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Abstract
We realize and numerically demonstrate the analogue of electromagnetically induced transparency (EIT) with a high-Q factor in a metal-dielectric bilayer terahertz metamaterial (MM) via bright-bright mode coupling and bright-dark mode coupling. The dielectric MM with silicon dimer rectangular-ring-resonator (Si-DRR) supports either a bright high-Q toroidal dipole resonance (TD) or a dark TD with infinite Q value, while plasmonic MM with metallic rectangular-ring-resonator (M-RR) supports a low-Q electric dipole resonance (ED). The results show that the near-field coupling between the dark TD and bright ED behaves just as that between the two bright modes, which is dependent on the Q factor of the TD resonance. Further, due to the greatly enhanced near-field coupling between the bright ED and dark TD, the coupling distance is significantly extended to about 1.9 times of the wavelength (in media), and robust EIT with large peak value over 0.9 and high Q-factor is achieved. The proposed bilayer MM provides a new EIT platform for design and applications in high-Q cavities, sensing, and slow-light based devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Electromagnetically induced transparency (EIT) originates from the interference between two different excitation pathways, giving rise to a sharp peak within a broad transmission dip [1,2]. This concept was later extended to classical optical systems as metamaterials (MMs) [3–6], The analogue of EIT in MMs has attracted significant attention owing to their excellent performances in filters, slow light-based devices, and biosensors [7–16]. There are two ways to realize the EIT in MMs. One is based on destructive interference between a bright mode that can be directly excited by incident electromagnetic waves and a dark mode that cannot be excited. The bandwidth or quality factor (Q) of the EIT transparency window can be easily adjusted by the asymmetry degree of MM structures [17–23]. The other is using bright-bright mode coupling, Q values of the EIT achieved are usually very low [24–33]. To achieve a high-Q EIT, it is necessary to have a large Q value contrast and a small resonance detuning between the two coupling modes [34]. Therefore, how to design a high-Q MM, and manipulate the detuning and coupling between a high-Q resonance and a low-Q mode have become two main problems in realizing high-Q EIT. In recent years, much progress has been made in achieving high-Q Fano resonance in all-dielectric MMs because of their free of ohmic loss of materials compared with their plasmonic counterparts [35–45]. For example, high-Q resonances can be easily obtained by changing the distance or size of two composing atoms in dimer-structured MMs, such as perforated high refractive dielectrics [46,47], silicon disks [48], or rectangular rings [49]. Regarding the second question, it is still difficult to design and control the detuning and near-field coupling of the two bright modes in single-layer MMs [50,51]. For the bilayer MMs, not only the two resonances can be independently designed, but also the near-field coupling of them can be effectively manipulated by relative position or distance of the two layers. However, there are few studies on this issue so far [52,53]; in addition, all reported EIT responses in one MM were realized via either bright-bright mode coupling or bright-dark mode coupling, not both, and the coupling distance between the two resonances was less than one wavelength [53–57].
In this work, we realized and numerically investigated the analogue of EIT with a high Q factor in a metal-dielectric bilayer terahertz MM. The dielectric MM with silicon dimer rectangular-ring-resonator (Si-DRR) supports either a bright high-Q toroidal dipole resonance (TD) or a dark TD with infinite Q value, while plasmonic MM with metallic rectangular-ring-resonator (M-RR) supports a low-Q electric dipole resonance (ED). We systematically studied the influences of structure parameters of M-RR and Si-DRR, and the layer thickness on the performance of the EIT induced by the near-field coupling of the TD and ED. The results show that the near-field coupling between the dark TD and bright ED is stronger than that between the two bright modes. Furthermore, due to the greatly enhanced near-field coupling between the bright ED and dark TD, the coupling distance is significantly extended to about 1.9 times of the wavelength (in media). Meanwhile, robust EIT with large peak value over 0.9 and high-Q factor was realized. The proposed bilayer MM provides a new EIT platform for design and applications in high-Q cavities, sensing, filtering, and slow-light based devices.
2. Structural design and simulation
2.1 Structural design
As shown in Fig. 1(a), the metal-dielectric bilayer MM we designed is composed of M-RR and Si-DRR arranged on the top and bottom of a crystalline quartz substrate with a thickness of h, and consider that THz wave polarized along the y axis is normally incident on it. We chose the quartz as a substrate because of its low absorption and ease fabrication [45]. Figure 1(b) shows unit cell of the bilayer MM, including high-resistance silicon DRR (blue) and plasmonic M-RR (yellow). Structure parameters of the Si-DRR are a1 = 380 µm, b1 = 180, w1 = 40 µm, the distance between the two RRs is s, and the thickness of silicon is 200 µm; the length, width and metallic line width of M-RR are a2, b2 and w2 = 6 µm, respectively; the metal thickness is 0.2 µm, and the period of the unit cell is Λx = Λy = 420 µm. Numerical simulations were performed by using Comsol software. In simulation, periodic boundary conditions were considered in the x and y directions, and a perfect matching layer (PML) was used in the z direction. The dielectric constants of quartz and silicon are 3.8 and 11.9, respectively, and the conductivity of the metal is set to be 3.56 ×107 S/m.
Fig. 1. (a) Schematic diagram of a metal-dielectric bilayer MM composed of Si-DRR and M-RR on the top and bottom of a quartz and illuminated by a normally incident THz wave polarized along the y-axis. (b) Unit cell of the bilayer MM. The geometric parameters are: Λx = Λy = 420 µm, a1 = 380 µm, b1 = 180 µm, w1 = 40 µm. M-RR has a length a2, width b2, and metal line width w2 = 6 µm. The thickness of silicon and metal are 200 µm and 0.2 µm, respectively.
2.2 High-Q TD resonance of Si-DRR
Considering an individual Si-DRR, it is obvious that the distances between two RRs in the unit cell s and in adjacent unit cell s’ satisfy: s + s’ = Λx – 2 × b1 = 60 µm. When s = s’ = 30 µm, the Si-RR is uniformly distributed along the x axis with a period of Λx/2; in this case the Si-DRR we called symmetric, otherwise it is asymmetric.
Firstly, we calculated the transmission spectrum of the individual asymmetric Si-DRR (i.e., without plasmonic M-RR) in the frequency range of 0.3–0.35 THz when s = 10 µm, as shown in Fig. 2(a). It can be clearly seen that an asymmetric Fano resonance with a Q value of about 380 appears at 0.331 THz (Q value is calculated by Fano formula fitting [34]). To understand the microscopic properties of the resonant multipoles, we use multipole decomposition calculation in Cartesian coordinates to obtain the contribution of the resonant multipole scattering power, as shown in Fig. 2(b), including the electric dipole Py, magnetic dipole Mx, toroidal dipole Ty, electric quadrupole Qe, and magnetic quadrupole Qm. The results show that the TD has the highest scattering power at the resonance and is the dominant multipole; the second largest dipole is Qm, which contributes 1/10 of TD to the resonance; and the contributions of ED, MD and Qe are all less than TD by more than 2 orders of magnitude. Therefore, this is a transverse TD resonance.
Fig. 2. (a) Calculated transmission spectrum of an individual Si-DRR when s = 10 µm. (b) Scattering power of different multipole moments. Py, Mx, Ty, Qe, and Qm are electric dipole ED, magnetic dipole MD, toroidal dipole TD, electric quadrupole, and magnetic quadrupole, respectively. (c), (d) Distributions of the electric and magnetic near-fields in the x-y plane and x-z plane at the resonance frequency of 0.331 THz, respectively.
The electric and magnetic near-field distributions at the resonance shown in Fig. 2(c) and 2(d) also verifies the excitation of the TD resonance. It can be clearly seen from Fig. 2(c) that clockwise and counterclockwise displacement current loops are excited in the left and right Si-RR, respectively; such pair of displacement current loops often leads to head-to-tail magnetic moment shown in Fig. 2(d), which indicates the formation of a TD moment along the y-axis.
Then, we studied the effect of the distance between two Si-RRs s on the resonance of TD. Figure 3 shows Q factor and resonance frequency calculated from transmission spectra with respect to s (see Table 1 for specific data). According to the mirror-symmetry of the structure, we known that a Si-DRR with spacing s and a Si-DRR with 60–s are actually identical, hence we can see from Fig. 3 that as s increases from 5 µm to 30 µm, Q values are exactly the same as those when s decreases from 55 µm to 30 µm, i.e., it is symmetrical about s = 30 µm. With the increase of s, the frequency and transmittance (not shown in the figure) of the TD resonance are almost unchanged, but the Q factor rises up quickly, from Q value of 241 when s = 5 µm to 1.6 ×105 when s = 29 µm. However, for a symmetric Si-DRR (s = 30 µm), Q value of the TD resonance becomes infinite (dark TD resonance). Therefore, we can get that the bright high-Q TD resonance is achieved by breaking the symmetry of Si-DRR. This can also be explained from the microscopic view of the electric and magnetic near-field distributions of the TD resonance [49]: when s = s’ = 30 µm, the intra- and inter-TD moments are of equal amplitude and opposite direction, and in a balanced state, thus the coupling of the TD mode to the incident THz wave is zero. Once the structural symmetry is broken (s$\; \ne \; $s’), the balanced state of intra- and inter-TD moments cannot be maintained, leading to the coupling of the transverse TD to the incidence. In addition, the intra-TD moment is stronger than inter-TD moments when s $< $ 30 µm, and the smaller s is, the larger the contrast between the intra- and inter-TD moment is.
Table 1. Q value of TD at different spacing s.
3. EIT in metal-dielectric bilayer MM
3.1 Near-field coupling of a low-Q ED and a high-Q TD
We calculated the transmission spectrum of an individual M-RR when a2 = 225 µm and b2 = 100 µm, as shown in Fig. 4(a). It can be seen that a typical ED resonance with a Q value of 7.8 is excited at 0.331 THz. The surface current distribution of M-RR at the resonance is shown in Fig. 4(b), the relative position of Si-DRR and TD moment Ty are also given in the figure. We can see that the surface current of M-RR (or electric dipole Py) is mainly distributed in two metallic wires of M-RR along the y-axis, while the toroidal dipole Ty is concentrated at the center between the two Si-RRs. The ED resonance of M-RR and TD resonance of Si-DRR designed are of large Q factor contrast and small frequency detuning. When the two resonators form a metal-dielectric bilayer MM with a separated distance h, EIT response will be excited due to the near-field coupling between the two resonances, as shown in Fig. 5 when h = 50 µm (other geometric parameters are the same as those used in Figs. 2 and 4). Transmissions of the individual M-RR (black dashed line) and Si-DRR (blue dashed line) are also given in the figure. We can clearly see an EIT transparency window (red solid line) with a peak value of 0.87 and a bandwidth of 5.7 GHz (Q = 58.7) induced by near-field coupling between the ED and intra-TD. Compared to the narrow band of the TD resonance, the EIT transparency window is largely broadened due to the strong interaction between the two resonances.
Fig. 4. Simulated transmission spectrum of an individual M-RR when a2 = 225 µm and b2 = 100 µm. (b) Surface current distribution of M-RR at the resonance. Si-DRR and its TD moment Ty are displayed as blue, red dotted arrow, respectively.
Fig. 5. Calculated transmission spectrum (red solid line) of a bilayer MM when s = 10 µm and h = 50 µm. Black dotted line and blue dotted line are the transmission spectra of the individual M-RR and Si-DRR, respectively.
The near-field coupling between the two resonances has a great influence on the EIT performance. Generally, the stronger the near field coupling of the two resonances, the wider the EIT transparency window. From the near-field distribution of the two resonances shown in Fig. 4(b), we can get that the near-field coupling of the two modes can be manipulated in the following three ways: 1) by the width of M-RR b2, this will directly change the near-field mode match between the TD and ED. 2) by Q factor of the TD resonance, which corresponds to the enhancement of electric and magnetic near-fields. 3) by the coupling distance between the two resonators, i.e., the thickness of the quartz substrate h. We will focus on the discussion of these three methods in the following section.
3.2 Influence of M-RR on EIT performance
We fixed the coupling distance h = 50 µm and spacing s = 10 µm for the Si-DRR (fixed Q value of 380 of the TD resonance), and investigated the influence of the width b2 of M-RR on the near-field coupling of the two resonances, meanwhile the length a2 of M-RR is readjusted such that the resonance frequency of the ED remains unchanged. Transmission spectra of the bilayer MM for six different values of b2 were calculated, as shown in Fig. 6. It can be seen that when b2 = 175 µm, the near-field mismatch of the ED and TD modes is large, their coupling is very weak, hence peak value of the EIT is only 0.28, and its line shape is largely asymmetric. With the decrease of b2, the near-field coupling between the two resonances increases, hence the EIT peak increases, and its bandwidth increases as well (Q factor decreases). For example, when b2 = 100 µm, the EIT peak and Q factor increase to 0.87 and 58.7, respectively, and the transparency window turns to be symmetrical. When b2 further decreases to 65 µm, the EIT peak reaches 0.93 and Q = 48.5, the EIT effect is largely saturated. Note that when b2 = 12 µm, metal ring of the MRR becomes metal wire, the near-field coupling between the two modes is the strongest among these six cases.
Fig. 6. EIT transparency window of the bilayer MM at different widths b2 of M-RR, when s = 10 µm for Si-DRR and coupling distance h = 50 µm.
3.3 Influences of Q factor of TD and coupling distance on EIT performance
Moreover, we studied the impact of Q factor of the TD resonance on the EIT performance, when M-RR is fixed of a2 = 225 µm, b2 = 100 µm and coupling distance h = 250 µm. Different Q values of the TD resonance are achieved by changing spacing s between the two Si-RRs (see Table 1). Figure 7(a) displays the peak and Q factor of the EIT with respect to spacing s in the range of 5–55 µm. It can be clearly seen that although the Q factor of the TD resonance is symmetrical about s = 30 µm, the peak and Q factor of the EIT are not symmetrical. This is easy to understand from the near-field coupling of the two resonances in Fig. 4(b) as follows: although the two TD resonances of Si-DRR with spacing s and with spacing 60–s belong to identical mode, their intra-TD moments are completely different (intra- and inter-TD moments of these two Si-DRRs are exactly interchangeable), therefore, EIT responses induced by the near-field coupling between the ED and the intra-TD in the two bilayer MMs are also different.
Fig. 7. Q factor (red dotted line) and peak (blue dotted line) of EIT with respect to spacing s when h = 250 µm (a) and 50 µm (b); with respect to coupling distance h when s = 20 µm (c) and 30 µm (d). For all cases, b2 = 100 µm.
When s increases from 5 µm to 30 µm, the Q factor of the TD resonance rises quickly, the near-field of intra-TD also enhances rapidly, thus its coupling with the ED resonance increases, leading to the increase of the EIT peak from 0.32 to 1.0. In addition, because of strong coupling of the two resonances, the EIT transparency window is largely broadened compared with the narrowband TD resonance, hence Q value of the EIT increases only from 71 to 367. As s further increases, the Q factor of the TD resonance decreases, meanwhile, the intra-TD becomes smaller than the inter-TD, which accelerates the decrease of the near-field coupling between the two modes. Therefore, the EIT peak drops remarkably, but the Q factor of the EIT keeps to rise to 568 due to the reduced broadening effect. The EIT response even disappears when s$\; >$ 40 µm.
Recall that the TD resonance is a dark mode with infinite Q value for symmetric Si-DRR (s = 30 µm), according to the continuity of the EIT peak and Q factor curves in Fig. 7(a), we can conclude that the near-field coupling between the dark TD and bright ED behaves just as that between the two bright modes, which is dependent on the Q factor of the TD resonance, i.e., the former is stronger than the latter. This result is different from those reported that the near-field coupling between the bright and dark modes usually take place in asymmetric MMs [20,23].
We also investigated the impact of the Q factor of TD on the EIT when h = 50 µm, as shown in Fig. 7(b). Due to the small coupling distance, the interaction of the two resonances is greatly enhanced. We can see that the EIT performance is quite different from that in Fig. 7(a). When s increases from 5 µm to 55 µm, the Q factor of the EIT not only is much smaller than that when h = 250 µm, but also decreases steadily instead of rising, which attributes to strong broadening effect of the interaction. However, the EIT peak first rises rapidly from 0.72 to 0.99 as s increases from 5 µm to 20 µm, then saturates and drops slowly, and keeps as high value as 0.66 even when s = 55 µm.
In order to achieve a higher Q-factor EIT, a simple way to do is to increase the thickness h for reducing the near-field coupling of the two modes. We calculated the influence of the coupling distance on the EIT for the bilayer MM at fixed s = 20 µm and s = 30 µm, as shown in Figs. 7(c) and 7(d), respectively. From Fig. 7(c), as the coupling distance h increases from 50 µm to 900 µm, the near-field coupling between the bright ED and bright TD decreases, leading to the rapid decrease of the EIT peak; meanwhile, there are two peaks appeared at h = 450 µm and 850 µm, which attribute to the Fabry–Pérot effect of the bilayer MM [53]. Thus, the effective coupling distance of the two modes is less than 300 µm. For the symmetric bilayer MM (s = 30 µm), the near-field coupling between the bright ED and dark TD is greatly enhanced; the EIT peak has a small fluctuation and maintains a large value over 0.85, and the Q factor rises remarkably and reaches over 105 as shown in Fig. 7(d). When h further increases to over 900 µm, the coupling of the two modes sharply drops, and the EIT response disappears. In this case, the near-field coupling distance is significantly extended to over 900 µm, i.e., 1.9 times of wavelength (in media), which was usually less than one wavelength in MMs reported thus far [53–57]. If we use metal wire instead of metal ring to further enhance the near-field coupling of the bright and dark modes, the EIT peak with smaller fluctuation and larger value over 0.90 can be obtained. Such long range EIT can be explained by good coupling ability of metal wire at THz frequencies [58].
Finally, it is well known that the Q factor of the resonance is dependent on both the material loss and radiative loss of the resonance mode, and low material loss is beneficial for achieving high-Q resonances. However, the Q factor of the EIT considered here is limited by the high-Q dielectric DRR. As a low-Q plasmonic MRR, it is not necessary to achieve a high-Q EIT by using superconducting material with lower material loss [59–61] instead of the metal. Moreover, due to the much larger mode volume of dielectric resonator, higher Q factor of the EIT can be achieved in plasmonic-dielectric bilayer MM than in all plasmonic bilayer MM.
4. Conclusion
In conclusion, we proposed and numerically demonstrated the analogue of EIT with a high Q factor in a metal-dielectric bilayer terahertz MM. The dielectric Si-DRR supports either a bright high-Q TD or a dark TD resonance with infinite Q value, while M-RR supports a low-Q ED resonance. We systematically investigated the influences of structure parameters of M-RR, Si-DRR, and layer thickness on the performance of the EIT induced by near-field coupling between the TD and ED resonances. The results show that the near-field coupling of the two resonances can be manipulated effectively and flexibly by the width of M-RR, Q factor of the TD resonance of DRR, and the coupling distance between the two resonators. Interestingly, we find that the near-field coupling between the bright ED and dark TD behaves just as that between the two bright modes, which is dependent on the Q factor of the TD resonance, i.e., the higher the Q factor of TD resonance, the stronger the near-field coupling of the two modes. This result is different from those reported that the near-field coupling between the bright and dark modes usually take place in asymmetric MMs. Furthermore, because of the greatly enhanced coupling of the bright ED and dark TD, the coupling distance is significantly extended to about 1.9 times of the wavelength (in media), which is less than one wavelength reported thus far. Meanwhile the peak of EIT maintains a large value over 0.9, indicating that Fabry–Pérot effect of the bilayer MM is greatly suppressed because of the strong near-field coupling of the two resonances. The proposed bilayer MM provides a new EIT platform that can also be extended to other wave bands such as optics or microwaves.
Funding
National Natural Science Foundation of China (61875179, 12004362); Science Research Foundation of Zhejiang Province (LGG19F050004); Primary Research and Development Plan of Zhejiang Province (2019C03114).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991). [CrossRef]
2. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997). [CrossRef]
3. 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]
4. 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]
5. S.-Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80(15), 153103 (2009). [CrossRef]
6. 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]
7. Z. Wei, X. Li, N. Zhong, X. Tan, X. Zhang, H. Liu, H. Meng, and R. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12(3), 641–647 (2017). [CrossRef]
8. T. A. Chen, I. W. Un, C. C. Wei, Y. J. Lu, D. P. Tsai, and T. J. Yen, “Alternating nanolayers of dielectric MgF2 and metallic Ag as hyperbolic metamaterials: probing surface states and optical topological phase transition and implications for sensing applications,” ACS Appl. Nano Mater. 4(2), 2211–2217 (2021). [CrossRef]
9. M. R. Forouzeshfard, S. Ghafari, and Z. Vafapour, “Solute concentration sensing in two aqueous solution using an optical metamaterial sensor,” J. Lumin. 230, 117734 (2021). [CrossRef]
10. Z. H. He, L. Q. Li, H. Q. Ma, L. H. Pu, H. Xu, Z. Yi, X. L. Cao, and W. Cui, “Graphene-based metasurface sensing applications in terahertz band,” Results Phys. 21, 103795 (2021). [CrossRef]
11. Z. Vafapour, A. Keshavarz, and H. Ghahraloud, “The potential of terahertz sensing for cancer diagnosis,” Heliyon 6(12), e05623 (2020). [CrossRef]
12. J. Zhang, N. Mu, L. H. Liu, J. H. Xie, H. Feng, J. Q. Yao, T. Chen, and W. R. Zhu, “Highly sensitive detection of malignant glioma cells using metamaterial-inspired THz biosensor based on electromagnetically induced transparency,” Biosens. Bioelectron. 185, 113241 (2021). [CrossRef]
13. E. S. Lari, Z. Vafapour, and H. Ghahraloud, “Optically tunable triple–band perfect absorber for nonlinear optical liquids sensing,” IEEE Sensors J. 20(17), 10130–10137 (2020). [CrossRef]
14. F. Yan, Q. Li, Z. W. Wang, H. Tian, and L. Li, “Extremely high Q-factor terahertz metasurface using reconstructive coherent mode resonance,” Opt. Express 29(5), 7015–7023 (2021). [CrossRef]
15. M. D. Fabrizio, S. Lupi, and A. D’Arco, “Virus recognition with terahertz radiation: drawbacks and potentialities,” J. Phys. Photonics 3, 032001 (2021). [CrossRef]
16. L. 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]
17. 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]
18. X. J. Liu, J. Q. Gu, R. Singh, Y. F. Ma, J. Zhu, Z. Tian, M. X. He, and J. G. Han, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(11), 113101 (2012). [CrossRef]
19. M. Wan, J. N. He, Y. L. Song, and F. Q. Zhou, “Electromagnetically induced transparency and absorption in plasmonic metasurfaces based on near-field coupling,” Phys. Lett. A 379(30-31), 1791–1795 (2015). [CrossRef]
20. B. Han, X. Li, C. Sui, J. Diao, X. Jing, and Z. Hong, “Analog of electromagnetically induced transparency in an E-shaped all-dielectric metasurface based on toroidal dipolar response,” Opt. Mater. Express 8(8), 2197–2207 (2018). [CrossRef]
21. J. Diao, B. Han, J. Yin, X. Li, T. Lang, and Z. Hong, “Analogue of electromagnetically induced transparency in an s-shaped all-dielectric metasurface,” IEEE Photonics J. 11(3), 1–10 (2019). [CrossRef]
22. 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]
23. N. Liu, L. Langguth, T. Weiss, J. Kastel, 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]
24. 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]
25. Z. Y. Li, Y. F. Ma, R. Huang, R. J. Singh, J. Q. Gu, Z. Tian, J. G. Han, and W. L. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express 19(9), 8912–8919 (2011). [CrossRef]
26. C. K. Chen, Y. C. Lai, Y. H. Yang, C. Y. Chen, and T. J. Yen, “Inducing transparency with large magnetic response and group indices by hybrid dielectric metamaterials,” Opt. Express 20(7), 6952–6960 (2012). [CrossRef]
27. F. Zhang, Q. Zhao, J. Zhou, and S. Wang, “Polarization and incidence insensitive dielectric electromagnetically induced transparency metamaterial,” Opt. Express 21(17), 19675–19680 (2013). [CrossRef]
28. R. Yahiaoui, J. A. Burrow, S. M. Mekonen, A. Sarangan, J. Mathews, I. Agha, and T. A. Searles, “Electromagnetically induced transparency control in terahertz metasurfaces based on bright-bright mode coupling,” Phys. Rev. B 97(15), 155403 (2018). [CrossRef]
29. L. Zhu, L. Dong, J. Guo, F. Y. Meng, and Q. Wu, “Tunable electromagnetically induced transparency in hybrid graphene/all-dielectric metamaterial,” Appl. Phys. A 123(3), 193 (2017). [CrossRef]
30. L. Zhu, X. Zhao, L. Dong, J. Guo, X. J. He, and Z. M. Yao, “Polarization-independent and angle-insensitive electromagnetically induced transparent (EIT) metamaterial based on bi-air-hole dielectric resonators,” RSC Adv. 8(48), 27342–27348 (2018). [CrossRef]
31. J. Ding, B. Arigong, H. Ren, J. Shao, M. Zhou, Y. K. Lin, and H. L. Zhang, “Dynamically tunable fano metamaterials through the coupling of graphene grating and square closed ring resonator,” Plasmonics 10(6), 1833–1839 (2015). [CrossRef]
32. T. Ma, Q. Huang, H. He, Y. Zhao, X. Lin, and Y. Lu, “All-dielectric metamaterial analogue of electromagnetically induced transparency and its sensing application in terahertz range,” Opt. Express 27(12), 16624–16634 (2019). [CrossRef]
33. J. Q. Gu, R. Singh, X. J. Liu, X. Q. Zhang, Y. F. Ma, S. Zhang, S. A. Maier, and Z. Tian, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012). [CrossRef]
34. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef]
35. W. Cao, R. Singh, I. A. I. Al-Naib, M. X. He, A. J. Taylor, and W. L. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. 37(16), 3366–3368 (2012). [CrossRef]
36. A. A. Basharin, V. Chuguevsky, N. Volsky, M. Kafesaki, and E. N. Economou, “Extremely high Q-factor metamaterials due to anapole excitation,” Phys. Rev. B 95(3), 035104 (2017). [CrossRef]
37. J. F. Algorri, D. C. Zografopoulos, A. Ferraro, B. Garcia-Camara, R. Beccherelli, and J. M. Sanchez-Pena, “Ultrahigh-quality factor resonant dielectric metasurfaces based on hollow nanocuboids,” Opt. Express 27(5), 6320–6330 (2019). [CrossRef]
38. G. D. Liu, X. Zhai, S. X. Xia, Q. Lin, C. J. Zhao, and L. L. Wang, “Toroidal resonance based optical modulator employing hybrid graphene-dielectric metasurface,” Opt. Express. 25(21), 26045–26054 (2017). [CrossRef]
39. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007). [CrossRef]
40. X. Wang, S. Li, and C. Zhou, “Polarization-independent toroidal dipole resonances driven by symmetry-protected BIC in ultraviolet region,” Opt. Express 28(8), 11983–11989 (2020). [CrossRef]
41. K. Koshelev, A. Bogdanov, and Y. Kivshar, “Meta-optics and bound states in the continuum,” Sci. Bull. 64(12), 836–842 (2019). [CrossRef]
42. Z. J. Liu, Y. Xu, Y. Lin, J. Xiang, T. H. Feng, Q. T. Cao, J. T. Li, S. Lan, and J. Liu, “High-Q quasibound states in the continuum for nonlinear metasurfaces,” Phys. Rev. Lett. 123(25), 253901 (2019). [CrossRef]
43. A. S. Kupriianov, Y. Xu, A. Sayanskiy, V. Dmitriev, Y. S. Kivshar, and V. R. Tuz, “Metasurface engineering through bound states in the continuum,” Phys. Rev. Appl. 12(1), 014024 (2019). [CrossRef]
44. K. Koshelev, S. Lepeshov, M. K. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum,” Phys. Rev. Lett. 121(19), 193903 (2018). [CrossRef]
45. S. Han, L. Q. Cong, Y. K. Srivastava, B. Qiang, M. V. Rybin, A. Kumar, R. Jain, W. X. Lim, V. C. Achanta, S. S. Prabhu, Q. J. Wang, Y. S. Kivshar, and R. Singh, “All dielectric active terahertz photonics driven by bound states in the continuum,” Adv. Mater. 31(37), 1901921 (2019). [CrossRef]
46. Y. Liu, Y. Luo, X. Jin, X. Zhou, K. Song, and X. Zhao, “High-Q fano resonances in asymmetric and symmetric all-dielectric metasurfaces,” Plasmonics 12(5), 1431–1438 (2017). [CrossRef]
47. C. B. Zhou, S. Y. Li, Y. Wang, and M. S. Zhan, “Multiple toroidal dipole Fano resonances of asymmetric dielectric nanohole arrays,” Phys. Rev. B 100(19), 195306 (2019). [CrossRef]
48. Y. He, G. T. Guo, T. H. Feng, Y. Xu, and A. E. Miroshnichenko, “Toroidal dipole bound states in the continuum,” Phys. Rev. B 98(16), 161112 (2018). [CrossRef]
49. X. Luo, X. J. Li, T. T. Lang, X. F. Jing, and Z. Hong, “Excitation of high Q toroidal dipole resonance in an all-dielectric metasurface,” Opt. Mater. Express 10(2), 358–368 (2020). [CrossRef]
50. L. Q. Cong and R. Singh, “Symmetry-protected dual bound states in the continuum in metamaterials,” Adv. Opt. Mater. 7(13), 1900383 (2019). [CrossRef]
51. D. R. Abujetas, A. Barreda, F. Moreno, A. Litman, J.-M. Geffrin, and J. A. Sanchez-Gil, “High-Q transparency band in all-dielectric metasurfaces induced by a quasi bound state in the continuum,” Laser Photon. Rev. 15(1), 2000263 (2021). [CrossRef]
52. A. Nagarajan, K. van Erve, and G. Gerini, “Ultra-narrowband polarization insensitive transmission filter using a coupled dielectric-metal metasurface,” Opt. Express 28(1), 773–787 (2020). [CrossRef]
53. F. Y. He, B. X. Han, X. J. Li, T. T. Lang, X. F. Jing, and Z. Hong, “Analogue of electromagnetically induced transparency with high-Q factor in metal-dielectric metamaterials based on bright-bright mode coupling,” Opt. Express 27(26), 37590–37600 (2019). [CrossRef]
54. S.-A. Biehs, V. M. Menon, and G. S. Agarwal, “Long-range dipole-dipole interaction and anomalous Förster energy transfer across a hyperbolic metamaterial,” Phys. Rev. B 93(24), 245439 (2016). [CrossRef]
55. C. L. Cortes and Z. Jacob, “Super-Coulombic atom-atom interactions in hyperbolic media,” Nat. Commun. 8(1), 14144 (2017). [CrossRef]
56. D. Bouchet, D. Cao, R. Carminati, Y. De Wilde, and V. Krachmalnicoff, “Long-range plasmon-assisted energy transfer between fluorescent emitters,” Phys. Rev. Lett. 116(3), 037401 (2016). [CrossRef]
57. Z. Guo, H. Jiang, Y. Li, H. Chen, and G. S. Agarwal, “Enhancement of electromagnetically induced transparency in metamaterials using long range coupling mediated by a hyperbolic material,” Opt. Express 26(2), 627–641 (2018). [CrossRef]
58. K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004). [CrossRef]
59. M. Ricci, N. Orloff, and S. M. Anlage, “Superconducting metamaterials,” Appl. Phys. Lett. 87(3), 034102 (2005). [CrossRef]
60. Z. Vafapour, M. D. utta, and M. A. Stroscio, “Sensing, switching and modulating applications of a superconducting tHz metamaterial,” IEEE Sensors J. 99, 1 (2021). [CrossRef]
61. P. Jung, A. V. Ustinov, and S. M. Anlage, “Progress in superconducting metamaterials,” Supercond Sci. Tech 27, 073001 (2014). [CrossRef]
