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Abstract
In this paper, a broadband tunable absorber based on bulk Dirac semimetal (BDS) in the far-infrared regime is studied. By optimizing the Femi energy and geometric size, the structure can achieve absorption levels greater than 90% in the 8.11-13.94 THz range, with a total thickness of 5.1 µm. Further, the bandwidth of this proposed absorber can be dynamically controlled by changing the Femi energy of the BDS instead of geometry. Meanwhile, the polarization and oblique incident angles in the TE and TM electromagnetic waves are also investigated. Finally, a new symmetry model is adopted to analyze the absorption mechanism, which is the innovation of this paper. This research result may provide potential applications for all types of optical photovoltaic devices and tunable biological chemistry sensors.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent decades, The research on 2D materials, such as metasurface [1], graphene [2], and phosphorus (BP) [3], have attracted extensive attention in the community of scholars due to their unique electromagnetic characteristics that don’t exist in nature. As a research branch of the 2D material-based devices, the metamaterial absorbers (MAs) have attracted intense attention in recent years [4]. However, most of these MA structures are made of traditional precious metals, such as gold, silver, or brass. Besides, for a designed absorber, the bandwidth and the spectral position of absorption peak are usually fixed at a certain value once the scheme of MAs is confirmed. To achieve the active tunability of the bandwidth, several methods have been adopted [5–9]. However, most of these absorbers are very hard to scale down to a higher frequency such as the THz or infrared regimes. Therefore, the quest for new materials that can enable extended spectral coverage, as well as simplified control schemes, is still to pursue.
Recently, as an optimized material, graphene has shown its promising potentials in THz and infrared absorber applications. The reason is that the surface conductivity σ of graphene is closely related to the Fermi energy EF. More important, EF can be dynamically changed by controlling the bias voltage. Meanwhile, actively tunable graphene-based plasmonic absorbers have been widely studied in the fields of electromagnetic radiation [10–13]. For most of the single-layer structure, however, the absorption bandwidth for the graphene-based metamaterial absorbers is usually relatively narrow [14,15]. More recently, a novel material bulk Dirac semimetal (BDS) which is widely known as three–dimensional (3D) graphene, arouses great interests among researchers for its superior advantages [16,17]. Similar to graphene, the electromagnetic properties of BDS can be controlled by changing its Fermi energy [18,19]. Comparing to graphene, a kind of one-atomic-layer material, another advantage of 3D BDS is that it’s easier to process and more stable, which has attracted a large number of scholars’ attention [20–25]. However, the work bandwidths of most of these BDS structures are still relatively narrow. Hence, it is necessary to solve the problem to achieve the initiative tunability of the absorption bandwidth in a simple way while keeping the size of the device constant.
In this paper, a broadband absorber that the bandwidth can be tunable by BDS in the far-infrared region is studied. numerical results show that the broadband BDS absorber presents an absorptance of more than 90% covering from 8.11 to 13.94 THz, with a total thickness of 4.56 µm (0.12λ at the lowest frequency). By varying an external gate voltage applied to the DBS, the absorption bandwidth of this proposed absorber can be continuously changed from 0 to 5.83 THz and the spectral position can be controlled. In addition, we also characterized the angular sensitivity of the proposed BDS absorber at oblique incidence. Further, to quantitatively understand the physical mechanism of the proposed absorber, a new symmetry model theory was applied to compare numerical simulation results.
2. Structure and materials
Figure 1 displays a single unit cell schematic of the designed BDS absorber. It is composed of a BDS film, a metal ground plane, and a dielectric spacer. The periods of the BDS absorber unit cell in the x and y directions are p. The top layer is a BDS film with four hollowed-out squares. Al2O3 dielectric is selected with the relative permittivity ɛr = 2.28 and tangential loss tgδ = 0.04. The metal ground plane is lossy gold whose thickness and conductivity are 0.2 µm and σ = 4.56×107 s/m, respectively. The designed BDS-based broadband tunable metamaterial absorber was numerically investigated by using the frequency domain solver of the commercial simulation software CST Microwave Studio which based on the FDTD method to obtain the transmission coefficient S21 and the reflection coefficient S11. In the simulation setup, the unit cell of the absorber was simulated with periodical boundary conditions set along with the x and y directions, and an open boundary condition is employed along the z-direction. The incident wave was vertical to the upper surface with the electric field polarized along the x-direction. Due to the 0.2 µm-thick bottom metallic mirror is thick enough to block all wave transmission, the absorptivity can be obtained by $A = 1 - {|{{S_{11}}} |^2}$.
Fig. 1. Schematic diagram and geometric parameters of the proposed broadband tunable metamaterial absorber: (a). Top view and (b) Side view of a unit cell. The geometrical parameters of the proposed structure are: p = 20 µm, l = 16 µm, l1 = l/$\sqrt 2 $ = 11.3 µm, l2 = l1/$\sqrt 2 $ = 8 µm, l3 = l2/$\sqrt 2 $ = 5.7 µm, α = 25°, t = 0.6 µm and h = 4.5 µm.
Under the conditions of low-temperature limit $T \ll {E_F}$, the permittivity of BDS was calculated by [26–28]:
According this equation, we can calculate the effective permittivity. Then we import these real and imaginary parts of permittivity into the characteristics of the new material in the CST, finishing the setting of BDS material.
3. Results and discussions
Figure 2 shows the absorptance and reflectance of the proposed BDS absorber for the Fermi energy EF = 60 meV when plane waves with transverse electric (TE, electric filed parallel to the x-axis) and transverse magnetic (TM, magnetic field parallel to the x-axis) polarizations are normally incident on the proposed absorber, respectively. It can find that the simulated absorption and refection curves exhibit a broadband absorption in the frequency range from 8.11 THz to13.94 THz with the absorptance more than 90%, and the relative absorption bandwidth is 52.87%. To display the superiority of this proposed absorber, the absorption performances about the recently reported THz broadband metamaterial absorbers are displayed in Table 1. Compared to these recent reports, this proposed absorber shows a wider bandwidth and the relative absorption bandwidth.
Table 1. Performance summary of the broadband metamaterial absorber made by BDS in the THz region
To better understand the tunable absorption mechanism of this proposed absorber, we investigated the electric field intensity distributions at several selected points for both TE and TM modes under normal incidence. Figures 3(a1)–(a4) indicate the electric field intensity distributions for TE mode at absorption peak frequency points of 7.1, 9.76, 11.42, and 13.18 THz, while Figs. 3(b1)–(b4) is for TM mode. A general trend can be found that the distributions of electric field are mainly distributed around the corners of the BDS pattern.
For TE mode, at the resonance frequency 7.1 THz as shown in Fig. 3(a1), the electric field is efficiently localized in the middle of the outer square, which indicate large charges are accumulated at the edge of the BDS pattern. As shown in Fig. 3 (a2)–(a4), the electric field intensities are concentrated at the corners of the outer and inner frames, and the intensity on the outer square decreases as the frequency increases, indicating the BDS patterns of the inner and outer square play an important role in the absorption of incident wave. For TM mode, the distributions of electric field are similar to that of TE mode. Only the position is rotated by 90°.Generally, the more electric fields confinement, the more absorption achievement. The energy assumption inside loss material such as BDS can be calculated by [23]:
where $\mathrm{\varepsilon ^{\prime\prime}}$ and V are the imaginary part of dielectric constant and volume of lossy material, respectively. El is the electric field inside the lossy materials. The imaginary parts of permittivity are very large in the range of 5-15 THz. Therefore, the energy consumption of the incident wave will be dissipated where the electric field is strong.In practical applications, incident angle insensitivity is a significant property and usually required for absorber. To study the dependency of absorption on incident angles, the color map of absorption performance versus incident angles and frequencies with EF = 60 meV for both TE and TM polarizations are displayed in Fig. 4. With the increase of the incident angles, it can be found that the peak absorption remains 90% at an angle of 40 degree. In addition, as the incident angle increase, the absorptance becomes weaker. When the incident angle reaches 50 degrees, it drops to about 80% for TE and TM polarizations at the frequency range of 8.11-13.94 THz. Furthermore, the dependence of the absorptance on polarization is also studied and shown in Fig. 5 due to the approximate rotational symmetry around the propagation axis, this absorber is not polarization sensitive. Hence, the designed broadband absorber can operate quite well over a relatively wide range of incident angles.
Fig. 4. Absorption performance of the proposed structure with incident angles θ ranging from 0° to 60° for (a) TE mode and (b) TM mode.
Fig. 5. Absorption performance of the proposed structure with different polarization angles φ for (a) TE mode and (b) TM mode.
Because the permittivity of BDS can be tuned by the Fermi energy, absorptance will be adjusted accordingly. Then we investigate the dependence of the absorptance on the EF. Figure 6 displayed the absorptance for TE and TM polarization at normal incidence with other parameters the same in Fig. 2. The black, magenta, and violet lines denote the results of EF = 50, 60, and 70 meV, respectively. Interestingly, in TE-polarized shown in Fig. 6(a), it can find that the working band can be converted from the narrowband absorption to wideband absorption merely by changing the Fermi energy. In addition, the first peak of the absorption exhibits blueshift as the Fermi energy increases. For TM-polarized cases shown in Fig. 6(b), the absorptance nearly immune from the change of the mode. Obviously, the absorption band for both TE- and TM-polarized incidence can be tuned dynamically tuned by changing the Femi energy. This phenomenon appears as color maps of the absorptance versus different Fermi energy and the frequency for TE and TM waves and shown in Fig. 7. Compared with Fig. 7(a) and 7(b), it is found that the change in polarization has little effect on absorption peak and bandwidth. At the same time, the maximum absorptance is 45% at 5 THz only when EF is 30 meV. Therefore, we can conclude that the absorption bandwidth is highly relayed on the Fermi energy of the BDS pattern.
Fig. 7. Absorption as a function of frequency and Fermi energy (EF) for (a) TE and (b) TM polarizations. The Fermi energy varies from 10 to 100 meV.
We need to study the influence of structure parameters on the absorption performance to evaluate the importance of geometry for practical manufacture. In Fig. 8, it shows the absorption spectra as functions of h, l and α with the Fermi energy EF = 60 meV for TE polarization, respectively. It can be observed from Fig. 8(a) and (b) that increasing h makes the bandwidth enlargement as well as the absorption magnitude. For h = 4.5 µm, the widest and highest absorption is achieved. Similarly, from Fig. 8(e) and (f), it can find that the peak absorptance gradually increases when the value of α increases from 0° to 45° in the first band. However, the bandwidth that meets the absorptance above 90% is reduced in the second band. Besides, the length of the BDS film would have a great influence on absorptance and bandwidth. Figure 8(c) and (d) show the simulation results for the absorption of the absorber structure with different length l. We can find that the first absorption spectra show a redshift with increasing of l. Moreover, the bandwidth, not absorptance of absorption spectra is increasing, but the bandwidth of 90% absorption is discrete when l is greater than 16 µm. From the above analysis, it can be found that the role of geometrical structures in improving the performance of this proposed absorber is very important and they are the trace of the optimization process.
Fig. 8. Influence of geometric parameters on the absorption performance while the other parameters are fixed. (a) Thickness of the substrate h; (c) length of the top layer l; (e) rotation angle of the second hollowed-out square α. Colormap of absorptance with (b) h varying from 1 µm to 5 µm; (d) l varying from 10 µm to 18 µm and (f) α varying from 0°to 45°.
4. Theoretical calculation with the symmetry model
To further reveal the absorption mechanism and gain the physical insight of the absorption origin for this BDS-based absorber, we have quantitatively analyzed the absorption mechanisms. Due to this proposed absorber backed by a metal plate, we introduced a new symmetry model theory to analyze the absorption mechanism [33]. The introduced new symmetry model is shown in Fig. 9(a), which constructed through two integrated composite layers in the form of mirror symmetry. For this symmetry model, S11 is equals to S22 and S21 equals to S12. For this symmetry model, the S parameters are obtained by CST, which can be written as:
Fig. 9. (a) Schematic of the symmetry model, and (b) comparison of the reflection loss curves produced by theoretical calculation and numerical simulation using the unit cell.
Where 2(h + t) = 10.2 µm is the total thickness of the symmetry model, k is the wave number of the incident wave in free space. n and z denote the refractive index and impedance, which can be deduced from Eqs. (3) and (4) [34]:
Then the equivalent permeability (µ) and permittivity (ɛ) can be calculated by:
Solving Eqs. (5)-(7) for ɛr and µr, and using the transmission line theory, the reflection loss (RL) can be expressed as:
5. Conclusion
In conclusion, a broadband and tunable metamaterial absorber based on Dirac semimetal is proposed. From the simulated and analyzed results, we can find the absorptance is greater than 90% in the range from 8.11 THz to 13.94 THz with the relative bandwidth of 52.87%. Simulated results clearly show that this proposed absorber display a broadband absorption in a wide range of incident angles up to 30° for both TE and TM polarization. Furthermore, the bias voltage and geometrical turnabilities of the absorber have also been researched under normal incidence. Based on the new symmetry model theory, the physical mechanism of absorption has been explained. This work may provide a new perspective on the design of Dirac-based tunable broadband absorbers, and the absorber design scheme can be easily scalable to other microwaves, terahertz, or visible regimes for various applications.
Funding
State Key Laboratory of Millimeter Waves (K202204).
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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