Open Access
Add to BibSonomyAbstract
In this paper, we numerically demonstrate that an actively controllable electromagnetic induced transparency (EIT) behavior can be obtained in a hybrid terahertz metamaterial. A unit cell of the hybrid metamaterial consists of a metallic split-ring resonator surrounded by a concentric graphene close-ring resonator, serving as superradiant and subradiant modes, respectively. The EIT-like effect results from the destructive interference caused by strong near field coupling between superradiant and subradiant mode resonators. A classical two-particle model is employed to theoretically study EIT-like behavior in the hybrid metamaterial, and the analytic results agree excellently with our numerical results. More importantly, by tuning Fermi energy based on electrical doping, the hybrid metamaterial can realize switching, modulation, and slow-light capabilities. Therefore, these results would exhibit potential applications in light storage and compact devices.
© 2016 Optical Society of America
1. Introduction
Electromagnetically induced transparency (EIT), caused by quantum destructive interference between two different excitation pathways, was first observed in a three level atomic system [1]. Recently, the classical oscillator systems can also realize the analogues of EIT effect. Moreover, this EIT-like effect originates from the interference of normal modes rather than from quantum interference [2,3]. Particularly, the EIT-like behavior in metamaterials attracts considerable attentions due to its outstandingly potential applications in slow-light devices [4,5], sensing [6], and quantum information storages [7]. Currently, the analogues of EIT effect in metamaterials are realized through two main approaches: the trapped mode resonance in asymmetric structure [8] and the coupling between bright and dark modes [9]. With the development of metamaterials, different EIT-like metamaterials have been proposed and experimentally demonstrated from microwave [10] to terahertz [11,12], near-infrared [13], visible [14], and even ultraviolet [15] regions. Unfortunately, most of the reported metamaterial-based EIT windows are inactive manipulation, which hinders their practical applications.
To actively control the EIT-like behavior, currently, different approaches have been employed to realize tunable EIT window and the associated group velocity. For example, thermal control of the EIT-like transmission was demonstrated in superconducting metamaterials [16,17]. Optical tuning of an EIT-like metamaterial integrating with photoconductive material was reported [18,19]. Recently, Micro-Electro-Mechanical Systems (MEMS) technology was also proposed to achieve controllability of EIT window [20,21]. However, those tunable methods depend highly on the nonlinear properties of active materials, which inevitably results in low modulation depth and range. In addition, the possibility and reliability for massive fabrication are still limited by complex structures and processes. Therefore, they are currently available only for laboratory experiments.
Since discovered in 2004, graphene has attracted considerable attention due to its excellent properties [22]. Recently, different tunable graphene-based metamaterials are designed and demonstrated by patterning or stacking graphene [23–27]. In this paper, we present an active control of EIT window in a hybrid terahertz metamaterial. Unit cell structure of the proposed hybrid metamaterial is composed of a graphene close-ring resonator and a metal split-ring resonator. The EIT window results from the destructive interference caused by strong near field coupling between two resonators. A classical two-particle model is also introduced to describe EIT-like effect in hybrid metamaterial. Moreover, further investigations find that the EIT window and the associated group delay can be actively tuned by changing Fermi energy of graphene resonator. Therefore, the proposed hybrid metamaterial with tunable EIT window response exhibits the potential applications in light storage and compact devices.
2. Design and simulation of EIT structure
In this paper, a hybrid terahertz metamaterial is designed to actively control EIT-like response, as shown in Fig. 1. Figure 1(a) shows schematic of the proposed hybrid metamaterial, and the unit cell is composed of a metallic split-ring resonator (MSRR) surrounded by a concentric graphene close-ring resonator (GCRR) (as shown in Fig. 1(b)). Here, all GCRR unit cells in the hybrid structure are electrically connected by the graphene wires to act as a top gate. Moreover, these structures are patterned on a light doped silicon substrate covered with a thin SiO2 layer (as shown in Fig. 1(c)). Within this hybrid structure, the GCRR structure serves as a superradiant mode, while the MSRR as a subradiant mode. If the resonance frequencies for MSRR and GCRR structures are very close to a particular frequency, the strong coupling between MSRR and GCRR structures may be established according to the coupling-mode theory [28] As a result, the destructive interference between two strongly coupled resonators causes the EIT-like behavior. More importantly, the EIT-like response can be actively tuned by electrical doping graphene, compared with the previously reported metallic EIT-like metamaterials [16–19].
Fig. 1 EIT structure based on the hybrid terahertz metamaterial: (a) schematic of hybrid terahertz metamaterial, (b) close-up view of unit cell, and (c) cross-sectional view of unit cell.
In order to explore EIT-like response of the hybrid metamaterial, numerical calculations based on finite difference time domain (FDTD) method are performed, where periodic boundary conditions are used for a unit cell in x- and y-directions, and z plane has a perfectly matched layer boundary condition. The plane wave polarizing along x-direction is normally incident to the structure surface along z-direction, as shown in Fig. 1(a). In our numerical calculations, the structural parameters of unit cell are as following: a = 100μm, b = 78μm, c = 30μm, d = 10μm, w1 = 5μm, w2 = 3μm, and g = 2μm, while the thicknesses of the SiO2 layer and silicon substrate are 300nm and 300um, respectively. In addition, the relative permittivities of the SiO2 and Si substrate are taken as 3.9 and 11.7 respectively, while the permittivity of metal gold is described by the Drude model with a plasmon frequency ωp of 1.366 × 1016rad/s and a collision frequency vc of 1.225 × 1014Hz. To simplify numerical calculations, we assumed the graphene to be an effective medium with thickness of tg = 0.34nm and relative complex permittivity of εr(ω) = 1 + jσ(ω)/(ωε0tg), in which the conductivity σ(ω) can be described as [29]:
Where ε0 is the permittivity of vacuum, ω is the frequency of incident wave, EF is the Fermi energy, Г is the scattering rate (Г = 2.4 THz), T is the temperature of the environment (T = 300 K), e is the charge of an electron, kB is the Boltzmann’s constant, ħ = h / 2π is the reduced Planck’s constant. When a bias voltage Vg is applied between the top and back gates (as shown in Fig. 1(c)), the carrier density and Fermi energy level in graphene can be dynamically controlled by electrical doping to tune the conductivity of graphene, as a result, actively controlling the propagation of terahertz wave.3. Results and discussions
To clarify underlying forming process of the EIT-like response, the transmission spectra and field distributions of three different structures, which are the isolated MSRR array, the isolated GCRR array, and their corresponding hybrid structure array (EIT structure), are calculated respectively, as shown in Fig. 2 and Fig. 3. For the isolated MSRR array, a narrow resonance with Q factor of 20.9 at 0.523THz is directly excited when the polarization of the excitation field is perpendicular to the gap of MSRR (as shown in Fig. 2(a)). At resonance dip, moreover, the induced surface currents on MSRR structure are the clockwise distributions, while the electric fields are mainly concentrated at the gap region (as shown in Figs. 2(b) and 2(c)). Therefore, the field behaviors in MSRR are a typical LC resonance [30]. For the isolated GCRR array with EF = 0.2eV, in contrast, a broad resonance with Q factor of 1.95 at 0.469THz is excited due to strong coupling interaction with incident wave, as shown in Fig. 2(d). Moreover, the surface currents on GCRR structure oscillate symmetrically in two arms parallel to the excited electric field, while the electric fields are focused at two sides of both arms perpendicular to the excited electric field, which is similar to dipole resonance (as shown in Figs. 2(e) and 2(f)) [31]. In addition, we also note that the Q factor of MSRR structure is about one order of magnitude larger than that of GCRR structure. Thus, the GCRR element with broad dipole resonance acts as superradiant mode that couples strongly to the radiation field, while the MSRR element with narrow LC resonance behaves as subradiant mode that couples only weakly to the radiation field.
Fig. 2 Calculated transmission spectra and field distributions of two isolated resonators: (a) LC resonance of MSRR, (b) surface currents on MSRR structure, (c) electric fields at the gap of MSRR structure, (d) dipole resonance of GCRR, (e) surface currents on GSRR structure, and (f) electric fields of GSRR structure.
Fig. 3 Calculated transmission spectrum and surface currents of the hybrid structure: (a) transmission spectrum, (b) 0.483THz, (c) 0.514THz, and (d) 0.564THz.
Next, when the GCRR and MSRR structures are integrated together to form a hybrid metamaterial structure, a sharp transmission peak between two transmission dips (0.483 THz and 0.564 THz) is observed at the frequency 0.514 THz (as shown in Fig. 3(a)). This phenomenon is well-known as the metamaterial-based EIT-like effect [32,33]. To understand physical nature of the EIT-like behavior in hybrid metamaterial, the surface currents at two resonance dips and the transparency peak are calculated. For the transmission dips, the surface currents are simultaneously excited in the GCRR and MSRR structures, which indicates the hybridization coupling model through near field coupling of the individual resonators (as shown in Fig. 3(b) and 3(d)). Here, the surface currents on two arms of the MSRR perpendicular to the excited electric field are antiparellel and cancel each other out, giving rise to nearly zero net current, while net currents on the arms of the GCRR and the MSRR parallel to the excited electric field are antiparallel and parallel to each other, respectively. Thus, the calculated current profiles associated with the two transmission dips (Fig. 3a) evidently reveal that the lower frequency dip stems from a bonding mode, and the higher frequency dip an antibonding mode, as observed in the previous reports [34,35]. For the transparency peak, however, the surface currents are localized within the MSRR structure of the coupled system, while the surface currents on the GCRR are completely suppressed due to the interaction with the constituent MSRR structure (as shown in Fig. 3(c)). As a result, the destructive interference between two resonators leads to a high transmission peak, as demonstrated in previous result [17].
As is well known, a remarkable characteristic of EIT-like response is strong dispersion in transparent window region. As expected, the transmission phase of our hybrid structure appears a sharp dispersion in the transparency window, in which a steep slope is obtained, as shown in gray region of Fig. 4(a). Meanwhile, we also notice that the transmission phase has two frequency segments due to anomalous and normal phase dispersions. Moreover, the strong normal phase dispersion can result in a large group delay enhancement at the transmission peak, as a result, increasing the traversing time of light passing through the entire structure [36]. This property indicates that our structure is very extremely attractive for slow-light applications [17]. According to Refs [37]. and [38], the group delay is calculated by the expression: τg = -dφ/dω where φ and ω = 2πf are the phase shift and frequency of transmission spectrum, respectively.
Figure 4(b) displays the calculated group delay of the proposed hybrid metamaterial. We find that the terahertz transmission experiences a group delay of about τg = 12.1ps in the sharp dispersion region (grey region in Fig. 4(b)). This indicates that a light pulse with a central frequency situated in the transparency window will be considerably slowed down when propagating through the hybrid metamaterial. Moreover, the achieved group delay in our structure is larger than the previously reported numerical results in the graphene complementary metamaterial [39,40]. Interestingly, we also obtained the negative group delay corresponding to fast light effect at nearby region of the transparency window, as experimentally observed in atomic EIT systems [41,42]. This phenomenon indicates that at nearby region of transparency window, this hybrid metamaterial completes the transition from slow to fast light, as a result, τg becomes negative (τg < 0). After this transition, the advancement of the time pulse increases until it reaches its maximum value (more negative τg). Beyond this point, τg decreases gradually and is closer to zero [43].
To elucidate underlying mechanism of EIT-like effect in the metamaterial, a widely used classical two-particle model is adopted to theoretically reveal the coupling characteristics between two resonators with varied incident field excitations [44]. In our structure, the GCRR and MSRR elements can be considered as both particles (superradiant and subradiant modes), and the coupling behavior between two modes can be analytically described by the following model [45]:
where , and , and represent the amplitudes, damping rates and effective masses of the superradiant and subradiant modes, respectively. and are resonance frequencies of the superradiant and subradiant modes, respectively. k and δ are the coupling coefficient and detuning resonant frequency between two modes respectively, while g1 and g2 are the geometric parameters indicating the coupling strength of superradiant and subradiant modes with incident field E0.To simplify the calculation process, g2 is assumed as zero due to larger Q-factor and weak interaction with incident field. Thus, the transmission coefficient of incident terahertz wave passing through hybrid metamaterial structure is described by the following equation [45,46]:
where is the wavelength in vacuum, while is the effective susceptibility of the EIT-like structure, which is obtained by Eq. (4)Here, P is the effective polarization of the EIT-like structure.According to Eq. (3), the analytical fit to the simulated transmission amplitudes is implemented. Figure 5 shows the fitted curves based on the analytic models for different Fermi energy. Obviously, the fitted curves agree extremely with the numerically simulated curves except for slight deviations caused either by a weak coupling of subradiant mode not considered in Eq. (3) or by the effects related to the periodicity of hybrid metamaterial [47], and this result demonstrates the validity of the analytical model. For the fitted analytical curves with different Fermi energy EF, the fitting parameters are listed in Tab. 1. We notice that for different Fermi energy, the damping rate of the superradiant mode is larger than of the subradiant mode, which results from the obviously different radiation losses of two particles. Interestingly, the damping rate doses not exhibit significant change when the Fermi energy increases from 0.05eV to 0.5eV, while the damping rate obviously increases from 0.043 to 0.245. These results indicate that the increase in Fermi energy enhances the losses of the subradiant resonator, namely suppressing the subradiant mode resonance, which hampers the destructive interference between the supperradiant and subradiant modes. As a result, the amplitude of the EIT peak is actively tuned.
Fig. 5 Comparison of the simulated transmission curve and the calculated transmission curve by two-particle model for different Fermi energy.
Table 1. Fitting parameters of the analytical models for different Fermi energy
Compared with the traditional EIT-like structure, the most obvious advantage of our hybrid metamaterial is active manipulation of EIT window by tuning Fermi energy based on electrical doping, which is highly desirable for the compact devices [48,49]. In order to examine tuning capacities of our hybrid structure, we further analyze the transmissions and absorptions of the hybrid metamaterial with different EF. 6. Figure 6(a) displays the transmission spectra of the hybrid structure with different EF. As expected, the amplitude of transparency window decreases gradually with Fermi energy of GCRR structure, as a result, an actively controllable transparency window is obtained in the hybrid structure. This tunable capacity can be attributed to change in resonance frequency of GCRR structure, in which the resonance frequency can be written as [39,40].
Based on this tunable characteristic, we can realize the switching and modulation devices in the interested frequency range. For example, the transmission amplitudes of EIT-like structure at 0.494THz are 0.84 and 0.06 when Fermi energy of GCRR structure are EF = 0.05eV and EF = 0.5eV, respectively (dash line in Fig. 6(a)). This result indicates that the transmission could be switched between 84% and 6% by changing Fermi energy obtained by tuning gate voltage. In addition, the absorptions of different Fermi energy are also calculated by A = 1-T-R, where T and R are the transmission and reflection coefficients. We notice that the absorption increases gradually with Fermi energy of GCRR structure, as shown in Fig. 6(b). For example, the peak absorption achieved is 53% for EF = 0.5eV, and shows an enhancement factor of 3.3 times compared with corresponding peak absorption of EF = 0.05eV. Moreover, the absorption is confined to a narrow line width spectral region, which may be interesting for applications in sensing [50].
Next, we further investigate the influence of Fermi energy on slow light effect, as shown in Fig. 7. As the Fermi energy increases from 0.05eV to 0.5eV, the transmission phase experiences a strong dispersion change, moreover, the phase dispersion becomes more and more obvious. Compare to all other Fermi energy, the steepest transmission phase slope is obtained as EF = 0.5eV, which indicates a large group delay [36]. As expected, for EF = 0.05eV, the group delay is 5.1ps, while as EF = 0.5eV, the group delay is 13.5ps. Moreover, the group delay increases gradually with the Fermi energy, shown in Fig. 7(b).
Fig. 7 Slow light effect of hybrid metamaterial with different Fermi energy: (a) transmission phase and (b) group delay.
For the practical application in slow light device, however, only talking about group delay is meaningless. Meanwhile, we should also consider the bandwidth of group delay. Generally, the delay-bandwidth product (DBP) is used to describe the highest slow light capacity range that the device potentially provides [51,52]. For our hybrid metamaterial with different Fermi energy, the group delay, DBP, Q-factor and amplitude of the corresponding EIT peak are shown in Tab. 2. We find that the group delay, BDP and corresponding Q-factor increase gradually with Fermi energy, while the corresponding amplitude of the EIT peak decreases. For example, for Fermi energy of 0.5eV, the hybrid metamaterial displays the maximum group delay, DBP and Q-factor as well as the minimum peak amplitude compared to all other Fermi energy, and their respective values are 13.5ps, 0.446, 15.7 and 0.443, respectively. Therefore, by tuning Fermi energy based on the electrical gate doping, the carrier concentration and corresponding conductivity of graphene can be substantially modulated. Thus, the near field coupling strength between two resonators is also adjusted, as a result, the EIT-like behavior in the hybrid structure can be actively controlled [39,40].
Table 2. Calculated group delay, DBP, Q-factor, and amplitude of hybrid metamaterial with different Fermi energy
To further investigate interactions between two resonators, next, we will theoretically analyze the influence of Fermi energy on the near field coupling between two resonators. Figure 8 shows the fitting values for k and δ as function of Fermi energy of graphene. We observed that the coupling coefficient k decreases gradually as increasing in Fermi energy. This indicates that the coupling strength between two resonators is weakened, as a result, leading to a narrow EIT-like window, and vice versa. Moreover, these results obtained by fitting are consistent with the simulated results shown in Fig. 6(a). In addition, we also notice that with Fermi energy increasing, the detuning resonance frequency δ gradually tends to a saturation value due to resonance frequency shift of GCRR structure.
4. Conclusions
In conclusion, we have numerically demonstrated an actively controllable EIT-like response in a hybrid metamaterial composed of MSRR surrounded by concentric GCRR array. Strong near field coupling between MSRR and GCRR elements leads to a destructive interference of the scattered fields, as a result, giving rise to an EIT-like phenomenon. A classical two-particle model is introduced to describe the EIT-like effect in hybrid metamaterial, and the model shows excellent agreement with the numerical simulation. Moreover, tuning Fermi energy obtained by electrical doping, the hybrid metamaterial exhibits the capabilities of switching, modulation, and slowing down the terahertz pulse. Therefore, this kind of hybrid metamaterials would exhibit potential applications in light storage and compact devices.
Funding
National Natural Science Foundation of China (51575149 and 51402075); Heilongjiang Province Natural Science Foundation of China (F201309); the Postdoctoral Science-Research Developmental Foundation of Heilongjiang Province (LBH-Q11082); the Youth Academic Backbone Support Plan of Heilongjiang Province Ordinary College (1253G026); Special Funds of Harbin Innovation Talents in Science and Technology Research (2014RFQXJ031); Science Funds for the Young Innovative Talents of HUST (2011F04).
References and links
1. K. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991). [CrossRef] [PubMed]
2. A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011). [CrossRef] [PubMed]
3. L. Dai, Y. Liu, and C. Jiang, “Plasmonic-dielectric compound grating with high group-index and transmission,” Opt. Express 19(2), 1461–1469 (2011). [CrossRef] [PubMed]
4. L. Zhu, F. Y. Meng, J. H. Fu, Q. Wu, and J. Hua, “Multi-band slow light metamaterial,” Opt. Express 20(4), 4494–4502 (2012). [CrossRef] [PubMed]
5. V. Kravtsov, J. M. Atkin, and M. B. Raschke, “Group delay and dispersion in adiabatic plasmonic nanofocusing,” Opt. Lett. 38(8), 1322–1324 (2013). [CrossRef] [PubMed]
6. R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014). [CrossRef]
7. R. Taubert, M. Hentschel, J. Kästel, and H. Giessen, “Classical analog of electromagnetically induced absorption in plasmonics,” Nano Lett. 12(3), 1367–1371 (2012). [CrossRef] [PubMed]
8. X. R. Jin, J. Park, H. Zheng, S. Lee, Y. Lee, J. Y. Rhee, K. W. Kim, H. S. Cheong, and W. H. Jang, “Highly-dispersive transparency at optical frequencies in planar metamaterials based on two-bright-mode coupling,” Opt. Express 19(22), 21652–21657 (2011). [CrossRef] [PubMed]
9. F. Y. Meng, F. Zhang, K. Zhang, Q. Wu, J.-Y. Kim, J.-J. Choi, B. Lee, and J.-C. Lee, “Low-loss magnetic metamaterial based on analog of electromagnetically induced transparency,” IEEE Trans. Magn. 47(10), 3347–3350 (2011). [CrossRef]
10. P. Tassin, L. Zhang, R. Zhao, A. Jain, T. Koschny, and C. M. Soukoulis, “Electromagnetically induced transparency and absorption in metamaterials: the radiating two-oscillator model and its experimental confirmation,” Phys. Rev. Lett. 109(18), 187401 (2012). [CrossRef] [PubMed]
11. L. Qin, K. Zhang, R. W. Peng, X. Xiong, W. Zhang, X. R. Huang, and M. Wang, “Optical-magnetism-induced transparency in a metamaterial,” Phys. Rev. B 87(12), 125136 (2013). [CrossRef]
12. Z. G. Dong, H. Liu, M. X. Xu, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Plasmonically induced transparent magnetic resonance in a metallic metamaterial composed of asymmetric double bars,” Opt. Express 18(17), 18229–18234 (2010). [CrossRef] [PubMed]
13. Z. Ye, S. Zhang, Y. Wang, Y. Park, T. Zentgraf, G. Bartal, X. Yin, and X. Zhang, “Mapping the near-field dynamics in plasmon-induced transparency,” Phys. Rev. B 86(15), 155148 (2012). [CrossRef]
14. 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]
15. C. Argyropoulos, F. Monticone, G. D’Aguanno, and A. Alù, “Plasmonic nanoparticles and metasurfaces to realize Fano spectra at ultraviolet wavelengths,” Appl. Phys. Lett. 103(14), 143113 (2013). [CrossRef]
16. C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107(4), 043901 (2011). [CrossRef] [PubMed]
17. W. Cao, R. Singh, C. H. Zhang, J. G. Han, M. Tonouchi, and W. L. Zhang, “Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013). [CrossRef]
18. J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012). [CrossRef] [PubMed]
19. X. Su, C. Ouyang, N. Xu, S. Tan, J. Gu, Z. Tian, R. Singh, S. Zhang, F. Yan, J. Han, and W. Zhang, “Dynamic mode coupling in terahertz metamaterials,” Sci. Rep. 5, 10823 (2015). [CrossRef] [PubMed]
20. P. Pitchappa, M. Manjappa, C. P. Ho, R. Singh, N. Singh, and C. K. Lee, “Active control of electromagnetically induced transparency analog in terahertz MEMS metamaterial,” Adv. Optical Mater. 4(4), 541–547 (2016). [CrossRef]
21. X. J. He, Q. X. Ma, P. Jia, L. Wang, T. Y. Li, F. M. Wu, and J. X. Jiang, “Dynamic manipulation of electromagnetically induced transparency with MEMS metamaterials,” Integr. Ferroelectr. 161(1), 85–91 (2015). [CrossRef]
22. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef] [PubMed]
23. Y. Zou, P. Tassin, T. Koschny, and C. M. Soukoulis, “Interaction between graphene and metamaterials: split rings vs. wire pairs,” Opt. Express 20(11), 12198–12204 (2012). [CrossRef] [PubMed]
24. Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, and D. Tang, “Critical coupling with graphene-based hyperbolic metamaterials,” Sci. Rep. 4, 5483 (2014). [CrossRef] [PubMed]
25. Y. Fan, Z. Liu, F. Zhang, Q. Zhao, Z. Wei, Q. Fu, J. Li, C. Gu, and H. Li, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015). [CrossRef] [PubMed]
26. Y. C. Fan, N. H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2(1), 151–156 (2015). [CrossRef]
27. H. Cheng, S. Q. Chen, P. Yu, W. W. Liu, Z. C. Li, J. X. Li, B. Y. Xie, and J. G. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3(12), 1744–1749 (2015). [CrossRef]
28. Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express 19(9), 8912–8919 (2011). [CrossRef] [PubMed]
29. B. Vasic, M. M. Jakovljevic, G. Isic, and R. Gajic, “Tunable metamaterials based on split ring resonators and doped graphene,” Appl. Phys. Lett. 103(1), 011102 (2013). [CrossRef]
30. 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]
31. B. Kanté, Y. S. Park, K. O’Brien, D. Shuldman, N. D. Lanzillotti-Kimura, Z. Jing Wong, X. Yin, and X. Zhang, “Symmetry breaking and optical negative index of closed nanorings,” Nat. Commun. 3, 1180 (2012). [CrossRef] [PubMed]
32. 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] [PubMed]
33. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Planar designs for electromagnetically induced transparency in metamaterials,” Opt. Express 17(7), 5595–5605 (2009). [CrossRef] [PubMed]
34. C. Y. Chen, I. W. Un, N. H. Tai, and T. J. Yen, “Asymmetric coupling between subradiant and superradiant plasmonic resonances and its enhanced sensing performance,” Opt. Express 17(17), 15372–15380 (2009). [CrossRef] [PubMed]
35. P. Q. Liu, I. J. Luxmoore, S. A. Mikhailov, N. A. Savostianova, F. Valmorra, J. Faist, and G. R. Nash, “Highly tunable hybrid metamaterials employing split-ring resonators strongly coupled to graphene surface plasmons,” Nat. Commun. 6, 8969 (2015). [CrossRef] [PubMed]
36. J. Wang, B. Yuan, C. Fan, J. He, P. Ding, Q. Xue, and E. Liang, “A novel planar metamaterial design for electromagnetically induced transparency and slow light,” Opt. Express 21(21), 25159–25166 (2013). [CrossRef] [PubMed]
37. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009). [CrossRef]
38. L. Zhang, P. Tassin, T. Koschny, C. Kurter, S. M. Anlage, and C. M. Soukoulis, “Large group delay in a microwave metamaterial analog of electromagnetically induced transparency,” Appl. Phys. Lett. 97(24), 241904 (2010). [CrossRef]
39. J. Ding, B. Arigong, H. Ren, M. Zhou, J. Shao, M. Lu, Y. Chai, Y. Lin, and H. Zhang, “Tuneable complementary metamaterial structures based on graphene for single and multiple transparency windows,” Sci. Rep. 4, 6128 (2014). [CrossRef] [PubMed]
40. J. X. Jiang, Q. F. Zhang, Q. X. Ma, S. T. Yan, F. M. Wu, and X. J. He, “Dynamically tunable electromagnetically induced reflection in terahertz complementary graphene metamaterials,” Opt. Mater. Express 5(9), 1962–1971 (2015). [CrossRef]
41. L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406(6793), 277–279 (2000). [CrossRef] [PubMed]
42. A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63(5), 053806 (2001). [CrossRef]
43. H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 9663 (2015). [CrossRef] [PubMed]
44. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency,” Phys. Rev. Lett. 102(5), 053901 (2009). [CrossRef] [PubMed]
45. F. Y. Meng, Q. Wu, D. Erni, K. Wu, and J. C. Lee, “Polarization-Independent Metamaterial Analog of Electromagnetically Induced Transparency for a Refractive-Index-Based Sensor,” IEEE Trans. Microw. Theory Tech. 60(10), 3013–3022 (2012). [CrossRef]
46. L. Zhu, F. Y. Meng, L. Dong, Q. Wu, B. J. Che, J. Gao, J. H. Fu, K. Zhang, and G. H. Yang, “Magnetic metamaterial analog of electromagnetically induced transparency and absorption,” J. Appl. Phys. 117(17), 17D146 (2015). [CrossRef]
47. T. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 7, 1245105 (2005).
48. X. Shi, D. Han, Y. Dai, Z. Yu, Y. Sun, H. Chen, X. Liu, and J. Zi, “Plasmonic analog of electromagnetically induced transparency in nanostructure graphene,” Opt. Express 21(23), 28438–28443 (2013). [CrossRef] [PubMed]
49. H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013). [CrossRef]
50. Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015). [CrossRef] [PubMed]
51. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]
52. X. G. Yin, T. H. Feng, S. Yip, Z. X. Liang, A. Hui, J. C. Ho, and J. Li, “Tailoring electromagnetically induced transparency for terahertz metamaterials: From diatomic to triatomic structural molecules,” Appl. Phys. Lett. 103(2), 021115 (2013). [CrossRef]
