We propose a broadband tunable metamaterial absorber with near-unity absorption in the terahertz regime based on a target-patterned graphene sheet. Due to gradient diameter modulation of the graphene sheet and circular symmetry of the unit cell, broadband and polarization-independent properties are achieved in the absorber. A full-wave numerical simulation is performed, and the results show that the absorber’s bandwidth of 90% terahertz absorption reaches 1.57 THz with a central frequency of 1.83 THz under normal incidence. At oblique incidence, the broadband absorption of the absorber remains more than 75% over a wide incidence angles up to 60for the transverse electric (TE) mode and 75for the transverse magnetic (TM) mode. Furthermore, tunable property is implemented and the peak absorption of the absorber can be tuned from 19% to near 100% by changing the Fermi energy of the graphene sheet from 0 to 0.9 eV via electrostatic doping. The absorber is scalable to the infrared and visible frequencies, which could be used as tunable sensors, filters and photovoltaic devices.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Metamaterial perfect absorbers (MPAs), a branch of metamaterials, currently have raised extensive interests as they are becoming a crucial component of high-resolution imaging, sensing and detecting systems in the terahertz regime [1–3]. MPAs are often realized by using lossy materials in periodic structures, and the basic mechanism of MPAs is that the incident electromagnetic fields are firmly confined and consumed inside the lossy materials [4–6]. As the first experimental demonstration of MPAs was implemented by Landy et al. in 2008 , where a classical sandwiched structure was presented and the incident electric and magnetic fields were independently absorbed by metamaterial resonators. From then on, large amount of structures of MPAs were proposed, but plenty of them were narrow in bandwidth [7–9].
The broadband property of MPAs is of great importance to the practical applications of optoelectronic devices, such as bolometers and solar energy-harvesting devices [10–13]. To achieve broadband absorption, various approaches have been investigated. One common strategy is to utilize multi-resonances by embracing multiple resonators with small differences in geometry size in one unit cell, and the continuously small different resonance frequencies can be merged to form a broadband absorption spectra [14–16]. Another approach of effective broadband structures is to overlay the multi-layered pattern with different geometry parameters separated by dielectric with different thicknesses [17–19]. Meanwhile, the tunable property of absorbers is more attractive in practice due to flexibility [20–22]. Compared with other new materials, graphene is a two-dimensional crystal composed of a monolayer of carbon atoms arranged in a honeycomb lattice and it is extensively adapted due to its fantastic electromagnetic properties [23–27]. Another remarkable property of graphene is that its Fermi level can be dynamically changed by applying an external gate voltage [28,29]. Up to now, multiple graphene-based structures of MPAs have been proposed in the microwave, infrared and terahertz regime [16,19,30–32], and polarization-independent and angle-insensitive broadband absorbers have attracted enormous interest.
On basis of previous work, a novel polarization-independent broadband absorber with near-unity absorption in the terahertz regime is presented here. By combining the gradient diameter of the graphene sheet with circular symmetry of the unit cell, polarization-independent and broadband properties are achieved simultaneously. The results show that the absorber’s normalized bandwidth with 90% terahertz absorption reaches 1.57 THz when the Fermi energy of graphene sheet is set as 0.7 eV under normal incidence. To better understand the mechanism of broadband absorption, the electric field distribution and surface current distribution of the structure are studied and discussed. Furthermore, the tunable property of the absorber is investigated and the peak absorption can be tuned from 19% to 100% by changing the Fermi energy of graphene from 0 to 0.9 eV via electrostatic doping.
2. Design and simulation
This designed unit cell of the metamaterial absorber is illustrated in Fig. 1. Figure 1(b) shows that the proposed absorber is a classical sandwich structure, which is composed of a target-patterned graphene resonator on the top layer and a continuous metallic ground plate spaced by a dielectric substrate. Gold is selected as the ground plate, whose conductivity is described by Drude model with a plasma frequencyrad/s and collision frequencyrad/s , and the thickness is. For the dielectric material, we adopt the low loss TOPAS polymer with permittivity  and the thickness is. As shown in the Fig. 1(b), the target-patterned graphene layer consists of one circle disk with radius, and an annulus with inner radiusand outer radius, which is separated by a gap. The perspective view is presented in Fig. 1(c). Graphene is chosen as the material of top layer and its conductivity can be expressed as (unit:)with the intraband and interband contributions from the Kubo formula [35,36]. In the Terahertz range, the photo energy ,, that the contribution of the interbandis negligible compared with the intrabandwhich can be expressed as:
In the modeling and simulation, frequency domain solver was selected and the simulated frequency range was set as 0.1 to 3.5 THz. In the boundary condition setting, the x-direction and y-direction were both set as unit cell and the two-sides of the z-direction were Floquet ports. To simulate the graphene more accurately, as the graphene is in fact a single-layer carbon atom material, the graphene sheet was modeled as an equivalent 2D surface impedance layer without thickness which was built from a closed planar circular curve extruding to a surface. Here, we assume the initial chemical potential of graphene is 0.7 eV, relaxation time , and the absolute temperature.The absorption of the absorber can be calculated as,which can be simplified as.The transmissionis due to the thickness of the golden ground layer () is much thicker than the skin depth of the incident terahertz wave. Theparameters can be obtained in the CST Microwave Studio simulation.
3. Results and discussion
To study the absorption spectra of the proposed broadband tunable metamaterial absorber, a numerical full-wave simulation has been performed based on the finite integration algorithm of CST Microwave Studio. We firstly investigate the absorption spectra under normal incidence with and without the graphene sheet, and the results are shown in Fig. 2. From the red curve(absorption spectra with graphene sheet), as expected, broadband absorption is observed that 90% absorption of the absorber reaches 1.57 THz, starting fromTHz toTHz, when the Fermi energy of graphene is set as 0.7 eV. When the graphene sheet is removed from the structure, zero absorption is noted, which is represented by the blue curve.
Additionally, we also investigate the influence of the thickness of TOPAS dielectric layer on the absorption. As shown in Fig. 3. The absorption curves appear a red shift when the thickness of TOPAS spacer increases from 24 to 30, and the peak absorption keeps increasing. Adhering to the principle of high absorption in a continuous bandwidth, we choose the thickness of as the best value. It should be noted that, in our calculation, we ignore the loss of TOPAS material itself because it is very low across the THz band.
To better understand the absorption mechanism, we further investigate the electric field distribution and surface current distribution of the absorber, as shown in Fig. 4 and Fig. 5, respectively. Figure 4(a) displays the electric field distribution of the absorber at 0.2, 0.8, 1.6, 2.2 THz in the TE mode, which are represented by the pictures from left to right, respectively. As shown from the first two pictures in Fig. 4(a), weak electric field appears in the structure at 0.2 THz, while a strong electric filed is concentrated on the circle gap and the space between two unit cells along the y-axis at 0.8 THz, respectively. It is easy to find, at 0.2 and 0.8 THz, there exists a classical absorption mechanism that consists of an electric resonance (realized by the top graphene layer) and a magnetic resonance (realized by the top and ground layer). It matches well with the results published in , Landy et al, and can be further verified by the following current distribution displayed in Fig. 5. When it comes to 1.6 and 2.2 THz, we can find from the next two pictures in the Fig. 4(a) that the graphene localized surface plasmon resonance is stimulated by the incident electromagnetic wave. Compared with the situation at 0.2 and 0.8 THz, the electric field spreads from the gap to almost the entire graphene pattern with a comparable lower electric field maximum amplitude, but the electric field among the graphene pattern is more uniform and stronger which agrees well with the absorption spectra given above. Figure 4(b) shows the electric field distribution in the TM mode, which is same as that in Fig. 4(a) when rotated by 90.
The surface current distribution on the front graphene layer and back ground layer is next investigated to further verify the results described by the electric field distribution. As shown in Fig. 5, at 0.2 and 0.8 THz, the maximum current on the top layer flow from bottom to top while it is inversed on the back ground layer, the current at 0.8 THz is larger than that at 0.2 THz, which agrees well with the electric field distribution described above. When it comes to the 1.6 THz, the surface current on the back ground layer is much different with the distribution at 0.8 and 0.2 THz. On the front graphene layer, the current emits from the bottom and converge on the top mainly along the center graphene and gap, and the current in the back ground layer keeps the same flow direction with the top layer, which is different with the magnetic resonance shown at 0.8 and 0.2 THz. The surface current distribution is mainly resulted by the graphene plasmon resonance which is consistent with the results described in , Vakil and Nader Engheta.
The absorption spectra of absorbers under different polarization angles and oblique incidence angles are essential to applicable devices. Firstly, the influence of polarization angles to the absorption of the absorber is investigated. As shown in Fig. 6, we can see that the absorption curve remains highly consistent when the polarization angles vary from 0to 90with a step width 10. The polarization-independent property of the absorber is mainly attributed to the circular symmetry of the unit cell, which consists of a cubic substrate and nummular pattern.
Next, the absorption spectra under oblique incidence in both the TE and TM modes are studied, as shown in Fig. 7(a) and Fig. 7(b), respectively. In the simulation, the incidence angles vary from 0to 80with the step width of 10. We can see the peak absorption keeps larger than 90% up to 70incidence angles for the TE mode and 65for the TM mode, respectively. Besides, the broadband absorption remains more than 75% with a bandwidth of 1.6 THz over a wide range of incidence angles up to 60for the TE mode and 75for the TM mode, respectively. Meanwhile, the absorption spectra occur a blue shift with increasing incidence angles.
Furthermore, the electrically tunable property of the broadband absorber is investigated at the end. Graphene is one kind of tunable material which is often used to tune the absorption amplitude. The surface conductivity of graphene sheet relates largely to its Fermi energy, which can be controlled by electrostatic doping or applying bias voltage [28,37]. Here, we implement the dynamically tunable property of the broadband absorber by varying the Fermi level of the graphene sheet located on the top layer of the unit cell. As shown in Fig. 8, the absorption amplitude changes from 19% to near 100% absorption with the Fermi energy varying from 0 to 0.9 eV. Here, the wide range of Fermi energy of graphene sheet can be modulated by sol-gel top gating method .
We proposed and demonstrated a broadband tunable metamaterial absorber which effectively takes advantage of the graphene surface plasmon resonance in the terahertz regime. Some valuable properties are found in the absorber, such as polarization-independence and angle-insensitivity. According to the full-wave numerical simulation, the results show a broadband width of 1.57 THz with a central frequency 1.83 THz under normal incidence when the Fermi level of graphene sheet is set as 0.7 eV. Besides, the absorption of the absorber remains unchanged for almost any polarization angles, and the broadband absorption remains more than 75% over a wide range of incidence angles up to 60for the TE mode and 75for the TM mode. Additionally, we performed analysis of the electric field distribution and surface current distribution of the absorber to better understand the mechanism of broadband absorption in the structure. The tunable property of the absorber is also investigated by controlling the Fermi level of graphene sheet located on the top layer, and the peak absorption can be tuned from 19% to near 100% by changing the chemical potential from 0 to 0.9 eV via sol-gel top gating method. The proposed absorber is designed with a compact single-layered graphene pattern which enables the ease of fabrication, and it can be scalable to the infrared and visible frequencies for many promising applications such as tunable sensors, filters and photovoltaic devices.
National Natural Science Foundation of China (NSFC) (51777023); China Postdoctoral Science Foundation (CPSF) (2017M622963, 2017M620411).
X. H. acknowledges the sponsorship of the China Scholarship Council.
1. C. Zhang, C. Huang, M. Pu, J. Song, Z. Zhao, X. Wu, and X. Luo, “Dual-band wide-angle metamaterial perfect absorber based on the combination of localized surface plasmon resonance and Helmholtz resonance,” Sci. Rep. 7(1), 5652 (2017). [CrossRef] [PubMed]
2. R. I. Stantchev, D. B. Phillips, P. Hobson, S. M. Hornett, M. J. Padgett, and E. Hendry, “Compressed sensing with near-field THz radiation,” Optica 4(8), 989–992 (2017). [CrossRef]
3. 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] [PubMed]
4. L. Huang and H. T. Chen, “A brief review on terahertz metamaterial perfect absorbers,” THz Sci. Technol. 6(1), 26–39 (2013).
9. B. X. Wang, G. Z. Wang, and L. L. Wang, “Design of a novel dual-band terahertz metamaterial absorber,” Plasmonics 11(2), 523–530 (2016). [CrossRef]
10. H. N. Tran, V. H. Nguyen, B. H. Nguyen, and D. L. Vu, “Light trapping and plasmonic enhancement in silicon, dye-sensitized and titania solar cells,” Adv. Nat. Sci.: Nanosci. Nanotechnol. 7, 013001 (2016).
11. B. Mulla and C. Sabah, “Multiband metamaterial absorber design based on plasmonic resonances for solar energy harvesting,” Plasmonics 11(5), 1313–1321 (2016). [CrossRef]
12. K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358, 5196 (2017).
13. N. Jiménez, V. Romero-García, V. Pagneux, and J. P. Groby, “Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems,” Sci. Rep. 7(1), 13595 (2017). [CrossRef] [PubMed]
14. Y. Zhang, Y. Li, Y. Cao, Y. Liu, and H. Zhang, “Graphene induced tunable and polarization-insensitive broadband metamaterial absorber,” Opt. Commun. 382, 281–287 (2017). [CrossRef]
17. J. Zhu, Z. Ma, W. Sun, F. Ding, Q. He, L. Zhou, and Y. Ma, “Ultra-broadband terahertz metamaterial absorber,” Appl. Phys. Lett. 105(2), 021102 (2014). [CrossRef]
18. S. Liu, H. Chen, and T. J. Cui, “A broadband terahertz absorber using multi-layer stacked bars,” Appl. Phys. Lett. 106(15), 151601 (2015). [CrossRef]
19. A. Fardoost, F. G. Vanani, and R. Safian, “Design of a multilayer graphene-based ultrawideband terahertz absorber,” IEEE Trans. NanoTechnol. 16(1), 68–74 (2017).
20. Y. Pang, J. Wang, Q. Cheng, S. Xia, X. Y. Zhou, Z. Xu, T. J. Cui, and S. Qu, “Thermally tunable water-substrate broadband metamaterial absorbers,” Appl. Phys. Lett. 110(10), 104103 (2017). [CrossRef]
21. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012). [CrossRef] [PubMed]
22. E. S. Torabi, A. Fallahi, and A. Yahaghi, “Evolutionary Optimization of Graphene-Metal Metasurfaces for Tunable Broadband Terahertz Absorption,” IEEE Trans. Antenn. Propag. 65(3), 1464–1467 (2017). [CrossRef]
23. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]
24. X. He, “Tunable terahertz graphene metamaterials,” Carbon 82, 229–237 (2015). [CrossRef]
27. C. Shi, X. He, F. Liu, F. Lin, and H. Zhang, “Investigation of graphene-supported tunable asymmetric terahertz metamaterials,” J. Opt. Soc. Am. B 35(3), 575–581 (2018). [CrossRef]
30. Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012). [CrossRef] [PubMed]
32. D. Yi, X. C. Wei, and Y. L. Xu, “Tunable Microwave Absorber Based on Patterned Graphene,” IEEE Trans. Microw. Theory Tech. 65(8), 2819–2826 (2017). [CrossRef]
33. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009). [CrossRef] [PubMed]
34. M. Faraji, M. K. Moravvej-Farshi, and L. Yousefi, “Tunable THz perfect absorber using graphene-based metamaterials,” Opt. Commun. 355, 352–355 (2015). [CrossRef]
35. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011). [CrossRef] [PubMed]
36. S. He and T. Chen, “Broadband THz absorbers with graphene-based anisotropic metamaterial films,” IEEE Trans. THz Sci. Technol. 3(6), 757–763 (2013).
37. C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011). [CrossRef] [PubMed]