A tunable metamaterial absorber is proposed in the terahertz regime. The amplitude and center frequency of the absorber can be tuned independently. Owing to the effective combination of graphene and strontium titanate (STO) in one metamaterial structure, the tunable properties of the amplitude and center frequency are implemented. The amplitude can be tuned by adjusting the chemical potential of graphene sheet, and center frequency can get a shift through temperature changes in the STO material. In a full-wave numerical simulation, the amplitude of the absorber can be tuned from approximately 100% to 35% with a fixed center frequency when chemical potential varies from 0.7 eV to 0.0 eV. The center frequency of the absorber can shift from 0.43 THz to 0.3 THz when temperature changes from 400 K to 200 K. The complex surface impedance of the graphene and permittivity of STO material in this research range are thoroughly examined, and the independently tunable mechanism of the absorber is explored by elucidating the electric field distribution. The influence of the oblique incidence of electromagnetic wave to the absorber is studied. The absorber can be scalable to the infrared and visible frequencies and demonstrates promising application on tunable sensors, filters, and photovoltaic devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The development of metamaterial perfect absorbers (MPAs) is based on metamaterials, but the disadvantage of high loss in metamaterials becomes a major advantage in MPAs. MPAs have attracted notable attention for its promising application in imaging, sensors, and solar harvesting [1–5]. The first MPAs were proposed and demonstrated at microwave frequency by Landy et al. in 2008; they achieved near-unity absorption through perfect impedance matching in free space by manipulating the permittivity and permeability of the metamaterial absorber independently . Consequently, several MPA structures have been proposed [5,7–10]; however, the practical application of MPAs remains limited because the absorption spectra of absorbers would be fixed once the structures of the absorbers are fabricated. Therefore, designing a robust tunable absorber is essential.
For the development of dynamically tunable metamaterial absorbers, several methods through which the amplitude and center frequency of an absorber can be tuned in various ways have been proposed [11–15]. Graphene, an active material with wonderful electromagnetic properties, is often used to tune absorber amplitude [7,16–18]. X. Zhang et al. used an H-shaped all-silicon optical tunable metamaterial absorber to tune the center frequency of an absorber; they demonstrated that resonance frequency presents a blue shift after pump beam excitation . A metamaterial consist of metallic split-ring resonators with embedded semiconductor InSb was reported, which enables the tuning of resonance frequency in the terahertz regime by changing the temperature of the semiconductor . Center frequency can be tuned by utilizing strontium titanate (STO) as substrate or film, whose permittivity is temperature-dependent, as demonstrated by R. Singh et al and Y. Jiao [20,21]. Although tunable absorbers have been extensively studied, only the amplitude or center frequency of the absorbers can be tuned in a single structure. A metamaterial absorber with independently tunable amplitude and center frequency has never been reported.
On the basis of previous work, a thermally and electrically tunable absorber is introduced and used in independently tuning amplitude and center frequency with the used of graphene and STO combination as one structure in the terahertz regime. In the proposed absorber, the amplitude tunable characteristic is achieved by adjusting the chemical potential of graphene sheet from 0.0 eV to 0.7 eV, and center frequency is tuned by changing the temperature of STO material from 400 K to 200 K. The results of full-wave numerical simulation show that the amplitude of the absorber can be tuned from approximately 100% to 35% with a fixed center frequency and center frequency can shift from 0.43 THz to 0.3 THz at nearly 100% peak absorption. The complex surface impedance of graphene and permittivity of the STO material are calculated in detail, and the tunable mechanism is explored by examining electric field distributions under different temperatures and chemical potentials.
2. Design and simulation
The designed metamaterial absorber is illustrated in Fig. 1. Figure 1(b) shows the four-layer unit cell of the metamaterial absorber. The structure from bottom to top is the metallic background layer, the dielectric layer of polymer dielectric layer, the strontium titanate (STO) material, and the patterned graphene layer. Figure 1(a) shows the top view of the unit cell. The length (py) and width (px) of the rectangle are 96 and 48 µm, respectively. The long axis (b) of the elliptical graphene pattern is 60 µm, and the short axis (a) is 30 µm. The schematic view is provided in Fig. 1(c). The terahertz wave is incident along the z-axis. In this structure, the background layer is made of gold with conductivity of , thickness (m) of 0.2 µm. A low loss TOPAS polymer is selected as one of the dielectric layer with permittivity (ε) of 2.35, and thickness (h1) 26 µm. Graphene and STO materials (h2 = 2 µm) have been thoroughly studied and accurately modeled by using calculated parameters.
In graphene materials, electrical conductivity is composed of intraband and interband contributions, which are expressed as. In the terahertz range, the contribution of the interband may be negligible compared with the intraband because of the photo energy,. Here, the intraband contribution can be calculated through the following equation :
In STO materials, complex relative permittivity is temperature dependent and can be expressed as follows [23,24]:
In the modeling and simulation, the CST software based on the finite integration algorithm is used with the frequency range set from 0.1 THz to 0.8 THz. At boundary conditions, shown in Fig. 1, the x-axis and y-axis are along the length and width of the rectangle structure, respectively, and are both set as a unit cell boundary. The two sides of z-axis are Floquet ports (18 modes), where terahertz wave vector occurs along the z-axis from top to bottom. For the characterization of the single-layer graphene material, an equivalent 2D surface impedance layer is adopted for modeling, which is built from a closed-elliptic curve extruding to the surface. Besides, initial conditions of the simulation are set as follows: 0.7 eV chemical potential, 0.1 ps relation time, and 400 K absolute temperature.
The designed MPAs can be treated as an effective medium because the structure size is considerably smaller than the wavelength of the incident terahertz wave . In the microwave studio, reflection and transmission are obtained from S parameters, where and , and the absorption can be calculated by
3. Results and discussion
To study the absorption spectrum of the metamaterial absorber, a full-wave numerical simulation is performed. Under initial conditions, reflection and absorption spectrum under normal incidence are represented in Fig. 2. A deep at 0.43 THz in the reflection curve marked as blue is observed, whereas the corresponding near-unity absorption spectrum is marked as red.
First, examining the tunable characteristics of the absorber is the focus of the study. The tunable property of the center frequency is achieved by employing the active STO material, whose permittivity is temperature dependent. The active material is simulated by calculating the temperature-dependent permittivity of STO material. As shown in Fig. 3(a), the frequency range of the study is from 0.1 THz to 0.8 THz. This range is consistent with the range of the absorption spectrum. The real part of the permittivity of the STO material is represented by different color curves as temperature changes. In these curves, the permittivity of STO material increases sharply at low temperatures. The value increases from 216 to 479 when the temperature is reduced from 400 K to 200 K with a step-width of 50 K. Figure 3(b) shows the relationship between STO material loss, temperature, and frequency. STO material loss increases with rising frequency but decreases with increasing temperature.
When the calculated permittivity of STO material is applied to the simulation, the center frequency tuning spectrum of the absorber can be obtained by changing the temperature of STO material. As shown in Fig. 4, the center frequency shifts from 0.43 THz to 0.3 THz when temperature changes from 400 K to 200 K, which are marked as red and cyan curves, respectively. The peak absorption rate is maintained above 99% when the frequency shifts.
The phase of the reflected wave as a function of frequency and temperature is plotted in Fig. 5, and the phases under different temperatures are marked by curves with diverse colors. It can be seen clearly that the phase changes obviously with different temperatures, the frequency point of phase reversal increases from 0.3 THz to 0.43 THz when the temperature varies from 200 K to 400 K. The phase change phenomenon agrees well with the phenomenon of frequency offset in Fig. 4.
The superior electromagnetic properties of graphene material are utilized for the application of the amplitude tunable characteristics of the absorber. The surface complex impedance of graphene sheet is largely related to its chemical potential, which can be adjusted through the application of a bias voltage. The wide range of Fermi energy of graphene sheet could be modulated by ion-gel top gating method [16,26,27]. Here, the complex surface impedance is presented because the equivalent 2D surface impedance model is adopted to simulate graphene, and the complex surface impedance of graphene under different temperatures and chemical potentials are calculated respectively. Firstly, the complex impedance of graphene sheet changing with different chemical potentialsis represented. As shown in Fig. 6(a) and 6(b), the real part and imaginary part of the complex surface impedance are plotted separately. Both the real part and imaginary part decreases sharply when the chemical potential increases from 0.0 eV to 0.7 eV, where maximum of the real part decreases from 1880 Ω to 120 Ω and the imaginary part changes from 110 Ω to 4 Ω. In the frequency ranging from 0.1 THz to 0.8 THz, the frequency increase shows minimal effect on the real part of complex surface impedance, while the values of imaginary part decrease significantly with increasing frequencies. Secondly, the relationship between the complex surface impedance and absolute temperature is illustrated in Fig. 6(c) and 6(d). It can be seen from Fig. 6(c), the real part of complex surface impedance doubles when the temperature is reduced from 400 K to 200 K, which is represented by the green and black dotted lines, respectively. However, at a fixed temperature, the value is almost constant. As depicted in Fig. 6(d), the maximum of imaginary part increases from 110 Ω to 208 Ω when the temperature varies from 400K to 200K, and the values also decrease with a higher frequency. It is worth to note that the effect of temperature on the surface impedance of graphene sheet is very weak when the chemical potential is high.
The amplitude tunable spectrum of the absorber can be obtained by using the calculation results of surface complex impedance. As shown in Fig. 7, the absorption amplitude of the absorber significantly changes when the chemical potential of graphene sheet is adjusted from 0.7 eV to 0.0 eV, and the absorption spectra are represented in various colors of the curves. The amplitude of absorption can be tuned from approximately 100% (marked as red, 0.7 eV) to 35% (marked as black, 0.0 eV), whereas center frequency is nearly unchanged.
The tunable mechanism is further explored by investigating the electric field distributions of the structure under different temperatures and chemical potentials. The center frequency of the absorber can be tuned by regulating the temperature. As shown in Fig. 8, the temperature is changed from 400 K to 200 K with a step-width 50 K, and the corresponding electric field distributions at different peak frequency points (0.43 THz, 0.4 THz, 0.37 THz, 0.34 THz and 0.3 THz) are provided one by one from left to right. Clearly, the electric field distributions are mainly concentrated at the upper and lower ends of the graphene pattern in all five frequencies or temperatures. This is mainly due to the excitation of vertical field of incident terahertz wave, and the resonance mode in the structure is not changed with different temperatures. Here, the graphene pattern layer functions as a conductor that works like an electric dipole absorbing the incident electric field.
Then, the electric distribution of the absorber at the resonant frequency of 0.43 THz under different chemical potential of graphene is illustrated, where temperature is set at 400 K. As shown in Fig. 9, the resonance gradually weakens when graphene chemical potential decreases from 0.7 eV to 0.0 eV due to the increase in the complex surface impedance of graphene. This result is consistent with the above discussions on graphene. Comparing Fig. 8 and Fig. 9, it can be found that the chemical potential of graphene owns a greater effect on the resonance than temperatures, which agrees well with the theoretical study of graphene complex impedance above.
The absorption spectra under oblique incidence in TE and TM modes are examined, which are shown as absorption contour maps in Fig. 10. Seemingly, the absorber sustains over 75% peak absorption when the incident angle is below 70° in both TE and TM modes, as depicted in Fig. 10(a) and 10(b), respectively. However, as the oblique incident angle increases, center frequency remains nearly unchanged in TE, whereas a blue shift from 0.43 THz to 0.55 THz occurs in TM mode. These results are mainly due to the changes in zero-reflection conditions under oblique incidences, the reflection coefficients for the TE and TM modes vary with the incident angels independently .
We designed and demonstrated an active tunable metamaterial absorber in the terahertz regime, whose amplitude and center frequency can be independently tuned based on graphene and STO material layers. Through a detailed study of active materials, the complex surface impedance of graphene under different chemical potentials and the permittivity of STO material under different temperatures were evaluated and used in the calculations. According to the full-wave numerical simulation, the absorber has an approximate 100% peak absorption at 0.43 THz, primary temperature of 400K, and chemical potential of 0.7 eV. On the tunable characteristics of the absorber, absorber center frequency can be tuned from 0.43 THz to 0.3 THz by changing the temperature from 400 K to 200 K, and peak absorption can be maintained above 99%. The amplitude of the absorber can be tuned from around 100% to 35% by adjusting the chemical potential of graphene from 0.0 eV to 0.7 eV, and the center frequencies is kept nearly unchanged. The tunable mechanism is explored by examining the electric field distribution of the structure at respective peak frequencies and different graphene chemical potentials. The proposed absorber can be scalable to infrared and visible frequencies and has promising applications in imaging, sensors, and solar harvesting.
National Natural Science Foundation of China (NSFC) (51777023); and China Postdoctoral Science Foundation (CPSF) (2017M620411).
1. Q. Liang, W. Yu, W. Zhao, T. Wang, J. Zhao, H. Zhang, and S. Tao, “Numerical study of the meta-nanopyramid array as efficient solar energy absorber,” Opt. Mater. Express 3(8), 1187–1196 (2013). [CrossRef]
2. X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011). [CrossRef] [PubMed]
4. K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2(1), 517 (2011). [CrossRef] [PubMed]
5. J. Y. Suen, K. Fan, W. J. Padilla, and X. Liu, “All-dielectric metasurface absorbers for uncooled terahertz imaging,” Optica 4(6), 601–604 (2017). [CrossRef]
7. H. Li, C. Ji, Y. Ren, J. Hu, M. Qin, and L. Wang, “Investigation of multiband plasmonic metamaterial perfect absorbers based on graphene ribbons by the phase-coupled method,” Carbon 141, 481–487 (2019). [CrossRef]
9. A. Li, X. Zhao, G. Duan, S. Anderson, and X. Zhang, “Diatom Frustule‐Inspired Metamaterial Absorbers: The Effect of Hierarchical Pattern Arrays,” Adv. Funct. Mater. 29(22), 1970151 (2019). [CrossRef]
11. L. Ye, Y. Chen, G. Cai, N. Liu, J. Zhu, Z. Song, and Q. H. Liu, “Broadband absorber with periodically sinusoidally-patterned graphene layer in terahertz range,” Opt. Express 25(10), 11223–11232 (2017). [CrossRef] [PubMed]
12. X. Zhao, Y. Wang, J. Schalch, G. Duan, K. Cremin, J. Zhang, C. Chen, R. D. Averitt, and X. Zhang, “Optically Modulated Ultra-Broadband All-Silicon Metamaterial Terahertz Absorbers,” ACS Photonics 6(4), 830–837 (2019). [CrossRef]
13. J. Schalch, G. Duan, X. Zhao, X. Zhang, and R. D. Averitt, “Terahertz metamaterial perfect absorber with continuously tunable air spacer layer,” Appl. Phys. Lett. 113(6), 61113 (2018). [CrossRef]
14. H. Kocer, S. Butun, B. Banar, K. Wang, S. Tongay, J. Wu, and K. Aydin, “Thermal tuning of infrared resonant absorbers based on hybrid gold-VO2 nanostructures,” Appl. Phys. Lett. 106(16), 161104 (2015). [CrossRef]
16. 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]
17. 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] [PubMed]
19. J. Zhu, J. Han, Z. Tian, J. Gu, Z. Chen, and W. Zhang, “Thermal broadband tunable terahertz metamaterials,” Opt. Commun. 284(12), 3129–3133 (2011). [CrossRef]
20. Y. Zhao, B. Li, C. Lan, K. Bi, and Z. Qu, “Tunable silicon-based all-dielectric metamaterials with strontium titanate thin film in terahertz range,” Opt. Express 25(18), 22158–22163 (2017). [CrossRef] [PubMed]
21. R. Singh, A. K. Azad, Q. X. Jia, A. J. Taylor, and H. T. Chen, “Thermal tunability in terahertz metamaterials fabricated on strontium titanate single-crystal substrates,” Opt. Lett. 36(7), 1230–1232 (2011). [CrossRef] [PubMed]
22. 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]
23. P. Kužel and F. Kadlec, “Tunable structures and modulators for THz light,” C. R. Phys. 9(2), 197–214 (2008). [CrossRef]
24. H. Nĕmec, P. Kuzel, L. Duvillaret, A. Pashkin, M. Dressel, and M. T. Sebastian, “Highly tunable photonic crystal filter for the terahertz range,” Opt. Lett. 30(5), 549–551 (2005). [CrossRef] [PubMed]
25. 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 Condens. Matter Mater. Phys. 65(19), 195104 (2002). [CrossRef]
26. Z. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. An, Y. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 41027 (2015). [CrossRef]
27. S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012). [CrossRef] [PubMed]
28. T. Wanghuang, W. Chen, Y. Huang, and G. Wen, “Analysis of metamaterial absorber in normal and oblique incidence by using interference theory,” AIP Adv. 3(10), 102118 (2013). [CrossRef]