Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Active Control and Large Group Delay in Graphene-Based Terahertz Metamaterials Wei Jia, Peiwen Ren, Yuanlin Jia, and Chunzhen Fan*
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School of Physical Science and Engineering, Zhengzhou University, Zhengzhou 450001, China ABSTRACT: A distinct plasmon-induced transparency (PIT) window has been realized in our novel design of |+|-shaped graphene metamaterials, which consist of two identical graphene strips and a cross-shaped graphene resonator in the right middle. The two strips serve as the dark resonator, and the cross-shaped graphene plays the bright one. Active control of the PIT window can be modulated from the on state to the off state only by breaking structure symmetry. Furthermore, the PIT window can be dynamically adjusted with different Fermi energies in a noncontact way. More importantly, the proposed metamaterial structure achieves a maximum group delay of 13.28 ps, which is much higher than that in the previous paper. In the case of sensing application, the position of the PIT window has been investigated with different embedded media, and it shows a linear function of the refraction index. This study may open up new avenues for the development of highly integrated optical filters, optical sensors, or integrated optical switches. optoelectronics and nanophotonics.27 Compared with those of noble metals, the Fermi energy of graphene can be flexibly adjusted through chemical doping or gate voltage. In 2015, Shi et al. have designed radiative graphene strips side by side to realize PIT in a non-quantum regime.28 Shang et al. reported a tunable PIT effect based on three-dimensional patterned graphene nanostrips.29 Tian et al. demonstrated a dynamically adjustable PIT effect with asymmetric H-shaped graphene metamaterials, which can be realized with different applied polarization angles.30 He et al. designed a PIT system by depositing a cut wire and double semicircular graphene ribbons on the dielectric substrate.31 At present, many graphene-based metamaterials have been proposed and investigated, but the group delay of the PIT structures mentioned above is not ideal in practice. In this work, we have designed a simple PIT plasmonic metamaterial, which includes a graphene-based |+| unit cell arranged periodically in the THz region. Specifically, the unit cell comprises two identical graphene strips and a cross-shaped resonator. The destructive interference induces a distinct transparency window originating from the near-field coupling of bright and dark modes. Such a PIT window can be effectively tuned from the on to off state through symmetry breaking, namely, the cross resonator is away from the right center position. The performance of the group delay with different Fermi energies is also explored in our work. Moreover, our proposed PIT system is sensitive to the
1. INTRODUCTION Metamaterials are a kind of artificial material with special electromagnetic properties mainly depending on their geometric arrangement, which are not available in nature.1 The study of metamaterials has achieved remarkable progress in the past decades due to their capability to control the characteristics of propagating waves in a desired way through carefully designing their structures.2 Electromagnetically induced transparency (EIT) originating from the destructive interference of a three-level atomic system is a quantum phenomenon, and it can greatly enhance the light transmission within an extremely narrow spectral range,3,4 which is accompanied by a large dispersion at the transparency window and results in a slow light effect.5−7 In 2008, Zhang et al. indicated that the quantum EIT phenomenon could occur in plasmonic metamaterials, overcoming the requirement of harsh experimental conditions based on non-quantum methods and paving a new way for the study of plasmonics.8 PIT is an analogue of the EIT effect. Owing to its unique optical characteristics, it has attracted significant interests in both theoretical and experimental research.9−13 It demonstrates great potential in the applications of sensing,14−18 quantum information storage,19 optical communication systems, optical switches,20,21 and so on. It should be noted that for traditional PIT metallic structures, it is not easy work to vary their performance without re-fabrication to change their geometric parameters. Recently, graphene has attracted much attention due to its excellent optical and electric properties.22−24 Having a singlelayer atomic thickness, it can stimulate both propagating and localized surface plasmon modes with negligible propagation loss,25,26 which makes it potentially useful in the field of © XXXX American Chemical Society
Received: May 17, 2019 Revised: June 25, 2019 Published: July 8, 2019 A
DOI: 10.1021/acs.jpcc.9b04693 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
is estimated simultaneously with the dielectric loss, providing a detailed range of charge transport characteristics in the materials. If the patterned graphene structure is tuned through hole doping, which can be initiated by exposing the sample to the nitric acid vapor for several minutes,38 the permittivity of graphene can be calculated through the equation ε = 1 + iσ(ω)/ε0tω where ε0 is the permittivity of vacuum and t is the thickness of the monolayer graphene layer. Figure 2 illustrates
refractive index change of the surrounding media, which is beneficial for the application in optical sensors.
2. MODEL AND METHOD Our designed structure of the graphene metamaterial is illustrated in Figure 1. The graphene layer is colored in gray,
Figure 1. Structure of the graphene-based |+| metamaterial on a dielectric substrate. (a) Overall structure where the incident light is along the z direction. (b) Unit cell with defined geometrical parameters. l = 12.5 μm, a = 6 μm, d = 1.5 μm, w = 1.5 μm. The periodicity is 20 μm in both x and y directions.
Figure 2. Real and imaginary parts of the graphene conductivity in the THz regime with different Fermi energies.
the real and imaginary parts of the graphene conductivity as a function of the incident THz frequency with different Fermi energies. It can be clearly found that the value of the real and imaginary parts decreased with larger Fermi energy, which gives us an effective way to tune the plasmon resonance of graphene in a non-contact way with different Fermi energies. Nowadays, there are several technologies for preparing one uniform monolayer of graphene, such as micromechanical stripping, thermal decomposition of SiC, chemical vapor deposition (CVD), and so on.39 Among them, CVD is the most popular one, which can produce graphene with high conductivity and field-effect mobility. After that, the patterned graphene shapes can be initiated through electron beam lithography (EBL) owing to their high resolution, usually up to 3 to 8 nm.40 Thus, the sample fabrication of the |+|-shaped graphene metamaterials are suggested in three propcedures:41 First, a large uniform monolayer graphene is grown on copper foil with a CVD technique. Second, the patterned graphene can be realized via standard lift-off processing. Finally, the gold electrodes are deposited on the sides of the monolayer graphene using the EBL step. In this way, the Fermi level of the patterned monolayer graphene can be independently shifted by changing the corresponding electric gating voltage between the Au electrode and the substrate.
and the substrate is in blue. Figure 1b represents the unit cell consisting of two identical graphene strips and a cross-shaped resonator; namely, it is a |+| pattern. The cross-shaped resonator is located right between these two strips. Figure 1a depicts the schematic diagram of the overall structure with a periodic array of the unit cell in the x−y plane. P represents the periodicity. The lengths of strips and the cross-shaped resonator are designated as l and a. The width is expressed as w. In addition, the spacing distance between strips and the cross-shaped resonator is indicated as d. The specific geometrical parameters are depicted elaborately in Figure 1b. In our calculations, the thickness of the monolayer graphene is taken as 1 nm, and the dielectric substrate is set as SiO2. The plane wave polarized along the x direction propagates perpendicularly along the z-axis to the structure surface. Both the transmission spectra as a function of the incident wavelength and the electric field distribution at each resonant peak are obtained with finite element calculations. The perfectly matched layer boundary is applied onto the computation domain consisting of only a unit cell. In the terahertz domain, the surface conductivity of graphene can be simplified and written as e 2E
3. RESULTS AND DISCUSSION In order to clarify the occurrence of a PIT phenomenon, the transmission spectra of our proposed |+| model are investigated in Figure 3. The curves of two graphene strips (black dotted line), a single cross-shaped resonator (red dashed, dotted line), and the combined structure (blue solid line) are illustrated in Figure 3a. When only two graphene strips exist, its transmittance is almost approaching 1.0. It cannot couple with the incident light in the terahertz region, acting as the dark mode. Meanwhile, for the case of only a cross-shaped structure, a dip appears at 4.22 THz, indicating the direct coupling with the incident light, acting as the bright mode. When two resonators are integrated together, a distinct transparency window with a transmittance of 90.7% is obtained at 4.16 THz. To deeply figure out the underlying physical origin of the PIT transmission window, Figure 3b−d shows the distributions of the electric field at each resonant peak labeled “b”, “c”, and “d”
i
32 where τ = μE F /evF 2 denotes the carrier σ(ω) = 2F π ℏ ω + iτ −1 relaxation lifetime and μ is the carrier density and is equal to 10,000 cm2 V−1 s−1. vF = c/300 represents the Fermi velocity.33 Relaxation time is used to describe the return from a certain state to an equilibrium state in a gradual physical process, and it depicts the process of physical state recovery. It can be controlled with an external applied gate voltage with the construction of a graphene field-effect transistor34 or chemical doping.35 In detail, a bias potential is applied between the ITO and a gold contact to electrically dope the graphene, which allowed us to controllably tune the electric potential over a sufficiently large range. Based on the plasma carrier model, the relaxation time of graphene can be determined from the voltage dependence of the complex permittivity ratio.36 Experimentally, with the field-induced time-resolved microwave conductivity technique,37 the real change in permittivity
B
DOI: 10.1021/acs.jpcc.9b04693 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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cross-shaped structure and two graphene strips. It can be clearly observed that when the lateral migration S increases from 0 to 3 μm, the transparency window becomes narrower, and the transmission peak decreases gradually, but the position of the transmission peak is almost unchanged in Figure 4a. When the lateral migration is further increased to 3.5 μm, the transparency window disappears completely, and a dip with a transmittance of 50.8% appears at 4.2 THz. Figure 4b−d illustrates the electric field distribution at the resonant peak with different S values. For the symmetry structure (S = 0 μm), the electric field mainly distributes on the vertical graphene strips. The dark mode interferes with the bright mode, inducing the appearance of the PIT window. With larger S, the electric field gradually transferred from the two strips to the cross-shaped resonator in Figure 4c. However, the electric field totally transfers to the cross-shaped structure with S = 3.5 μm in Figure 4d. The bright mode of the cross-shaped resonator induces the resonant dip at 4.20 THz. Therefore, the PIT window can be easily modulated from the on to off state with different lateral migrations, which shadows great application in optical switches. It should be pointed out that the conductivity of graphene depends largely on Fermi energy, which can be tuned by chemical doping or electrostatic gating.42 Figure 5 shows the
Figure 3. (a) Transmission spectra of the parallel vertical strips, crossshaped structure, and both of them. (b−d) Distributions of the electric field for the corresponding points “b”, “c”, and “d” in panel (a).
in Figure 3a. The electric field in Figure 3b mainly distributes at the edge of the graphene strips, and its intensity is extremely weak. For the cross-shaped graphene structure in Figure 3c, the electric field distributes at the edge of the horizontal strip with a very high electric field intensity. Meanwhile, for the combined structures in Figure 3d, the enhanced electric field mainly distributes on the vertical graphene strips, and the electric field on the cross-shaped structure becomes weaker. This proves that the electric field energy transfers from the cross-shaped structure to the parallel vertical graphene strips, resulting from the near-field coupling of bright and dark modes. Finally, the destructive interference induces a distinct transparency window. To modulate the PIT window, we explore the influence on it through breaking the structure symmetry as shown in Figure 4. S denotes the lateral displacement between the center of the
Figure 5. Contour plot of the transmittance in the graphene-based |+| metamaterial with different Fermi energies in the THz region.
contour plot of the transmittance with different Fermi energies in our proposed |+| structure. It is also clearly found that with the increase of Fermi energy, the corresponding position of the transparency window moves toward a higher frequency region; namely, an obvious blue shift phenomenon occurs with an increased Fermi energy. It can be well understood through the following relationship f ∝ E F .43 One notable feature of the PIT effect is the phase dispersion around the region of the transparency window. Here, we dϕ introduce the group delay τg = − dω to describe the slow light capability where ϕ is the transmission phase shift and ω is the angular frequency.44 Figure 6a shows the transmission phase shift with different Fermi energies, and it moves to the highfrequency region with larger Fermi energy. Figure 6b depicts the corresponding group delay. When the Fermi energy is 1.1 eV, the group delay can reach as high as 13.28 ps, which is higher than that in the previous work. It has strategic significance in designing compact slow light devices with ultrafast response. In terms of sensing performance, transmission peaks are sensitive to the surrounding medium, which means that small perturbations of the refractive index can result in dramatic shifts of the resonance or line shape. Figure 7a plots the simulated PIT spectra with different refractive indices at room
Figure 4. (a) Transmission spectra as a function of the incident frequency are presented with different lateral displacements S in our proposed structure. (b−d) Electric field distributions for the corresponding points “b”, “c”, and “d” in panel (a). C
DOI: 10.1021/acs.jpcc.9b04693 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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4. CONCLUSIONS In summary, we have numerically and theoretically analyzed the PIT effect in THz metamaterials consisting of two identical graphene strips and a cross-shaped resonator. The PIT effect is induced by the destructive interference of bright−dark resonators. The performance of the PIT effect can be influenced by breaking structure symmetry, which results in an optical switcher with on and off states. Moreover, the transparency window can also be controlled over a broad frequency range by varying the Fermi energy of the graphene. Group delay has also been studied in depth, and it is found that such a PIT structure achieved a maximum group delay of 13.28 ps. Finally, we discuss the response of the PIT window as a function of surrounding media. This work may offer new possibilities for applications in the terahertz regime, such as slow light, biosensing, and spectral filters.
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Figure 6. Optical dispersion characteristics in the graphene-based |+| metamaterial structure illustrated with different Fermi energies: (a) transmission phase and (b) group delay.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Chunzhen Fan: 0000-0003-2137-6923 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is supported by the Key Science and Technology research project of Henan Province (162102210164 and 1721023100107) and the Natural Science Foundation of Henan Educational Committee (17A140002).
Figure 7. (a) Transmission spectra with different refractive indices of surrounding media. (b) Corresponding relationship of the resonant PIT peak with varying refractive indices of surrounding media.
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REFERENCES
(1) Smith, D. R.; Pendry, J. B.; Wiltshire, M. C. K. Metamaterials and Negative Refractive Index. Science 2004, 305, 788−792. (2) Liu, Y.; Zhang, X. Metamaterials: A New Frontier of Science and Technology. Chem. Soc. Rev. 2011, 40, 2494−2507. (3) Harris, S. E.; Field, J. E.; Imamoğlu, A. Nonlinear Optical Processes Using Electromagnetically Induced Transparency. Phys. Rev. Lett. 1990, 64, 1107−1110. (4) Boller, K. J.; Imamoğlu, A.; Harris, S. E. Observation of Electromagnetically Induced Transparency. Phys. Rev. Lett. 1991, 66, 2593−2596. (5) Leonhardt, U. A Laboratory Analogue of the Event Horizon Using Slow Light in An Atomic Medium. Nature 2002, 415, 406−409. (6) Tian, Y.; Ding, P.; Fan, C. Tunable Plasmon-Induced Transparency in Plasmonic Metamaterial Composed of Three Identical Rings. Opt. Eng. 2017, 56, 107106. (7) Izadshenas, S.; Zakery, A.; Vafapour, Z. Tunable Slow Light in Graphene Metamaterial in A Broad Terahertz Range. Plasmonics 2018, 13, 63−70. (8) Zhang, S.; Genov, D. A.; Wang, Y.; Liu, M.; Zhang, X. PlasmonInduced Transparency in Metamaterials. Phys. Rev. Lett. 2008, 101, No. 047401. (9) Papasimakis, N.; Fedotov, V. A.; Zheludev, N. I.; Prosvirnin, S. L. Metamaterial Analog of Electromagnetically Induced Transparency. Phys. Rev. Lett. 2008, 101, 253903. (10) Liu, N.; Langguth, L.; Weiss, T.; Kästel, J.; Fleischhauer, M.; Pfau, T.; Giessen, H. Plasmonic Analogue of Electromagnetically Induced Transparency at The Drude Damping Limit. Nat. Mater. 2009, 8, 758−762. (11) Tassin, P.; Zhang, L.; Koschny, T.; Economou, E. N.; Soukoulis, C. M. Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency. Phys. Rev. Lett. 2009, 102, No. 053901.
temperature when the embedded media are perfluorohexane (n = 1.251), water (n = 1.330), 60% glucose solution (n = 1.439), benzene (n = 1.501), and carbon disulfide (n = 1.628). For the composite system with different concentrations, the effective medium theory can be employed to arrive at the effective dielectric constant. As an example, the 60% glucose solution represents a known quantity of glucose mixed with a known quantity of water. We can arrive at the effective dielectric constant of the embedding solution on the proposed structure according to the effective medium equaution45 ε − εeff ε − εeff +f 2 =0 (1 − f ) 1 ε1 + 2εeff ε2 + 2εeff Here, f is the volume fraction of the glucose solution. ε1, ε2, and εeff represent the dielectric constants of water, glucose solution, and the complex solution, respectively. According to the relationship between the effective dielectric constant of the complex medium, the effective refractive index of the complex medium can be obtained through the equation neff = εeff . The refractive index of the substrate is 1.5 and remains unchanged throughout the simulation. According to the calculation data, we can find that the transmission spectra exhibit an obvious red shift with the increase in the refractive index of the surrounding media. Moreover, the position of the transparency window is linearly related to the refractive index of the surrounding media as shown in Figure 7b. It is demonstrated that the graphene-based PIT structure is of potential interest in plasmon resonance sensors. D
DOI: 10.1021/acs.jpcc.9b04693 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C (12) Gu, J.; Singh, R.; Liu, X.; Zhang, X.; Ma, Y.; Zhang, S.; Maier, S. A.; Tian, Z.; Azad, A. K.; Chen, H.-T.; et al. Active Control of Electromagnetically Induced Transparency Analogue in Terahertz Metamaterials. Nat. Commun. 2012, 3, 1151. (13) Bagci, F.; Akaoglu, B. A Polarization Independent Electromagnetically Induced Transparency-Like Metamaterial with Large Group Delay and Delay-Bandwidth Product. J. Appl. Phys. 2018, 123, 173101. (14) Liu, N.; Weiss, T.; Mesch, M.; Langguth, L.; Eigenthaler, U.; Hirscher, M.; Sönnichsen, C.; Giessen, H. P. Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing. Nano Lett. 2010, 10, 1103−1107. (15) Singh, R.; Cao, W.; Al-Naib, I.; Cong, L.; Withayachumnankul, W.; Zhang, W. Ultrasensitive terahertz Sensing with high-Q Fano Resonances in Metasurfaces. Appl. Phys. Lett. 2014, 105, 171101. (16) Liu, S. D.; Yang, Z.; Liu, R.-P.; Li, X.-Y. High Sensitivity Localized Surface Plasmon Resonance Sensing Using A Double Split Nanoring Cavity. J. Phys. Chem. C 2011, 115, 24469−24477. (17) Wu, D. J.; Jiang, S. M.; Liu, X. J. Fano-Like Resonances in Asymmetric Homodimer of Gold Elliptical Nanowires. J. Phys. Chem. C 2012, 116, 13745−13748. (18) Jia, W.; Ren, P. W.; Tian, Y. C.; Fan, C. Z. Dynamically Tunable Optical Properties in Graphene-Based Plasmon-Induced Transparency Metamaterials. Chin. Phys. B 2019, 28, No. 026102. (19) Taubert, R.; Hentschel, M.; Kästel, J.; Giessen, H. Classical Analog of Electromagnetically Induced Absorption in Plasmonics. Nano Lett. 2012, 12, 1367−1371. (20) Chen, J.; Wang, P.; Chen, C.; Lu, Y.; Ming, H.; Zhan, Q. Plasmonic EIT-Like Switching in Bright-Dark-Bright Plasmon Resonators. Opt. Express 2011, 19, 5970−5978. (21) Safavi-Naeini, A. H.; Alegre, T. P. M.; Chan, J.; Eichenfield, M.; Winger, M.; Lin, Q.; Hill, J. T.; Chang, D. E.; Painter, O. Electromagnetically Induced Transparency and Slow Light with Optomechanics. Nature 2011, 472, 69−73. (22) Novoselov, K. S.; Fal’ko, V. I.; Colombo, L.; Gellert, P. R.; Schwab, M. G.; Kim, K. A Roadmap for Graphene. Nature 2012, 490, 192−200. (23) Xu, X.; Zhang, Q.; Yu, Y.; Chen, W.; Hu, H.; Li, H. Naturally Dried Graphene Aerogels with Superelasticity and Tunable Poisson’s Ratio. Adv. Mater. 2016, 28, 9223−9230. (24) Li, D.; Wang, W.; Zhang, H.; Zhu, Y.; Zhang, S.; Zhang, Z.; Zhang, X.; Yi, J.; Wei, W. Graphene-Induced Modulation Effects on Magnetic Plasmon in Multilayer Metal-Dielectric-Metal Metamaterial. Appl. Phys. Lett. 2018, 112, 131101. (25) Gao, W.; Shu, J.; Qiu, C.; Xu, Q. Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances. ACS Nano 2012, 6, 7806−7813. (26) Gao, W.; Shi, G.; Jin, Z.; Shu, J.; Zhang, Q.; Vajtai, R.; Ajayan, P. M.; Kono, J.; Xu, Q. Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene. Nano Lett. 2013, 13, 3698− 3702. (27) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666−669. (28) Shi, X.; Su, X.; Yang, Y. Enhanced Tunability of Plasmon Induced Transparency in Graphene Strips. J. Appl. Phys. 2015, 117, 143101. (29) Shang, X. J.; Zhai, X.; Li, X. F.; Wang, L. L.; Wang, B. X.; Liu, G. D. Realization of Graphene-Based Tunable Plasmon-Induced Transparency by The Dipole-Dipole Coupling. Plasmonics 2016, 11, 419−423. (30) Tian, Y.-C.; Jia, W.; Ren, P.-W.; Fan, C.-Z. Tunable Plasmon Induced Transparency Based on Asymmetric H-Shaped Graphene Metamaterials. Chin. Phys. B 2018, 27, 124205. (31) He, X.; Liu, F.; Lin, F.; Shi, W. Graphene Patterns Supported Terahertz Tunable Plasmon Induced Transparency. Opt. Express 2018, 26, 9931−9944.
(32) Stauber, T.; Peres, N. M. R.; Castro Neto, A. H. Conductivity of Suspended and Non-Suspended Graphene at Finite Gate Voltage. Phys. Rev. B 2008, 78, No. 085418. (33) Liu, Z.; Bai, B. Ultra-Thin and High-Efficiency Graphene Metasurface for Tunable Terahertz Wave Manipulation. Opt. Express 2017, 25, 8584−8592. (34) Murata, Y.; Calzolari, A.; Heun, S. Tuning Hydrogen Adsorption on Graphene by Gate Voltage. J. Phys. Chem. C 2018, 122, 11591−11597. (35) Guo, B.; Fang, L.; Zhang, B.; Gong, J. R. Graphene Doping: A Review. Insci. J. 2011, 1, 80−89. (36) Choi, W.; Nishiyama, H.; Ogawa, Y.; Ueno, Y.; Furukawa, K.; Takeuchi, T.; Tsutsui, Y.; Sakurai, T.; Seki, S. Plasma Carriers on Graphene: Relaxation of Plasma Carriers in Graphene: An Approach by Frequency-Dependent Optical Conductivity Measurement (Advanced Optical Materials 14/2018). Adv. Opt. Mater. 2018, 6, 1870054. (37) Choi, W.; Tsutsui, Y.; Sakurai, T.; Seki, S. Complex Permittivity Analysis Revisited: Microwave Spectroscopy of Organic Semiconductors with Resonant Cavity. Appl. Phys. Lett. 2017, 110, 153303. (38) Yan, H.; Low, T.; Guinea, F.; Xia, F.; Avouris, P. Tunable Phonon-Induced Transparency in Bilayer Graphene Nanoribbons. Nano Lett. 2014, 14, 4581−4586. (39) Near, R.; Tabor, C.; Duan, J.; Pachter, R.; El-Sayed, M. Pronounced Effects of Anisotropy on Plasmonic Properties of Nanorings Fabricated by Electron Beam Lithography. Nano Lett. 2012, 12, 2158−2164. (40) Yang, R.; Zhang, L.; Wang, Y.; Shi, Z.; Shi, D.; Gao, H.; Wang, E.; Zhang, G. An Anisotropic Etching Effect in the Graphene Basal Plane. Adv. Mater. 2010, 22, 4014−4019. (41) Liu, T.; Wang, H.; Liu, Y.; Xiao, L.; Zhou, C.; Liu, Y.; Xu, C.; Xiao, S. Independently Tunable Dual-Spectral Electromagnetically Induced Transparency in A Terahertz Metal-Graphene Metamaterial. J. Phys. D: Appl. Phys. 2018, 51, 415105. (42) García de Abajo, F. J. Graphene Plasmonics: Challenges and Opportunities. ACS Photonics 2014, 1, 135−152. (43) Koppens, F. H. L.; Chang, D. E.; García de Abajo, F. J. Graphene Plasmonics: A Platform for Strong Light−Matter Interactions. Nano Lett. 2011, 11, 3370−3377. (44) Lu, H.; Liu, X.; Mao, D. Plasmonic Analog of Electromagnetically Induced Transparency in Multi-Nanoresonator-Coupled Waveguide Systems. Phys. Rev. A. 2012, 85, No. 053803. (45) Huang, J. P.; Yu, K. W. Enhanced Nonlinear Optical Responses of Materials: Composite Effects. Phys. Rep. 2006, 431, 87−172.
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