Abstract

Stereometamaerials can fully utilize the 3D degrees of freedom to exploit the coupling and hybridization between multiple split ring resonators (SRRs), enabling more extraordinary resonances and properties over their planar counterparts. Here we propose and numerically study a kind of structure based on connected SRRs sharing their gap in a rotational fashion. It is shown that there are three typical resonance modes in such cage-like SRR (C-SRR) stereometamaterial in the communication and near infrared range. In the order of increasing energy, these modes can be essentially ascribed to magnetic torodial dipole, magnetic dipole, and a mixture of electric-dipole and magnetic toroidal dipole. We show that the latter two are derived from the second-order mode in the corresponding individual SRR, while the first one from the fundamental one. The highest energy mode remains relatively “dark” in an individual C-SRR due to the high-order feature and the rotational symmetry. However, they are all easily excitable in a C-SRR array, offering multiband filtering functionality.

© 2014 Optical Society of America

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References

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  1. 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]
  2. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
    [Crossref] [PubMed]
  3. C. M. Soukoulis and M. Wegener, “Past achievements and further challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5(9), 523–530 (2011).
  4. H. C. Guo, N. Liu, L. W. Fu, T. P. Meyrath, T. Zentgraf, H. Schweizer, and H. Giessen, “Resonance hybridization in double split-ring resonator metamaterials,” Opt. Express 15(19), 12095–12101 (2007).
    [Crossref] [PubMed]
  5. Z. J. Yang, Z. S. Zhang, Z. H. Hao, and Q. Q. Wang, “Strong bonding magnetic plasmon hybridizations in double split-ring resonators,” Opt. Lett. 37(17), 3675–3677 (2012).
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    [Crossref] [PubMed]
  7. Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
    [Crossref]
  8. N. Liu, H. Liu, S. N. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
    [Crossref]
  9. 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]
  10. Y. W. Huang, W. T. Chen, P. C. Wu, V. A. Fedotov, N. I. Zheludev, and D. P. Tsai, “Toroidal lasing spaser,” Sci Rep 3, 1237 (2013).
    [Crossref] [PubMed]
  11. Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. G. Lu, X. B. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012).
    [Crossref]
  12. V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant transparency and non-trivial non-radiating excitations in toroidal metamaterials,” Sci Rep 3, 2967 (2013).
    [Crossref] [PubMed]
  13. G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic field of elementary time-dependent toroidal sources,” J. Phys. Math. Gen. 28(16), 4565–4580 (1995).
    [Crossref]
  14. V. M. Dubovik and V. V. Tugushev, “Toroid moments in electrodynamics and solid-state physics,” Phys. Rep. 187(4), 145–202 (1990).
    [Crossref]
  15. R. R. Lewis, “Anapole moments of atoms,” Phys. Rev. A 48(6), 4107–4112 (1993).
    [Crossref] [PubMed]
  16. A. Ceulemans, L. Chibotaru, and P. W. Fowler, “Molecular anapole moments,” Phys. Rev. Lett. 80(9), 1861–1864 (1998).
    [Crossref]
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    [Crossref] [PubMed]
  18. Z. G. Dong, P. Ni, J. Zhu, X. B. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012).
    [Crossref] [PubMed]
  19. P. B. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  20. Q. Zhang, J. J. Xiao, and S. L. Wang, “Optical characteristics associated with magnetic resonance in toroidal metamaterials of vertically coupled plasmonic nanodisks,” J. Opt. Soc. Am. B 31(5), 1103–1108 (2014).
    [Crossref]

2014 (1)

2013 (3)

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

Y. W. Huang, W. T. Chen, P. C. Wu, V. A. Fedotov, N. I. Zheludev, and D. P. Tsai, “Toroidal lasing spaser,” Sci Rep 3, 1237 (2013).
[Crossref] [PubMed]

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant transparency and non-trivial non-radiating excitations in toroidal metamaterials,” Sci Rep 3, 2967 (2013).
[Crossref] [PubMed]

2012 (4)

2011 (1)

C. M. Soukoulis and M. Wegener, “Past achievements and further challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5(9), 523–530 (2011).

2009 (1)

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

2007 (2)

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]

H. C. Guo, N. Liu, L. W. Fu, T. P. Meyrath, T. Zentgraf, H. Schweizer, and H. Giessen, “Resonance hybridization in double split-ring resonator metamaterials,” Opt. Express 15(19), 12095–12101 (2007).
[Crossref] [PubMed]

2004 (3)

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]

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

I. I. Naumov, L. Bellaiche, and H. Fu, “Unusual phase transitions in ferroelectric nanodisks and nanorods,” Nature 432(7018), 737–740 (2004).
[Crossref] [PubMed]

1998 (1)

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

1995 (1)

G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic field of elementary time-dependent toroidal sources,” J. Phys. Math. Gen. 28(16), 4565–4580 (1995).
[Crossref]

1993 (1)

R. R. Lewis, “Anapole moments of atoms,” Phys. Rev. A 48(6), 4107–4112 (1993).
[Crossref] [PubMed]

1990 (1)

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

1972 (1)

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

Afanasiev, G. N.

G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic field of elementary time-dependent toroidal sources,” J. Phys. Math. Gen. 28(16), 4565–4580 (1995).
[Crossref]

Bellaiche, L.

I. I. Naumov, L. Bellaiche, and H. Fu, “Unusual phase transitions in ferroelectric nanodisks and nanorods,” Nature 432(7018), 737–740 (2004).
[Crossref] [PubMed]

Ceulemans, A.

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

Chau, Y. F.

Chen, H.

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

Chen, W. T.

Chibotaru, L.

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

Christy, R.

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

Dong, Z. G.

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. G. Lu, X. B. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012).
[Crossref]

Z. G. Dong, P. Ni, J. Zhu, X. B. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012).
[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]

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]

Enkrich, C.

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

Fan, Y. C.

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

Fedotov, V.

Fedotov, V. A.

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant transparency and non-trivial non-radiating excitations in toroidal metamaterials,” Sci Rep 3, 2967 (2013).
[Crossref] [PubMed]

Y. W. Huang, W. T. Chen, P. C. Wu, V. A. Fedotov, N. I. Zheludev, and D. P. Tsai, “Toroidal lasing spaser,” Sci Rep 3, 1237 (2013).
[Crossref] [PubMed]

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]

Fowler, P. W.

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

Fu, H.

I. I. Naumov, L. Bellaiche, and H. Fu, “Unusual phase transitions in ferroelectric nanodisks and nanorods,” Nature 432(7018), 737–740 (2004).
[Crossref] [PubMed]

Fu, L. W.

Giessen, H.

Guo, H. C.

Hao, Z. H.

Ho, Y. Z.

Huang, Y. W.

Johnson, P. B.

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

Kafesaki, M.

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]

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]

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]

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

Lewis, R. R.

R. R. Lewis, “Anapole moments of atoms,” Phys. Rev. A 48(6), 4107–4112 (1993).
[Crossref] [PubMed]

Li, H. Q.

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

Li, J. Q.

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. G. Lu, X. B. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012).
[Crossref]

Linden, S.

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

Liu, H.

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

Liu, N.

Lu, C. G.

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. G. Lu, X. B. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012).
[Crossref]

Meyrath, T. P.

Naumov, I. I.

I. I. Naumov, L. Bellaiche, and H. Fu, “Unusual phase transitions in ferroelectric nanodisks and nanorods,” Nature 432(7018), 737–740 (2004).
[Crossref] [PubMed]

Ni, P.

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).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Rho, J.

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. G. Lu, X. B. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012).
[Crossref]

Rogacheva, A. V.

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant transparency and non-trivial non-radiating excitations in toroidal metamaterials,” Sci Rep 3, 2967 (2013).
[Crossref] [PubMed]

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.

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant transparency and non-trivial non-radiating excitations in toroidal metamaterials,” Sci Rep 3, 2967 (2013).
[Crossref] [PubMed]

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]

Schweizer, H.

Soukoulis, C. M.

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

C. M. Soukoulis and M. Wegener, “Past achievements and further challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5(9), 523–530 (2011).

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

Stepanovsky, Y. P.

G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic field of elementary time-dependent toroidal sources,” J. Phys. Math. Gen. 28(16), 4565–4580 (1995).
[Crossref]

Tsai, D. P.

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant transparency and non-trivial non-radiating excitations in toroidal metamaterials,” Sci Rep 3, 2967 (2013).
[Crossref] [PubMed]

Y. W. Huang, W. T. Chen, P. C. Wu, V. A. Fedotov, N. I. Zheludev, and D. P. Tsai, “Toroidal lasing spaser,” Sci Rep 3, 1237 (2013).
[Crossref] [PubMed]

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]

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]

Wang, Q. Q.

Wang, S. L.

Wegener, M.

C. M. Soukoulis and M. Wegener, “Past achievements and further challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5(9), 523–530 (2011).

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

Wei, Z. Y.

Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

Wu, P. C.

Xiao, J. J.

Yang, Z. J.

Yin, X. B.

Z. G. Dong, P. Ni, J. Zhu, X. B. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012).
[Crossref] [PubMed]

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. G. Lu, X. B. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012).
[Crossref]

Zentgraf, T.

Zhang, Q.

Zhang, X.

Z. G. Dong, P. Ni, J. Zhu, X. B. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012).
[Crossref] [PubMed]

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. G. Lu, X. B. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012).
[Crossref]

Zhang, Z. S.

Zheludev, N. I.

V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant transparency and non-trivial non-radiating excitations in toroidal metamaterials,” Sci Rep 3, 2967 (2013).
[Crossref] [PubMed]

Y. W. Huang, W. T. Chen, P. C. Wu, V. A. Fedotov, N. I. Zheludev, and D. P. Tsai, “Toroidal lasing spaser,” Sci Rep 3, 1237 (2013).
[Crossref] [PubMed]

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]

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. F.

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

Zhu, J.

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. G. Lu, X. B. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012).
[Crossref]

Z. G. Dong, P. Ni, J. Zhu, X. B. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012).
[Crossref] [PubMed]

Zhu, S. N.

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

Appl. Phys. Lett. (2)

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]

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. G. Lu, X. B. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. Math. Gen. (1)

G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic field of elementary time-dependent toroidal sources,” J. Phys. Math. Gen. 28(16), 4565–4580 (1995).
[Crossref]

Nat. Photonics (2)

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

C. M. Soukoulis and M. Wegener, “Past achievements and further challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5(9), 523–530 (2011).

Nature (1)

I. I. Naumov, L. Bellaiche, and H. Fu, “Unusual phase transitions in ferroelectric nanodisks and nanorods,” Nature 432(7018), 737–740 (2004).
[Crossref] [PubMed]

Opt. Express (3)

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of the stereometamaterial. (a) Feature sizes of the constitution SRR where l 1 =300 nm, l 2 =200 nm, w=50 nm, g=75 nm and the dashed line labels the rotation axis (z-axis) for generating the C-SRR stereometamaterials. (b) and (c) unit cell of the C-SRR array with periods P x and P z =600 nm, respectively. (b) The incident light is incoming with k-vector parallel to two of the SRRs and perpendicular to the other two SRRs. (c) The C-SRR is rotated by 45þ degree with respect to the normal direction of the array plane.
Fig. 2
Fig. 2 (a) Scattering cross section of single SRR and an individual cage-SRR (C-SRR). (b) and (c) the surface current corresponding to the resonance peaks of single SRR. Background color is for the current intensity.
Fig. 3
Fig. 3 (a) Simulated transmission of the two dimensional arrays shown in Fig. 1(b), with periodic boundary conditions for P x =600 nm, 700 nm, and 800 nm. The vertical dot line represents the frequency of | ω 2 mode in single SRR. (b) Dispersion of radiated power from the various multipole moments when P x =700 nm.
Fig. 4
Fig. 4 Surface current density (arrows) maps corresponding to the three transmission dips in Fig. 3. (a), (d) and (g) for the C-SRR unit cell. (b), (e) and (h) schematic diagram of the induced current and effective electric dipole moment (blue arrow), magnetic dipole moment (green arrows), toroidal dipole moment (red arrow), and accumulated charges (“+” and “-“). (c), (f) and (i) currents on sheets I and II of the C-SRR in Figs. 4(a), 4(d) and 4(g), correspondingly.
Fig. 5
Fig. 5 (a) Simulated transmission of the two dimensional arrays shown in the situation of Fig. 1(c). The gray dot line represents the second-order mode | ω 2 of single SRR. (b) Dispersion of the radiated powers of various multipole moments for P x =700 nm.
Fig. 6
Fig. 6 Same as Fig. 4, while the C-SRR unit is rotated by 45þ degree with respect to the normal direction of the array plane [see Fig. 1(c)].

Equations (6)

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P= 1 iω j d 3 r
M= 1 2c ( r×j ) d 3 r
T= 1 10c [ ( rj )r2 r 2 j ] d 3 r
Q αβ (e) = 1 i2ω [ r α j β + r β j α 2 3 ( rj ) δ αβ ] d 3 r
Q αβ (m) = 1 3c [ ( r×j ) α r β + ( r×j ) β r α ] d 3 r
I CSRR = 2 ω 4 3 c 3 | P | 2 + 2 ω 4 3 c 3 | M | 2 + 4 ω 5 3 c 4 Im( P * T )+ 2 ω 6 3 c 5 | T | 2 + ω 6 5 c 5 | Q αβ (e) | 2 + ω 6 40 c 5 | Q αβ (m) | 2 ...

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