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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 16 — Jul. 30, 2012
  • pp: 17581–17590
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Highly-dispersive electromagnetic induced transparency in planar symmetric metamaterials

Xiqun Lu, Jinhui Shi, Ran Liu, and Chunying Guan  »View Author Affiliations


Optics Express, Vol. 20, Issue 16, pp. 17581-17590 (2012)
http://dx.doi.org/10.1364/OE.20.017581


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Abstract

We propose, design and experimentally demonstrate highly-dispersive electromagnetically induced transparency (EIT) in planar symmetric metamaterials actively switched and controlled by angles of incidence. Full-wave simulation and measurement results show EIT phenomena, trapped-mode excitations and the associated local field enhancement of two symmetric metamaterials consisting of symmetrically split rings (SSR) and a fishscale (FS) metamaterial pattern, respectively, strongly depend on angles of incidence. The FS metamaterial shows much broader spectral splitting than the SSR metamaterial due to the surface current distribution variation.

© 2012 OSA

1. Introduction

Electromagnetically induced transparency (EIT) is a coherent optical nonlinearity which renders a medium transparent over a narrow spectral range within an absorption line [1

1. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]

]. EIT phenomenon gives rise to important effects such as ultraslow group velocity and enhancing nonlinear interactions between light and a medium, however, cumbersome experimental conditions are often involved in achieving EIT phenomenon, such as cryogenic temperatures and high intensity lasers.

During the past decade, metamaterials consisting of subwavelength electromagnetic resonators have attracted tremendous amount of interest [2

2. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef] [PubMed]

4

4. N. I. Zheludev, “Applied physics: the road ahead for metamaterials,” Science 328(5978), 582–583 (2010). [CrossRef] [PubMed]

], due to their unusual properties (e.g. negative refraction, invisibility and perfect lens). More recently, metamaterials are engineered to realize an intriguing classical analogy with famous quantum phenomenon such as EIT phenomenon [5

5. N. Papasimakis and N. I. Zheludev, “Metamaterial-induced transparency,” Opt. Photon. News 20(10), 22–27 (2009). [CrossRef]

] and Fano resonance [6

6. 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] [PubMed]

]. The asymmetric Fano resonance, which has long been known as a characteristic feature of interacting quantum systems, has more recently been found in plasmonic nanostructures and metamaterials. Under certain conditions a Fano resonance can be regarded as the classical analogue of electromagnetically induced transparency. These conditions are: (i) sufficiently small frequency detuning between the two coupled resonances; (ii) strongly contrasting resonance linewidths; and (iii) appropriate resonance amplitudes [6

6. 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] [PubMed]

]. When coherent coupling between the two resonances occurs, destructive interference can suppress the absorption of the broader resonance, resulting in an induced transparency window [7

7. 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]

9

9. 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]

]. Subsequently, metamaterial analogy of EIT phenomenon has been widely investigated in a wide range of literatures [10

10. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102(5), 053901 (2009). [CrossRef] [PubMed]

30

30. 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]

]. The steep dispersion of EIT and Fano resonance profile promises applications in slow light, sensor, nonlinear and switching applications. The EIT phenomenon in metamaterials is generally realized by the bright-dark mode coupling [10

10. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102(5), 053901 (2009). [CrossRef] [PubMed]

26

26. Y. Tamayama, T. Nakanishi, and M. Kitano, “Variable group delay in a metamaterial with field-gradient-induced transparency,” Phys. Rev. B 85(7), 073102 (2012). [CrossRef]

] or the bright-bright mode coupling [7

7. 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]

, 8

8. 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]

, 27

27. V. A. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. I. Zheludev, “Temperature control of Fano resonances and transmission in superconducting metamaterials,” Opt. Express 18(9), 9015–9019 (2010). [CrossRef] [PubMed]

30

30. 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]

]. Classical analogy of EIT effect in metamaterials was initially observed in arrays of asymmetrically split rings (ASRs) [7

7. 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]

], consisting of two wire arcs with a broken symmetry, serving as the bright modes for certain polarized wave. The asymmetric coupling between the bright modes can excite a high-Q mode formed by counter-propagating currents (i.e. a so-called trapped mode resonance that is associated with an asymmetric Fano-type line shape), revealing EIT transmission peak. The quality factor of such trapped-mode resonance is mainly limited by losses and attempts to compensate or eliminate Joule losses using optically-pumped gain media such as superconducting metamaterials [15

15. C. Kurter, P. Tassin, L. Zhang, Th. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetic induced transparency with a metal/superconductor hybrid metamaterial,” Phys. Rev. Lett. 107, 043901 (2011).

, 27

27. V. A. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. I. Zheludev, “Temperature control of Fano resonances and transmission in superconducting metamaterials,” Opt. Express 18(9), 9015–9019 (2010). [CrossRef] [PubMed]

] and semiconductor quantum dots [31

31. E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009). [CrossRef] [PubMed]

, 32

32. K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010). [CrossRef] [PubMed]

] have been reported. The tunability of EIT effect is another key issue. Tuning of an EIT phenomenon was observed when crossing the superconducting transition temperature of a superconducting metamaterial [15

15. C. Kurter, P. Tassin, L. Zhang, Th. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetic induced transparency with a metal/superconductor hybrid metamaterial,” Phys. Rev. Lett. 107, 043901 (2011).

, 27

27. V. A. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. I. Zheludev, “Temperature control of Fano resonances and transmission in superconducting metamaterials,” Opt. Express 18(9), 9015–9019 (2010). [CrossRef] [PubMed]

]. Most generally, the properties of EIT effect can mostly be controlled by the metamaterial design [7

7. 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]

13

13. 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]

] or changing the location of one resonator [22

22. X. R. Jin, J. W. Park, H. Y. Zheng, S. J. Lee, Y. P. Lee, J. Y. Rhee, K. W. Kim, H. S. Cheong, and W. H. Jang, “Highly-dispersive transparency at optical frequencies in planar metamaterials based on two-bright-mode coupling,” Opt. Express 19(22), 21652–21657 (2011). [CrossRef] [PubMed]

]. However, it is extremely difficult to change the geometrical size of elements or move one resonator once they are fabricated. Therefore, a practical way of controlling EIT is desirable for developing EIT-type metamaterials for real applications. Active manipulation of plasmonic EIT was proposed and the tunability of EIT was only investigated theoretically in this scheme [17

17. Y. H. Lu, J. Y. Rhee, W. H. Jang, and Y. P. Lee, “Active manipulation of plasmonic electromagnetically-induced transparency based on magnetic plasmon resonance,” Opt. Express 18(20), 20912–20917 (2010). [CrossRef] [PubMed]

]. Even though the mechanical control has the disadvantage for high-speed applications, it is significant for active manipulation of EIT phenomenon.

In this paper, we report that high-dispersive EIT can be achieved in two types of planar single-layered metamaterials that consist of symmetrically split rings (SSR) and fish-scale (FS) pattern, respectively. The active tuning of EIT is demonstrated theoretically and experimentally and it can be efficiently switched and controlled via the angle of incidence. The local field enhancement is achieved through engaging so-called trapped modes, sub-radiant high-Q current modes. The local energy density enhancement can be adjusted from 80 to about 3000 times the incident wave’s energy density simply by tilting the metamaterial relative to the incident beam. Both metamaterials considered is single-layered and simple, offering an easy-to-implement way of achieving EIT tunability in metamaterials in the broad frequency domain.

2. Metamaterial samples

We investigated EIT tuning in two model meta-surfaces based on SSR and FS wire patterns, falling into the wallpaper symmetry groups pmm and pmg, respectively, see Fig. 1
Fig. 1 Metamaterial structures. (a) The angle of incidence а is measured between the incident wave vector k and the metamaterial's surface normal n. Here metamaterial transmission is studied for y-polarized electromagnetic waves at oblique incidence which is realized by tilting the metamaterials around their y axis. (b) Symmetrically split ring (SSR) unit cell. (c) Fishscale (FS) unit cell.
. The SSRs consist of two identical wire arcs and the FS structure is assembled from pairs of identical “U”-shapes connected to form continuous wires, thus neither structure allows the excitation of anti-symmetric currents at normal incidence. Both metamaterials consist of square meta-molecule arrays with a period of 15 mm, rendering the structures non-diffracting at any angle of incidence for frequencies below 10 GHz. The metamaterial patterns with an overall size of about 200 × 200mm2 were etched from 35 µm copper cladding covering FR4 PCB substrates of t = 1.6 mm thickness. The width of the metallic strips was 0.8mm. Detailed dimensions of the SSR and FS unit cells are given in Figs. 1(b) and 1(c), respectively. We note that the FS metamaterial had previously attracted attention for its invisibility, magnetic mirror properties [33

33. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, and N. I. Zheludev, “Planar electromagnetic metamaterial with a fish scale structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056613 (2005). [CrossRef] [PubMed]

, 34

34. V. A. Fedotov, A. V. Rogacheva, N. I. Zheludev, P. L. Mladyonov, and S. L. Prosvirnin, “Mirror that does not change the phase of reflected waves,” Appl. Phys. Lett. 88(9), 091119 (2006). [CrossRef]

] and EIT phenomenon [8

8. 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]

], where a bilayered FS metamaterial is necessary for the trapped-mode excitation.

In metamaterials, trapped-mode resonances belonging to a family of Fano resonances are usually observed in structures with intrinsic symmetry breaking, for example in ASRs [7

7. 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]

] or pairs of ring resonators of different size [28

28. N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94(21), 211902 (2009). [CrossRef]

]. At normal incidence, such intrinsic symmetry breaking of the metamaterial structure is essential to allow the excitation of EIT phenomenon in metamaterials. Here we investigate transparency induced by extrinsic symmetry breaking provided by an oblique incidence. In contrast to normal incidence, where the incident wave excites the entire metamaterial interface in phase, at oblique incidence the wave fronts “roll across” the meta-surface, exciting different parts of the unit cell at different times. We will see that this phase lag allows and controls the excitation of the anti-symmetric currents underpinning EIT transmission peak.

3. Experimental and simulated results

The SSR and FS metamaterials were measured at angles of incidence from 0° to 50° in the 4-9 GHz frequency range. The experiments were carried out in an anechoic chamber using broadband horn antennas (Schwarzbeck BBHA9120D) equipped with dielectric lens concentrators and a vector network analyzer (Agilent E8364B). Corresponding transmission spectra and the associated modes of excitation were also simulated using the commercial software (CST Microwave Studio) in the frequency domain, where copper was treated as a perfect electric conductor and a relative permittivity ε = 4.05−i0.05 was assumed for the lossy dielectric substrate. For the results presented below, both the polarization of incident waves and the axis around which the metamaterial was tilted to achieve the oblique incidence were parallel to the SSR wires and the straight FS wires (i.e. the y axis), see Fig. 1.

Figure 2
Fig. 2 Transmission spectra. (a)-(b) Measured and (c)-(d) simulated transmission spectra of the SSR and FS metamaterials as a function of the angle of incidence α for incident y-polarized electromagnetic waves. The insets indicate types of metamaterials.
shows the measured and simulated metamaterial transmission spectra as a function of the angle of incidence α. Apparently, EIT phenomenon can be switched and manipulated by angles of incidence. At normal incidence onto either metamaterial the y-polarization can only excite one resonance (III) at about 6.4 GHz, which we will later identify as a simple symmetric dipole resonance. However, when the metamaterial patterns are tilted around the y axis, a second transmission minimum I - which is not present at normal incidence - appears at a slightly lower frequency. Remarkably, a narrow pass band II discussed in terms of EIT [27

27. V. A. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. I. Zheludev, “Temperature control of Fano resonances and transmission in superconducting metamaterials,” Opt. Express 18(9), 9015–9019 (2010). [CrossRef] [PubMed]

, 28

28. N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94(21), 211902 (2009). [CrossRef]

] forms in between the transmission minima I and III. This pass band has a strong dependence on the angle of incidence, which differs for the SSR and FS metamaterials. In case of SSRs [see Fig. 2(a)], the spectral separation of the transmission resonances I and III is independent of the angle of incidence α. However, with increasing α the pass band II at about f = 5.2 GHz becomes more pronounced and its quality factor measured as Q = f/Δf increases to about 23 at α = 50° (peak width Δf = 0.23 GHz at 3 dB below maximum). The FS metamaterial shows a remarkably different behavior, see Fig. 2(b). Its pass band II at 5.8 GHz broadens dramatically from Q = 27 to about 10 as the angle of incidence is increased from α = 10° to 50° and simultaneously the spectral separation of the surrounding transmission minima increases about 3-fold. There is a good agreement between the simulated and experimental results shown in Fig. 2, but the experimental results are a little worse than the simulated ones due to scattering losses during the experiment. Figure 2(c) and 2(d) illustrate that the maximum of the quality factor for SRR metamaterial is 30.4 at the angle of incidence α = 50° with the resonant frequency f = 5.17 GHz and the width Δf = 0.17 GHz while the maximum of the quality factor for FS metamaterial is about 50 at the angle of incidence α = 10° with the resonant frequency f = 6.11 GHz and the width Δf = 0.12 GHz, which are summarized in Fig. 3(c)
Fig. 3 Energy density enhancement and quality factor at the resonant modes. (a)-(b) Magnitude of the electromagnetic energy density 0.1 mm above the surface, relative to the energy density of the incident y-polarized wave at α = 50° for the SSR metamaterial and at α = 10° for the FS metamaterial. The modes shown here correspond to the resonances I, II, and III marked in Fig. 2. (c)-(d) Quality factor and peak energy density enhancement for the pass band II as a function of the angle of incidence. Square and triangle symbols correspond to the SSR and FS metamaterials, respectively (dashed lines - simulations, solid lines - experiments).
.

For metamaterials with symmetric patterns like those discussed here anti-symmetric current configurations are forbidden, but only at normal incidence. The origin of EIT-type resonances appearing at oblique incidence can be traced to the excitation of trapped modes [7

7. 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]

, 28

28. N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94(21), 211902 (2009). [CrossRef]

]. Remarkably, strong magnetic dipole generated by anti-parallel propagating surface currents confines most electromagnetic energy near the surface of the planar metamaterial, which gives rise to giant local field energy density enhancement. The factor of near-field energy density enhancement is calculated as the ratio of the magnitude of the electromagnetic energy density 0.1mm above the SSR and FS metamaterial relative to the energy density of incident y-polarized wave. The energy distribution maps of the SSR metamaterial at α = 50° and FS metamaterial at α = 10° are shown in Fig. 3(a) and 3(b). In case of the SSR metamaterial, this trapped mode consists of currents of equal magnitude oscillating in anti-phase in the two wire arcs, while in the FS pattern the currents in neighboring bends have the same magnitude but oscillate in opposite directions. In either case, radiation losses are very weak, as emission from opposite arcs/bends would destructively interfere in the far-field and therefore electromagnetic energy is trapped at the meta-surface. As a consequence, the magnitude of the excited currents can become very large, ensuring a high quality factor of the pass band, see Fig. 3(c). In particular this results in a remarkably large local energy density enhancement relative to the incident wave, which can be tuned from 80 to 2900 for the FS metamaterial and from 170 to 3700 in case of the SSR metamaterial, see Fig. 3(d). This tunable trapping of electromagnetic energy is of interest for various sensing applications and achieving strong optical nonlinearities.

The transmission phase changes of the FS and SRR metamaterials at α = 50° are illustrated in Fig. 4(a)
Fig. 4 Phase change and group index across the FS and SSR metamaterial as a function of frequency at an incident angle of α = 50° (dashed lines-simulations, solid lines-experiments). Gray boxes indicate areas of sharp normal phase dispersion.
and 4(c). The transmission window studied here is accompanied by a very sharp normal phase dispersion that, as was recently pointed out in Refs. 8

8. 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]

and 9

9. 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]

, renders the response of the structure a metamaterial analog of EIT. Despite the metamaterials vanishing thickness of ~λ/35, it can potentially be used for achieving long pulse delays. In fact, the phase dispersion of the FS metamaterial at α = 10° is much stronger (not shown here). The group index is roughly estimated according to ng = c0 dk/dω = - (c0/t) dΦ /dω [17

17. Y. H. Lu, J. Y. Rhee, W. H. Jang, and Y. P. Lee, “Active manipulation of plasmonic electromagnetically-induced transparency based on magnetic plasmon resonance,” Opt. Express 18(20), 20912–20917 (2010). [CrossRef] [PubMed]

, 24

24. Z. G. Dong, P. G. Ni, J. Zhu, and X. Zhang, “Transparency window for the absorptive dipole resonance in a symmetry-reduced grating structure,” Opt. Express 20(7), 7206–7211 (2012). [CrossRef] [PubMed]

, 35

35. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009). [CrossRef]

], where c0 is the speed of light in vacuum, Φ is the transmission phase, ω is the angular frequency and t is the thickness of metamaterials. In Fig. 4(b) and 4(d), the group indices are the same order as those in Ref. 35

35. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009). [CrossRef]

[35

35. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009). [CrossRef]

]. The high group index corresponds to an increased traversing time of light through the entire structure. There is a good agreement between the simulated and measured results despite the fabrication error and random error in experiments.

4. Spectral splitting of the SSR and FS metamaterials

It is difficult to produce a simple and accurate estimate for the resonant frequency for the polarized incident radiation considered here at the normal incidence [33

33. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, and N. I. Zheludev, “Planar electromagnetic metamaterial with a fish scale structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056613 (2005). [CrossRef] [PubMed]

], however, the resonances appear when the wavelength of excitation in the strip is approximately equal to the full length of the metallic wire within the unit cell. Under the oblique incidence, the resonant frequencies seem more sophisticated to be estimated. Asymmetric shifts of SRR and FS metamaterials are used to describe the hybridization strength of the dipolar-active and dipolar-inactive modes quantitatively [29

29. C. Y. Chen, I. W. Un, N. H. Tai, and T. J. Yen, “Asymmetric coupling between subradiant and superradiant plasmonic resonances and its enhanced sensing performance,” Opt. Express 17(17), 15372–15380 (2009). [CrossRef] [PubMed]

], defined as ω+ω, where ω+and ω correspond to the resonant frequencies of the resonances III and I. ωFS+ andωFS shift progressively to blue and red with increasing angles of incidence, respectively, while ωSSR+ and ωSSR are kept nearly unchanged in Fig. 5(a)
Fig. 5 Resonant frequency and asymmetric shift. (a) ω+ andω of SSR and FS metamaterials. ω+and ω+ correspond to the resonant frequencies of the resonances I and III marked in Fig. 2. (b) Asymmetric shifts ω+ω of SSR and FS metamaterials. Square and triangle symbols correspond to the SSR and FS metamaterials, respectively.
. The asymmetric shifts describe the resonant feature straightforwardly shown in Fig. 5(b). It is obvious that the asymmetric coupling of SRR metamaterial is much weaker than that of FS metamaterial when the angle of incidence increases.

Next, it is necessary to explicate why the resonant frequencies of the resonances III and I in the FS metamaterial shift progressively to blue and red with increasing angles of incidence, while the resonant frequencies of the resonances III and I in the SSR metamaterial are almost kept unmoved. Oblique incidence leads to a small delay between the excitation of the two arcs of the SSR or halves of the FS-wire, meanwhile a small portion of magnetic component propagates across the surface of the metamaterial, rendering the whole system symmetry broken. This delay is sufficient to allow the excitation of an anti-symmetric trapped current mode associated with transmission minimum I and maximum II. Different from the SSR metamaterial with two separated arms, the “U” elements are being physically connected. The conductive coupling contributes to spectral separation [36

36. N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. (Deerfield Beach Fla.) 20(23), 4521–4525 (2008). [CrossRef]

]. For the connected structures, the spectral splitting that is directly correlated with the electromagnetic coupling strength is substantially enhanced. In particular, the redshift of the anti-symmetric modes (lower frequency resonance I) is weaker than the blueshift of the symmetric modes (higher frequency resonance III), which is contrary to the result in Ref. 36

36. N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. (Deerfield Beach Fla.) 20(23), 4521–4525 (2008). [CrossRef]

[36

36. N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. (Deerfield Beach Fla.) 20(23), 4521–4525 (2008). [CrossRef]

]. On the other hand, the large spectral splitting of the FS metamaterial is linked to the surface current distribution variation due to the oblique incidence, illustrated in Fig. 6
Fig. 6 Normalized absolute surface current distribution of resonant modes I, II and III in the FS metamaterial at α = 10° and α = 50°. (a)-(b) Absolute surface current of the FS metamaterial at φ0 = 0°. φ0 denotes initial phase of incident waves. (c)-(d) Absolute surface current of the FS metamaterial at φ0 = 90°. Arrows qualitatively indicate the instantaneous directions and magnitudes of the current flows. The dashed circles indicate the locations of the nodes in the surface current maps.
. It is clearly seen in Fig. 6(a) and 6(c) or Fig. 6(b) and 6(d) that the surface current distribution in two adjacent unit cells is greatly influenced by phase φ0 of incident waves. Whatever angles of incidence and phase of incident waves are, the response of the resonances I and II in the FS metamaterial is mostly dominated by anti-phase surface currents in the FS bends while in-phase surface currents contribute to the response of the resonance III. At α = 10°, there are four nodes of the surface current for each resonance in Fig. 6(a), marked by the dashed circles. At α = 50°, the resonance II still has four nodes, however, three nodes for the resonance I and five nodes for the resonance III due to large surface current distribution variation. The variation of nodes never occurs in the SSR metamaterial with two separated arcs. The additional current nodes require higher energies of the electromagnetic field to excite the particular surface current modes [37

37. C. Rockstuhl, F. Lederer, C. Etrich, Th. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14(19), 8827–8836 (2006). [CrossRef] [PubMed]

]. Therefore, the resonant frequencies of the resonances III and I in the FS metamaterial shift progressively to blue and red with increasing angles of incidence, much stronger than that of the SSR metamaterial.

5. Conclusions

In summary, we experimentally and numerically demonstrated that highly-dispersive EIT-type transmission band can be switched and controlled via angles of incidence. In particular, we have realized (i) trapped mode on/off switching, (ii) tuning of highly-dispersive EIT transmission band, (iii) tuning of the resonance quality factor and (iv) a controlled 35-fold increase of local energy density enhancement via the angle of incidence for simple, planar model structures based on SSRs and a FS wire pattern. These structures are well-suited for existing microfabrication and nanofabrication technologies and tuning via the angle of incidence can be easily applied anywhere in the electromagnetic spectrum. The variation of surface current nodes provides an insight into large spectral splitting of the FS metamaterial and explains the reason that the resonant frequencies of the resonances III and I in the FS metamaterial shift progressively to blue and red with increasing angles of incidence. The EIT-like behavior of the SSR and FS metamaterials makes them promising candidates for “slow light” applications, while local energy density enhancement provides in interesting platform for nonlinear, gain metamaterials and the lasing spaser.

Acknowledgments

The author thanks Dr. Plum and Prof. Zheludev for useful discussions. This work was supported by the Natural Science Foundation of Heilongjiang Province in China under Grant No. LC201006, in part by the National Science Foundation of China under Grant No. 11104043, in part by the China Postdoctoral Science Foundation under Grant No. 2012M511171, in part by the Special Foundation for Harbin Young Scientists under Grant No. 2012RFLXG030.

References and Links

1.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]

2.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef] [PubMed]

3.

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011). [CrossRef] [PubMed]

4.

N. I. Zheludev, “Applied physics: the road ahead for metamaterials,” Science 328(5978), 582–583 (2010). [CrossRef] [PubMed]

5.

N. Papasimakis and N. I. Zheludev, “Metamaterial-induced transparency,” Opt. Photon. News 20(10), 22–27 (2009). [CrossRef]

6.

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] [PubMed]

7.

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]

8.

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]

9.

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]

10.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102(5), 053901 (2009). [CrossRef] [PubMed]

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.

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]

13.

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]

14.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Planar designs for electromagnetically induced transparency in metamaterials,” Opt. Express 17(7), 5595–5605 (2009). [CrossRef] [PubMed]

15.

C. Kurter, P. Tassin, L. Zhang, Th. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetic induced transparency with a metal/superconductor hybrid metamaterial,” Phys. Rev. Lett. 107, 043901 (2011).

16.

Y. Lu, X. Jin, H. Zheng, Y. P. Lee, J. Y. Rhee, and W. H. Jang, “Plasmonic electromagnetically-induced transparency in symmetric structures,” Opt. Express 18(13), 13396–13401 (2010). [CrossRef] [PubMed]

17.

Y. H. Lu, J. Y. Rhee, W. H. Jang, and Y. P. Lee, “Active manipulation of plasmonic electromagnetically-induced transparency based on magnetic plasmon resonance,” Opt. Express 18(20), 20912–20917 (2010). [CrossRef] [PubMed]

18.

J. Zhang, S. Xiao, C. Jeppesen, A. Kristensen, and N. A. Mortensen, “Electromagnetically induced transparency in metamaterials at near-infrared frequency,” Opt. Express 18(16), 17187–17192 (2010). [CrossRef] [PubMed]

19.

Z. G. Dong, H. Liu, J. X. Cao, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett. 97(11), 114101 (2010). [CrossRef]

20.

Z. G. Dong, H. Liu, M. X. Xu, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Plasmonically induced transparent magnetic resonance in a metallic metamaterial composed of asymmetric double bars,” Opt. Express 18(17), 18229–18234 (2010). [CrossRef] [PubMed]

21.

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]

22.

X. R. Jin, J. W. Park, H. Y. Zheng, S. J. Lee, Y. P. Lee, J. Y. Rhee, K. W. Kim, H. S. Cheong, and W. H. Jang, “Highly-dispersive transparency at optical frequencies in planar metamaterials based on two-bright-mode coupling,” Opt. Express 19(22), 21652–21657 (2011). [CrossRef] [PubMed]

23.

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]

24.

Z. G. Dong, P. G. Ni, J. Zhu, and X. Zhang, “Transparency window for the absorptive dipole resonance in a symmetry-reduced grating structure,” Opt. Express 20(7), 7206–7211 (2012). [CrossRef] [PubMed]

25.

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

26.

Y. Tamayama, T. Nakanishi, and M. Kitano, “Variable group delay in a metamaterial with field-gradient-induced transparency,” Phys. Rev. B 85(7), 073102 (2012). [CrossRef]

27.

V. A. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. I. Zheludev, “Temperature control of Fano resonances and transmission in superconducting metamaterials,” Opt. Express 18(9), 9015–9019 (2010). [CrossRef] [PubMed]

28.

N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94(21), 211902 (2009). [CrossRef]

29.

C. Y. Chen, I. W. Un, N. H. Tai, and T. J. Yen, “Asymmetric coupling between subradiant and superradiant plasmonic resonances and its enhanced sensing performance,” Opt. Express 17(17), 15372–15380 (2009). [CrossRef] [PubMed]

30.

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]

31.

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009). [CrossRef] [PubMed]

32.

K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010). [CrossRef] [PubMed]

33.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, and N. I. Zheludev, “Planar electromagnetic metamaterial with a fish scale structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(5), 056613 (2005). [CrossRef] [PubMed]

34.

V. A. Fedotov, A. V. Rogacheva, N. I. Zheludev, P. L. Mladyonov, and S. L. Prosvirnin, “Mirror that does not change the phase of reflected waves,” Appl. Phys. Lett. 88(9), 091119 (2006). [CrossRef]

35.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009). [CrossRef]

36.

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. (Deerfield Beach Fla.) 20(23), 4521–4525 (2008). [CrossRef]

37.

C. Rockstuhl, F. Lederer, C. Etrich, Th. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14(19), 8827–8836 (2006). [CrossRef] [PubMed]

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(260.5740) Physical optics : Resonance
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: May 23, 2012
Revised Manuscript: July 10, 2012
Manuscript Accepted: July 10, 2012
Published: July 18, 2012

Citation
Xiqun Lu, Jinhui Shi, Ran Liu, and Chunying Guan, "Highly-dispersive electromagnetic induced transparency in planar symmetric metamaterials," Opt. Express 20, 17581-17590 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-17581


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References

  1. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys.77(2), 633–673 (2005). [CrossRef]
  2. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004). [CrossRef] [PubMed]
  3. Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev.40(5), 2494–2507 (2011). [CrossRef] [PubMed]
  4. N. I. Zheludev, “Applied physics: the road ahead for metamaterials,” Science328(5978), 582–583 (2010). [CrossRef] [PubMed]
  5. N. Papasimakis and N. I. Zheludev, “Metamaterial-induced transparency,” Opt. Photon. News20(10), 22–27 (2009). [CrossRef]
  6. 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] [PubMed]
  7. 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]
  8. 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]
  9. 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]
  10. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett.102(5), 053901 (2009). [CrossRef] [PubMed]
  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. 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]
  13. 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]
  14. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Planar designs for electromagnetically induced transparency in metamaterials,” Opt. Express17(7), 5595–5605 (2009). [CrossRef] [PubMed]
  15. C. Kurter, P. Tassin, L. Zhang, Th. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetic induced transparency with a metal/superconductor hybrid metamaterial,” Phys. Rev. Lett.107, 043901 (2011).
  16. Y. Lu, X. Jin, H. Zheng, Y. P. Lee, J. Y. Rhee, and W. H. Jang, “Plasmonic electromagnetically-induced transparency in symmetric structures,” Opt. Express18(13), 13396–13401 (2010). [CrossRef] [PubMed]
  17. Y. H. Lu, J. Y. Rhee, W. H. Jang, and Y. P. Lee, “Active manipulation of plasmonic electromagnetically-induced transparency based on magnetic plasmon resonance,” Opt. Express18(20), 20912–20917 (2010). [CrossRef] [PubMed]
  18. J. Zhang, S. Xiao, C. Jeppesen, A. Kristensen, and N. A. Mortensen, “Electromagnetically induced transparency in metamaterials at near-infrared frequency,” Opt. Express18(16), 17187–17192 (2010). [CrossRef] [PubMed]
  19. Z. G. Dong, H. Liu, J. X. Cao, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett.97(11), 114101 (2010). [CrossRef]
  20. Z. G. Dong, H. Liu, M. X. Xu, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Plasmonically induced transparent magnetic resonance in a metallic metamaterial composed of asymmetric double bars,” Opt. Express18(17), 18229–18234 (2010). [CrossRef] [PubMed]
  21. 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]
  22. X. R. Jin, J. W. Park, H. Y. Zheng, S. J. Lee, Y. P. 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. Express19(22), 21652–21657 (2011). [CrossRef] [PubMed]
  23. 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]
  24. Z. G. Dong, P. G. Ni, J. Zhu, and X. Zhang, “Transparency window for the absorptive dipole resonance in a symmetry-reduced grating structure,” Opt. Express20(7), 7206–7211 (2012). [CrossRef] [PubMed]
  25. X. J. Liu, J. Q. Gu, R. Singh, Y. F. Ma, J. Zhu, Z. Tian, M. X. He, J. G. Han, and W. L. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100(13), 131101 (2012). [CrossRef]
  26. Y. Tamayama, T. Nakanishi, and M. Kitano, “Variable group delay in a metamaterial with field-gradient-induced transparency,” Phys. Rev. B85(7), 073102 (2012). [CrossRef]
  27. V. A. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. I. Zheludev, “Temperature control of Fano resonances and transmission in superconducting metamaterials,” Opt. Express18(9), 9015–9019 (2010). [CrossRef] [PubMed]
  28. N. Papasimakis, Y. H. Fu, V. A. Fedotov, S. L. Prosvirnin, D. P. Tsai, and N. I. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett.94(21), 211902 (2009). [CrossRef]
  29. 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. Express17(17), 15372–15380 (2009). [CrossRef] [PubMed]
  30. 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]
  31. E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express17(10), 8548–8551 (2009). [CrossRef] [PubMed]
  32. K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot luminescence in plasmonic metamaterials,” Phys. Rev. Lett.105(22), 227403 (2010). [CrossRef] [PubMed]
  33. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, and N. I. Zheludev, “Planar electromagnetic metamaterial with a fish scale structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.72(5), 056613 (2005). [CrossRef] [PubMed]
  34. V. A. Fedotov, A. V. Rogacheva, N. I. Zheludev, P. L. Mladyonov, and S. L. Prosvirnin, “Mirror that does not change the phase of reflected waves,” Appl. Phys. Lett.88(9), 091119 (2006). [CrossRef]
  35. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B80(19), 195415 (2009). [CrossRef]
  36. N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. (Deerfield Beach Fla.)20(23), 4521–4525 (2008). [CrossRef]
  37. C. Rockstuhl, F. Lederer, C. Etrich, Th. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express14(19), 8827–8836 (2006). [CrossRef] [PubMed]

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