absorption is proposed [19–21]. In some special areas, such as selective thermal emitters and solar–thermal energy harvesting, it is highly desirable to realize perfect absorption over a broad spectral band.
Hence, various structures have been proposed to obtain light absorption over a wide spectral band. The main mechanisms for realizing broadband absorption are combining similar resonators with different sizes in one unit cell [22,23] or multiple resonance coupling [24]. Up to now, broadband absorbers were realized with different structures such as metallic gratings [25–29], plasmonic metamaterials [30–33], and nanocomposites [34,35]. Especially in optical frequency, broadband MMA is widely applied in solar energy harvesting. For example, broadband MMA based on plasmonic materials can be used to improve absorption in photovoltaic devices [36]. MMAs have great potential in solar cell cooling to avoid adverse influences on efficiency and reliability caused by increased temperature [37,38]. Therefore, although there are many creative applications for perfect MMAs, broadband studies to achieve practical applications are still significant.
In this paper, we propose an ultrabroadband MMA based on coupling of Mie scattering, electric dipole (ED) and SPP resonances, which consists of amorphous silicon (a-Si) nanostructure and titanium (Ti) layer. The impacts of various geometry parameters and incident light conditions on absorption are also analyzed. Furthermore, polarization-independent properties can be realized by changing the dielectric structure to centrosymmetric. The centrosymmetric structure demonstrates ultrabroadband absorption from ultraviolet (UV) to near-infrared (NIR). The absorptivity is higher than 90% from 250 nm to 1115 nm and average absorption over this band is higher than 97.11%. In addition, absorption remains higher than 90% for transverse magnetic (TM) and higher than 80% for transverse electric (TE) polarized waves over a wide incident angle range (up to 60°). This MMA has great potential in optical applications such as photodetectors, sensors, imaging, and harvesting solar energy.
2. Structure and results
Figure 1(a) shows a schematic of the proposed MMA, which consists of periodic dielectric strips supported by a Ti substrate. A groove is etched in the middle with two inclined planes on the sides of each dielectric strip. The structure of the dielectric strips is characterized by the periodic interval d, heights h1 and h2, gap width g, bottom width w, and inclined plane width q. We select a-Si as the dielectric material because of its wide applications and large dissipative loss at UV [39–41], and select Ti for its high loss property [30]. Fabrication of the proposed metamaterial is compatible with nanofabrication technologies such as electron beam lithography or nanoimprinting lithography [16,42]. The periodic of the proposed absorber is along the x-direction, and is infinite in the y-direction. To ensure the proposed absorber has subwavelength structure for the operating wavelength, the period is set as d = 250 nm. The electric field incidents along the negative z-direction with polarization along x-direction. The transmission T of the proposed structure is zero, because the Ti film thickness, t = 200 nm, is greater than the penetration depth of the incident light. Thus, the absorption A is given by A = 1 – R, where R is reflection.
Fig. 1. (a) The schematic of the proposed absorber (left) and a magnified unit cell (right). Here the optimized geometric parameters are h1 = 90 nm, h2 = 35 nm, w = 200 nm, g = 60 nm, and q = 20 nm. The Ti film has a thickness of t = 200 nm. (b) The absorption spectrum of our proposed MMA. P1, P2, and P3 are the absorption peaks at 482 nm, 596 nm, and 868 nm. The incident waves are x-polarized.
The structure parameters are optimized by a genetic algorithm (GA) [43] coupled with finite element method (FEM) using COMSOL Multiphysics software. First, we set the range of structural parameters with 5 nm steps to reduce the search space, and GA randomly generates structural parameters. Our simulation wavelength range is from 350 nm to 1200 nm. Then, FEM is used to calculate the absorption of each randomly generated structure. The ideal value of absorption is set at 1, and is integrated into a fitness function. The objective of the GA optimization algorithm is to maximize the following fitness function:
where N = 850 is the wavelength range. Optimized parameters are obtained through iterations of GA, until the stop criterion is satisfied [44]. In the simulation process, the refractive indexes of a-Si and Ti are adopted from Pierce et al. [45] and Johnson et al. [46], respectively. The refractive index of the ambient medium is assumed to be na = 1. Figure 1(b) shows the absorption spectrum of the optimized MMA in a broadband from 350 to 1200 nm, and the inset shows a partial amplification. The optimized MMA clearly shows high absorption, over 90%, from 382 nm to 1100 nm. The average absorption of the structure can be calculated by3. Principle and discussions
To further understand the physical mechanism of the designed MMA, we plot the magnetic field (|H|) distributions in Figs. 2(a)–2(d) and electric field (|E|) distributions in Figs. 2(e)–2(f) of x-polarized light with normal incidence corresponding to the resonant wavelengths 382 nm, 482 nm, 596 nm, and 868 nm. As shown in Fig. 2(a), the magnetic field is localized in the gap between the two vertical bars and between two unit cells at their bases. As shown in Fig. 2(e), electric field distribution consists of two pairs of EDs in the upper and lower parts of the vertical bars. This illustrates the existence of electric dipole resonance (EDR) in the short wavelength range. From Fig. 2(b), Mie modes are excited by the incident wave in the vertical bars of the dielectric structure [47], and part of the magnetic field is localized in the gap. Meanwhile, as shown in Fig. 2(f), the electric dipoles in the upper part of the vertical bars lead to localization of the electric field, indicating that the corresponding absorption band benefits from the coupling of EDR and Mie resonance.
Fig. 2. (a)–(d) Magnetic field |H| distributions and (e)–(h) electric field |E| distributions of cross-sections in y-direction.
For the long wavelength range as shown in Fig. 2(d), the magnetic field is concentrated at the dielectric-substrate interface, indicating the first-order SPP resonance dominates absorption. In Fig. 2(c), the majority of the magnetic field is confined to the vertical dielectric bars, a result of Mie resonance; and a minority of the magnetic field is confined to the dielectric-substrate interface, which results from the second-order SPP resonance. This indicates that the efficient absorption around P2 results from coupling between SPP resonance and Mie resonance, and the Mie resonance plays a leading role. The electric field distributions in Figs. 2(g) and 2(h), which correspond to the magnetic field distributions in Figs. 2(c) and 2(d), further show the localization of the electric field.
In general, the vertical dielectric bars of the proposed structure can be viewed as Mie resonators, which trap EM waves with multiple internal reflections [47,48]. When the structure is illuminated with the electric field parallel to the x-direction, Mie modes can form in the vertical bars and behave as magnetic resonances. To satisfy the boundary condition at the interface between air and the dielectric, the electric field inside the vertical bars is tangential to the boundaries. As a result, displacive eddy currents appear in the vertical bars along the y-direction to enhance the restriction of the magnetic field.
Meanwhile, SPP resonance develops at the interface between the substrate and dielectric. The high loss property of Ti results in a relatively large Q factor of the resonance, which improves the absorption bandwidth. At short wavelengths, the charges gathering in the vertical bars form EDR, which can constrain the electric field in the gaps. In addition, the internal Mie resonance is leaky for the subwavelength size of vertical bars, which implies it is broadband and interacts more effectively with the EDR and SPP resonance [49]. Therefore, the broadband absorption of the proposed absorber can be attributed multiple resonance coupling.
The influence of geometric parameters on absorption spectra is analyzed in detail. Absorption spectra as functions of h1, g, h2, d, q, and w, with the other parameters unchanged, are shown in Figs. 3(a)–3(f), respectively. The three dark red bands correspond to the three resonance peaks in Fig. 1. P1 redshifts with increasing h1, in Fig. 3(a), and hardly moves with changes in other geometric parameters. Figures 2(b) and 3(f) show that the Mie resonance appears in the middle of the vertical bars and EDR appears at the top of the vertical bars. Based on this analysis, P1 results from EDR and Mie resonance coupling. Changes in h1 will affect the coupling distance of EDR and Mie resonances, which result in P1 shifting.
Fig. 3. Demonstration of geometry effects on absorption performance with normally incident x-polarized light: (a) h1, (b) g, (c) h2, (d) d, (e) q, and (f) w, which are marked in Fig. 1(a). P1 and P2 are marked by the white dashed and dot-dashed line. The calculated wavelengths of P3 from Eq. (6) are shown by the white dotted line, and the black dashed lines mark the absorption spectrum at the optimal geometric parameters.
As shown in Fig. 3(b), P2, which is mainly generated from Mie resonance, blueshifts with increasing g. This can be explained with the following analysis. According to Mie resonance theory, the resonance wavelength can be described as [50]:
where D is the effective width of the vertical dielectric bars and nb is the refractive index of a-Si. The effective width of the vertical bars is reduced with an increase of g. From Eq. (3), the wavelength of Mie resonance blueshifts. Similarly, the wavelength of Mie resonance blueshifts as q increases, as shown in Fig. 3(e). Changing the other geometric parameters in Fig. 3 has a negligible impact on the effective width of the vertical bars, so there are no obvious shifts in P2.From Fig. 3, it is obvious that the influences of geometric parameters on P3 are more complex than those on P1 and P2. We explain the reason for the complex changes of P3 as follows. At the interface of the dielectric bars and the substrate, the frequency of the SPP resonance can be given by:
where εeff and ωP = 8.5×1015 rad/s are the effective permittivity of the dielectric bars and the plasma frequency of the substrate, respectively. The effective permittivity can be approximated as [51,52]:It is worth noting in Fig. 3(c) that with increasing h2, a strong absorption peak appears around 300 nm. To explain this phenomenon, the magnetic field and electric field distributions at 315 nm are shown in Figs. 4(a) and 4(b), with h2 = 80 nm. As shown in Fig. 4(a), the magnetic distribution means that no Mie resonance exists in this band. The electric field distribution and electric field lines in Fig. 4(b) further support our analysis above and indicate that there are three pairs of dipoles in the upper and lower parts of the dielectric bars. Therefore, the peak is generated from the contribution of the localization of the electric field caused by multiple EDRs.
Fig. 4. (a) Magnetic field distributions |H| and (b) electric field distributions |E| of the cross-section in y-direction at 315 nm. Red arrows in (b) illustrate electric field lines. The incident waves are x-polarized.
We also investigated the influence of incidence and polarization angles on absorption performance with TE waves. As shown in Fig. 5(a), with increasing incidence angle, average absorption remains above 90% within the range from 0° to 30°, and average absorption remains above 70% within the range of from 0° to 60°. As illustrated in Fig. 5(b), the average absorption keeps a high level when polarization angles are less than 45°. However, in the range from 45° to 90°, absorption decreases with increasing polarization angle. These results show that the proposed absorber for linear polarized light has high polarization and incident angular tolerance, up to ±45° and ±30°, respectively.
Fig. 5. Absorption maps with changes to (a) incidence angle (the incident waves are x-polarized) and (b) polarization angle.
Figure 6(a) shows the simulated absorption spectrum for both x-polarized and y-polarized light at normal incidence. An ultrabroadband with high absorption can be obtained for x-polarized light, but a narrow absorption peak appears for y-polarized light. This suggests that the proposed absorber is polarization-dependent. Absorption as a function of polarization angle with normally incident x-polarized light at 900 nm is shown in Fig. 6(b). Absorption of the proposed absorber is almost linearly proportional to the polarization angle of the incident light. This polarization sensitivity property is beneficial for polarization detection and sensing.
Fig. 6. (a) Absorption spectrum under the illumination of x-polarized and y-polarized normal incidence. (b) The absorptivity (red) and reflectivity (blue) as a function of polarization angle with normally incident wave at 900 nm.
4. Polarization-independent absorber
To induce polarization-independent behavior, we change the structure of the proposed MMA to centrosymmetry. As shown in Fig. 7(a) the modified structure is arranged periodically in x and y-directions. In Section 3, we showed that the absorber has high UV absorption, and through parameter optimization we extended the wavelength range from 250 nm to 1200 nm. The optimized parameters are d = 250 nm, h1 = 50 nm, h2 = 90 nm, w = 200 nm, g = 60 nm, and q = 15 nm.
Fig. 7. (a) Schematic of the designed polarization-independent structure with cross-sections in x and y-direction. (b) The absorption spectrum of the designed polarization-independent absorber with normally incident x-polarized light. (c) The absorption spectra of designed polarization-independent absorber with changing polarization angle from 0° to 90°.
The absorption spectrum of the polarization-independent absorber with normally incident x-polarized light is shown in Fig. 7(b). It is worth mentioning that absorptivity in the UV band is higher than 90%. The average absorption from 250 nm to 1115 nm is 97.11%. The peak absorptivity is 99.98% at 896 nm. Comparing the proposed polarization-independent absorber with some previous similar works as detailed in Table 1, the proposed MMA can achieve broadband absorption with the least number of layers. Figure 7(c) shows that the absorption spectra of the designed polarization-independent structure are highly consistent with changing polarization angle from 0° to 90°. The absorption spectra of absorbers under different oblique incidence angles are also important to applicable devices. As shown in Figs. 8(a) and 8(b), the absorption spectra under oblique incidence angles in the TE and TM modes are calculated, respectively. The average absorption remains greater than 80% for TE mode and greater than 90% for TM mode up to 60° incidence angles.
Fig. 8. Absorption maps with changing incidence angle of (a) TE and (b) TM waves. The incident waves are x-polarized and y-polarized, respectively.
Table 1. Comparison between the proposed absorber and some similar absorbers
5. Conclusion
In this study, we proposed an ultrabroadband MMA based on multiple resonance coupling. The polarization-dependent characteristic can realize nearly perfect absorption from visible to NIR. In this range, the absorber exhibits an average absorption of 97.75% and maximum absorption reaches 99.92%. By adjusting the structure of the absorber, the polarization-independent characteristic can achieve nearly perfect absorption from UV to NIR. The absorptivity is higher than 90% in a broadband from 250 nm to 1115 nm, and the average absorption over this band is higher than 97.11%. Realization of broadband perfect absorption benefits from Mie, electric dipole and SPPs resonances in the designed metamaterial structure. The proposed MMA has great potential in optical applications, such as photodetectors, sensors, imaging, and harvesting solar energy.
Funding
National Natural Science Foundation of China (11144007, 11274188, 51472174); Natural Science Foundation of Shandong Province (ZR2017MF059); Optoelectronics Think Tank Foundation of Qingdao.
Disclosures
The authors declare no conflicts of interest.
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