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Abstract
A functionally tunable and absorption-tunable terahertz (THz) metamaterial absorber based on vanadium dioxide (VO2) and graphene is proposed and verified numerically. Based on phase transition properties of VO2 and tunability of graphene, the switching performance between ultra-broadband and narrow-band near-perfect absorption can be achieved. We simulate and analyze the characteristics of the constructed model by finite element analysis. Theoretical calculations show that when VO2 is in the metallic state and the graphene Fermi energy is 0 eV, the designed absorber can perform ultra-broadband absorption. The absorber achieves greater than 95% absorption in the 2.85 - 10THz range. When VO2 is in the insulating state and the graphene Fermi energy is 0.7 eV, more than 99.5% absorption can be achieved at 2.3 THz. The absorption rate can be tuned by changing the conductivity of VO2 and the Fermi energy of graphene. Moreover, the proposed absorber displays good polarization insensitivity and wide incident angle stability. The design may have potential applications in terahertz imaging, sensing, electromagnetic shielding and so on.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Generally speaking, the range of terahertz waves is generally between 0.1 and 10THz. In recent decades, with the development of new technologies, terahertz science and technology have also ushered in rapid development [1–3]. The excellent characteristics of terahertz wave make it have good application prospects in military radar [4], medical detection [5], imaging [6], communications [7] and sensing [8] and so on. These applications require high-response devices, but natural materials with high response in terahertz band are limited. Since the concept of metamaterial was proposed by John Pendry [9], it has developed rapidly. Especially in the terahertz band, metamaterial has better electromagnetic responses than natural materials [10]. Metamaterial-based terahertz absorbers have been extensively studied in recent years [11,12]. However, many current metamaterial-based absorbers can only achieve a single function and do not have adjustable characteristics once they are fabricated. Therefore, how to realize high-performance tunable metamaterial absorber has become a hot spot in terahertz technology.
In order to achieve the tunable function of absorbers in the terahertz band, some materials are used to devise metamaterial devices, such as graphene [13], vanadium dioxide (VO2) [14–16], Dirac semimetal film (DSF) [17], liquid crystal [18], Insb [19], etc. Absorbers made of these materials achieve narrowband, multiband, and broadband absorption tuning. As a functional metal oxide material, VO2 has a unique phase transition characteristic, and it will undergo a reversible transition from a metallic state to an insulating state at around 341 K [20]. This unique property makes it become a popular choice for tunable absorbers. In addition, as a two-dimensional material, electrical conductivity and carrier mobility of graphene can be dynamically adjusted by chemical doping or electrostatic doping, and it also has good performance in terahertz absorbers [21,22]. Recently, some devices based on VO2 and graphene have been published to acquire different functionalities. For example, Liu et al. designed an absorber based on graphene and VO2 materials, which can achieve switching of broadband and double-band absorption and the adjustment of absorption intensity [23]. Zhang et al. designed a switchable absorber for multiband and broadband absorption [24]. However, there are still some aspects that can be improved, such as simpler structure, higher absorptance and wider bandwidth. From this perspective, we design a metamaterial absorber based on VO2 and graphene. The device achieves high absorption rate, broadband and tunable functions.
In this paper, a tunable broadband-narrowband switchable absorber is proposed based on graphene and VO2 materials. When VO2 is in the metallic state, the absorber achieves nearly complete absorption in the broadband range of 2.85 - 10 THz. The absorption rate can be adjusted by utilizing the phase transition properties of VO2. When VO2 is in the insulation state, the absorber switches to a narrow-band absorber. The absorber can achieve an absorption rate of 0.995 at 2.3 THz. Furthermore, the phenomenon of broadband absorption by the absorber is explained using electric field distribution and impedance matching theory. The proposed absorber may have promising applications in the field of terahertz imaging, detecting and sensing.
2. Design and method
The 3D diagram and geometric parameters of the designed absorber are shown in Fig. 1. The unit structure from top to bottom is a graphene pattern layer, a dielectric layer (SiO2), VO2 pattern layer, and a metal mirror layer. As shown, the structure of this absorber unit repeats with a period of p = 35 µm in the xy plane. The thickness of the gold at the bottom is h1 = 10 µm. The metal as a reflective layer can ensure that all incident electromagnetic waves are reflected. The thickness of the SiO2 dielectric on the gold mirror is h2 = 7.5 µm, and the thickness of the SiO2 between the graphene layer and the VO2 layer is h3 = 7 µm. The dielectric constant of two dielectric layers is ε = 2.45 [25]. The thickness of VO2 layer is 0.1 µm, and geometric parameters are w1 = 28 µm, w2 = 1 µm, w3 = 7.5 µm, w4 = 11 µm. The radius and thickness of the top graphene disk are R = 10 µm and h = 1 nm.
Fig. 1. (a) The three-dimensional schematic of the unit cell of the designed absorber. (b) x-y plane of VO2 layer. (c) x-y plane of graphene layer.
The surface conductivity of graphene can be described by Kubo's formula [26]:
The Fermi energy of graphene can be modulated by electrostatic bias. In this paper, Fermi energy level is chosen as Ef = 0.7 eV and carrier relaxation time τ = 0.2 ps for narrowband absorption.
The Drude model also allows us to characterize VO2 and Au optically in the terahertz range, The dielectric constant of gold can be expressed as:
in the formula, plasma frequency ${\omega _{p1}}$ is 1.37 × 1016 s-1 and the collision frequency ${\gamma _1}$ is 1.23 × 1014 s-1 [28].For VO2, the Drude model can be used to describe its dielectric constant in the terahertz range [29]:
In this paper, the finite element theory is used to simulate. In the simulation, periodic boundary conditions are set in X and Y directions. Floquet port is set in Z direction. Through simulation, the narrow-band and wide-band absorption spectra of the proposed terahertz metamaterial absorber in the insulating and metallic states of VO2 are obtained. In the simulation, the absorptivity can be expressed as:
where, A, R and T are respectively expressed as absorptivity, reflectance and transmittance, $R = {|{{S_{11}}} |^2}$, $T = {|{{S_{21}}} |^2}$. $|{{S_{11}}} |$ and $|{{S_{21}}} |$ represent reflection coefficient and transmission coefficient, respectively. Since the bottom metal can completely reflect electromagnetic wave, the transmittance T is 0, which is simplified as $A = 1 - R$ [31].3. Results and discussion
The simulation results are shown in Fig. 3. Through simulations, the absorptions of absorbers with different functions (broadband absorption and narrowband absorption) and different polarization modes (TE, TM) are obtained. In the ultra-wideband range of 2.85 - 10 THz, the absorptance of the device is greater than 95%. The bandwidth of the absorber is 7.15 THz, covering almost entire terahertz band. Figure 3(a) shows that when VO2 changes phase under the influence of temperature, the device can achieve switching between narrowband and ultra-broadband by adjusting the Fermi energy of graphene. When the Fermi energy of graphene is 0.7 eV and VO2 is in the insulating state (${\sigma _{V{O_2}}} = 200$S/m), the absorber realizes the function of narrow-band absorption, and the absorption rate at 2.3 THz is greater than 99.5%. Meanwhile, when the Fermi energy of graphene is 0.0 eV and temperature rises to the phase transition temperature, VO2 is in the metallic state (${\sigma _{V{O_2}}} = 200000$S/m), the absorber achieves the ultra-broadband absorption function. The absorber achieves an average absorption rate of over 95% over an ultra-broadband range of 2.85 to 10 THz. Moreover, it can be seen from Fig. 3(b) and (c) that the TE and TM modes are the same absorption.
Fig. 3. (a) Curve of broadband absorption (blue line) and curve of narrowband absorption (red line). (b) Absorption curves of vertically polarized (TE wave) and parallel polarized (TM wave) electromagnetic waves when ${\sigma _{V{O_2}}} = 2 \times {10^5}$S/m and ${E_f} = 0.0$eV with vertical incidence. (c) Absorption curves of vertically polarized (TE wave) and parallel polarized (TM wave) electromagnetic waves when ${\sigma _{V{O_2}}} = 2 \times {10^2}$ S/m and ${E_f} = 0.7$eV with vertical incidence.
In order to explain the absorption mechanism of the absorber, Fig. 4–5 show the electric and magnetic field distribution of broadband absorption and narrowband absorption. The electric field of the incident wave is polarized along the y-axis. Figure 4 shows the electric field intensity and surface current distribution of the VO2 layer and the bottom gold layer at 3.25 THz, 6.25 THz, 7.1 THz and 10THz. Through Fig. 4(a) and Fig. 5(a)-(d), the electric field is concentrated between the VO2 patches at 3.25 THz, and the upper and lower patches form a VO2 resonator. With the increase of frequency, the electric field between VO2 patches decreases at 6.25 THz and 7.1 THz, and the internal edge electric field increases. At 10 THz, the electric field is concentrated at the edge of VO2. We can conclude that the resonance in lower frequency band is mostly caused by the coupling between the VO2 sheets while high frequency resonance is caused by the electric dipole resonance of a single VO2 sheet. According to the surface current distribution in Fig. 4(a)-(d) and the magnetic field distribution of each frequency in Fig. 5(e)-(h), at 3.25 THz, 6.25 THz and 7.1 THz, the antiparallel current between the VO2 patch and the bottom gold layer forms a loop. Therefore, the VO2 dielectric layer in the middle can be regarded as a magnetic dipole, forming a strong magnetic resonance. At the frequency of 10 THz, the surface current direction of VO2 patch is parallel to the surface current direction on the gold layer, forming an electrical resonance. Therefore, under the combined action of magnetic resonance and electrical resonance, the incident electromagnetic wave is consumed within the resonant cavity, enhancing the absorption [32]. Figure 6 shows the current distribution of the top graphene and the bottom metal layer during narrow-band absorption. VO2 is now in an insulated state, equivalent to a dielectric. The antiparallel current between the graphene patch and the bottom metal layer at 2.3 THz forms a loop, generating an artificial magnetic moment. Accordingly, near-perfect absorption occurs at a particular frequency.
Fig. 4. Electric field distribution and current density in VO2 patch and base metal with broadband absorption at (a) 3.25 THz, (b) 6.25 THz, (c) 7.1 THz and (d) 10 THz.
Fig. 5. (a) - (d) displays the electric field of the absorber on the xz-direction cross-section at frequencies of 3.25 THz, 6.25 THz, 7.1 THz and 10 THz, respectively. (e) - (h) displays the magnetic field of the absorber on the xz-direction cross-section at frequencies of 3.25 THz, 6.25 THz, 7.1 THz and 10 THz, respectively.
Fig. 6. Electric field distribution and current density in graphene patch and bottom metal with narrowband absorption at 2.3 THz.
To further figure out the intrinsic physical mechanism of the proposed broadband absorption phenomenon, impedance matching theory is used. The absorption rate of the absorber can be expressed as:
Figure 8 shows the tunable function of the absorber in broadband and narrow bands. Figure 8(a) shows that when the Fermi energy of graphene is 0.0 eV, the conductivity of VO2 during heating (40°C - 80°C) changes from 200 S/m - 200000 S/m [35]. VO2 transitions from an insulating state to a metallic state, and the absorber forms a traditional metal-dielectric-metal structure. The broadband absorber realizes switching between total reflection and perfect absorption. Figure 8(b) shows that when VO2 is in the insulating state, adjusting the graphene Fermi energy (0.0 - 0.7eV) can dynamically adjust the absorption rate at 2.3 THz from 1% to 99%. The switchable and adjustable function of broadband and narrowband is realized, this can also be called the switching function of the terahertz absorber.
Fig. 8. (a) Broadband absorption curve of absorber during heating. (b) Narrow band absorption curve of absorber during Fermi energy change.
Considering the possible errors in the actual fabrication process of the structure, we discuss the influence of structure parameters on broadband and narrowband absorption. In Fig. 9, we plot the effect of the structural parameters (w1, w2, w3, w4) of the VO2 patch and the thickness of the dielectric (h2) on the absorption. It can be seen from Fig. 9(a) and (b) that when w1 decreases or w2 increases, low-frequency absorption spectrum appears blue-shifted. This is because the resonance effect of terahertz waves is affected when the structural size of VO2 is changed. The coupling between low frequency VO2 patches makes the absorptance high. Therefore, when size is changed, the coupling between the VO2 decreases leading to decrease in the absorptance. From Fig. 9(c) and (d), it can be concluded that when the size of w3 and w4 changes, the effect on the absorptance is small. The absorber remains high broadband absorption characteristics. In Fig. 9(e), we can see effect of different thicknesses of the dielectric layers on the absorption effect. When the thickness of the dielectric layer h2 increases in the range of 6.5 µm to 8.5 µm, the absorption effect in higher frequency band increases while the absorption effect in lower frequency band decreases. Considering the overall absorption effect, when the parameters are optimized 7.5 µm was chosen as the dielectric layer thickness. Above all, we can conclude that the absorber structure has good practical production process tolerance.
Fig. 9. (a) - (d) are the effects of VO2 patch parameters w1, w2, w3 and w4 on the absorption rate, respectively. (e) is the influence of the thickness of the dielectric layer h2 on the absorption rate.
In Fig. 10, the scanning absorption spectra of the key parameters R, h3, which affect the narrowband absorption effect are plotted. Meanwhile, VO2 is in the state of insulation, and the conductivity σ = 200 S/m., it can be seen from Fig. 10(a) that with the increase of the graphene disk radius, the absorption peak appears red-shifted. The absorption rate does not change significantly, so this parameter change has little effect on the absorption. As the thickness of the silicon dioxide layer h2 increases, the absorption efficiency increases. As shown in Fig. 10(b), in the range of 6 - 8 µm, the absorptance at 2.3 THz also increases gradually with the increase of thickness, but some smaller high-order absorption peaks appeared. The thickness of 7 µm was finally selected after comprehensive consideration. The absorption effect of narrow-band absorption is less affected by parameters, and the errors in the production process can also be ignored.
Fig. 10. (a) The effect of the graphene disk radius R on the absorption rate. (b) The effect of the silicon dioxide dielectric layer h1 on the absorption rate.
In order to investigate the absorption effect of the absorber under oblique incidence, broadband and narrowband absorption spectra were simulated under a wide range of incidence angles. In the simulation, the angle of incidence is the angle between incident electromagnetic wave and the Z direction, and the angle of incidence varies from 0° to 80° in 10° steps. Figure 11(a) and (b) are the absorption spectra of the broadband absorber under TE and TM polarized waves, respectively. When the incident angle is less than 60°, it still maintains good broadband absorption characteristics. For TM polarized waves, a blue shift occurs when the incident angle is greater than 40°. Figure 11(c) and (d) show the narrow-band absorptance of TE wave and TM wave as a function of frequency and incident angle. The absorptance of both polarizations decreases with the increase of incident angle. When the incident angle is kept below 50°, the dependence of the absorption on the incident angle is relatively weak, and the absorption rate drops rapidly. Figure 11(e) and (f) show the absorption spectra of the proposed absorber with the polarization angles of normal incident waves varied from 0° to 90°. It is clear that the proposed absorber is insensitive to the polarization angle.
Fig. 11. Angular dependence of broadband absorptance for (a) TE polarization and (b) TM polarization.
In fact, VO2 and graphene have been widely used in terahertz absorbers. Terahertz absorbers based on these two materials have realized narrowband absorption, broadband absorption [36,37], switching between narrowband absorption and broadband absorption [23,24,38–40] and other functions. Compared with various devices listed in Table 1, our device has better performance in broadband absorption. It shows that proposed structure in this paper has an ultra-broadband and high absorptance.
Table 1. Comparisons between the proposed structure and other publications.
4. Conclusion
In conclusion, a bifunctional absorption modulator based on a hybrid VO2 graphene structure is proposed. Using the phase transition properties of VO2 and changing the chemical potential of graphene, functional switching of metamaterial devices and independent tuning of their absorption properties can be achieved. When VO2 is in the state of metallic and the graphene Fermi energy is 0 eV, the metamaterial device can be used as a tunable ultra-broadband absorber, absorbing more than 95% in the range of 2.85 - 10 THz, and the relative bandwidth is about 110%. At this time, by adjusting the conductivity of the VO2 pattern, the absorption of the broadband function can be flexibly adjusted. In addition, the ultra-broadband absorber has good absorption performance, and the absorptance is maintained above 90% over a wide range of incident angles up to 60°. When VO2 is insulating, the design acts as a narrowband absorber to convert the graphene Fermi energy from changing 0.0 eV to 0.7 eV can greatly change the absorption rate of this absorber. The design is strongly polarization-independent and works well over a wide range of incidence angles. The design provides a new avenue for the development of terahertz filtering and modulation devices.
Funding
National Natural Science Foundation of China (61905091, 62005095, 62104080).
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.
References
1. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]
2. I. F. Akyildiz, C. Han, and S. Nie, “Combating the Distance Problem in the Millimeter Wave and Terahertz Frequency Bands,” IEEE Commun. Mag. 56(6), 102–108 (2018). [CrossRef]
3. H. Li, C. Zheng, H. Xu, J. Li, C. Song, J. Li, L. Wu, F. Yang, Y. Zhang, W. Shi, and J. Yao, “Diatomic terahertz metasurfaces for arbitrary-to-circular polarization conversion,” Nanoscale 14(35), 12856–12865 (2022). [CrossRef]
4. Q. Yang, B. Deng, H. Wang, Y. Zhang, and Y. Qin, “Translation compensation and micro-Doppler extraction for precession ballistic targets with a wideband terahertz radar,” J. Electron. Imaging 27(1), 1 (2018). [CrossRef]
5. N. Qi, Z.-Y. Zhang, and Y.-H. Xiang, “Application of Terahertz Technology in Medical Testing and Diagnosis,” Spectrosc. Spectr. Anal. 33(8), 2064–2070 (2013). [CrossRef]
6. N. Lyu, J. Zuo, Y. Zhao, and C. Zhang, “Terahertz Synthetic Aperture Imaging with a Light Field Imaging System,” Electronics 9(5), 830 (2020). [CrossRef]
7. M. Hasan, S. Arezoomandan, H. Condori, and B. Sensale-Rodriguez, “Graphene terahertz devices for communications applications,” Nano Commun.Netw. 10, 68–78 (2016). [CrossRef]
8. M. Chen, L. Singh, N. Xu, R. Singh, W. Zhang, and L. Xie, “Terahertz sensing of highly absorptive water-methanol mixtures with multiple resonances in metamaterials,” Opt. Express 25(13), 14089–14097 (2017). [CrossRef]
9. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]
10. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef]
11. H. Li and J. Yu, “Bifunctional terahertz absorber with a tunable and switchable property between broadband and dual-band,” Opt. Express 28(17), 25225–25237 (2020). [CrossRef]
12. J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Broadband terahertz absorber with a flexible, reconfigurable performance based on hybrid-patterned vanadium dioxide metasurfaces,” Opt. Express 28(12), 17832–17840 (2020). [CrossRef]
13. J. Zhu, C. Wu, and Y. Ren, “Broadband terahertz metamaterial absorber based on graphene resonators with perfect absorption,” Results Phys. 26, 104466 (2021). [CrossRef]
14. H. Li, W. Xu, Q. Cui, Y. Wang, and J. Yu, “Theoretical design of a reconfigurable broadband integrated metamaterial terahertz device,” Opt. Express 28(26), 40060–40074 (2020). [CrossRef]
15. Z. Song, K. Wang, J. Li, and Q. H. Liu, “Broadband tunable terahertz absorber based on vanadium dioxide metamaterials,” Opt. Express 26(6), 7148–7154 (2018). [CrossRef]
16. L. Chen and Z. Song, “Simultaneous realizations of absorber and transparent conducting metal in a single metamaterial,” Opt. Express 28(5), 6565–6571 (2020). [CrossRef]
17. Z. Li, T. Wang, H. Zhang, D. Li, and Y. Zhang, “Tunable bifunctional metamaterial terahertz absorber based on Dirac semimetal and vanadium dioxide,” Superlattices Microstruct. 155(4), 106921 (2021). [CrossRef]
18. L. Wang, S. Ge, W. Hu, M. Nakajima, and Y. Lu, “Graphene-assisted high-efficiency liquid crystal tunable terahertz metamaterial absorber,” Opt. Express 25(20), 23873–23879 (2017). [CrossRef]
19. H. Liu, G. Ren, Y. Gao, B. Zhu, B. Wu, H. Li, and S. Jian, “Tunable Terahertz Plasmonic Perfect Absorber Based on T-Shaped InSb Array,” Plasmonics 11(2), 411–417 (2016). [CrossRef]
20. F. J. Morin, “Oxides Which Show a Metal-to-Insulator Transition at the Neel Temperature,” Phys. Rev. Lett. 3(1), 34–36 (1959). [CrossRef]
21. K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012). [CrossRef]
22. H. Li, J. Li, C. Zheng, H. Xu, F. Yang, J. Li, Z. Yue, W. Shi, Y. Zhang, and J. Yao, “Dual-band giant spin-selective full-dimensional manipulation of graphene-based chiral meta-mirrors for terahertz waves,” Opt. Express 30(12), 22292–22305 (2022). [CrossRef]
23. W. Liu and Z. Song, “Terahertz absorption modulator with largely tunable bandwidth and intensity,” Carbon 174(25), 617–624 (2021). [CrossRef]
24. B. Zhang and K.-D. Xu, “Switchable and tunable bifunctional THz metamaterial absorber,” J. Opt. Soc. Am. B 39(3), A52–A60 (2022). [CrossRef]
25. Y. T. Zhao, B. Wu, B. J. Huang, and Q. Cheng, “Switchable broadband terahertz absorber/reflector enabled by hybrid graphene-gold metasurface,” Opt. Express 25(7), 7161–7169 (2017). [CrossRef]
26. Hanson and W. George, “Dyadic Green's functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]
27. S. Ke, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Plasmonic absorption enhancement in periodic cross-shaped graphene arrays,” Opt. Express 23(7), 8888–8900 (2015). [CrossRef]
28. Z. Li, Z. Yi, T. Liu, L. Liu, X. Chen, F. Zheng, J. Zhang, H. Li, P. Wu, and P. Yan, “Three-band perfect absorber with high refractive index sensing based on an active tunable Dirac semimetal,” Phys. Chem. Chem. Phys. 23(32), 17374–17381 (2021). [CrossRef]
29. J. Li, X. Chen, Z. Yi, H. Yang, Y. Tang, Y. Yi, W. Yao, J. Wang, and Y. Yi, “Broadband solar energy absorber based on monolayer molybdenum disulfide using tungsten elliptical arrays,” Mater. Today Energy 16, 100390 (2020). [CrossRef]
30. F. Fan, Y. Hou, Z.-W. Jiang, X.-H. Wang, and S.-J. Chang, “Terahertz modulator based on insulator-metal transition in photonic crystal waveguide,” Appl. Opt. 51(20), 4589–4596 (2012). [CrossRef]
31. N. Tang, Y. Li, F. Chen, and Z. Han, “In situ fabrication of a direct Z-scheme photocatalyst by immobilizing CdS quantum dots in the channels of graphene-hybridized and supported mesoporous titanium nanocrystals for high photocatalytic performance under visible light,” RSC Adv. 8(73), 42233–42245 (2018). [CrossRef]
32. N. Mou, S. Sun, H. Dong, S. Dong, Q. He, L. Zhou, and L. Zhang, “Hybridization-induced broadband terahertz wave absorption with graphene metasurfaces,” Opt. Express 26(9), 11728–11736 (2018). [CrossRef]
33. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002). [CrossRef]
34. K. Zhang, F. Xia, S. Li, Y. Liu, and W. Kong, “Actively tunable multi-band terahertz perfect absorber due to the hybrid strong coupling in the multilayer structure,” Opt. Express 29(18), 28619–28630 (2021). [CrossRef]
35. J. A. Bossard, L. Lin, S. Yun, L. Liu, D. H. Werner, and T. S. Mayer, “Near-ideal optical metamaterial absorbers with super-octave bandwidth,” ACS Nano 8(2), 1517–1524 (2014). [CrossRef]
36. X. M. Du, F. P. Yan, W. Wang, S. Y. Tan, L. N. Zhang, Z. Y. Bai, H. Zhou, and Y. F. Hou, “A polarization- and angle-insensitive broadband tunable metamaterial absorber using patterned graphene resonators in the terahertz band,” Opt. Laser Technol. 132, 106513 (2020). [CrossRef]
37. W. Liu, J. Xu, and Z. Song, “Bifunctional terahertz modulator for beam steering and broadband absorption based on a hybrid structure of graphene and vanadium dioxide,” Opt. Express 29(15), 23331–23340 (2021). [CrossRef]
38. Z. Song, A. Chen, and J. Zhang, “Terahertz switching between broadband absorption and narrowband absorption,” Opt. Express 28(2), 2037–2044 (2020). [CrossRef]
39. M. Zhang and Z. Song, “Switchable terahertz metamaterial absorber with broadband absorption and multiband absorption,” Opt. Express 29(14), 21551–21561 (2021). [CrossRef]
40. H. Zhu, Y. Zhang, L. Ye, Y. Li, Y. Xu, and R. Xu, “Switchable and tunable terahertz metamaterial absorber with broadband and multi-band absorption,” Opt. Express 28(26), 38626–38637 (2020). [CrossRef]
