Abstract

The toroidal response is numerically investigated in a multifold double-ring metamaterials at the antibonding magnetic-dipole mode (i.e., antiparallel magnetic dipoles in one double-ring fold). This intriguing toroidal resonance in metamaterials is considered as a result of the magnetoelectric effect due to the broken balance of the electric near-field environment. We demonstrate that the toroidal dipole response in metamaterials can improve the quality factor of the resonance spectrum. In viewing of the design flexibility on the double-ring geometry, such toroidal metamaterials will offer advantages in application potentials of toroidal dipolar moment.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
    [CrossRef] [PubMed]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  3. J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79(12), 121104 (2009).
    [CrossRef]
  4. 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]
  5. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
    [CrossRef]
  6. T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
    [CrossRef] [PubMed]
  7. Y.-W. Huang, W. T. Chen, P. C. Wu, V. Fedotov, V. Savinov, Y. Z. Ho, Y.-F. Chau, N. I. Zheludev, and D. P. Tsai, “Design of plasmonic toroidal metamaterials at optical frequencies,” Opt. Express 20(2), 1760–1768 (2012).
    [CrossRef] [PubMed]
  8. N. Papasimakis, V. A. Fedotov, K. Marinov, and N. I. Zheludev, “Gyrotropy of a metamolecule: wire on a torus,” Phys. Rev. Lett. 103(9), 093901 (2009).
    [CrossRef] [PubMed]
  9. K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007).
    [CrossRef]
  10. W. C. Haxton, C.-P. Liu, and M. J. Ramsey-Musolf, “Nuclear anapole moments,” Phys. Rev. C Nucl. Phys. 65(4), 045502 (2002).
    [CrossRef]
  11. A. Ceulemans, L. F. Chibotaru, and P. W. Fowler, “Molecular anapole moments,” Phys. Rev. Lett. 80(9), 1861–1864 (1998).
    [CrossRef]
  12. W. C. Haxton, “Atomic parity violation and the nuclear anapole moment,” Science 275(5307), 1753–1754 (1997).
    [CrossRef]
  13. V. M. Dubovik and V. V. Tugushev, “Toroid moments in electrodynamics and solid-state physics,” Phys. Rep. 187(4), 145–202 (1990).
    [CrossRef]
  14. M. Fiebig, D. Frohlich, K. Kohn, S. Leute, T. Lottermoser, V. V. Pavlov, and R. V. Pisarev, “Determination of the Magnetic symmetry of Hexagonal Manganites by Second Harmonic Generation,” Phys. Rev. Lett. 84(24), 5620–5623 (2000).
    [CrossRef] [PubMed]
  15. C. M. Dutta, T. A. Ali, D. W. Brandl, T.-H. Park, and P. Nordlander, “Plasmonic properties of a metallic torus,” J. Chem. Phys. 129(8), 084706 (2008).
    [CrossRef] [PubMed]
  16. Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express 18(21), 22412–22417 (2010).
    [CrossRef] [PubMed]
  17. 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. P. Ding, E. J. Liang, L. Zhang, Q. Zhou, and Y. X. Yuan, “Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(1), 016604 (2009).
    [CrossRef] [PubMed]
  19. 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]
  20. 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]
  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. 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]
  25. 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]
  26. K. Aydin, I. M. Pryce, and H. A. Atwater, “Symmetry breaking and strong coupling in planar optical metamaterials,” Opt. Express 18(13), 13407–13417 (2010).
    [CrossRef] [PubMed]
  27. 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]
  28. 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]
  29. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
    [CrossRef]

2012

2010

2009

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]

P. Ding, E. J. Liang, L. Zhang, Q. Zhou, and Y. X. Yuan, “Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(1), 016604 (2009).
[CrossRef] [PubMed]

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]

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]

N. Papasimakis, V. A. Fedotov, K. Marinov, and N. I. Zheludev, “Gyrotropy of a metamolecule: wire on a torus,” Phys. Rev. Lett. 103(9), 093901 (2009).
[CrossRef] [PubMed]

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79(12), 121104 (2009).
[CrossRef]

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]

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

2008

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]

C. M. Dutta, T. A. Ali, D. W. Brandl, T.-H. Park, and P. Nordlander, “Plasmonic properties of a metallic torus,” J. Chem. Phys. 129(8), 084706 (2008).
[CrossRef] [PubMed]

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]

2007

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]

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]

K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007).
[CrossRef]

2006

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

2004

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [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), 2943–2945 (2004).
[CrossRef]

2002

W. C. Haxton, C.-P. Liu, and M. J. Ramsey-Musolf, “Nuclear anapole moments,” Phys. Rev. C Nucl. Phys. 65(4), 045502 (2002).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

2000

M. Fiebig, D. Frohlich, K. Kohn, S. Leute, T. Lottermoser, V. V. Pavlov, and R. V. Pisarev, “Determination of the Magnetic symmetry of Hexagonal Manganites by Second Harmonic Generation,” Phys. Rev. Lett. 84(24), 5620–5623 (2000).
[CrossRef] [PubMed]

1998

A. Ceulemans, L. F. Chibotaru, and P. W. Fowler, “Molecular anapole moments,” Phys. Rev. Lett. 80(9), 1861–1864 (1998).
[CrossRef]

1997

W. C. Haxton, “Atomic parity violation and the nuclear anapole moment,” Science 275(5307), 1753–1754 (1997).
[CrossRef]

1990

V. M. Dubovik and V. V. Tugushev, “Toroid moments in electrodynamics and solid-state physics,” Phys. Rep. 187(4), 145–202 (1990).
[CrossRef]

Ali, T. A.

C. M. Dutta, T. A. Ali, D. W. Brandl, T.-H. Park, and P. Nordlander, “Plasmonic properties of a metallic torus,” J. Chem. Phys. 129(8), 084706 (2008).
[CrossRef] [PubMed]

Atwater, H. A.

Aydin, K.

Boardman, A. D.

K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007).
[CrossRef]

Brandl, D. W.

C. M. Dutta, T. A. Ali, D. W. Brandl, T.-H. Park, and P. Nordlander, “Plasmonic properties of a metallic torus,” J. Chem. Phys. 129(8), 084706 (2008).
[CrossRef] [PubMed]

Buchwald, W. R.

Cao, J.-X.

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]

Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express 18(21), 22412–22417 (2010).
[CrossRef] [PubMed]

Ceulemans, A.

A. Ceulemans, L. F. Chibotaru, and P. W. Fowler, “Molecular anapole moments,” Phys. Rev. Lett. 80(9), 1861–1864 (1998).
[CrossRef]

Chau, Y.-F.

Chen, C.-Y.

Chen, W. T.

Chibotaru, L. F.

A. Ceulemans, L. F. Chibotaru, and P. W. Fowler, “Molecular anapole moments,” Phys. Rev. Lett. 80(9), 1861–1864 (1998).
[CrossRef]

Ding, P.

P. Ding, E. J. Liang, L. Zhang, Q. Zhou, and Y. X. Yuan, “Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(1), 016604 (2009).
[CrossRef] [PubMed]

Dong, J.

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79(12), 121104 (2009).
[CrossRef]

Dong, Z. G.

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]

Dong, Z.-G.

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]

Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express 18(21), 22412–22417 (2010).
[CrossRef] [PubMed]

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]

Dorpe, P. V.

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]

Dubovik, V. M.

V. M. Dubovik and V. V. Tugushev, “Toroid moments in electrodynamics and solid-state physics,” Phys. Rep. 187(4), 145–202 (1990).
[CrossRef]

Dutta, C. M.

C. M. Dutta, T. A. Ali, D. W. Brandl, T.-H. Park, and P. Nordlander, “Plasmonic properties of a metallic torus,” J. Chem. Phys. 129(8), 084706 (2008).
[CrossRef] [PubMed]

Economou, E. 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), 2943–2945 (2004).
[CrossRef]

Fan, S.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Fedotov, V.

Fedotov, V. A.

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[CrossRef] [PubMed]

N. Papasimakis, V. A. Fedotov, K. Marinov, and N. I. Zheludev, “Gyrotropy of a metamolecule: wire on a torus,” Phys. Rev. Lett. 103(9), 093901 (2009).
[CrossRef] [PubMed]

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]

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]

K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007).
[CrossRef]

Fiebig, M.

M. Fiebig, D. Frohlich, K. Kohn, S. Leute, T. Lottermoser, V. V. Pavlov, and R. V. Pisarev, “Determination of the Magnetic symmetry of Hexagonal Manganites by Second Harmonic Generation,” Phys. Rev. Lett. 84(24), 5620–5623 (2000).
[CrossRef] [PubMed]

Fleischhauer, M.

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]

Fowler, P. W.

A. Ceulemans, L. F. Chibotaru, and P. W. Fowler, “Molecular anapole moments,” Phys. Rev. Lett. 80(9), 1861–1864 (1998).
[CrossRef]

Frohlich, D.

M. Fiebig, D. Frohlich, K. Kohn, S. Leute, T. Lottermoser, V. V. Pavlov, and R. V. Pisarev, “Determination of the Magnetic symmetry of Hexagonal Manganites by Second Harmonic Generation,” Phys. Rev. Lett. 84(24), 5620–5623 (2000).
[CrossRef] [PubMed]

Fu, Y. H.

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]

Genov, D. A.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

Giessen, H.

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]

Halas, N. J.

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]

Hao, F.

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]

Haxton, W. C.

W. C. Haxton, C.-P. Liu, and M. J. Ramsey-Musolf, “Nuclear anapole moments,” Phys. Rev. C Nucl. Phys. 65(4), 045502 (2002).
[CrossRef]

W. C. Haxton, “Atomic parity violation and the nuclear anapole moment,” Science 275(5307), 1753–1754 (1997).
[CrossRef]

Ho, Y. Z.

Huang, Y.-W.

Joannopoulos, J. D.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Kaelberer, T.

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[CrossRef] [PubMed]

Kafesaki, M.

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79(12), 121104 (2009).
[CrossRef]

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]

Kästel, J.

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]

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), 2943–2945 (2004).
[CrossRef]

Kim, J.

Kohn, K.

M. Fiebig, D. Frohlich, K. Kohn, S. Leute, T. Lottermoser, V. V. Pavlov, and R. V. Pisarev, “Determination of the Magnetic symmetry of Hexagonal Manganites by Second Harmonic Generation,” Phys. Rev. Lett. 84(24), 5620–5623 (2000).
[CrossRef] [PubMed]

Koschny, T.

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]

Koschny, Th.

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79(12), 121104 (2009).
[CrossRef]

Langguth, L.

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]

Lederer, F.

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]

Lei, S.-Y.

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]

Leute, S.

M. Fiebig, D. Frohlich, K. Kohn, S. Leute, T. Lottermoser, V. V. Pavlov, and R. V. Pisarev, “Determination of the Magnetic symmetry of Hexagonal Manganites by Second Harmonic Generation,” Phys. Rev. Lett. 84(24), 5620–5623 (2000).
[CrossRef] [PubMed]

Li, T.

Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express 18(21), 22412–22417 (2010).
[CrossRef] [PubMed]

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]

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]

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]

Liang, E. J.

P. Ding, E. J. Liang, L. Zhang, Q. Zhou, and Y. X. Yuan, “Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(1), 016604 (2009).
[CrossRef] [PubMed]

Liu, C.-P.

W. C. Haxton, C.-P. Liu, and M. J. Ramsey-Musolf, “Nuclear anapole moments,” Phys. Rev. C Nucl. Phys. 65(4), 045502 (2002).
[CrossRef]

Liu, H.

Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express 18(21), 22412–22417 (2010).
[CrossRef] [PubMed]

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]

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]

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]

Liu, N.

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]

Lottermoser, T.

M. Fiebig, D. Frohlich, K. Kohn, S. Leute, T. Lottermoser, V. V. Pavlov, and R. V. Pisarev, “Determination of the Magnetic symmetry of Hexagonal Manganites by Second Harmonic Generation,” Phys. Rev. Lett. 84(24), 5620–5623 (2000).
[CrossRef] [PubMed]

Maier, S. A.

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]

Marinov, K.

N. Papasimakis, V. A. Fedotov, K. Marinov, and N. I. Zheludev, “Gyrotropy of a metamolecule: wire on a torus,” Phys. Rev. Lett. 103(9), 093901 (2009).
[CrossRef] [PubMed]

K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007).
[CrossRef]

Nordlander, P.

C. M. Dutta, T. A. Ali, D. W. Brandl, T.-H. Park, and P. Nordlander, “Plasmonic properties of a metallic torus,” J. Chem. Phys. 129(8), 084706 (2008).
[CrossRef] [PubMed]

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]

Papasimakis, N.

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[CrossRef] [PubMed]

N. Papasimakis, V. A. Fedotov, K. Marinov, and N. I. Zheludev, “Gyrotropy of a metamolecule: wire on a torus,” Phys. Rev. Lett. 103(9), 093901 (2009).
[CrossRef] [PubMed]

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]

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]

Park, T.-H.

C. M. Dutta, T. A. Ali, D. W. Brandl, T.-H. Park, and P. Nordlander, “Plasmonic properties of a metallic torus,” J. Chem. Phys. 129(8), 084706 (2008).
[CrossRef] [PubMed]

Pavlov, V. V.

M. Fiebig, D. Frohlich, K. Kohn, S. Leute, T. Lottermoser, V. V. Pavlov, and R. V. Pisarev, “Determination of the Magnetic symmetry of Hexagonal Manganites by Second Harmonic Generation,” Phys. Rev. Lett. 84(24), 5620–5623 (2000).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

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

Pfau, T.

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]

Pisarev, R. V.

M. Fiebig, D. Frohlich, K. Kohn, S. Leute, T. Lottermoser, V. V. Pavlov, and R. V. Pisarev, “Determination of the Magnetic symmetry of Hexagonal Manganites by Second Harmonic Generation,” Phys. Rev. Lett. 84(24), 5620–5623 (2000).
[CrossRef] [PubMed]

Prosvirnin, S. L.

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]

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]

Pryce, I. M.

Ramsey-Musolf, M. J.

W. C. Haxton, C.-P. Liu, and M. J. Ramsey-Musolf, “Nuclear anapole moments,” Phys. Rev. C Nucl. Phys. 65(4), 045502 (2002).
[CrossRef]

Rockstuhl, C.

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]

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).
[CrossRef] [PubMed]

Savinov, V.

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Singh, R.

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]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

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

Sonnefraud, Y.

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]

Soref, R.

Soukoulis, C. M.

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79(12), 121104 (2009).
[CrossRef]

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]

Tai, N.-H.

Tsai, D. P.

Y.-W. Huang, W. T. Chen, P. C. Wu, V. Fedotov, V. Savinov, Y. Z. Ho, Y.-F. Chau, N. I. Zheludev, and D. P. Tsai, “Design of plasmonic toroidal metamaterials at optical frequencies,” Opt. Express 20(2), 1760–1768 (2012).
[CrossRef] [PubMed]

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[CrossRef] [PubMed]

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]

Tugushev, V. V.

V. M. Dubovik and V. V. Tugushev, “Toroid moments in electrodynamics and solid-state physics,” Phys. Rep. 187(4), 145–202 (1990).
[CrossRef]

Un, I.-W.

Wang, B.

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79(12), 121104 (2009).
[CrossRef]

Wang, F. M.

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]

Wang, F.-M.

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]

Wang, S.-M.

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]

Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express 18(21), 22412–22417 (2010).
[CrossRef] [PubMed]

Weiss, T.

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]

Wiltshire, M. C. K.

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

Wu, P. C.

Xu, M.-X.

Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express 18(21), 22412–22417 (2010).
[CrossRef] [PubMed]

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]

Yen, T.-J.

Yuan, Y. X.

P. Ding, E. J. Liang, L. Zhang, Q. Zhou, and Y. X. Yuan, “Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(1), 016604 (2009).
[CrossRef] [PubMed]

Zhang, L.

P. Ding, E. J. Liang, L. Zhang, Q. Zhou, and Y. X. Yuan, “Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(1), 016604 (2009).
[CrossRef] [PubMed]

Zhang, S.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

Zhang, W.

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]

Zhang, X.

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]

Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express 18(21), 22412–22417 (2010).
[CrossRef] [PubMed]

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

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]

Zheludev, N.

K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007).
[CrossRef]

Zheludev, N. I.

Y.-W. Huang, W. T. Chen, P. C. Wu, V. Fedotov, V. Savinov, Y. Z. Ho, Y.-F. Chau, N. I. Zheludev, and D. P. Tsai, “Design of plasmonic toroidal metamaterials at optical frequencies,” Opt. Express 20(2), 1760–1768 (2012).
[CrossRef] [PubMed]

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[CrossRef] [PubMed]

N. Papasimakis, V. A. Fedotov, K. Marinov, and N. I. Zheludev, “Gyrotropy of a metamolecule: wire on a torus,” Phys. Rev. Lett. 103(9), 093901 (2009).
[CrossRef] [PubMed]

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]

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]

Zhou, J.

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79(12), 121104 (2009).
[CrossRef]

Zhou, Q.

P. Ding, E. J. Liang, L. Zhang, Q. Zhou, and Y. X. Yuan, “Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(1), 016604 (2009).
[CrossRef] [PubMed]

Zhu, S. N.

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]

Zhu, S.-N.

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]

Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express 18(21), 22412–22417 (2010).
[CrossRef] [PubMed]

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]

Zhu, Z.-H.

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]

Appl. Phys. Lett.

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]

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]

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]

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]

J. Chem. Phys.

C. M. Dutta, T. A. Ali, D. W. Brandl, T.-H. Park, and P. Nordlander, “Plasmonic properties of a metallic torus,” J. Chem. Phys. 129(8), 084706 (2008).
[CrossRef] [PubMed]

Nano Lett.

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]

Nat. Mater.

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]

Nat. Phys.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

New J. Phys.

K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007).
[CrossRef]

Opt. Express

Phys. Rep.

V. M. Dubovik and V. V. Tugushev, “Toroid moments in electrodynamics and solid-state physics,” Phys. Rep. 187(4), 145–202 (1990).
[CrossRef]

Phys. Rev. B

J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79(12), 121104 (2009).
[CrossRef]

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]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Phys. Rev. C Nucl. Phys.

W. C. Haxton, C.-P. Liu, and M. J. Ramsey-Musolf, “Nuclear anapole moments,” Phys. Rev. C Nucl. Phys. 65(4), 045502 (2002).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

P. Ding, E. J. Liang, L. Zhang, Q. Zhou, and Y. X. Yuan, “Antisymmetric resonant mode and negative refraction in double-ring resonators under normal-to-plane incidence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(1), 016604 (2009).
[CrossRef] [PubMed]

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]

Phys. Rev. Lett.

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]

M. Fiebig, D. Frohlich, K. Kohn, S. Leute, T. Lottermoser, V. V. Pavlov, and R. V. Pisarev, “Determination of the Magnetic symmetry of Hexagonal Manganites by Second Harmonic Generation,” Phys. Rev. Lett. 84(24), 5620–5623 (2000).
[CrossRef] [PubMed]

N. Papasimakis, V. A. Fedotov, K. Marinov, and N. I. Zheludev, “Gyrotropy of a metamolecule: wire on a torus,” Phys. Rev. Lett. 103(9), 093901 (2009).
[CrossRef] [PubMed]

A. Ceulemans, L. F. Chibotaru, and P. W. Fowler, “Molecular anapole moments,” Phys. Rev. Lett. 80(9), 1861–1864 (1998).
[CrossRef]

Science

W. C. Haxton, “Atomic parity violation and the nuclear anapole moment,” Science 275(5307), 1753–1754 (1997).
[CrossRef]

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
[CrossRef] [PubMed]

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

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Unit-cell schematic of the toroidal metamaterial by rotating the double-ring structure with respect to the oo’ rotation axis. The outer and inner rings are shown in different colors for eye guide. (a) The planar double ring structure (1-fold). (b) The 3-fold double-ring structure with 60-degree intervals between neighboring folds.

Fig. 2
Fig. 2

Magnetic field distributions for torus-like double-ring metamaterials. All plots are in the middle yz-plane of the structure. (a) and (b) 1-fold double-ring structure. Antiparallel magnetic dipoles are resonantly confined in the double-ring gap. (c) and (d) 2-fold structure with crossed double rings. Note that the same magnetic resonant mode is shared for the crossed double-ring folds. (e) and (f) 4-fold double-ring structure with a 45-degree rotation interval. The toroidal dipole response with closed head-to-tail magnetic dipole distribution is clearly formed (Black arrows indicate the directions of the magnetic field located around the double-ring gaps).

Fig. 3
Fig. 3

The magnitude distribution of the induced surface current (x-component) at the toroidal dipole resonance. Antiparallel current directions are induced for each of the inner-and-outer edge pairs of the double rings, and thus the toroidal dipole moment is collectively formed.

Fig. 4
Fig. 4

(a) Transmittance spectra for multifold double-ring metamaterials, where a high quality factor (Q) is obtained for the well-shaped torus-like metamolecule (4-fold case). The incident wave propagates along the z-direction with polarized electric-field component in the x-direction, as specified in Fig. 1. (b) The scattering powers of toroidal dipole ( T x ), electric dipole ( P x ), electric quadrupole ( Q e ), magnetic dipole ( M y ), and magnetic quadrupole ( Q m ) calculated from the 4-fold structure. The yellow shadow is for eye guide.

Metrics