Open Access
Add to BibSonomy
Abstract
In this paper, we design a polarization-independent and angle-insensitive broadband THz graphene metamaterial absorber based on the surface plasmon-polaritons resonance. Full-wave simulation is conducted, and the results show that the designed metamaterial absorber has an absorption above 99% in the frequency range from 1.23 THz to 1.68 THz, which refers to a very high standard. Furthermore, the absorber has the properties of tunability, and the absorption can be nearly adjusted from 1% to 99% by varying the Fermi energy level of the graphene from 0 eV to 0.7 eV. In the simulation, when the incident angles of TE and TM waves change from 0° to 60°, the average absorption keeps greater than 80%. The proposed absorber shows promising performance, which has potential applications in developing graphene-based terahertz energy harvesting and thermal emission.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials are able to realize many properties not found in natural materials [1,2]. In recent years, metamaterials have unlocked a number of unique optical properties for manipulating electromagnetic (EM) waves at subwavelength scale, such as the wave amplitude [3,4], wave polarization state [5,6], phase change [7,8], and nonlinearity [9]. Absorption is an important approach in controlling electromagnetic wave amplitude, and metamaterial absorbers have many applications in the field of optics [10]. In 2008, Landy et al. experimentally first demonstrate a metamaterial absorber, where the absorber combines two distinct metallic resonators to realize perfect absorption in the gigahertz band [11]. Due to the significance from the perspective of research and the practical applications, absorber performance with different band has shown more interests in the past years [12–15]. Graphene, a 2D material with a single layer of carbon atoms arranged in a hexagonal lattice, has an abundance of new physical and chemical properties [16]. And its Fermi energy level (EF) can be dynamically adjusted by means of electrical or chemical doping, which grants its optical properties widely applicable in tunable metamaterial optical devices [17,18]. Due to the unique optical property of graphene, graphene sheet has been studied as metal like material and applied in the surface plasmon applications. And a diverse number of graphene narrowband absorbers [19–23] and other metamaterials [24–27] have been proposed.
By using special implementations of graphene, such as integrating multiple resonators [28–31], multilayered structures [32,33], and utilizing metal or dielectric structures with adjustable graphene layers [34,35], perfect broadband absorber breaks the limitations of narrow band. However, it is worth noting that most broadband absorbers are based on a low reference absorption standard of greater than 90%. In fact, the corresponding bandwidths of more than 99% absorption for these broadband absorbers are fairly narrow. Besides, it is of great significance to study the tunable characteristics of absorber with high switching ratio in a wide range in practical applications. Hence, the research prospect of the tunable broadband absorber with higher absorption and large-scale regulation remains highly intriguing.
In this paper, we propose a polarization-independent, and angle-insensitive broadband metamaterial absorber with extremely high absorptivity based on the localized surface plasmon (LSP) and propagating surface plasmon (PSP). The proposed absorber is composed of a gold mirror, dielectric layers and graphene nanostructures consisting of a single layer of graphene concentric rings and crosses (GCRC). In full-wave simulations, absorption over 90% is realized in the range of 1.10–1.86 THz. In addition, from 1.23 to 1.68 THz the absorber exhibits a high absorption of above 99%. The mechanism of nearly perfect absorption is studied via electric and magnetic field distributions. We then investigate the influence of the size of dielectric layer and graphene patterns on the absorption. Meanwhile, the influence of incident conditions is also investigated, with results showing that the proposed absorber is insensitive to polarization and oblique incident angles. Moreover, the absorption strength can be controlled by adjusting the Fermi energy level. This type of metamaterial absorber has many potential applications in THz tunable devices such as smart absorbers, imaging, and optical switch.
2. Structure and simulation
The schematic of the tunable polarization-independent graphene broadband absorber is shown in Fig. 1, which contains a single layer of GCRC array separated from an optically thick gold mirror by a dielectric substrate. The dielectric material is considered to be non-dispersive with relative dielectric constant ɛ = 3.4. On the top of the graphene lies an ion-gel layer with a thickness of 1 µm, which serves as a transparent spacer layer with high capacitance between the top gate contact and the bottom layer of GCRC. The dielectric constant of the ion-gel layer is ɛig = 1.82. The Fermi energy level of the graphene layer can be adjusted by tuning the external voltage of the ion-gel via the top Au electrode [29,36,37]. For experimental characterization, the proposed GCRC metamaterial can be fabricated by electro-beam lithography and ion-beam sputter deposition [38,39]. The quantitative estimate between Fermi energy level and the voltage is [36]:
where V is the gate voltage, n is the carrier density and C is the capacitance of the gate. The dielectric constant of bulk gold (Au) is described by the Drude model with plasma frequency ωp = 4.35π × 1015 rad/s and damping constant ωτ = 13π × 1012 rad/s [28], and the layer has a thickness of 200 nm. The geometric parameters of a unit cell of the GCRC are shown in Figs. 1(b) and 1(c). The lattice constant is p = 73 µm and the thickness of the dielectric substrate is h = 30 µm. The graphene ring has an inner radius of R1 = 25 µm and the outer radius of R2 = 35 µm; the graphene cross has a width of W = 18 µm and length of L = 30 µm. The center symmetric graphene nanostructures allow for polarization-independence in the proposed broadband absorber.
Fig. 1. (a) Schematic of the designed broadband absorber. (b) and (c) The geometrical parameters of the GCRC metamaterial absorber.
In our numerical simulations, the graphene layer is described by an effective surface conductivity mode. The conductivity of graphene from the Kubo formula is described with interband and intraband contributions as [18,20,23]:
Here, we assume the initial Fermi energy level of graphene is 0.7 eV, relaxation time τ = 0.2 ps, and the absolute temperature T = 300 K. To investigate the proposed GCRC metamaterial absorber, a numerical full-wave simulation was performed based on the finite element method (FEM) by the commercial software COMSOL Multiphysics. The simulations use adaptive fine mesh settings. A unit cell of the proposed structure is simulated using periodic boundary condition. The absorption can be given by A(ω) = 1 − |S11 (ω)|2 − |S21 (ω)|2, where |S11 (ω)|2 is the reflection and |S21 (ω)|2 is the transmission. The S parameters can be obtained in the FEM simulation. Since the gold layer is thick enough to block the incident terahertz wave and no energy is allowed to transmit through the GCRC metamaterial absorber, the absorption can be simplified as A(ω) = 1 − |S11 (ω)|2.
The working principle of the GCRC metamaterial absorbers can be understood as follows. When the incident waves illuminate the metamaterials, anti-parallel currents are generated from the both bottom metallic and top graphene layers, resulting in a strong magnetic resonance. When the graphene and the metallic layer are very close, strong coupling effect leads to an extremely strong near fields that can be dissipated by the lossy graphene [29]. Meanwhile, illuminated by the incident waves, LSP modes or PSP modes will be excited inside the graphene nanostructures, which enhance the absorption effectively [39].
3. Results and discussions
First, we consider the case where x-polarized waves normally illuminate on the GCRC metamaterials absorber. The proposed absorber exhibits a high absorptivity of above 90% from 1.10 to 1.86 THz and above 99% from 1.23 to 1.68 THz in Fig. 2, which indicates nearly perfect absorption. The peaks of absorption band are located at f1 (1.29THz) and f2 (1.61THz) with the absorptivity great than 99.9%. To clarify their physical origins, the absorption spectra of two simplified graphene metamaterials with the original GCRC structure replaced by solo rings and crosses are plotted in Fig. 2 with green dashed line and blue dotted line, respectively. We can see that neither the solo rings nor crosses can achieve broadband absorption, which indicates the excellent absorption effect is the result of the combination of the two structures.
Fig. 2. Simulated absorption spectra of solo ring (green dashed line), solo cross (blue dotted line), and the GCRC (red solid line) structures with x-polarized incident waves.
In order to understand the physical origins of the absorption, we investigate the electric field amplitude distributions of the GCRC absorber. From Figs. 3(a)–3(d), the spatial distributions of the electric field can be clearly divided into two categories. As shown in Figs. 3(a) and 3(b), a dipole resonance mode is supported by the edges of the horizontal arms in the graphene crosses. The electric field is concentrated in the gaps between the graphene rings and crosses along the x-direction. While in Figs. 3(c) and 3(d), a quadrupole resonance mode is generated from the four corners of the horizontal arms of the graphene crosses. The electric field of this mode is primarily concentrated on surface of the horizontal arms of the graphene crosses.
Fig. 3. Left: Spatial distributions of the electric field intensity in a single unit cell of GCRC (z-direction), calculated at 1.10 THz (a), 1.29 THz (b), 1.61 THz (c), and 1.81 THz (d). Right: Spatial distributions of the electric field intensity in a single unit cell of solo rings (e) and solo crosses (f) at their absorption peaks (z-direction). Bottom: Spatial distributions of the electric field intensity in a single unit cell of GCRC (y-direction), calculated at 1.10 THz (g), 1.29 THz (h), 1.61 THz (i), and 1.81 THz (g). Spatial distributions of the magnetic field intensity in a single unit cell of GCRC (y-direction), calculated at 1.10 THz (k), 1.29 THz (l), 1.61 THz (m), and 1.81 THz (n). The incident waves are x-polarized.
Figures 3(g)–3(j) show the electric field distributions along the y-direction, where the electric field spreads from the gap to uniformly cover almost both horizontal arms of the graphene crosses. The electric field is mainly located in the gap of the graphene rings and crosses, implying that LSP mode are excited in the GCRC absorber, and the electric field is strongly confined to the interface of the graphene and dielectric, implying that PSP mode are excited. Two different resonance modes are also observed from magnetic field distributions plotted in Figs. 3(k)–3(n). Therefore, at f1 the LSP mode dominates the absorption, while at f2 the PSP mode dominates the absorption. It can be clearly seen that as the frequency increases, the surface plasmon-polaritons (SPP) modes change, and the two modes coexist in the middle part of the absorption band.
To better understand the function of the solo rings and crosses in the total absorption, we calculate the electric field amplitude corresponding to the respective absorption peaks of the structures under illumination of x-polarized waves. As shown in Fig. 3(e), the electric field of solo ring at the absorption-peak 1.40 THz is mainly localized on the inside of the rings along the polarization direction of incident electric field. From Fig. 3(f) solo graphene crosses can only produce a quadrupole resonance and excite PSP mode in the studied band and the electric field distribution of solo cross at the absorption-peak 1.50 THz is similar to that in Figs. 3(c) and 3(d). But when adding a ring to the structure, a dipole resonance generated and LSP mode is excited. Comparing the absorption spectra of solo graphene and the combined structure of rings and crosses in Fig. 2, the absorption of the combined structure is significantly increased. Therefore, it is the graphene rings that induce the dipole resonance and LSP mode and also enhance the quadrupole resonance mode of the graphene crosses. Meanwhile, the coupling of LSP and PSP resonance modes achieves the more desirable absorptivity and bandwidth.
Next, we further investigate the influence of dielectric thickness h and lattice constant p on absorption while keeping other parameters fixed. As shown in Figs. 4(a) and 4(b), the increase of h and p lead to a redshift of the PSP-dominated peak. This is because that the increased h or p leads to an increased effective dielectric constant of the resonant mode. The following formula can qualitatively explain this change.
where ${\varepsilon _{eff}}\; $ is the effective dielectric constant and ${\omega _P}$ is the plasma frequency of graphene which is related to ${\sigma _\omega }$. Comparing with the PSP-dominated peak, the shift of LSP-dominated peak is relatively small. This suggests that in the proposed GCRC metamaterial absorber, the dielectric constant of the substrate mainly affects the PSP resonance mode. The change of absorption in Fig. 4(a) is due to the Fabry–Perot effect in the substrate layer. For h = 30 µm, the effective impedance of the absorber matches that of free space at the resonance frequency, so that all of the reflection from the structure vanished [19]. Thus, the overall incident waves are absorbed in the structure.Fig. 4. Absorption spectra of the absorber with different thicknesses of dielectric layer (a), lattice constants (b), and lengths (c) and widths (d) of the graphene crosses. The incident waves are x-polarized.
The absorption of the GCRC is also related to the geometric parameters of the graphene nanostructure. We investigate the influence of L and W on absorption with other parameters fixed. The absorption as a function of length L of the cross is indicated in Fig. 4(c). The LSP-dominated peak has a clearly blue shift as L decreases. The LSP mode occurs when the graphene plasmon resonances resonate along the length L of the graphene cross, and the resonance condition can be denoted as [20]:
where kL = ${\omega _{LSP}}\sqrt {{\varepsilon _{eff}}} $, ${\varepsilon _{eff}}$, ${\omega _Q},\; $δ, and Leqv represent the effective dielectric constant, resonance angular frequency, phase change at the edges of the horizontal arms and equivalent resonance length of the horizontal arm, respectively. j is an integer, and can be defined as 1 under the condition that the incident wavelength is far greater than L. Therefore, the resonance frequency can be simplified as [41]:From Eq. (6), the resonant frequency is proportional to the effective length Leqv, so the LSP-dominated peak blue shifts with decreases in L. Moreover, as L decreases, the PSP-dominated peak is initially unchanged as the effective dielectric constant is insensitive to L. However, when L drops to 15 µm, the absorption spectrum approaches that of the solo ring in Fig. 2. This is because the decrease in L makes the gap of the graphene ring and cross wider, so that the coupling between them becomes weaker. Meanwhile, when L = 15 µm, the graphene cross becomes a rectangle, and the PSP resonance of the original cross structure disappears. Therefore, the absorption is reduced and the absorption spectrum becomes similar to that of the solo rings.
The evolution of the absorption spectra with varying width W of the graphene cross is illustrated in Fig. 4(d). For the graphene cross, the effective dielectric constant ${\varepsilon _{eff}}$ mainly depends on the width W, and ${\varepsilon _{eff}}$ increases as W decreases. When W ${\ll} $ L, the narrower graphene strip suggests a larger ${\varepsilon _{eff}}$ [42]. On the other hand, when W approaches to L, the PSP resonance in the horizontal arms of graphene crosses cannot be neglected and L dominates the absorption gradually [41]. As a result, the PSP-dominated peak experiences a redshift and the range of the shift decreases with the increase in W. The LSP-dominated peak also experiences a redshift and reduced absorption with increase in W. From the analysis of Fig. 4, the dielectric constant has very little effect on the LSP resonance mode in the structure. Therefore, the redshift of the LSP-dominated peak is due to the change in W influencing the coupling between the graphene rings and crosses, which then influence the induction of the resonance in graphene rings to LSP resonance in the crosses.
In addition, the effect of the different polarization angles and incident angles on the GCRC absorber are investigated in Figs. 5(a)–5(c). Figure 5(a) depicts the absorption spectra of the proposed absorber with the polarization angles of normal incident waves varied from 0° to 90°. The absorptivity of different polarization angles remains strictly consistent, which indicates that the GCRC absorber is polarization-independent for normally incident waves. This is mainly due to center symmetric graphene nanostructures of the unit cell. Figures 5(b) and 5(c) depict the absorption contour map in both TE and TM modes with incident angle varied from 0° to 60°. It is observed that the absorption band blue shifts slightly in TE mode with the increase of incident angle, which is mainly because the parasitic resonances generated at large incident angle [31]. As incident angle increases, the absorption bandwidth of TM mode becomes narrower and a higher-order mode appears. Meanwhile, as the incident angle increases, it is inevitable that the absorption rate decreases due to the weaker interaction between the incident wave and graphene patterns. Nonetheless, the average absorption from 1.10 to 1.86 THz remains greater than 80% with a wide range (60°) of incident angle for both TE and TM mode. In general, the absorption of the proposed absorber is insensitive to the incident angle.
Fig. 5. (a) Absorption contour map of the GCRC absorber for normally incident TE waves with polarization angles from 0° to 90°. (b) and (c) Absorption contour maps of the absorber as a function of incident angle and frequency under oblique incident angle from 0° to 60° for the TE mode and TM mode, respectively.
Finally, we investigate the dynamically tunable property of the proposed GCRC absorber. As shown in Eq. (3), the surface conductivity of graphene is closely related to its Fermi energy level in the THz band. The Fermi energy level of graphene can be modulated by applying a bias voltage. Here the dynamically tunable property of the GCRC absorber can be realized by changing the Fermi energy level of the graphene rings and crosses. We plot the absorption spectra of the absorber in Fig. 6 with different Fermi energy levels of the graphene sheets illuminated by x-polarized THz waves. It is seen that the broadband absorption from 1.23 to 1.68 THz can be nearly tuned from 1 to 99% by varying the Fermi energy levels of graphene from 0 to 0.7 eV. This indicates that the designed metamaterial has a potential application in optical switch. The comparison of the absorption frequency band (FB), fractional bandwidth (BW), and absorptivity regulation (The minimum absorption of state ON to maximum absorption of state OFF at the operating bandwidth) of the proposed absorber with some others’ work are shown in Table 1, which shows that the proposed absorber has the advantage of ultra-broadband and tunable.
Fig. 6. Absorption spectra of the GCRC absorber for different Fermi energy levels of graphene from 0 to 0.7 eV. The incident waves are x-polarized.
Table 1. The comparison between references and our work.
4. Conclusion
In conclusion, a dynamically tunable, polarization-independent, and angle-insensitive broadband metamaterial absorber based on graphene surface plasmon resonance is numerically investigated at THz frequencies. The proposed absorber is designed by the combination of a gold mirror, dielectric layer and graphene nanostructures. According to the full-wave FEM simulation, it has a broadband absorption above 90% from 1.10 to 1.86 THz, and absorption above 99% from 1.23 to 1.68 THz. The average absorption of the absorber remains greater than 80% with the incident angles from 0° to 60° for TE and TM waves. The polarization-independent property benefits from the centrosymmetric graphene nanostructures. In addition, the absorption can be nearly tuned from 1% to 99% by changing the Fermi energy level of the graphene. Our results provide a new method to design broadband tunable absorption metamaterials in THz and other wavebands. The proposed absorber has high modulation depth and significant potential in applications of thermal emitters, photovoltaic devices, smart absorbers, and active optical switch.
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 that there are no conflicts of interest related to this article.
References
1. A. M. Shaltout, V. M. Shalaev, and M. L. Brongersma, “Spatiotemporal light control with active metasurfaces,” Science 364(6441), eaat3100 (2019). [CrossRef]
2. S. Sun, Q. He, J. Hao, S. Xiao, and L. Zhou, “Electromagnetic metasurfaces: physics and applications,” Adv. Opt. Photonics 11(2), 380–479 (2019). [CrossRef]
3. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef]
4. J. Zhou, Y. Hu, T. Jiang, H. Ouyang, H. Li, Y. Sui, H. Hao, J. You, X. Zheng, Z. Xu, and X. A. Cheng, “Ultrasensitive polarization-dependent terahertz modulation in hybrid perovskites plasmon-induced transparency devices,” Photonics Res. 7(9), 994–1002 (2019). [CrossRef]
5. C. C. Chang, Z. Zhao, D. Li, A. J. Taylor, S. Fan, and H. T. Chen, “Broadband Linear-to-Circular Polarization Conversion Enabled by Birefringent Off-Resonance Reflective Metasurfaces,” Phys. Rev. Lett. 123(23), 237401 (2019). [CrossRef]
6. J. Li, Y. Yang, J. Li, Y. Zhang, Z. Zhang, H. Zhao, F. Li, T. Tang, H. Dai, and J. Yao, “All-Optical Switchable Vanadium Dioxide Integrated Coding Metasurfaces for Wavefront and Polarization Manipulation of Terahertz Beams,” Adv. Theory Simul. 3(1), 1900183 (2020). [CrossRef]
7. K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6(11), 782–787 (2012). [CrossRef]
8. Y. Kim, P. C. Wu, R. Sokhoyan, K. Mauser, R. Glaudell, G. Kafaie Shirmanesh, and H. A. Atwater, “Phase Modulation with Electrically Tunable Vanadium Dioxide Phase-Change Metasurfaces,” Nano Lett. 19(6), 3961–3968 (2019). [CrossRef]
9. B. Sain, C. Meier, and T. Zentgraf, “Nonlinear optics in all-dielectric nanoantennas and metasurfaces: a review,” Adv. Photonics 1(2), 024002 (2019). [CrossRef]
10. V. C. Su, C. H. Chu, G. Sun, and D. P. Tsai, “Advances in optical metasurfaces: fabrication and applications [Invited],” Opt. Express 26(10), 13148–13182 (2018). [CrossRef]
11. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef]
12. I. Koirala, C. S. Park, S. S. Lee, and D. Y. Choi, “Angle tolerant transmissive color filters exploiting metasurface incorporating hydrogenated amorphous silicon nanopillars,” Chin. Opt. Lett. 17(8), 082301 (2019). [CrossRef]
13. L. Lei, F. Lou, K. Tao, H. Huang, X. Cheng, and P. Xu, “Tunable and scalable broadband metamaterial absorber involving VO2-based phase transition,” Photonics Res. 7(7), 734–741 (2019). [CrossRef]
14. Z. Yan, Q. Zhu, M. Wan, X. Lu, X. Pu, C. Tang, and L. Yu, “Graphene ultraviolet ultrahigh-Q perfect absorption for nanoscale optical sensing,” Opt. Express 28(5), 6095–6101 (2020). [CrossRef]
15. A. Safaei, S. Modak, A. Vazquez-Guardado, D. Franklin, and D. Chanda, “Cavity-induced hybrid plasmon excitation for perfect infrared absorption,” Opt. Lett. 43(24), 6001–6004 (2018). [CrossRef]
16. F. H. Koppens, D. E. Chang, and F. Javier Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011). [CrossRef]
17. 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]
18. K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017). [CrossRef]
19. P. Sun, C. You, A. Mahigir, T. Liu, F. Xia, W. Kong, G. Veronis, J. P. Dowling, L. Dong, and M. Yun, “Graphene-based dual-band independently tunable infrared absorber,” Nanoscale 10(33), 15564–15570 (2018). [CrossRef]
20. D. Wu, M. Wang, H. Feng, Z. Xu, Y. Liu, F. Xia, K. Zhang, W. Kong, L. Dong, and M. Yun, “Independently tunable perfect absorber based on the plasmonic properties in double-layer graphene,” Carbon 155, 618–623 (2019). [CrossRef]
21. F. Liu and E. Cubukcu, “Tunable omnidirectional strong light-matter interactions mediated by graphene surface plasmons,” Phys. Rev. B 88(11), 115439 (2013). [CrossRef]
22. Y. Liu, R. Zhong, J. Huang, Y. Lv, C. Han, and S. Liu, “Independently tunable multi-band and ultra-wide-band absorbers based on multilayer metal-graphene metamaterials,” Opt. Express 27(5), 7393–7404 (2019). [CrossRef]
23. L. Ye, F. Zeng, Y. Zhang, and Q. H. Liu, “Composite graphene-metal microstructures for enhanced multiband absorption covering the entire terahertz range,” Carbon 148, 317–325 (2019). [CrossRef]
24. S. X. Xia, X. Zhai, L. L. Wang, and S.-C. Wen, “Plasmonically induced transparency in double-layered graphene nanoribbons,” Photonics Res. 6(7), 692–702 (2018). [CrossRef]
25. F. Zeng, L. Ye, L. Li, Z. Wang, W. Zhao, and Y. Zhang, “Tunable mid-infrared dual-band and broadband cross-polarization converters based on U-shaped graphene metamaterials,” Opt. Express 27(23), 33826–33839 (2019). [CrossRef]
26. D. Drosdoff, A. D. Phan, and L. M. Woods, “Transverse Electric Mode for Near-Field Radiative Heat Transfer in Graphene-Metamaterial Systems,” Adv. Opt. Mater. 2(11), 1038–1042 (2014). [CrossRef]
27. J. Bai, S. Zhang, F. Fan, S. Wang, X. Sun, Y. Miao, and S. Chang, “Tunable broadband THz absorber using vanadium dioxide metamaterials,” Opt. Commun. 452, 292–295 (2019). [CrossRef]
28. X. Huang, W. He, F. Yang, J. Ran, B. Gao, and W. L. Zhang, “Polarization-independent and angle-insensitive broadband absorber with a target-patterned graphene layer in the terahertz regime,” Opt. Express 26(20), 25558–25566 (2018). [CrossRef]
29. 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]
30. T. Wang, Y. Zhang, H. Zhang, and M. Cao, “Dual-controlled switchable broadband terahertz absorber based on a graphene-vanadium dioxide metamaterial,” Opt. Mater. Express 10(2), 369–386 (2020). [CrossRef]
31. J. Han and R. Chen, “Tunable broadband terahertz absorber based on a single-layer graphene metasurface,” Opt. Express 28(20), 30289–30298 (2020). [CrossRef]
32. Z. Xu, D. Wu, Y. Liu, C. Liu, Z. Yu, L. Yu, and H. Ye, “Design of a Tunable Ultra-Broadband Terahertz Absorber Based on Multiple Layers of Graphene Ribbons,” Nanoscale Res. Lett. 13(1), 143 (2018). [CrossRef]
33. M. Rahmanzadeh, H. Rajabalipanah, and A. Abdolali, “Multilayer graphene-based metasurfaces: robust design method for extremely broadband, wide-angle, and polarization-insensitive terahertz absorbers,” Appl. Opt. 57(4), 959–968 (2018). [CrossRef]
34. F. Gao, Z. Zhu, W. Xu, J. Zhang, C. Guo, K. Liu, X. Yuan, and S. Qin, “Broadband wave absorption in single-layered and nonstructured graphene based on far-field interaction effect,” Opt. Express 25(9), 9579–9586 (2017). [CrossRef]
35. M. Nourbakhsh, E. Zareian-Jahromi, and R. Basiri, “Ultra-wideband terahertz metamaterial absorber based on Snowflake Koch Fractal dielectric loaded graphene,” Opt. Express 27(23), 32958–32969 (2019). [CrossRef]
36. M. Chen, Z. Xiao, X. Lu, F. Lv, and Y. Zhou, “Simulation of dynamically tunable and switchable electromagnetically induced transparency analogue based on metal-graphene hybrid metamaterial,” Carbon 159, 273–282 (2020). [CrossRef]
37. X. Jiang, Z. Zhang, K. Wen, G. Li, J. He, and J. Yang, “A Triple-Band Hybridization Coherent Perfect Absorber Based on Graphene Metamaterial,” Appl. Sci. 10(5), 1750 (2020). [CrossRef]
38. C. Wang, W. Liu, Z. Li, H. Cheng, Z. Li, S. Chen, and J. Tian, “Dynamically Tunable Deep Subwavelength High-Order Anomalous Reflection Using Graphene Metasurfaces,” Adv. Opt. Mater. 6(3), 1701047 (2018). [CrossRef]
39. Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. M. Ajayan, F. J. G. d. Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014). [CrossRef]
40. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011). [CrossRef]
41. 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]
42. A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011). [CrossRef]
