Abstract

We experimentally and numerically study the nature of coupling between laterally paired terahertz metamaterial split-ring resonators. Coupling is shown to modify the inductive–capacitive (LC) resonances resulting in either red or blue-shifting. Results indicate that tuning of the electric and magnetic coupling parameters may be accomplished not by changing the orientation or density of SRRs, but by a design modification at the unit cell level. These experiments illustrate additional degrees of freedom in tuning the electromagnetic response, which offers a path to more robust metamaterial designs.

© 2011 OSA

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  1. J. B. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
  2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
    [PubMed]
  3. 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).
    [PubMed]
  4. C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
    [PubMed]
  5. H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
    [PubMed]
  6. J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, and W. Zhang, “Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations,” Opt. Express 16(3), 1786–1795 (2008).
    [PubMed]
  7. R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16(9), 6537–6543 (2008).
    [PubMed]
  8. 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).
    [PubMed]
  9. R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “The impact of nearest neighbor interaction on the resonances in terahertz metamaterial,” Appl. Phys. Lett. 94(2), 021116 (2009).
  10. R. S. Penciu, K. Aydin, M. Kafesaki, Th. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures,” Opt. Express 16(22), 18131–18144 (2008).
    [PubMed]
  11. N. Feth, M. König, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation,” Opt. Express 18(7), 6545–6554 (2010).
    [PubMed]
  12. O. Sydoruk, E. Tatartschuk, E. Shamonina, and L. Solymar, “Analytical formulation for the resonant frequency of split rings,” J. Appl. Phys. 105(1), 014903 (2009).
  13. F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanism of split ring resonators: theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007) (b).
  14. R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “Coupling between a dark and bright eigenmode in a terahertz metamaterial,” Phys. Rev. B 79(8), 085111 (2009).
  15. N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
  16. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
    [PubMed]
  17. 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).
  18. D. Grischkowsky, S. Keiding, M. Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7(10), 2006 (1990).
  19. 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 (2004).
  20. Computer Simulation Technology (CST), Darmstadt, Germany.
  21. R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Asymmetric planar terahertz metamaterials,” Opt. Express 18(12), 13044–13050 (2010).
    [PubMed]
  22. R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).

2010

2009

O. Sydoruk, E. Tatartschuk, E. Shamonina, and L. Solymar, “Analytical formulation for the resonant frequency of split rings,” J. Appl. Phys. 105(1), 014903 (2009).

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

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).

R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “The impact of nearest neighbor interaction on the resonances in terahertz metamaterial,” Appl. Phys. Lett. 94(2), 021116 (2009).

2008

2007

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanism of split ring resonators: theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007) (b).

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).
[PubMed]

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

2006

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[PubMed]

2004

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).
[PubMed]

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 (2004).

2001

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

1999

J. B. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).

1990

Al-Naib, I. A. I.

Averitt, R. D.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[PubMed]

Aydin, K.

Brener, I.

Busch, K.

Chen, H. T.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[PubMed]

Economou, E. N.

R. S. Penciu, K. Aydin, M. Kafesaki, Th. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures,” Opt. Express 16(22), 18131–18144 (2008).
[PubMed]

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 (2004).

Edwards, D. J.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanism of split ring resonators: theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007) (b).

Enkrich, C.

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).
[PubMed]

Exter, M.

Fattinger, C.

Faulkner, G.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanism of split ring resonators: theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007) (b).

Fedotov, V. A.

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).
[PubMed]

Feth, N.

Frimmer, M.

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).

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

Giessen, H.

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

Gossard, A. C.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[PubMed]

Grischkowsky, D.

Han, J.

Hao, T.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanism of split ring resonators: theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007) (b).

Hesmer, F.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanism of split ring resonators: theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007) (b).

Holden, A.

J. B. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).

Husnik, M.

Kafesaki, M.

R. S. Penciu, K. Aydin, M. Kafesaki, Th. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures,” Opt. Express 16(22), 18131–18144 (2008).
[PubMed]

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 (2004).

Kaiser, S.

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

Katsarakis, N.

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 (2004).

Keiding, S.

Koch, M.

Koenderink, A. F.

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).

König, M.

Koschny, T.

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).
[PubMed]

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 (2004).

Koschny, Th.

Lederer, F.

R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “The impact of nearest neighbor interaction on the resonances in terahertz metamaterial,” Appl. Phys. Lett. 94(2), 021116 (2009).

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

Linden, S.

N. Feth, M. König, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation,” Opt. Express 18(7), 6545–6554 (2010).
[PubMed]

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

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).
[PubMed]

Liu, M.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

Liu, N.

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

Niegemann, J.

O’Hara, J. F.

Ozbay, E.

Padilla, W. J.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[PubMed]

Papasimakis, N.

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).
[PubMed]

Penciu, R. S.

Pendry, J. B.

J. B. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).

Prosvirnin, S. L.

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).
[PubMed]

Radkovskaya, A. A.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanism of split ring resonators: theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007) (b).

Robbins, D.

J. B. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).

Rockstuhl, C.

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

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

R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “The impact of nearest neighbor interaction on the resonances in terahertz metamaterial,” Appl. Phys. Lett. 94(2), 021116 (2009).

Rose, M.

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).
[PubMed]

Schultz, S.

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

Sersic, I.

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).

Shamonin, M.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanism of split ring resonators: theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007) (b).

Shamonina, E.

O. Sydoruk, E. Tatartschuk, E. Shamonina, and L. Solymar, “Analytical formulation for the resonant frequency of split rings,” J. Appl. Phys. 105(1), 014903 (2009).

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanism of split ring resonators: theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007) (b).

Shelby, R. A.

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

Singh, R.

R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Asymmetric planar terahertz metamaterials,” Opt. Express 18(12), 13044–13050 (2010).
[PubMed]

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

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

R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “The impact of nearest neighbor interaction on the resonances in terahertz metamaterial,” Appl. Phys. Lett. 94(2), 021116 (2009).

R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16(9), 6537–6543 (2008).
[PubMed]

J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, and W. Zhang, “Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations,” Opt. Express 16(3), 1786–1795 (2008).
[PubMed]

Smirnova, E.

Smith, D. R.

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

Solymar, L.

O. Sydoruk, E. Tatartschuk, E. Shamonina, and L. Solymar, “Analytical formulation for the resonant frequency of split rings,” J. Appl. Phys. 105(1), 014903 (2009).

Soukoulis, C. M.

R. S. Penciu, K. Aydin, M. Kafesaki, Th. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures,” Opt. Express 16(22), 18131–18144 (2008).
[PubMed]

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

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).
[PubMed]

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 (2004).

Stannigel, K.

Stevens, C. J.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanism of split ring resonators: theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007) (b).

Stewart, W.

J. B. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).

Sydoruk, O.

O. Sydoruk, E. Tatartschuk, E. Shamonina, and L. Solymar, “Analytical formulation for the resonant frequency of split rings,” J. Appl. Phys. 105(1), 014903 (2009).

Tatartschuk, E.

O. Sydoruk, E. Tatartschuk, E. Shamonina, and L. Solymar, “Analytical formulation for the resonant frequency of split rings,” J. Appl. Phys. 105(1), 014903 (2009).

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanism of split ring resonators: theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007) (b).

Taylor, A. J.

Verhagen, E.

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).

Wang, Y.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

Wegener, M.

N. Feth, M. König, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation,” Opt. Express 18(7), 6545–6554 (2010).
[PubMed]

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

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).
[PubMed]

Zhang, S.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

Zhang, W.

R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Asymmetric planar terahertz metamaterials,” Opt. Express 18(12), 13044–13050 (2010).
[PubMed]

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

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

R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “The impact of nearest neighbor interaction on the resonances in terahertz metamaterial,” Appl. Phys. Lett. 94(2), 021116 (2009).

J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, and W. Zhang, “Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations,” Opt. Express 16(3), 1786–1795 (2008).
[PubMed]

R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16(9), 6537–6543 (2008).
[PubMed]

Zhang, X.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

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Computer Simulation Technology (CST), Darmstadt, Germany.

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Figures (5)

Fig. 1
Fig. 1

Optical microscope images of the fabricated MM samples. (a) through (c) show the symmetric gap to gap coupled SRRs, MM1 to MM3, (d) and (e) show the SRRs in which the gaps of the split rings were displaced in opposite directions, (f) shows the MM5 array. The dimensions of the unit cells are indicated in the figure. The unit cell periodicity for all samples is identical.

Fig. 2
Fig. 2

Measured (a) and simulated (b) transmission magnitudes for the MM1 to MM3 samples when the gap is fixed at the center of the arm but the inter-ring separation in the unit cell is changed. The cyan line in figure b defines the position of the resonance for the isolated SRR at around 0.46 THz.

Fig. 3
Fig. 3

Measured (a) and simulated (b) transmission magnitudes for the coupled SRRs MM3 to MM5 when the gaps are displaced from the center of the arm but the inter-ring separation is fixed at 2 μm.

Fig. 4
Fig. 4

The simulated electric field distributions for the coupled SRRs MM1 (a), MM3 (b) and MM5 (c). Arrows indicate the direction of the electric field while arrow color and size indicate field strength. Red and green arrows correspond to the magnitude of strong and weak fields, respectively. The polarity of the induced electronic charges on the SRR arms is indicated in the figure. The contribution from fringing capacitance is stronger in MM1 (a) compared to MM3 (b) due to the similar polarity of the induced charges in the adjacent arms of the coupled SRRs. With the displacement of the gaps (MM5), an additional capacitive contribution arises in the central part of the adjacent gap bearing arms of the coupled SRRs (c).

Fig. 5
Fig. 5

Numerical simulations of single (a) and symmetric gap coupled (b) SRR systems. In both of the systems of SRRs, 0 µm, 0.5 µm and 1.0 µm undercut of the metallization is taken into considerations. In the case of a single SRR design, the 1.0 µm undercut blue shifts the resonance by 16 GHz (a). The same undercut shifts the resonance only 6 GHz for a coupled SRR unit cell similar to MM3 (b).

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