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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 17 — Aug. 26, 2013
  • pp: 19675–19680
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Polarization and incidence insensitive dielectric electromagnetically induced transparency metamaterial

Fuli Zhang, Qian Zhao, Ji Zhou, and Shengxiang Wang  »View Author Affiliations


Optics Express, Vol. 21, Issue 17, pp. 19675-19680 (2013)
http://dx.doi.org/10.1364/OE.21.019675


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Abstract

In this manuscript, we demonstrate numerically classical analogy of electromagnetically induced transparency (EIT) with a windmill type metamaterial consisting of two dumbbell dielectric resonator. With proper external excitation, dielectric resonators serve as EIT bright and dark elements via electric and magnetic Mie resonances, respectively. Rigorous numerical analyses reveal that dielectric metamaterial exhibits sharp transparency peak characterized by large group index due to the destructive interference between EIT bright and dark resonators. Furthermore, such EIT transmission behavior keeps stable property with respect to polarization and incidence angles.

© 2013 OSA

1. Introduction

Recently, metamaterial microstructures have been employed to mimic electromagnetically induced transparency (EIT) behavior of atomic system [1

1. 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] [PubMed]

6

6. 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]

]. A sharp transmission peak along with steep normal dispersion results in large value of group index, which is of great interest to the enhancement of group delay and slow light control [7

7. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]

]. To resemble classical EIT behavior, various metamaterial based approaches including “trapped mode” [1

1. 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] [PubMed]

4

4. R. Singh, I. A. I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011). [CrossRef]

] and destructive interference between isolated bright and dark elements were proposed [5

5. 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]

, 6

6. 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]

, 8

8. X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(13), 131101 (2012). [CrossRef]

19

19. J. Chen, P. Wang, C. Chen, Y. Lu, H. Ming, and Q. Zhan, “Plasmonic EIT-like switching in bright-dark-bright plasmon resonators,” Opt. Express 19(7), 5970–5978 (2011). [CrossRef] [PubMed]

]. For the latter case, bright and dark elements generally have same resonance frequencies, around which bright element can be excited by the incident beam directly while dark elements do not coupled directly to external wave, but can be excited by local field of bright element resonance via near field coupling.

In the letter, we propose a windmill type dielectric EIT metamaterial at terahertz regime. Instead of isolated dark and bright elements for EIT metamaterial, herein elementary unit is a unified cell composed of two orthogonal dumbbell dielectric resonators, which serves as bright and dark elements via electric and magnetic Mie resonance, respectively. Rigorous numerical results reveal a typical EIT transmission peak along with large group index occurs around 0.5 THz. Besides, such behavior shows independent property to incidence angle and polarization.

2. Results and discussion

Figure 1
Fig. 1 Schematic view of windmill shape EIT metamaterial (a) periodic array and (b) elementary cell. The geometry parameters are as follows: l = 98, w = 62, t = s = 20, ax = ay = 240 (unit: μm).
depicts schematically configuration for dielectric EIT metamaterial. A windmill configuration is proposed as a combination of two identical dumbbell type twisted by 90°. Each dumbbell cell consists of two square bricks separated by a dielectric bar. The whole dielectric metamaterial array is patterned on a fused quartz substrate (εQuartz = 3.794 + 0.003i) [26

26. M. N. Afsar and H. Ding, “A novel open-resonator system for precise measurement of permittivity and loss-tangent,” IEEE Trans. Instrum. Meas. 50(2), 402–405 (2001). [CrossRef]

]. Dielectric layer is assumed as Titanium oxide (TiO2) with a relative large permittivity and moderate dielectric loss at terahertz frequencies (εTiO2 = 114, tanδTiO2 = 0.01) [27

27. H. Němec, C. Kadlec, F. Kadlec, P. Kuzel, R. Yahiaoui, U.-C. Chung, C. Elissalde, M. Maglione, and P. Mounaix, “Resonant magnetic response of TiO2 microspheres at terahertz frequencies,” Appl. Phys. Lett. 100(6), 061117 (2012). [CrossRef]

]. The geometrical parameters are given in the caption of Fig. 1. The scattering response of EIT metamaterial is calculated by using 3D full wave frequency domain package, High Frequency Structure Simulator (HFSS).

According to two-resonator-model for EIT metamaterial [5

5. 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]

, 6

6. 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]

], it is obvious that two dumbbell resonators are required. That means one dumbbell is electrically coupled directly to the incident beam as bright element and the other one, whose resonance cannot be observed directly for normal incidence, acts as a dark element. Finally, a windmill type configuration is formed by two dumbbell resonators for EIT metamaterial design. Figure 2(c) presents the scattering parameters of windmill metamaterial under normal incidence with electric polarization along x axis. Clearly, a typical EIT-like transmission spectrum with one sharp peak located at 0.483 THz and two transmission dips at 0.465 and 0.528 THz can be observed. Compared to the resonance frequency of bright/dark element, slightly frequency shift of EIT peak mainly attributes to the overlap of middle parts of twisted dumbbell resonators.

To look insight the underlying physics for such dielectric metamaterial, local electric field distributions of transmission peak and dips are monitored and given in Fig. 3
Fig. 3 Local electric field distribution for dielectric EIT metamaterial at various frequencies: (a) f = 0.465 THz (b) f = 0. 485 THz (c) f = 0.528THz.
. At the transmission dips around EIT windows, as shown in Figs. 3(a) and 3(c), linearly oscillated displacement currents are excited along the vertical dumbbell resonator, which is directly coupled to incident electric field, hence, leading to vanishing transmission. Subsequent local magnetic field produced by displacement currents along vertical dumbbell further induces anti-orientation circular displacement currents distribution inside two square bricks of horizontal dumbbell. At the transmission peak frequency, as presented in Fig. 3(b), most local displacement currents are localized inside two square bricks of horizontal dumbbell and mere displacement currents are observed along the vertical dumbbell, due to destructive interference between resonance modes of dark and bright resonators.

Employing a well-established retrieval algorithm [28

28. X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco Jr, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004). [CrossRef] [PubMed]

], electromagnetic parameters including effective index, n, can be obtained. The group index, ng = n + ωdn/dω, is further calculated and presented in Fig. 4
Fig. 4 Group index and imaginary part of phase index for dielectric windmill type EIT metamaterial.
. Within the EIT transmission window, the group index experiences strong dispersion. The peak value over 100 for group index and low value of imaginary part of effective index reveal great interest of potential application in slow light control.

Figure 5(a)
Fig. 5 (a) Transmission spectra as a function of frequency and polarization angle. Local electric field distribution at EIT peak frequency f = 0.485 THz under incidence polarization of (b) ϕ = 30°and (c) ϕ = 135°. Inset shows the electric polarization varies with respect to x axis.
presents the transmission spectra as a function of frequency and polarization angle off to x axis. Electric polarization angle off to x axis varying 180° were investigated, even though only four polarization angles were plotted. As incident polarization varies, transmission spectra difference is so minor that can be negligible, clearly demonstrating the polarization independence property of dielectric EIT metamaterial. Local electric field distribution at EIT transmission peak under various polarization excitations were given in Figs. 5(b) and 5(c). When the incident polarization is off to x axis, accumulation of local field is no longer concentrated inside two dielectric bricks of single dumbbell resonator, despite the amplitude distribution mainly depends on polarization angle. This is because two orthogonal dielectric bars can be excited by incident electric field components along x and y axes, consequently, such electromagnetic energy can be finally transferred into corresponding dielectric brick resonators. Actually, local field interference between bright elements plays an important role to design a polarization insensitive property. As reported in Ref. 25

25. 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] [PubMed]

, construction/destruction interference of local fields of two orthogonal bright elements can result in the enhancement or elimination of EIT effect, when polarization angles are 135° and 45°, respectively. On the contrary, dielectric brick resonators’ locations at the vertex of dielectric bar in this manuscript ensure these dark elements can only be excited by single bright element under various polarizations. Furthermore, symmetric configuration of windmill microstructure leads to unchanged resonance frequencies of bright and dark elements. As a consequence, EIT behavior is independent of varying polarization.

Figure 6
Fig. 6 Oblique incidence as a function of frequency for dielectric EIT metamaterial. (a) TE and (b) TM mode.
displays EIT metamaterial transmission spectra as a function of frequency and incident angle under TE and TM modes. As shown in Fig. 6, for normal incidence, dumbbell metamaterial shows the same EIT transmission characteristics for TE and TM polarizations. With increasing incident direction angle off to z axis, θ, EIT peaks shows a stable behavior for both TE and TM modes. A maximum frequency shift is around 0.03 THz, accounting for 6% with respect to central frequency. Even though, EIT transmission feature remains under oblique incident up to 75° off to z axis. Obviously, this shows the advantage of dielectric metamaterial in the realization of planar isotropic EIT structure.

3. Conclusions

In conclusion, we present a full dielectric windmill type EIT metamaterial at terahertz frequency. With proper design, electric and magnetic Mie resonances of dumbbell resonator enable superradiant and subradiant resonance nature under different excitation. Rigorous numerical analyses verify such planar dielectric metamaterial exhibits typical EIT transmission peak along with large value of group index. Due to symmetry configuration, windmill type EIT metamaterial possesses a nearly independent characteristic of EIT transmission feature on polarization and incidence angle. Furthermore, recent advance on magnetic sputtering approach and lithography [29

29. F. Ponchel, X. Lei, D. Rémiens, G. Wang, and X. Dong, “Microwave evaluation of Pb0.4Sr0.6TiO3 thin films prepared by magnetron sputtering on silicon: performance comparison with Ba0.3Sr0.7TiO3 thin films,” Appl. Phys. Lett. 99(17), 172905 (2011). [CrossRef]

] to prepare dielectric film enables the feasibility of dielectric EIT metamaterial at terahertz as proposed in this manuscript. Considering strict requirement for polarization independence in real application, it can be expected that this work will be useful to promote the development of EIT metamaterial and slow light device.

Acknowledgments

We gratefully acknowledge the financial support from National Natural Science Foundation of China (Grant Nos. 61101044, 61275176, 11274198, 51032003), National High Technology Research and Development Program of China (863 Program) (Grant No. 2012AA030403), Aeronautical Science Foundation of China (Grant No. 20120153001), NPU Foundation for Fundamental Research (Grant No. JCY20130138), and NPU Aoxiang Star Project, and Project-sponsored by SRF for ROCS, SEM.

References and links

1.

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] [PubMed]

2.

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]

3.

R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express 19(7), 6312–6319 (2011). [CrossRef] [PubMed]

4.

R. Singh, I. A. I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011). [CrossRef]

5.

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]

6.

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]

7.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]

8.

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(13), 131101 (2012). [CrossRef]

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.

W. Cao, R. Singh, I. A. IAl-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q darkmode plasmonic fano metamaterials,” Opt. Lett. 37, 3366 (2012).

11.

R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “Coupling between a dark and a bright eigenmode in a terahertz metamaterial,” Phys. Rev. B 79(8), 085111 (2009). [CrossRef]

12.

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]

13.

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]

14.

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mater. Express 1(3), 391–399 (2011). [CrossRef]

15.

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]

16.

J. Shao, J. Li, J. Li, Y.-K. Wang, Z.-G. Dong, P. Chen, R.-X. Wu, and Y. Zhai, “Analogue of electromagnetically induced transparency by doubly degenerate modes in a U-shaped metamaterial,” Appl. Phys. Lett. 102(3), 034106 (2013). [CrossRef]

17.

A. E. Çetin, A. Artar, M. Turkmen, A. A. Yanik, and H. Altug, “Plasmon induced transparency in cascaded π-shaped metamaterials,” Opt. Express 19(23), 22607–22618 (2011). [CrossRef] [PubMed]

18.

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]

19.

J. Chen, P. Wang, C. Chen, Y. Lu, H. Ming, and Q. Zhan, “Plasmonic EIT-like switching in bright-dark-bright plasmon resonators,” Opt. Express 19(7), 5970–5978 (2011). [CrossRef] [PubMed]

20.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101(2), 027402 (2008). [CrossRef] [PubMed]

21.

F. Zhang, L. Kang, Q. Zhao, J. Zhou, and D. Lippens, “Magnetic and electric coupling effects of dielectric metamaterial,” New J. Phys. 14(3), 033031 (2012). [CrossRef]

22.

B.-I. Popa and S. A. Cummer, “Compact dielectric particles as a building block for low-loss magnetic metamaterials,” Phys. Rev. Lett. 100(20), 207401 (2008). [CrossRef] [PubMed]

23.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett. 98(15), 157403 (2007). [CrossRef] [PubMed]

24.

A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in all-dielectric oligomers,” Nano Lett. 12(12), 6459–6463 (2012). [CrossRef] [PubMed]

25.

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] [PubMed]

26.

M. N. Afsar and H. Ding, “A novel open-resonator system for precise measurement of permittivity and loss-tangent,” IEEE Trans. Instrum. Meas. 50(2), 402–405 (2001). [CrossRef]

27.

H. Němec, C. Kadlec, F. Kadlec, P. Kuzel, R. Yahiaoui, U.-C. Chung, C. Elissalde, M. Maglione, and P. Mounaix, “Resonant magnetic response of TiO2 microspheres at terahertz frequencies,” Appl. Phys. Lett. 100(6), 061117 (2012). [CrossRef]

28.

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco Jr, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004). [CrossRef] [PubMed]

29.

F. Ponchel, X. Lei, D. Rémiens, G. Wang, and X. Dong, “Microwave evaluation of Pb0.4Sr0.6TiO3 thin films prepared by magnetron sputtering on silicon: performance comparison with Ba0.3Sr0.7TiO3 thin films,” Appl. Phys. Lett. 99(17), 172905 (2011). [CrossRef]

OCIS Codes
(260.5430) Physical optics : Polarization
(160.3918) Materials : Metamaterials
(230.4555) Optical devices : Coupled resonators

ToC Category:
Metamaterials

History
Original Manuscript: June 1, 2013
Revised Manuscript: July 19, 2013
Manuscript Accepted: July 28, 2013
Published: August 14, 2013

Citation
Fuli Zhang, Qian Zhao, Ji Zhou, and Shengxiang Wang, "Polarization and incidence insensitive dielectric electromagnetically induced transparency metamaterial," Opt. Express 21, 19675-19680 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-19675


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References

  1. 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] [PubMed]
  2. 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]
  3. R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express19(7), 6312–6319 (2011). [CrossRef] [PubMed]
  4. R. Singh, I. A. I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett.99(20), 201107 (2011). [CrossRef]
  5. 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]
  6. 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]
  7. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today50(7), 36 (1997). [CrossRef]
  8. X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100(13), 131101 (2012). [CrossRef]
  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. W. Cao, R. Singh, I. A. IAl-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q darkmode plasmonic fano metamaterials,” Opt. Lett.37, 3366 (2012).
  11. R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “Coupling between a dark and a bright eigenmode in a terahertz metamaterial,” Phys. Rev. B79(8), 085111 (2009). [CrossRef]
  12. 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. B80(15), 153103 (2009). [CrossRef]
  13. 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. Express19(9), 8912–8919 (2011). [CrossRef] [PubMed]
  14. Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mater. Express1(3), 391–399 (2011). [CrossRef]
  15. 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]
  16. J. Shao, J. Li, J. Li, Y.-K. Wang, Z.-G. Dong, P. Chen, R.-X. Wu, and Y. Zhai, “Analogue of electromagnetically induced transparency by doubly degenerate modes in a U-shaped metamaterial,” Appl. Phys. Lett.102(3), 034106 (2013). [CrossRef]
  17. A. E. Çetin, A. Artar, M. Turkmen, A. A. Yanik, and H. Altug, “Plasmon induced transparency in cascaded π-shaped metamaterials,” Opt. Express19(23), 22607–22618 (2011). [CrossRef] [PubMed]
  18. 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]
  19. J. Chen, P. Wang, C. Chen, Y. Lu, H. Ming, and Q. Zhan, “Plasmonic EIT-like switching in bright-dark-bright plasmon resonators,” Opt. Express19(7), 5970–5978 (2011). [CrossRef] [PubMed]
  20. Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett.101(2), 027402 (2008). [CrossRef] [PubMed]
  21. F. Zhang, L. Kang, Q. Zhao, J. Zhou, and D. Lippens, “Magnetic and electric coupling effects of dielectric metamaterial,” New J. Phys.14(3), 033031 (2012). [CrossRef]
  22. B.-I. Popa and S. A. Cummer, “Compact dielectric particles as a building block for low-loss magnetic metamaterials,” Phys. Rev. Lett.100(20), 207401 (2008). [CrossRef] [PubMed]
  23. L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett.98(15), 157403 (2007). [CrossRef] [PubMed]
  24. A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in all-dielectric oligomers,” Nano Lett.12(12), 6459–6463 (2012). [CrossRef] [PubMed]
  25. 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. Express20(7), 6952–6960 (2012). [CrossRef] [PubMed]
  26. M. N. Afsar and H. Ding, “A novel open-resonator system for precise measurement of permittivity and loss-tangent,” IEEE Trans. Instrum. Meas.50(2), 402–405 (2001). [CrossRef]
  27. H. Němec, C. Kadlec, F. Kadlec, P. Kuzel, R. Yahiaoui, U.-C. Chung, C. Elissalde, M. Maglione, and P. Mounaix, “Resonant magnetic response of TiO2 microspheres at terahertz frequencies,” Appl. Phys. Lett.100(6), 061117 (2012). [CrossRef]
  28. X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(1), 016608 (2004). [CrossRef] [PubMed]
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