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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 17 — Aug. 16, 2010
  • pp: 18229–18234
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Plasmonically induced transparent magnetic resonance in a metallic metamaterial composed of asymmetric double bars

Zheng-Gao Dong, Hui Liu, Ming-Xiang Xu, Tao Li, Shu-Ming Wang, Shi-Ning Zhu, and X. Zhang  »View Author Affiliations


Optics Express, Vol. 18, Issue 17, pp. 18229-18234 (2010)
http://dx.doi.org/10.1364/OE.18.018229


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Abstract

We demonstrate that the trapped magnetic resonance mode can be induced in an asymmetric double-bar structure for electromagnetic waves normally incident onto the double-bar plane, which mode otherwise cannot be excited if the double bars are equal in length. By adjusting the structural geometry, the trapped magnetic resonance becomes transparent with little resonance absorption when it happens in the dipolar resonance regime, a phenomenon so-called plasmonic analogue of electromagnetically induced transparency (EIT). This planar EIT-like metamaterial offers a great geometry simplification by combining the radiant and subradiant resonant modes in a single double-bar resonator.

© 2010 OSA

1. Introduction

For conventional metamaterials, the spatial distances between discrete elements were generally out of the touch of neighboring near fields localized around individual elements, and consequently the plasmonic interactions of nearby metal structures could be neglected. Though this treatment was feasible to study the average effect in terms of the effective medium approximation (such as left-handed metamaterials), it is not applicable to interparticle-coupled metamaterials, for which great interest has been provoked recently because the plasmon coupling between adjacent metallic elements can induce many attractive electromagnetic properties [1

1. H. Liu, Y. M. Liu, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Coupled magnetic plasmonsin metamaterials,” Phys. Stat. Solidi B 246(7), 1397–1406 (2009). [CrossRef]

3

3. T. Li, H. Liu, F. M. Wang, Z. G. Dong, S. N. Zhu, and X. Zhang, “Coupling effect of magnetic polariton in perforated metal/dielectric layered metamaterials and its influence on negative refraction transmission,” Opt. Express 14(23), 11155–11163 (2006). [CrossRef] [PubMed]

]. For example, the plasmon hybridization in neighboring elements can split the resonant spectrum and obtain a great optical activity [4

4. H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies,” Phys. Rev. B 76(7), 073101 (2007). [CrossRef]

], while the plasmonic analogue of electromagnetically induced transparency (EIT) in metamaterials, usually composed of dual resonators [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]

11

11. 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]

], is a result of plasmon coupling between a radiative eigenmode (e.g., dipolar resonance) in one resonator and a subradiant eigenmode (e.g., quadrupolar resonance) in the adjacent resonator in a manner of destructive interference.

Generally, intriguing properties in coupled metamaterials are resulted from various plasmon coupling configurations with either structural symmetry or asymmetry. A straight configuration is to squeeze the element interval and thus the near-field coupling can be significantly enhanced between metal elements, including those symmetric elements equivalent in both metal shape and spatial arrangement [12

12. I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009). [CrossRef]

]. In contrast, spatially and/or structurally asymmetric configurations usually take an astonishing role in modifying the electromagnetic responses in coupled metamaterials. Spatially asymmetric coupling, i.e., rotating or translating the neighboring homomorphic elements with respect to one another can lead to optical activity or additional dark-mode excitation, respectively [4

4. H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies,” Phys. Rev. B 76(7), 073101 (2007). [CrossRef]

,13

13. A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8(8), 2171–2175 (2008). [CrossRef] [PubMed]

]. On the other hand, structurally asymmetric coupling happens by deliberately breaking the element symmetry in shape as well as in size, such as concentric double rings [14

14. Z. G. Dong, M. X. Xu, S. Y. Lei, H. Liu, T. Li, F. M. Wang, and S. N. Zhu, “Negative refraction with magnetic resonance in a metallic double-ring metamaterial,” Appl. Phys. Lett. 92(6), 064101 (2008). [CrossRef]

,15

15. 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]

], ring-disk composite [16

16. F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett. 8(11), 3983–3988 (2008). [CrossRef] [PubMed]

], asymmetric split-ring pairs [17

17. 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]

,18

18. 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]

], and mismatched nanoparticle pairs [19

19. L. V. Brown, H. Sobhani, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Heterodimers: plasmonic properties of mismatched nanoparticle pairs,” ACS Nano 4(2), 819–832 (2010). [CrossRef] [PubMed]

]. A common coupling characteristic for such size or shape asymmetry in adjacent elements is the Fano-type resonance with a transmission dip closely accompanied with a transmission peak [14

14. Z. G. Dong, M. X. Xu, S. Y. Lei, H. Liu, T. Li, F. M. Wang, and S. N. Zhu, “Negative refraction with magnetic resonance in a metallic double-ring metamaterial,” Appl. Phys. Lett. 92(6), 064101 (2008). [CrossRef]

18

18. 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]

,20

20. 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]

]. In this work, we numerically demonstrate that a trapped magnetic/quadrupolar resonance with Fano-type profile is excitable by introducing asymmetry in a double-bar structure. A plasmonically induced transparency can be obtained when this trapped magnetic resonance coincides with a dipolar resonance. It is emphasized that this planar design based on a simple double-bar structure takes a great convenience for experimental treatment in comparison with various EIT-like metamaterials studied in literatures [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]

11

11. 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]

], which are usually either in three dimensions or with complex planar geometry.

2. Plasmonic metamaterial and numerical model

Figure 1
Fig. 1 (Color online) Structural schematic of the metallic double-bar metamaterial. Only a single double-bar layer in the propagation direction is considered in simulations.
shows a schematic illustration of the metallic metamaterial and the polarization of incident light. The bar geometry with length 1=200nm, width w=30nm, thinckness t=30nm, and the gap between double bars is g=30nm. The translating parameters for the double bars are: px=250nm, py=600nm, and pz=100nm. The substrate is quartz with index of refraction ns=1.55, and the metallic structure is immerged in a host medium with index of refraction nh=1.94. Under the polarization situation of incident waves with electric field along the bar length, dipolar oscillation is an excitable bright mode, whereas the quadrupolar eigenmode with antiparallel induced currents inherent to the double parallel bars is subradiant/dark because the double bars are electrically equivalent for their same lengths. In our simulations [21

21. Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96(4), 044104 (2010). [CrossRef]

,22

22. F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016604 (2007). [CrossRef] [PubMed]

], perfect electric and magnetic boundaries are used in compliance with the incident polarization configuration, and the metal is defined by using Drude dispersion with ωp=1.37×1016s1 and γ=1.2×1014s1, where γ is three times of the theoretical bulk value in order to account for nanofabrication tolerances [7

7. 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]

,8

8. 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]

].

3. Results and discussions

Figures 2(a)
Fig. 2 (Color online) Transmission spectra of the double-bar metamaterial with (a) symmetric bar lengths 1=1=200nm, (b) symmetric bar lengths 1=1=120nm, and (c) asymmetric bar lengths 1=200nm and 1=120nm. Magnetic field distributions for five resonances in (a)-(c) are shown in the right panel (d)-(h), respectively.
and 2(b) show the calculated transmission spectra for the symmetric double-bar structure with equal bar lengths 1=200nm and 120nm, respectively. It is found that dipolar resonances occur near f1=162THz and f2=248THz, respectively. As is known, the asymmetric mode (i.e., the quadrupolar resonant mode with antiparallel induced current at the surface of the double-bar structure) cannot be excited magnetically since the magnetic field component is parallel to the double-bar plane, also it cannot be excited electrically because the symmetric double bars (i.e., bars in the same length) are equivalent with respect to the polarized electric field. However, by breaking the length symmetry of the double bars, e.g., keeping the length of one of the double bars as 1=200nm while shortening the length of another bar to be 1=120nm, a third resonant mode, in addition to these two dipolar resonances as presented in Figs. 2(a) and 2(b), can be induced around f3=202THzwith a Fano-type transmission spectrum [Fig. 2(c)]. This additional mode confines a strong intensity of magnetic field in the gap of the asymmetric double bars, and thus is a nonradiative/trapped magnetic resonance with antiparallel induced currents on the double bar surfaces. To confirm these dipolar and quadrupolar modes, magnetic field distributions are presented in Figs. 2(d)2(h), corresponding to five resonances in Figs. 2(a)2(c), respectively.

The additional magnetic resonance is induced electrically since the asymmetric double-rod structure is not equivalent with respect to the polarized electric field of the incident light, and it is physically similar to the electrically excited magnetic resonance in split-ring resonators [23

23. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004). [CrossRef]

]. Nevertheless, it should be of interest that a plasmon version of the EIT phenomenon can be obtained in this asymmetric double-bar metamaterial, if structural parameters are adjusted to make the trapped magnetic resonance locate within the frequency regime of the dipolar resonance. As shown in Fig. 3
Fig. 3 (Color online) EIT-like transmittance and absorbance in the asymmetric double-bar metamaterial with some adjusted structural scales as follows: 1=157nm, 1=117nm, g=40nm, Px=240nm, and Py=590nm. The orange vertical shadow indicates the position of the transparency window and absorption dip, while the inset presents the localized magnetic field distribution for the transparency window.
, when the dipolar and quadrupolar resonances coincide, the latter one will become transparent around 200 THz. In different to the EIT phenomenon in an atomic system, the intrinsic metal loss in the metamaterial cannot be eliminated at the optical spectrum [7

7. 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]

]. This transparency window, as well as the corresponding narrow dip at the middle portion of the dipolar absorption profile, is a result of the destructive interference between the two excitation pathways, namely, direct excitation of the radiative dipolar plasmon oscillation and indirect excitation of the nonradiative quadrupolar plasmon oscillation [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]

,7

7. 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]

].

According to the interpretation for a plasmonic analogue of EIT phenomenon [4

4. H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies,” Phys. Rev. B 76(7), 073101 (2007). [CrossRef]

8

8. 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]

], the incident waves excite the dipolar plasmon state, and then this excited dipolar oscillation plasmonically couples to the quadrupolar oscillation. Transparency window would be formed if there is a destructive interference between the direct excitation pathway of dipolar plasmon oscillation and the indirect excitation pathway of quadrupolar plasmon oscillation. During this process, radiative plasmon state transfers the exciting electromagnetic resonance to the subradiant plasmon state through the aid of near-field plasmon coupling. Note that this plasmon coupling in EIT-like metamaterials happens at a same resonance frequency of two different resonant modes [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]

11

11. 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]

]. In contrast, the optical nonlinearity is inherent in an atomic EIT system where a control light is different to a probe light in frequency [24

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

,25

25. C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70(1), 37–41 (2002). [CrossRef]

]. Here, the plasmon coupling in a manner of destructive interference acts as the control factor which determines the absorption or transparency of the probe/incident light. If the plasmon coupling does not exist for these two resonant modes, there should be a resonant dip (absorption) in the transmission spectrum, instead of an EIT-like resonant transparency, as presented in Fig. 2(c). Notice that the EIT-like peak can never be obtained in the double-bar structure unless a structural asymmetry will be introduced. Moreover, the occurrence of EIT not only depends on the bar scales and the bar-bar gap, but it also depends on the periodic array intervals. The latter dependence should imply the importance of the ordered arrangement on the EIT occurrence. In fact, since such transparency window in EIT-like characteristic is a result of destructive interference between dark and bright resonances, any disorder in the structural arrangement, or even fabrication imperfections of element size and position, will break or disturb the coherent coupling between elements, and thus is not preferred for a significant EIT-like window.

Another characteristic of EIT-like resonance in metamaterials is the large group index that is useful for slowing down the electromagnetic propagation in nanoplasmonic devices. To characterize this property for the EIT-like transmission peak in the asymmetric double-bar metamaterial as presented in Fig. 3, the group index dispersion is calculated. It is found that the maximum group index can reach a value of 27 at the transparency window (Fig. 4
Fig. 4 (Color online) Group index of the EIT-like asymmetric double-bar metamaterial with structural parameters as presented in Fig. 3. The bulk value of the loss factor γbu1k (circle line) is considered to evaluate the influence of the metal damping constant on the group index.
, red solid line). Note that a loss factor γ=1.2×1014s1, triple the bulk value of gold, has been considered for the simulation. If the bulk value γbu1k=4.08×1013s1 is used for the gold in the Drude formula, the maximum value of the group index can reach a value as large as 62 (Fig. 4, black circle line). This difference in the maximum value of the group index indicates how much it can be affected by the metal loss factor in the Drude formula. Interestingly, negative group index can be found in the dipolar resonance regime, this is known as superluminal wave propagation, a common characteristic to lossy metamaterials [26

26. V. Yannopapas, “Sign of the refractive index in lossy metamaterials,” Opt. Commun. 282(20), 4152–4156 (2009). [CrossRef]

], and was experimentally observed in atomic EIT systems [27

27. L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406(6793), 277–279 (2000). [CrossRef] [PubMed]

,28

28. A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63(5), 053806 (2001). [CrossRef]

].

4. Summary

In summary, in addition to the dipolar resonant mode, an electrically excited quadrupolar mode with Fano-type profile can be induced in a metallic double-bar metamaterial by breaking the length symmetry. The radiative dipolar plasmon oscillation cannot only absorb the polarized light, but also it can interact destructively with the subradiant quadrupolar mode through the near-field plasmon coupling. Consequently, a transparency resonance can be obtained instead of an absorption one due to destructive interference between these two resonant modes. It is emphasized that this asymmetric double-bar structure is currently the most simplified EIT-like metamaterial by combining the radiant and subradiant resonant modes in a single double-bar resonator, and thus would take great convenience for future experimental study of plasmonic EIT phenomenon.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 10874081, No. 10904012, and No. 60990320), the National Key Projects for Basic Researches of China (No. 2010CB630703), and the Research Fund for the Doctoral Program of Higher Education of China (No. 20090092120031).

References and links

1.

H. Liu, Y. M. Liu, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Coupled magnetic plasmonsin metamaterials,” Phys. Stat. Solidi B 246(7), 1397–1406 (2009). [CrossRef]

2.

M. Decker, S. Linden, and M. Wegener, “Coupling effects in low-symmetry planar split-ring resonator arrays,” Opt. Lett. 34(10), 1579–1581 (2009). [CrossRef] [PubMed]

3.

T. Li, H. Liu, F. M. Wang, Z. G. Dong, S. N. Zhu, and X. Zhang, “Coupling effect of magnetic polariton in perforated metal/dielectric layered metamaterials and its influence on negative refraction transmission,” Opt. Express 14(23), 11155–11163 (2006). [CrossRef] [PubMed]

4.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies,” Phys. Rev. B 76(7), 073101 (2007). [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.

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]

7.

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]

8.

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]

9.

V. Yannopapas, E. Paspalakis, and N. V. Vitanov, “Electromagnetically induced transparency and slow light in an array of metallic nanoparticles,” Phys. Rev. B 80(3), 035104 (2009). [CrossRef]

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.

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]

12.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009). [CrossRef]

13.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8(8), 2171–2175 (2008). [CrossRef] [PubMed]

14.

Z. G. Dong, M. X. Xu, S. Y. Lei, H. Liu, T. Li, F. M. Wang, and S. N. Zhu, “Negative refraction with magnetic resonance in a metallic double-ring metamaterial,” Appl. Phys. Lett. 92(6), 064101 (2008). [CrossRef]

15.

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]

16.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett. 8(11), 3983–3988 (2008). [CrossRef] [PubMed]

17.

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]

18.

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]

19.

L. V. Brown, H. Sobhani, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Heterodimers: plasmonic properties of mismatched nanoparticle pairs,” ACS Nano 4(2), 819–832 (2010). [CrossRef] [PubMed]

20.

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]

21.

Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. 96(4), 044104 (2010). [CrossRef]

22.

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(1), 016604 (2007). [CrossRef] [PubMed]

23.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004). [CrossRef]

24.

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

25.

C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70(1), 37–41 (2002). [CrossRef]

26.

V. Yannopapas, “Sign of the refractive index in lossy metamaterials,” Opt. Commun. 282(20), 4152–4156 (2009). [CrossRef]

27.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406(6793), 277–279 (2000). [CrossRef] [PubMed]

28.

A. Dogariu, A. Kuzmich, and L. J. Wang, “Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity,” Phys. Rev. A 63(5), 053806 (2001). [CrossRef]

OCIS Codes
(160.3918) Materials : Metamaterials
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Metamaterials

History
Original Manuscript: July 16, 2010
Revised Manuscript: August 4, 2010
Manuscript Accepted: August 4, 2010
Published: August 9, 2010

Citation
Zheng-Gao Dong, Hui Liu, Ming-Xiang Xu, Tao Li, Shu-Ming Wang, Shi-Ning Zhu, and X. Zhang, "Plasmonically induced transparent magnetic resonance in a metallic metamaterial composed of asymmetric double bars," Opt. Express 18, 18229-18234 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-18229


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References

  1. H. Liu, Y. M. Liu, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Coupled magnetic plasmonsin metamaterials,” Phys. Stat. Solidi B 246(7), 1397–1406 (2009). [CrossRef]
  2. M. Decker, S. Linden, and M. Wegener, “Coupling effects in low-symmetry planar split-ring resonator arrays,” Opt. Lett. 34(10), 1579–1581 (2009). [CrossRef] [PubMed]
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