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Abstract
We investigated the electromagnetically induced transparency (EIT)-like effects in planar metamaterials (MMs) at microwave (GHz) frequencies. The specific MMs that were used in this study consist of cut-wire resonator/ring resonator, which achieved the dual EIT-like effects in a single-layer through the bright- and quasi-dark-mode coupling and the lattice mode coupling. In addition, by varying the distance between the two resonators, the quad-band EIT spectral response in the microwave region was obtained, and the group refractive index at the EIT-like resonance of proposed design reached up to 4,000. This study provides the design approach to the multispectral EIT-like effects and might suggest potential applications in a variety of fields, for example, low-loss slow-light device, multiple switching sensor, and other sensing devices.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The EIT leads to a sharp transparency window within a broad absorption band by the quantum interference effect between atomic ensembles [1]. This phenomenon allows a transmission window with a spectrum of extreme dispersion and high Q factor of the transmission peak, which causes a slow-light effect, improves the nonlinearity associated with the near-resonant effect. This is desirable for sensing, quantum optical memories and slow-light devices [2–6]. The EIT can be extended to the classical optical systems by using plasmonic MMs, which is defined as the EIT-like effect [7]. It is generally very attractive because it can be used to control the dynamic response and potentially extend the application range using the resonant elements of MM structure. The EIT has been extensively studied in MM structures, including nanoparticle and nano-slot structures [8,9]. One way of inducing transmission using MMs is the unit cell coupling of bright-dark resonances via the Fano type of interference [10]. The EIT phenomenon can be obtained by breaking the structural symmetry or subwavelength-scale coupling [11–14]. Commonly, for the near-field subwavelength-scale coupling, it can be interpreted by the coupling between a radiative bright resonator that strongly couples with the incident light, and a dark resonator that weakly couples to the incident light. Another way to obtain the EIT is to control the lattice coupling by changing the lattice constant of MM structure [15]. The lattice mode resonance is observed owing to the discontinuity of dispersion curve at the medium-substrate interface. These are also called as the diffraction modes or the Wood anomalies, and their spectral positions depend on the periodicity of unit cell and the incident angle of excitation field [16,17]. The recent studies have shown that a plasmonic MM system, based on a dipole-quadruple-mode coupling, can be obtained, which can be applied to the MM applications where the EIT optical resonance operates in the multiple frequency domains [18–20]. Generally, the multi-spectral EIT effects are generated by the coupling that occurs in multilayered or stacked structure [21,22]. However, the fabrication of these complex structures is time-consuming and requires the processes for surface planarization and layering in a multi-level stacking, which severely hinder the fundamental applications. If the multi-spectral EIT resonance can be realized in a single-layer structure, it offers advantages in the applications of multi-wavelength biosensing [23–25].
In this paper, we demonstrate the major contribution of dipole-quadrupole and lattice mode coupling to strong Fano resonance in cut-wire resonator and ring resonator (CWR and RR) system, and achieve a multi-spectral EIT by simply moving the RR. The coupling between pure dipoles creates a transmission window. By moving the RR to increase the coupling strength (∆d≠4 mm), the dipole-quadrupole mode of RR appears as a transparency window. Furthermore, the lattice mode coupling was controlled by adjusting the lattice constants of structure array, and sharp transmission was further observed. This study clearly shows that, by changing the coupling strength between two resonators, multiple transmission windows can be induced. There is a great advantage of being able to control multiple transmission windows with a simple structure.
2. Simulation and experimental setup
To obtain the scattering parameters, the numerical calculation was performed by using the commercial finite-integration software, CST Microwave Studio. For the simulation, in the tetrahedral mesh, the periodic boundary conditions were assigned to be an infinite periodic array in the x and the y directions and open for the z direction in the environment of free space. The transmission spectra were calculated using T(ω) = |S21(ω)|2. And the size of fabricated samples was made to be 400 × 400 mm2 in order to include an area sufficient to be irradiated by the microwave beam. It is made from a printed circuit board consisting of a copper film with a thickness of 0.035mm covered on a 0.1-mm-thick FR4 substrate. The metallic pattern was fabricated by using the conventional photolithography method. The transmission spectra were measured in a microwave anechoic chamber. Two standard-gain horn antennas were used as the transmitting and the receiving antennas, which were connected to a Hewlett Packard E8362B network analyzer. The distance between middle point of two antennas and sample was kept at 150 cm for the measurements to remove the near-field effects.
3. Results and discussion
The MM of proposed structure comprises of a CWR and an RR, and is designed in a way that they can exhibit the EIT effect with bright- and quasi-dark-mode coupling between CWR and RR. The schematic diagram of proposed MM geometry is shown in Fig. 1(a). In the proposed geometry, represents the width of CWR as well as RR, h represents the height of CWR, r denotes the radius of RR, and ∆d stands for the distance between two resonators, therefore, ∆d = 4 and ∆d ≠ 4 represent symmetric and asymmetric, respectively. The periodicity of MM is denoted by and is taken to be 22 mm. We have set w = 2, h = 10 and r = 6 mm. The distance ∆d between CWR and RR structures is varied in our study to examine the modulation response of EIT effect. The CWR and the RR are constructed on FR4 substrates with a copper thickness t = 0.035 mm with an electric conductivity of 5.8 × 107 S/m. The 0.1-mm-thick FR4 with a dielectric constant of 3.9 and a loss tangent of 0.025 is used as the substrate. The numerical calculations were performed by using the finite-element frequency-domain solver in CST Microwave Studio. The MM geometry is simulated under the unit cell boundary condition in the x-y plane. We set open boundary condition along the direction of light propagation. The wave, having an electric-field polarization along the y direction, is perpendicularly incident to the plane. Figures 1(b) and 1(c) present the simulated transmission spectra of CWR alone and RR alone, respectively, under the y polarizaion. When the plane wave is vertically illuminated with y polarization, the CWR and the RR can be directly excited at 11 GHz as bright and quasi-dark mode, respectively. In addition, the second resonance occurs near 15 GHz, which is the excitation associated with the periodicity of unit cell. Generally speaking, the metallic periodic MM is excited by incident EM wave in the slab dielectric waveguide through diffraction, as it can be partially regarded as a two-dimensional grating called the MM grating [26]. The Q-factor is defined as ω0/∆ωFWHM, and the ratio of resonant frequency to the FWHM (full width at half maximum) is calculated for each of the two resonators. The fundamental mode of CWR shows low radiation loss, narrow bandwidth and high Q (QCWR-1 = 16.48), and the second resonance also reveals a narrow bandwidth and a high Q (QCWR-2 = 24.95). In case of the RR, there are a broad bandwidth and a low Q (QRR-1 = 4.59) in the fundamental mode, but a relatively high Q (QRR-2 = 13.87) in the second resonance. Figure 1(d) presents the simulated transmission curve of our proposed structure. Interestingly, when the CWR and the RR are combined as in Fig. 1(a), the dual transparency window is demonstrated for the symmetric configuration. For transmission peakI, the CWR and the RR, which serve as the bright and the quasi-dark mode as shown in Figs. 1(b) and 1(c), respectively, resonate at the same frequency and they exhibit the bright- and quasi-dark-mode coupling. The coupling between CWR and RR induces a sharp transparency window with a transmission of 88% at 10.1 GHz. In addition, transmission peakII occurs owing to the coupling with the lattice resonance occurring near 15 GHz, resulting in 87% transmission at 15.5 GHz.
Fig. 1 (a) Schematic view of the unit cell of proposed design with the geometrical parameters. Simulated spectra of the transmission at the normal incidence for (b) CWR alone (c) RR alone. (d) Simulated spectra depicting the transmission window for the CWR-RR structure (∆d = 4 mm).
Figure 2 shows the simulated transmission spectra of the planar asymmetric MM structure (∆d = 3, 2, and 1 mm). These three CWR/RR structures have the same geometry parameters as in Fig. 1, except different distance between two resonators. When the CWR/RR forms an asymmetric structure, the third and the fourth transmission (III and IV) appear as shown in Fig. 2. In the vicinity of ω = 12.7 GHz (where is the frequency of EIT peak III), due to the destructive interference between the two modes, the original resonance dip of resonator is replaced by a narrow transparency window by two adjacent split resonances at ω1 = 12.2 and ω2 = 13.6 GHz. In addition, the destructive interference due to the lattice mode coupling replaces the original resonance dip around ω = 14.6 GHz (where ω is the frequency of EIT peak IV) with a narrow transparency window by two adjacent split resonances at ω1 = 13.6 and ω2 = 14.7 GHz. The coupling between two types of resonator modes can be manipulated by changing the distance, which is expected to be employed for the transmission switching.
Fig. 2 Transmission spectra of the CWR/RR structure by varying the distance between two resonators ∆d = (a) 3, (b) 2 and (c) 1 mm.
Figure 3 demonstrates the experimental results for three cases. The EIT-like peak is observed experimentally and was in a fairly good agreement with the simulation. Particularly, the coupling varies with the distance between resonators and the multi-spectral EIT, including additional transmission peaks, is clearly observed. The resonance frequency between simulation and experiment is slightly shifted. This might be because the real permittivity value of dielectric substrate differs from that used in the simulation. The narrow transparency window is generally associated with steep dispersion, resulting in a significantly-reduced group velocity of wave propagation. This is, a slow-light effect, which is one of the important features of the EIT-like phenomenon. Figure 4(a) presents the group index of wave for transmission peak III, defined by ng = Re(n) + ω[dRe(n)/dω]. The calculated maximal group index in the transparency window is given, with respect to the CWR/RR at a fixed lattice periodicity. The group index is enhanced rapidly as the distance between CWR and RR increases. In Fig. 4(b), the large group index over 4000 can be obtained with the proposed simple structure for ∆d = 3 mm. The corresponding Q value of EIT-like transmission with respect to the distance between two resonators is shown in Fig. 4(a), and is over 90 when ∆d > 3 mm. This high Q value is mainly due to the narrow resonance of Fano dip, induced by the coupling between two resonators. As in the inset of Fig. 4(b), we also calculated the group delay time, defined by tg = –dφ(ω)/dω, where φ is the transmission phase. For ∆d = 3 mm, at transmission peak III, a time delay of 26 ns occurs, which slows down the wave pulse. Figure 4(c) shows the surface-current distribution corresponding to transmission peak III for ∆d = 3 mm. The antiparallel current between CWR and RR is formed strongly, and thus the total magnetic moment in the x direction is cancel out. That is, scattering field is suppressed owing to the destructive interference between two resonators, resulting in a transparency window. GHz radiation through the region between CWR and RR with out-of-phase current flows can be a possible reason for the group delay observed in this structure, and the slow light with low loss is produced at the center of the transparency window.
Fig. 3 Simulated and measured transmission spectra for Δd = (a) 4, (b) 3, (c) 2 and (d) 1 . The sample is shown as inset.
Fig. 4 (a) Group index (red) and Q-factor (blue) of transmission peak III with respect to the distance between two resonators. (b) Dependence of the group index on frequency as obtained from the scattering parameters. Inset in (b) shows the obtained group-delay plot for Δd = 3 mm. (c) Surface-current distribution corresponding to transmission peak III.
To further elucidate the coupling between the two radiative modes, the distribution of z component of the electric field in the transmission dip at 13.4 GHz for ∆d = 4 mm, and 12.2 and 13.7 GHz for ∆d = 1 mm are shown in Figs. 5(c)–5(e), respectively. In the comparison of Figs. 5(c) and 5(d), the dipole excitation of CWR is suppressed by the coherent coupling with the quadrupole excitation in the RR, giving rise to the Fano dip in the spectrum of CWR/RR structure as shown in Fig. 5(b). Due to the narrow gap between the resonators, a strongly-confined dipolar field of CWR induces excitation of the quadrupole plasmon mode by inducing the electron displacement in the RR. In this way, the dipole mode of CWR is strongly coupled to the quadrupole one in the RR. Therefore, we can understand that this transmission peak III is made by the interaction between electric dipole and electric quadrupole. However, the asymmetric quadrupole excitation occurs, which results in a resonance in the low-frequency region, unlike the conventional quadrupole resonance. As shown in Figs. 5(d) and 5(e), region 1 corresponds to 12.2 GHz and region 2 to 13.7 GHz. For this reason, the resonance appears at a frequency different from the conventional one. To provide a quantitative description of the EIT system based on dipole and quadrupole coupling, we consider a three-oscillator EIT model. The dipole antenna of our MM is represented by an oscillator DP (dipole) driven by an external electric field. The quadrupole antenna is represented by oscillators QP1 and QP2 (quadrupoles), which can only be excited by coupling with oscillator DP. From the coupled differential equations, the energy dissipation as a function of frequency is obtained as follow [27,28]:
where A is given by:Here, (ωDP, ωQP1, and ωQP2) and (γDP, γQP1, and γQP2) are the resonance frequencies and the damping rates of three oscillators, respectively. κQP1 and κQP2 defines the coupling coefficient between oscillators DP and QP1, and oscillators DP and QP2, respectively. The values of damping rates γDP, γQP1, and γQP2 are calculated to be 3.49, 1.32, and 1.44 GHz, respectively. In addition, we obtain the values of κQP1 and κQP2 at 2.23 and 2.42 GHz, respectively, for the CWR/RR structure, resulting from the corresponding transmission peak, which leads to the sharp transmission window in the dipole absorption.Fig. 5 Simulated transmission spectra at the normal incidence for Δd = (a) 4 and (b) 1 mm. Distribution of the z component of electric field in the transmission dip at (c) 13.4 GHz for Δd = 4 mm, (d) 12.2 and (e) 13.7 GHz for Δd = 1 mm.
To investigate the effect of lattice mode on the MM resonance, we consider an MM sample consisting of CWR and RR with a square lattice constant varied as shown in Fig. 6(a). This Fig. 6 show the unit cell dimensions of the CWR/RR samples with varying lattice constants/periodicities, p = 21, 22 and 23 mm. These MM samples are designed so that the characteristics of MM resonance do not change by keeping the geometry of unit cell the same for all three samples. However, the resonance frequency of lattice mode is continuously adjusted by changing the lattice constant along the x and the y axis of sample. The diffraction frequency for lattice is determined by the following simplified diffraction equation for a periodic square lattice with the normal incidence;
where c is the velocity of light in vacuum, n is the refractive index of substrate, P is the periodicity of structure, and (i, j) are the pair of indexes defining the order of lattice mode [29]. For case of the second-order lattice mode (SOLM), (0, 2), the equation above is expressed as fdiff = (c/nP)*2, where the frequency of lattice mode varies in inverse proportion to the periodicity. In this work, to illustrate the origin of transmission peak II, the mode-splitting effect was observed. We performed the numerical simulations to investigate the confined electric field in the lattice-matched hybrid modes of transmission peak II (p = 22 and 23 mm), as shown in Fig. 6(b). The strong confined electric field was seen for each resonance mode at p = 22 mm as the surface currents remained, which was highly radiative. In addition, at p = 23 mm, when the lattice mode frequency was closely matched to the structural resonance, the surface currents were still in strong electric-field confinement. The role of SOLM in the mode-splitting effect was confirmed, and through this coupling between the eigen-resonance of MM and the lattice mode, the split resonances red-shifted and their spectral line-width changed. Furthermore, this could lead to suppression of the radiative loss that gave rise to extraordinary transmission and maintain the amplitude of transmission with 79%. We also numerically investigate the effect of SOLM on the dipolar resonance emerging at 13.9 GHz for the incident wave. As the periodicity of structure increases to be 23 mm, a strong coupling between the MM eigen-resonance and the SOLM is confirmed, resulting in a sharp transparency (transmission peak IV at 13.9 GHz) at the center of CWR/RR resonance. In addition, when the lattice constant increases from 22 to 23 mm, the red-shift of SOLM with respect to the MM resonance results in a red-shift of the observed transmission peak, as shown in Fig. 6(a). In this way, the transparency is controlled by the lattice mode propagating on the substrate surface. In Figs. 6(c) and 6(d), the surface-current distribution of resonant dip for p = 21 mm and that in the transmission frequency region for p = 22 mm are confirmed. When the CWR dipole resonance matches with the SOLM (p = 22 mm), the propagation of energy on the surface of substrate interacts with the CWR dipole resonance to induce antiparallel currents inside the RR and on the surface of CWR. This opposite current interferes destructively to cause the field cancellation at the resonance, leading to sharp transmission peaks and steep dispersion in the system. Thus, the MM resonance properties are modified by the effect of lattice mode, which leads to a sharp transmission characteristic by changing the dipole type of CWR to the quadrupole.Fig. 6 (a) Transmission spectra of the CWR/RR structure at a fixed distance (Δd = 1 mm) with respect to the lattice constants/periodicities, p = 21, 22 and 23 mm. Also, transmission amplitude for each peak with respect to the periodicity. Surface-current distributions for MM periodicity of (b) 22 and 23 mm. Surface-current distributions at (c) Δd = 1 mm, p = 21 mm and 13.8 GHz, and (d) Δd = 1 mm, p = 22 mm and 14.6 GHz.
4. Conclusions
This study reports the investigation of EIT-like effects in MM consisting of CWR and RR. We have successfully implemented the multi-spectral EIT-like effect in the single-layer structure through manipulation of dipole-quadrupole and lattice-mode coupling. By moving the RR, the dipole and the quadrupole modes of CWR and RR were excited, and the lattice coupling could be controlled. In particular, the near-field coupling strength between CWR and RR increased with the movement of RR, and the harmonic lattice mode could enhance the Q-factor of all the CWR/RR resonances. The near-field coupling between CWR and RR and the coupling of lattice mode to the resonators lead to an intensified adjacent split-resonances behavior, giving rise to extraordinary transmission peak. We successfully explained the reason why the double-peak spectrum was converted into the quad-peak one. The experimental transmission spectra were obtained to verify the rationality of simulation, and the measurement results turned out to be fit well with the simulation. The obtained results in this paper give some contributions to the flourishing areas of MM with potential applications such as switching sensors and slow-light devices at multiple frequencies.
Funding
Ministry of Science, ICT and Future Planning.
Acknowledgments
This work was supported by the NRF fund by MSIP, Korea (No. 2017R1A2B4003916).
References
1. Y. Tamayama, K. Yasui, T. Nakanishi, and M. Kitano, “Electromagnetically induced transparency like transmission in a metamaterial composed of cut-wire pairs with indirect coupling,” Phys. Rev. B Condens. Matter Mater. Phys. 89(7), 75120 (2014). [CrossRef]
2. S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82(23), 4611–4614 (1999). [CrossRef]
3. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef] [PubMed]
4. M. D. Lukin, S. F. Yelin, and M. Fleischhauer, “Entanglement of atomic ensembles by trapping correlated photon states,” Phys. Rev. Lett. 84(18), 4232–4235 (2000). [CrossRef] [PubMed]
5. N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing,” Nano Lett. 10(4), 1103–1107 (2010). [CrossRef] [PubMed]
6. V. Yannopapas, E. Paspalakis, and N. V. Vitanov, “Electromagnetically induced transparency and slow light in an array of metallic nanoparticles,” Phys. Rev. B Condens. Matter Mater. Phys. 80(3), 35104 (2009). [CrossRef]
7. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 47401 (2008). [CrossRef] [PubMed]
8. Z.-J. Yang, Z.-H. Hao, H.-Q. Lin, and Q.-Q. Wang, “Plasmonic Fano resonances in metallic nanorod complexes,” Nanoscale 6(10), 4985–4997 (2014). [CrossRef] [PubMed]
9. A. Artar, A. A. Yanik, and H. Altug, “Multispectral plasmon induced transparency in coupled meta-atoms,” Nano Lett. 11(4), 1685–1689 (2011). [CrossRef] [PubMed]
10. N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101(25), 253903 (2008). [CrossRef] [PubMed]
11. K. Aydin, I. M. Pryce, and H. A. Atwater, “Symmetry breaking and strong coupling in planar optical metamaterials,” Opt. Express 18(13), 13407–13417 (2010). [CrossRef] [PubMed]
12. R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “Coupling between a dark and a bright eigenmode in a terahertz metamaterial,” Phys. Rev. B Condens. Matter Mater. Phys. 79(8), 85111 (2009). [CrossRef]
13. Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014). [CrossRef] [PubMed]
14. 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]
15. C. Sui, B. Han, T. Lang, X. Li, X. Jing, and Z. Hong, “Electromagnetically induced transparency in an all-dielectric metamaterial-waveguide with large group index,” IEEE Photonics J. 9(5), 1 (2017). [CrossRef]
16. C. H. Yi, Y. J. Yoo, Y. J. Kim, K. W. Kim, Y. P. Lee, and J. Y. Rhee, “Role of Wood’s anomaly in the performance of metamaterial absorbers with periodicity comparable to wavelength,” J. Phys. D Appl. Phys. 49(19), 195103 (2016). [CrossRef]
17. S. Yang, Z. Liu, Z. X. Xia, E. Yiwen, C. Tang, Y. Wang, J. Li, L. Wang, and C. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016). [CrossRef]
18. W. Y. Li, X. Zhai, X.-J. Shang, S.-X. Xia, M. Qin, and L.-L. Wang, “Multi-spectral plasmon induced transparency based on three-dimensional metamaterials,” Opt. Mater. Express 7(12), 4269–4276 (2017). [CrossRef]
19. V. M. Acosta, K. Jensen, C. Santori, D. Budker, and R. G. Beausoleil, “Electromagnetically induced transparency in a diamond spin ensemble enables all-optical electromagnetic field sensing,” Phys. Rev. Lett. 110(21), 213605 (2013). [CrossRef] [PubMed]
20. J. Kim, R. Soref, and W. R. Buchwald, “Multi-peak electromagnetically induced transparency (EIT)-like transmission from bull’s-eye-shaped metamaterial,” Opt. Express 18(17), 17997–18002 (2010). [CrossRef] [PubMed]
21. D. Wu, Y. Liu, L. Yu, Z. Yu, L. Chen, R. Li, R. Ma, C. Liu, J. Zhang, and H. Ye, “Plasmonic metamaterial for electromagnetically induced transparency analogue and ultra-high figure of merit sensor,” Sci. Rep. 7(1), 45210 (2017). [CrossRef] [PubMed]
22. A. Ourir, B. Gallas, L. Becerra, J. de Rosny, and P. Dahoo, “Electromagnetically induced transparency in symmetric planar metamaterial at THz wavelengths,” Photonics 2(1), 308–316 (2015). [CrossRef]
23. K. V. Sreekanth, M. ElKabbash, Y. Alapan, E. I. Ilker, M. Hinczewski, U. A. Gurkan, and G. Strangi, “Hyperbolic metamaterials-based plasmonic biosensor for fluid biopsy with single molecule sensitivity,” EPJ Appl. Metamat. 4, 1 (2017). [CrossRef]
24. Y. Lee, S.-J. Kim, H. Park, and B. Lee, “Metamaterials and metasurfaces for sensor applications,” Sensors (Basel) 17(8), 1726 (2017). [CrossRef] [PubMed]
25. X. He, Q. Zhang, G. Lu, G. Ying, F. Wu, and J. Jiang, “Tunable ultrasensitive terahertz sensor based on complementary graphene metamaterials,” RCS Adv. 6(57), 52212–52218 (2016). [CrossRef]
26. N. Born, I. Al-Naib, C. Jansen, R. Singh, J. V. Moloney, M. Scheller, and M. Koch, “Terahertz metamaterials with ultrahigh angular sensitivity,” Adv. Opt. Mater. 3(5), 642–645 (2015). [CrossRef]
27. 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]
28. M. Miyata, J. Hirohata, Y. Nagasaki, and J. Takahara, “Multi-spectral plasmon induced transparency via in-plane dipole and dual-quadrupole coupling,” Opt. Express 22(10), 11399–11406 (2014). [CrossRef] [PubMed]
29. M. Manjappa, Y. K. Srivastava, and R. Singh, “Lattice-induced transparency in planar metamaterials,” Phys. Rev. B 94(16), 161103 (2016). [CrossRef]
