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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 16 — Aug. 1, 2011
  • pp: 15363–15370
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Plasmonic-induced optical transparency in the near-infrared and visible range with double split nanoring cavity

Shao-Ding Liu, Zhi Yang, Rui-Ping Liu, and Xiu-Yan Li  »View Author Affiliations


Optics Express, Vol. 19, Issue 16, pp. 15363-15370 (2011)
http://dx.doi.org/10.1364/OE.19.015363


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Abstract

Abstract: Plasmonic-induced optical transparency with double split nanoring cavity is investigated with finite difference time domain method. The coupling between the bright third-order mode of split nanoring with one gap and the dark quadrupole mode of split nanoring with two gaps leads to plasmonic analogue of electromagnetically induced transparency. The transparence window is easily modified to the near-infrared and visible range. Numerical results show a group index of 16 with transmission exceeding 0.76 is achieved for double split nanoring cavity. There is large cavity volume of double split nanoring, and the field enhancement inside the cavity is homogenous. Double split nanoring cavity could be a good platform for slow light and sensing applications.

© 2011 OSA

1. Introduction

Electromagnetically induced transparency (EIT) in atomic physics is the result of a quantum destructive interference between two pathways induced by another field, which can make an absorptive medium transparent to the probe field [1

1. K. J. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991). [CrossRef] [PubMed]

]. EIT is useful for many applications, such as slow light propagation, transfer of quantum correlation, and nonlinear optical processes [2

2. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999). [CrossRef]

4

4. S. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82(23), 4611–4614 (1999). [CrossRef]

]. But the special experimental conditions block the practical application of EIT in atomic system, and EIT-like behavior in classical systems has been developed [5

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

11

11. 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]

]. Among these methods, plasmonic analogues of EIT in metallic nanostructures have been attracted much attention in recent years. Compared to EIT in atomic medium, plasmonic-induced optical transparency can be operated in room temperature, also it has wide bandwidth and easy to integrate [11

11. 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]

]. The EIT analogue in metallic nanostructure is considered as the plasmon coupling between a radiative mode and a subradiative mode through a manner of destructive interference. A lot of nanostructures have been proposed and demonstrated to realize plasmonic-induced optical transparency, such as dipole antennas [11

11. 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]

17

17. 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]

], fish scales metallic patterns [18

18. 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]

], detuned electrical dipoles [19

19. 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]

,20

20. S. I. Bozhevolnyi, A. B. Evlyukhin, A. Pors, M. G. Nielsen, M. Willatzen, and O. Albrektsen, “Optical transparency by detuned electrical dipoles,” N. J. Phys. 13(2), 023034 (2011). [CrossRef]

], split ring resonators [21

21. P. Tassin, L. Zhang, Th. 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]

29

29. M. Kang, H.-X. Cui, Y. Li, B. Gu, J. Chen, and H.-T. Wang, “Fano-Feshbach resonance in structural symmetry broken metamaterials,” J. Appl. Phys. 109(1), 014901 (2011). [CrossRef]

], array of metallic nanoparticles [30

30. 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]

], and plasmonic-waveguide system [31

31. R. D. Kekatpure, E. S. Barnard, W. Cai, and M. L. Brongersma, “Phase-coupled plasmon-induced transparency,” Phys. Rev. Lett. 104(24), 243902 (2010). [CrossRef] [PubMed]

35

35. L. Dai, Y. Liu, and C. Jiang, “Plasmonic-dielectric compound grating with high group-index and transmission,” Opt. Express 19(2), 1461–1469 (2011). [CrossRef] [PubMed]

]. It has been found plasmonic-induced optical transparency is particular useful for switching [36

36. 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]

], slow light [37

37. L. Zhang, P. Tassin, T. Koschny, C. Kurter, S. M. Anlage, and C. M. Soukoulis, “Large group delay in a microwave metamaterial analog of electromagnetically induced transparency,” Appl. Phys. Lett. 97(24), 241904 (2010). [CrossRef]

], and sensing applications [38

38. 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]

40

40. 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]

].

2. Spectra of SNRs

The solid line of Fig. 1(a)
Fig. 1 (a) Extinction and scattering cross sections of Ag SNR-I under normal incident excitation, (b) Field enhancement (|E|/|Einc|) distribution of the third-order mode at the cross section of SNR-I. (c) Spectra of SNR-II under grazing incident excitation, (d) Field enhancement distribution of the quadrupole mode of SNR-II, where the polarization vector is indicated by arrows. The geometry parameters W = 40 nm, g = 30 nm, R = 180 nm, r = 105 nm, and the thickness T = 25 nm. The inset of Fig. 1(a) is the spectra of SNR-I with R = 65 nm.
shows the extinction spectrum of a SNR-I, where finite difference time domain (FDTD) method is used to calculate the spectra [50

50. A. Taflove and S. C. Hagness, Computational electrodynamics: The finite-difference time-domain method (Artech House, Boston, 2005).

], silver is selected as the material due to low intrinsic loss, the dielectric response is modeled with a Drude fit to the experimental data (ε∞ = 1, plasma frequency ωp = 1.366 × 1016 rad/s, and collision frequency νc = 3.07 × 1013 Hz) [51

51. P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

], and the electric permittivity of surrounding medium is supposed to be 1. The field enhancement distribution of the resonance around 249 THz (λ = 1206 nm) at the cross section of SNR-I is represented in Fig. 1(b), and the arrows indicate the polarization vector, it can be found the resonance is the third-order mode of SNR-I [45

45. A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, “Multiple plasmon resonances from gold nanostructures,” Appl. Phys. Lett. 90(14), 143105 (2007). [CrossRef]

]. The dashed line in Fig. 1(a) is the scattering spectrum of SNR-I, there is a large scattering efficiency of the third-order mode, leading to a wide line width with a quality factor Q ≈7.9. Thus the third-order mode of SNR-I could serve as a “bright atom” in the EIT-like plasmonic system.

Figure 1(c) represents the extinction and scattering spectra of a SNR-II that under grazing incident excitation. The resonance with higher energy around 328 THz (λ = 915 nm) is the dipole mode, which has a large scattering efficiency. Figure 1(d) shows the field enhancement distribution of the resonance with lower energy around 252 THz (λ = 1188 nm) at the cross section of SNR-II, one can find it is the quadrupole mode of SNR-II. As the bonding dipole mode of a pair of nanorod [11

11. 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]

], the quadrupole mode of SNR-II cannot be excited under normal incident excitation, and it has counter propagating currents on the two side of SNR-II, therefore, there is no direct electrical dipole coupling with the radiation wave, leading to a low scattering efficiency, and the line width is much narrower than that of SNR-I. The quality factor of the quadrupole mode of SNR-II Q ≈44, and the quadrupole mode of SNR-II could serve as a “dark atom”.

3. Plasmonic analogue of EIT with DSNR cavity

Align the two kings of SNRs together to form a DSNR cavity as shown in Fig. 2(a)
Fig. 2 (a) Geometry of DSNR cavity, where δ is the center offset between the two rings. (b) Transmission spectra of DSNRs with δ = 0 for different numbers of layers, where the geometry parameters are the same as Fig. 1, the unit cell size is 600 × 600 × 240 nm3, and the inset show the natural logarithm of peak transmission versus the number of layers along the propagation direction at the transparency frequency. (c) Field enhancement distribution at the cross section of DSNR cavity with incident frequency 245 THz, (d) 234 THz, and (e) 258 THz, where the polarization vector is indicated by arrows.
, one can expect the bright third-order mode of SNR-I can be excited by the incident wave directly, and the excitation of the dark quadrupole mode of SNR-II by SNR-I coupling back to the bright third-order mode of SNR-I, leading to an EIT-like transmission. Figure 2(b) shows the transmission spectra of DSNRs with center offset δ = 0 for different numbers of layers, where DSNRs are arranged periodically with a spacing of 600 nm in the x-y plane and a spacing of 240 nm in the z (propagation) direction. There is a transmission peak around 245 THz (λ = 1224 nm) within a broader absorption band, which is similar to the transmission usually observed in an atomic EIT system [1

1. K. J. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991). [CrossRef] [PubMed]

]. The inset in Fig. 2(b) shows the natural logarithm of peak transmission versus the number of layers along the propagation direction at the transparency frequency, the transparent peak decreases with the increase of the layers due to loss in the metal, and a linear relation between the natural logarithm of peak transmission versus number of layers is observed, which indicate a single propagating mode dominates for light traversing through the metamaterial [11

11. 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]

,20

20. S. I. Bozhevolnyi, A. B. Evlyukhin, A. Pors, M. G. Nielsen, M. Willatzen, and O. Albrektsen, “Optical transparency by detuned electrical dipoles,” N. J. Phys. 13(2), 023034 (2011). [CrossRef]

]. The calculations also show the relative change of the group index at transmission peak is within 5% for different numbers of layers. Figure 2(c) shows the field enhancement distribution at transmission peak position, where one layer is used in the following calculations, since the layer thickness is large enough to avoid the inter-layer coupling. There is a large field enhancement around SNR-II, and the field enhancement is homogenous inside the cavity, while the resonance of SNR-I is suppressed, causing by the destructive interference of the bright and dark modes between the two rings. Field enhancement distributions of the two transmission dips around 234 THz and 258 THz are represented in Fig. 2(d) and 2(e), respectively. There are strong SP coupling between the two rings for the dip around 234 THz, the polarization vector indicate the charge distributions on the two rings are different, and in the viewpoint of plasmon hybridization theory [54

54. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]

], it can be recognized as the bonding mode. The field enhancement between the two rings for the dip around 258 THz is weak, and it can be recognized as the antibonding mode.

Unlike an atomic EIT system, where the coupling between two energy levels is realized with a pump beam, the coupling between the radiative and dark atoms in the plasmonic EIT system is determined by their spatial separation. Figure 3(a)
Fig. 3 (a) Transmission spectra of DSNR cavities with different center offset δ. (b) The dispersion of the phase. (c) The maximum transmission efficiency versus δ and its corresponding group index.
shows the transmission spectra of DSNR cavities with different center offset δ between the two rings. When δ = 0, there is the minimum coupling strength between the two rings, and the maximum transmission is about 0.76. Increase or decrease the offset δ to 20 or −20 nm, the coupling strength becomes stronger, leading to the broadening of the transparence window, and the transmission is increased to about 0.82. Slow light is one of the most important applications for EIT system, and the group index ng of DSNR cavities will be investigated in the following. The dispersions of transmission phase with different offset δ are represented in Fig. 3(b). ng is then calculated according to the following formula,
ng=cvg=cHτg=cHdφ(ω)dω
(1)
where c is the speed of light in vacuum, vg is the group velocity in the media, τg is the delay time, φ(ω) is the phase as a function of the angular frequency ω, and H is the spacing in the z direction. The maximum transmission efficiency versus δ and its corresponding ng are shown in Fig. 3(c). A maximum group index of 16 with transmission 0.76 is achieved for δ = 0. The transmission is increasing with the increase or decrease of δ, while the group index is decreasing on the contrary. For δ = 0, the transparency bandwidth Δλ ≈33 nm estimated from the transmission spectra using the excess loss level of 1 dB, the propagation loss is about 1.7 dB per 240 nm thick unit cell. The propagation length L is about 0.613 μm, and one can estimate the bandwidth-delay product λ−2ΔλL(ng-1) ≈0.2, which is smaller than that of dipole antennas [20

20. S. I. Bozhevolnyi, A. B. Evlyukhin, A. Pors, M. G. Nielsen, M. Willatzen, and O. Albrektsen, “Optical transparency by detuned electrical dipoles,” N. J. Phys. 13(2), 023034 (2011). [CrossRef]

]. But it has been shown the bandwidth-delay product is affected by the dimensions of a unit cell [20

20. S. I. Bozhevolnyi, A. B. Evlyukhin, A. Pors, M. G. Nielsen, M. Willatzen, and O. Albrektsen, “Optical transparency by detuned electrical dipoles,” N. J. Phys. 13(2), 023034 (2011). [CrossRef]

], enlarge the unit cell size to 1000 × 1000 × 240 nm3, the transmission peak is moved to about 243 THz, the transparency bandwidth Δλ ≈56 nm, the propagation loss is decreased to about 1.01 dB per unit cell, ng is decreased to about 8, and the bandwidth-delay product is enlarged to about 0.26.

With the small space between the inner and outer SNRs as shown in Fig. 2(a), there always has a relative strong coupling between the two rings. To further decrease the coupling strength to get larger group index, one can move the inner ring out as shown in the inset of Fig. 4
Fig. 4 The maximum transmission efficiency versus the distance d and its corresponding group index, where the inner ring is moved out, and the unit cell size is 820 × 600 × 240 nm3.
, where d is the distance between the two rings. The circular points in Fig. 4 indicate the relationship between the maximum transmission efficiency and separation d. The transmission is decreasing with the increase of d for the coupling becomes weaker. The variation of the corresponding group index with the maximum transmission is represented by the square points in Fig. 4, where the increase of the group index persists up to d = 30 nm, and a maximum group index of 25 is achieved, at where the transmission is about 0.41. The inter-layer space is sufficiently large, and one can get a larger group index by decreasing the layer thickness.

Modify the geometry parameters of DSNR cavity, the transparence window can be adjusted to the visible range easily. Figure 5(a)
Fig. 5 (a) Transmission spectra of DSNR cavities with different δ, where the transparence window is moved into the visible range, and the geometry parameters W = 20 nm, g = 20 nm, R = 97 nm, r = 50 nm, T = 80 nm, and the unit cell size is 400 × 400 × 240 nm3. (b) The maximum transmission efficiency versus δ and its corresponding group index. (c) The maximum transmission efficiency versus d and its corresponding group index, where the inner ring is moved out, and the unit cell size is 500 × 500 × 240 nm3.
shows the transmission spectra of modified structure with different offset, where the spacing in the x-y plane is 400 nm. The transparence widow is moved to 414 THz (λ = 725 nm) when δ = 0. Figure 5(b) represents the maximum transmission efficiency versus δ and its corresponding group index. A maximum group index of 17 with transmission 0.74 is achieved for δ = 0. The transparency bandwidth Δλ ≈13 nm when δ = 0, the propagation loss is about 2.54 dB per unit cell, one can estimate the bandwidth-delay product is about 0.16, and one can enlarge the unit cell size to get a larger bandwidth-delay product. The maximum transmission efficiency versus d and its corresponding group index when the inner ring is moved out are represented in Fig. 5(c), where the increase of the group index persists up to d = 18 nm, and a maximum group index of 27 is achieved, at where the transmission is about 0.42.

4. Conclusion

In summary, plasmonic-induced optical transparency with DSNR cavity is theoretically investigated. The coupling between the bright third-order mode of SNR-I and the dark quadrupole mode of SNR-II leads to an EIT-like transmission. The transparence window is easily modified to the NIR and visible range. A maximum group index reaching 16 with transmission exceeding 0.76 is achieved for DSNR cavity, and one can get a larger group index when moving the inner ring out. There is large cavity volume of DSNR, and the field enhancement inside the cavity is homogenous. DSNR cavity could be useful for slow light and sensing applications.

Acknowledgments

This work was supported by the fund of Taiyuan University of Technology for young teachers.

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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]

40.

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]

41.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90(5), 057401 (2003). [CrossRef] [PubMed]

42.

T. G. Habteyes, S. Dhuey, S. Cabrini, P. J. Schuck, and S. R. Leone, “Theta-shaped plasmonic nanostructures: bringing “dark” multipole plasmon resonances into action via conductive coupling,” Nano Lett. 11(4), 1819–1825 (2011). [CrossRef] [PubMed]

43.

E. M. Larsson, J. Alegret, M. Käll, and D. S. Sutherland, “Sensing characteristics of NIR localized surface plasmon resonances in gold nanorings for application as ultrasensitive biosensors,” Nano Lett. 7(5), 1256–1263 (2007). [CrossRef] [PubMed]

44.

F. Hao, E. M. Larsson, T. A. Ali, D. S. Sutherland, and P. Nordlander, “Shedding light on dark plasmons in gold nanorings,” Chem. Phys. Lett. 458(4–6), 262–266 (2008). [CrossRef]

45.

A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, “Multiple plasmon resonances from gold nanostructures,” Appl. Phys. Lett. 90(14), 143105 (2007). [CrossRef]

46.

A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tuneable visible resonances in crescent shaped nano-split-ring resonanctors,” Appl. Phys. Lett. 91(9), 093109 (2007). [CrossRef]

47.

S. D. Liu, Z. S. Zhang, and Q. Q. Wang, “High sensitivity and large field enhancement of symmetry broken Au nanorings: effect of multipolar plasmon resonance and propagation,” Opt. Express 17(4), 2906–2917 (2009). [CrossRef] [PubMed]

48.

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]

49.

J. Kim, R. Soref, and W. R. Buchwald, “Multi-peak electromagnetically induced transparency (EIT)-like transmission from bull’s-eye-shaped metamaterial,” Opt. Express 18(17), 17997–18002 (2010). [CrossRef] [PubMed]

50.

A. Taflove and S. C. Hagness, Computational electrodynamics: The finite-difference time-domain method (Artech House, Boston, 2005).

51.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

52.

M. G. Nielsen, A. Pors, R. B. Nielsen, A. Boltasseva, O. Albrektsen, and S. I. Bozhevolnyi, “Demonstration of scattering suppression in retardation-based plasmonic nanoantennas,” Opt. Express 18(14), 14802–14811 (2010). [CrossRef] [PubMed]

53.

A. Pors, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “From plasmonic nanoantennas to split-ring resonators: tuning scattering strength,” J. Opt. Soc. Am. B 27(8), 1680–1687 (2010). [CrossRef]

54.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.5740) Physical optics : Resonance
(160.3918) Materials : Metamaterials

ToC Category:
Optics at Surfaces

History
Original Manuscript: June 13, 2011
Revised Manuscript: July 20, 2011
Manuscript Accepted: July 20, 2011
Published: July 26, 2011

Citation
Shao-Ding Liu, Zhi Yang, Rui-Ping Liu, and Xiu-Yan Li, "Plasmonic-induced optical transparency in the near-infrared and visible range with double split nanoring cavity," Opt. Express 19, 15363-15370 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-15363


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  40. 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]
  41. J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90(5), 057401 (2003). [CrossRef] [PubMed]
  42. T. G. Habteyes, S. Dhuey, S. Cabrini, P. J. Schuck, and S. R. Leone, “Theta-shaped plasmonic nanostructures: bringing “dark” multipole plasmon resonances into action via conductive coupling,” Nano Lett. 11(4), 1819–1825 (2011). [CrossRef] [PubMed]
  43. E. M. Larsson, J. Alegret, M. Käll, and D. S. Sutherland, “Sensing characteristics of NIR localized surface plasmon resonances in gold nanorings for application as ultrasensitive biosensors,” Nano Lett. 7(5), 1256–1263 (2007). [CrossRef] [PubMed]
  44. F. Hao, E. M. Larsson, T. A. Ali, D. S. Sutherland, and P. Nordlander, “Shedding light on dark plasmons in gold nanorings,” Chem. Phys. Lett. 458(4–6), 262–266 (2008). [CrossRef]
  45. A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, “Multiple plasmon resonances from gold nanostructures,” Appl. Phys. Lett. 90(14), 143105 (2007). [CrossRef]
  46. A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tuneable visible resonances in crescent shaped nano-split-ring resonanctors,” Appl. Phys. Lett. 91(9), 093109 (2007). [CrossRef]
  47. S. D. Liu, Z. S. Zhang, and Q. Q. Wang, “High sensitivity and large field enhancement of symmetry broken Au nanorings: effect of multipolar plasmon resonance and propagation,” Opt. Express 17(4), 2906–2917 (2009). [CrossRef] [PubMed]
  48. 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]
  49. J. Kim, R. Soref, and W. R. Buchwald, “Multi-peak electromagnetically induced transparency (EIT)-like transmission from bull’s-eye-shaped metamaterial,” Opt. Express 18(17), 17997–18002 (2010). [CrossRef] [PubMed]
  50. A. Taflove and S. C. Hagness, Computational electrodynamics: The finite-difference time-domain method (Artech House, Boston, 2005).
  51. P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
  52. M. G. Nielsen, A. Pors, R. B. Nielsen, A. Boltasseva, O. Albrektsen, and S. I. Bozhevolnyi, “Demonstration of scattering suppression in retardation-based plasmonic nanoantennas,” Opt. Express 18(14), 14802–14811 (2010). [CrossRef] [PubMed]
  53. A. Pors, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “From plasmonic nanoantennas to split-ring resonators: tuning scattering strength,” J. Opt. Soc. Am. B 27(8), 1680–1687 (2010). [CrossRef]
  54. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]

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