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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 14 — Jul. 15, 2013
  • pp: 16975–16979
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Electromagnetic dipole coupling mechanism in layered terahertz metamaterials

Jeongmook Choi, Hyunseung Jung, Hojin Lee, and Hyunyong Choi  »View Author Affiliations


Optics Express, Vol. 21, Issue 14, pp. 16975-16979 (2013)
http://dx.doi.org/10.1364/OE.21.016975


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Abstract

Interplay between adjacent dipoles is an experimental priori for designing artificially-engineered structure because the dipole coupling is one critical factor for determining the electromagnetic response in metamaterials. Although numerous investigations have been performed to study the coupling effect of the split-ring resonator (SRR), the interlayer dipole coupling of its complementary SRR, called C-SRR, has been largely unexplored. Here, we present experimental and theoretical investigations on the electromagnetic coupling effect in the two stacks of layered C-SRR structures. By adjusting the relative lateral distance between the two-dimensionally stacked meta-structures, we observe that the confined magnetic dipole plays an important role in determining the resonance frequency and the bandwidth broadening of the C-SRR, exhibiting an exactly opposite behavior to the SRR structure. Our investigation provides experimental basis for developing frequency tunable three-dimensional metamaterial devices.

© 2013 OSA

1. Introduction

Metamaterial has attracted substantial attention due to the exotic electromagnetic response to the incident light. It consists of a periodic unit cell, called meta-atom, whose physical dimension is typically much smaller than the wavelength of the light [1

1. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef] [PubMed]

,2

2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]

]. When the incident light is illuminated on the meta-atoms, electromagnetic dipoles are formed on the metallic surface, in which the light excites collective oscillations of free electrons that lead to the surface plasmon mode [2

2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]

,3

3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

]. These dipoles strongly interact with the adjacent ones, resulting in interesting and yet unnatural phenomenon such as negative [4

4. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

8

8. H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, “Tunable terahertz metamaterials with negative permeability,” Phys. Rev. B 79(24), 241108 (2009). [CrossRef]

] or extremely high refractive index [9

9. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011). [CrossRef] [PubMed]

]. Numerous studies conducted so far have included optical properties of meta-structures focusing on the spectral region of specific resonance with narrow bandwidth. For example, split-ring resonator (SRR), one of the most widely investigated metamaterials, has been explored and has achieved tunable resonance frequency and bandwidth by adjusting the dipole coupling via controlling the geometrical parameters [10

10. C. Rockstuhl, F. Lederer, C. Etrich, T. 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]

,11

11. C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1-2), 219–227 (2006). [CrossRef]

], periodicity [2

2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]

,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] [PubMed]

,13

13. R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010). [CrossRef]

] and stacking layers [14

14. N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]

,15

15. E. Ekmekci, C. Strikwerda, K. Fan, G. Keiser, X. Zhang, G. Turhan-Sayan, and R. D. Averitt, “Frequency tunable terahertz metamaterials using broadside coupled split-ring resonators,” Phys. Rev. B 83(19), 193103 (2011). [CrossRef]

]. Although the SRR have been extensively studied [1

1. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef] [PubMed]

,2

2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]

,10

10. C. Rockstuhl, F. Lederer, C. Etrich, T. 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]

,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] [PubMed]

,14

14. N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]

18

18. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef] [PubMed]

], not much explored structure is its complementary one where the metallic (open) patterns in SRR are replaced with the corresponding open (metallic) patterns [17

17. H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007). [CrossRef] [PubMed]

,19

19. F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004). [CrossRef] [PubMed]

,20

20. T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007). [CrossRef]

].

Complementary split-ring resonator (C-SRR) is a reversed structure of the SRR. Since it is composed of periodic unit slit where the metallic surfaces in the SRR are replaced with the open slit, the electromagnetic dipole coupling in the C-SRR structure is based on the localized guided mode of magnetic dipole rather than the surface plasmon mode [20

20. T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007). [CrossRef]

]. So far, the electromagnetic response of the C-SRR structures have been analyzed and compared with the SRR structure using Babinet’s principle [19

19. F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004). [CrossRef] [PubMed]

,20

20. T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007). [CrossRef]

]. According to the Babinet’s principle, the electromagnetic response of reflection and transmission of the C-SRR is reversed to that of the SRR under complementary light illumination. However, the principle strictly holds only for the isolated two-dimensional planar layer, and it is expected that the dipole coupling in the layered C-SRR exhibits different coupling behaviors as compared to the layered SRR. Although the interpretation of the C-SRR response could be relied on the optical symmetry of the SRR electric dipole, there exists no simple complementary optical quantity in determining the reverse behaviors of the layered C-SRR as to the layered SRR, and no experimental studies have been reported on the vertically stacked C-SRR metamaterials.

Here, we report direct experimental measurements of the coupling effect in the double-layered C-SRR. We present the terahertz (THz) time-domain spectroscopy (THz-TDS) measurements of the dipole coupling mechanism in the layered C-SRR structures, and the result is compared to that of the layered SRR structures. Specifically, the top and bottom layer of both C-SRR and SRR samples are laterally shifted to control the amount of coupling strength between adjacent unit cells. By increasing the spatial shift between the two layers (top and bottom layers), we have observed a large spectral shift over 40% in the resonance frequency of both layered C-SRR and SRR structures. In addition, we show that the bandwidth can be tunable as much as 30% compared to the structures with no lateral shift, all of which can be explained by the interaction of the electric or magnetic dipole with the adjacent meta-atoms.

2. Sample design and experimental method

The proposed metamaterial structures are fabricated by conventional photolithography. First, 5 μm of polyimide is spin coated on silicon wafer and then 200 nm-thick gold with 20 nm-thick chromium adhesion layer is deposited by an electron-beam evaporator. The bottom layer is patterned by the lift-off technique to form C-SRR structures. As a spacer layer, 3μm of polyimide is spin coated over the bottom metallic structure. After the spacer layer is cured, the second C-SRR array structures are deposited and patterned. The layer-to-layer alignment is achieved by the conventional aligner system (EVG 640). Finally, 5 μm of polyimide is spin coated and cured as a passivation layer, and the completed polyimide filter is peeled off from the silicon wafer.

The dimensions of the periodic C-SRR are designed to have a peak resonance frequency ranging from 1.26 THz to 1.83 THz (depending on the lateral shift), considering the transmission characteristics of the polyimide film that shows a high transparent optical property at frequency range of 0.5 ~3 THz. The geometrical parameters of the proposed double-layered C-SRR structure are shown in Fig. 1(a)
Fig. 1 Geometry of proposed metamaterial structures. Schematics of the double-layered C-SRR (a) and SRR (b) are shown with the following geometrical parameters: width w = 30 μm, length l = 90 μm, and overlap distance s = 0, 15, 30, and 45 μm. Insets are the optical microscopy images of both structures with periodicity p = 135 μm. The incident THz field is directed downwards with the rotated polarization of 90 ° for the C-SRR compared to the SRR.
. In order to compare with the SRR, we also fabricate the inverse structure with same geometry. Figure 1(b) shows the double-layered SRR: the unit-cell width is w = 30 μm and the length is l = 90 μm. The overlap distance along the lateral direction between the bottom and the top meta-atom array is s = 0, 15, 30, and 45 μm. The insets of Fig. 1(a) and 1(b) are the optical microscopy images of the C-SRR and the SRR structures with periodicity p = 135 μm at s = 0 μm. The polarization of the incident THz field to the C-SRR is rotated by 90° compared to the SRR’s as shown in Fig. 1 by the Babinet’s principle [19

19. F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004). [CrossRef] [PubMed]

,20

20. T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007). [CrossRef]

].

For the THz-TDS measurement, we have employed an ultrafast regenerative amplifier system with a repetition rate of 250 kHz (Coherent RegA 9050). Ultrashort 50 fs pulse with 800 nm central wavelength are focused on a 500 μm thick <110> ZnTe crystal. It produces THz pulses covering 0.5 ~3 THz range by optical rectification. The THz field is focused with a 90° off-axis parabolic mirror onto the samples with the focus diameter of about 1 mm. For the THz detection, an identical pair of the ZnTe is used for the electro-optic sampling measurement. In order to keep the humidity level below 1%, the whole THz set-up is the enclosed and purged with dry air. To characterize the electromagnetic responses of the proposed arrays over THz range, we have used conventional THz-TDS measurement [21

21. N. Hasegawa, T. Löffler, M. Thomson, and H. G. Roskos, “Remote identification of protrusions and dents on surfaces by terahertz reflectometry with spatial beam filtering and out-of-focus detection,” Appl. Phys. Lett. 83(19), 3996–3998 (2003). [CrossRef]

,22

22. T. Löffler, M. Kreß, M. Thomson, T. Hahn, N. Hasegawa, and H. G. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semicond. Sci. Technol. 20(7), S134–S141 (2005). [CrossRef]

]. Transmission in THz frequency-domain is obtained from THz field through the samples E(ω) divided by the THz reference field E0(ω).

3. Results and discussion

The measured THz transmission spectra of the double-layered C-SRR with respect to the overlap distance s are plotted in Fig. 2(a)
Fig. 2 Measured transmission spectra of the double-layered C-SRR (symbols) with various s = 0, 15, 30, and 45 μm and the simulation results (lines) performed by high frequency structure simulator (HFSS) (a). Inset of (a) is the measured transmission spectra of the double-layered SRR with the same s. The resonance frequency (b) and the 3 dB bandwidth (c) of both structures with the simulation results (lines) are shown as a function of the s.
. The incident magnetic field is vertically polarized as shown in the right inset of Fig. 2(a). As shown in Fig. 2(a), we observe the resonant transmission enhancement in the C-SRR structures [17

17. H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007). [CrossRef] [PubMed]

,19

19. F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004). [CrossRef] [PubMed]

,20

20. T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007). [CrossRef]

]. Blue shift of the resonance frequency is qualitatively well reproduced by the finite-element numerical simulation shown as thin solid lines in Fig. 2(a). In the left inset of Fig. 2(a), we present the transmission spectra of the double-layered SRR to compare the spectral characteristics between the two structures. The data show that the SRR structures show the resonant transmission decrease, as expected from the Babinet’s principle.

In order to investigate the effect of the s, we plot the resonance frequency and the 3 dB bandwidth as a function of s in Fig. 2(b) and 2(c), respectively. The slight discrepancies between the experiment and the simulations (solid lines) are attributed to deviations of the geometry and surface roughness of the structures [10

10. C. Rockstuhl, F. Lederer, C. Etrich, T. 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]

]. By increasing s, we find that the resonance frequency is blue-shifted over 44% in the double-layered C-SRR. On the other hand, a large red-shift is observed in the double-layered SRR. For the spectral broadening, the 3dB bandwidths of the split-ring resonators (both C-SRR and SRR) show opposite behaviors, namely the bandwidth gets narrower with increasing s for the C-SRR while it shows a broader feature with increasing s for the SRR. These observations indicate that the coupling mechanism of two structures is different with respect to s.

For further analysis of the dipole coupling effects, we compare the measured transmission spectra of the single and the double layered structures for the two split-ring resonators with s = 0 μm. The measured THz transmission spectra for the single- and double-layer structures (both C-SRR and SRR) are shown in Fig. 3
Fig. 3 Measured transmission spectra of the single and the double layered SRR (a) and the corresponding C-SRR structures (b) at s = 0 μm. The antisymmetric plasmon mode ωa and the symmetric plasmon mode ωs (both arise from the coupling of the two meta-atoms between the stacked layers) are clearly shown in the SRR; however, the resonance frequency ωc is hardly changed for the single and the double layered C-SRR.
. For the SRR, two plasmon resonances at 0.9 THz and 1.61 THz are observed as depicted in Fig. 3(a). These plasmon modes can be understood by the plasmon hybridization of the electric dipole [18

18. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef] [PubMed]

,23

23. 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]

27

27. N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl. 49(51), 9838–9852 (2010). [CrossRef] [PubMed]

]. The induced electric dipoles on the metallic rings by THz excitation are strongly coupled transversely along the vertical direction, and this coupling generates so called antisymmetric plasmon mode ωa (0.9 THz) and symmetric plasmon mode ωs (1.61 THz) via stacking exactly the same structure. As shown in the Fig. 3(a), the transverse coupling between the top and the bottom layer causes a frequency blue-shift compared to the single-layer SRR. However, Fig. 3(b) shows that the resonance ωc in the double layered C-SRR does not change in contrast to the single layer C-SRR. Because light is confined inside the open slits in the C-SRR, no charge oscillations are excited in the C-SRR (due to the absence of metallic rings) and the magnetic dipoles are induced between the effective slits in the layered C-SRR [19

19. F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004). [CrossRef] [PubMed]

,20

20. T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007). [CrossRef]

]. The fact that there is negligible shift of the resonance frequency in the C-SRR at s = 0 μm underlies the apparently different coupling mechanism between the SRR and the C-SRR structures.

The central issue to address in this paper is the dependence of coupling effect on s. In Fig. 4(a)
Fig. 4 Top and cross-sectional views of both split-ring resonators with s (a). The length of electric dipole aSRR (red arrows) in the SRR does not change with s; whereas the length of magnetic dipole aC-SRR varies because the magnetic dipoles are induced in the effective slits. By increasing s, the coupling distance dx is decreased (increased) in SRR (C-SRR). (b) Calculated local magnetic field distribution of the double-layered C-SRR and the corresponding optical microscopy images. Strong field enhancements at the edge of the effective slits represent the induced magnetic dipoles. The effective slit length leff decreases with increasing s as shown in optical microscopy images.
, we plot the top and cross-sectional views of the layered structures with their induced electromagnetic dipoles (indicated by arrow). Here, we consider only the major resonance mode for the SRR (the symmetric plasmon mode ωs in the SRR). By increasing s, while the transverse electric-dipole coupling between the upper and the lower plane becomes weak, the longitudinal coupling becomes strong since the electric-dipole coupling length dx is reduced for the SRR. Both the transverse and the longitudinal coupling thus lead to the decreased resonance frequency (a red-shift feature) with increased broadening in the double-layered SRR [26

26. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19(21), 3628–3632 (2007). [CrossRef]

,27

27. N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl. 49(51), 9838–9852 (2010). [CrossRef] [PubMed]

]. On the other hand, the magnetic dipole length aC-SRR in the double-layered C-SRR is reduced with increasing s, which leads to the resonance blue-shift; note that the electric dipole length aSRR in the double-layered SRR does not change with respect to the s. In contrast to the double-layered SRR, we note that the coupling length dx in the C-SRR increases, thereby the spectral bandwidth of the double-layered C-SRR becomes narrower [27

27. N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl. 49(51), 9838–9852 (2010). [CrossRef] [PubMed]

].

More insight can be obtained from the local field distribution. In Fig. 4(b), we shows the calculated results of the local magnetic field distribution based on the finite difference time domain (FDTD) method and the corresponding optical microscopy images of the layered C-SRR with respect to the s. As expected, the local field enhancement at the edge of the effective slits is clearly observed, confirming the induced magnetic dipoles in the C-SRR. Note that the length between field-enhancement spots decreases as increasing s because the effective slit length leff is decreased as shown in the optical microscopy images of Fig. 4(b). Therefore, we can confirm that the magnetic field is confined in the effective slits and the dipole coupling of the C-SRR shows different behaviors compared to the double-layered SRR with respect to the s.

4. Conclusion

In conclusion, we have investigated electromagnetic dipole coupling in layered SRR and C-SRR. Using identical meta-atom arrays of the layered C-SRR and SRR, we have observed that the electromagnetic dipoles are strongly coupled with adjacent unit cells with the overlap distance. Since excited modes in both structures cannot be attributed to the same mode, the resonance features show qualitatively different coupling behaviors with respect to the s. In the layered SRR, it is the surface plasmon mode by the electric charge oscillation on the metallic surface. On the other hand, the localized guided mode via the confined magnetic dipole plays an important role in determining the spectral characteristics of the layered C-SRR. Our results are expected to provide experimental basis for designing layered three-dimensional metamaterial devices.

Acknowledgments

The work at Yonsei (Jeongmook Choi and Hyunyong Choi) was supported by Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No.2011-0013255). The work at Soongsil (Hyunseung Jung and Hojin Lee) was supported by the Human Resources Development program (No.20124010203160) of the Korea Institute of Energy Technology Evaluation and Panning (KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy.

References and links

1.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef] [PubMed]

2.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]

3.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

4.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

5.

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

6.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]

7.

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007). [CrossRef] [PubMed]

8.

H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, “Tunable terahertz metamaterials with negative permeability,” Phys. Rev. B 79(24), 241108 (2009). [CrossRef]

9.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011). [CrossRef] [PubMed]

10.

C. Rockstuhl, F. Lederer, C. Etrich, T. 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]

11.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1-2), 219–227 (2006). [CrossRef]

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] [PubMed]

13.

R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010). [CrossRef]

14.

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]

15.

E. Ekmekci, C. Strikwerda, K. Fan, G. Keiser, X. Zhang, G. Turhan-Sayan, and R. D. Averitt, “Frequency tunable terahertz metamaterials using broadside coupled split-ring resonators,” Phys. Rev. B 83(19), 193103 (2011). [CrossRef]

16.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005). [CrossRef] [PubMed]

17.

H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007). [CrossRef] [PubMed]

18.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef] [PubMed]

19.

F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004). [CrossRef] [PubMed]

20.

T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007). [CrossRef]

21.

N. Hasegawa, T. Löffler, M. Thomson, and H. G. Roskos, “Remote identification of protrusions and dents on surfaces by terahertz reflectometry with spatial beam filtering and out-of-focus detection,” Appl. Phys. Lett. 83(19), 3996–3998 (2003). [CrossRef]

22.

T. Löffler, M. Kreß, M. Thomson, T. Hahn, N. Hasegawa, and H. G. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semicond. Sci. Technol. 20(7), S134–S141 (2005). [CrossRef]

23.

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]

24.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004). [CrossRef]

25.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006). [CrossRef] [PubMed]

26.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19(21), 3628–3632 (2007). [CrossRef]

27.

N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl. 49(51), 9838–9852 (2010). [CrossRef] [PubMed]

OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(260.5740) Physical optics : Resonance
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: June 18, 2013
Manuscript Accepted: June 28, 2013
Published: July 9, 2013

Citation
Jeongmook Choi, Hyunseung Jung, Hojin Lee, and Hyunyong Choi, "Electromagnetic dipole coupling mechanism in layered terahertz metamaterials," Opt. Express 21, 16975-16979 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-14-16975


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References

  1. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science303(5663), 1494–1496 (2004). [CrossRef] [PubMed]
  2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science306(5700), 1351–1353 (2004). [CrossRef] [PubMed]
  3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
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  5. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004). [CrossRef] [PubMed]
  6. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007). [CrossRef]
  7. C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science315(5808), 47–49 (2007). [CrossRef] [PubMed]
  8. H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, “Tunable terahertz metamaterials with negative permeability,” Phys. Rev. B79(24), 241108 (2009). [CrossRef]
  9. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature470(7334), 369–373 (2011). [CrossRef] [PubMed]
  10. C. Rockstuhl, F. Lederer, C. Etrich, T. 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]
  11. C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B84(1-2), 219–227 (2006). [CrossRef]
  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] [PubMed]
  13. R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett.97(24), 241108 (2010). [CrossRef]
  14. N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics3(3), 157–162 (2009). [CrossRef]
  15. E. Ekmekci, C. Strikwerda, K. Fan, G. Keiser, X. Zhang, G. Turhan-Sayan, and R. D. Averitt, “Frequency tunable terahertz metamaterials using broadside coupled split-ring resonators,” Phys. Rev. B83(19), 193103 (2011). [CrossRef]
  16. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005). [CrossRef] [PubMed]
  17. H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express15(3), 1084–1095 (2007). [CrossRef] [PubMed]
  18. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater.7(1), 31–37 (2008). [CrossRef] [PubMed]
  19. F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett.93(19), 197401 (2004). [CrossRef] [PubMed]
  20. T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B76(3), 033407 (2007). [CrossRef]
  21. N. Hasegawa, T. Löffler, M. Thomson, and H. G. Roskos, “Remote identification of protrusions and dents on surfaces by terahertz reflectometry with spatial beam filtering and out-of-focus detection,” Appl. Phys. Lett.83(19), 3996–3998 (2003). [CrossRef]
  22. T. Löffler, M. Kreß, M. Thomson, T. Hahn, N. Hasegawa, and H. G. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semicond. Sci. Technol.20(7), S134–S141 (2005). [CrossRef]
  23. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422 (2003). [CrossRef] [PubMed]
  24. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett.4(5), 899–903 (2004). [CrossRef]
  25. H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett.6(4), 827–832 (2006). [CrossRef] [PubMed]
  26. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater.19(21), 3628–3632 (2007). [CrossRef]
  27. N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl.49(51), 9838–9852 (2010). [CrossRef] [PubMed]

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