Abstract

Magnetic resonance in metamaterials is basically formed by an optically induced current loop that, when arranged in a specific order, can exhibit exotic features. In this work, we numerically study the magnetic-resonance-associated optical characteristics in strongly coupled plasmonic nanodisks, which are shown to support various magnetic resonances for vertical polarization (E-field out of the disk plane). To identify these modes, which are essentially relevant to the optically induced current loops, we calculate the optical spectrum, the radiation powers from multipole moments, and the resonant magnetic field pattern. It is shown that the lowest-order resonances are sequentially magnetic dipole mode, magnetic quadrupole mode, and toroidal mode. The surface charge density, the induced current density, and the magnetic near-field are carefully examined for these modes, which show that these modes are quite differently located in both spectrum and real space, bearing distinct symmetry nature. In view of that, we introduce a concentric and nonconcentric air hole in the disks, as a small perturbation, to tune their resonance. It is found that both the radii of the air hole and its position are capable to shift the resonant frequencies. However, their impacts are interestingly distinct with respect to the mode order. These results can provide a useful way to adjust the optical properties of the metamaterials constructed by double disks.

© 2014 Optical Society of America

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2013 (4)

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

Z. G. Dong, J. Zhu, X. B. Yin, J. Q. Li, C. G. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87, 245429 (2013).

Q. Zhang, J. J. Xiao, X. M. Zhang, Y. Yao, and H. Liu, “Reversal of optical binding force by Fano resonance in plasmonic nanorod heterodimer,” Opt. Express 21, 6601–6608 (2013).
[CrossRef]

Q. Zhang and J. J. Xiao, “Multiple reversals of optical binding force in plasmonic disk-ring nanostructures with dipole-multipole Fano resonances,” Opt. Lett. 38, 4240–4243 (2013).
[CrossRef]

2012 (4)

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, 1760–1768 (2012).
[CrossRef]

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101, 144015 (2012).

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11, 426–431 (2012).
[CrossRef]

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
[CrossRef]

2011 (3)

2010 (4)

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

R. K. Zhao, P. Tassin, T. Tassin, T. Koschny, and C. M. Soukoulis, “Optical forces in nanowire pairs and metamaterials,” Opt. Express 18, 25665–25676 (2010).
[CrossRef]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[CrossRef]

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

2008 (1)

2007 (3)

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007).

H. K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, and V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076–1083 (2007).
[CrossRef]

C. Noguez, “Surface plasmons on metal nanoparticles: the influence of shape and physical environment,” J. Phys. Chem. C 111, 3806–3819 (2007).
[CrossRef]

2006 (2)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

A. K. Sarychev, G. Shvets, and V. M. Shalaev, “Magnetic plasmon resonance,” Phys. Rev. E 73, 036609 (2006).
[CrossRef]

2005 (2)

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

L. J. Sherry, S. H. Chang, G. C. Schatz, and R. P. V. Duyne, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

2002 (1)

E. E. Radescu and G. Vaman, “Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles,” Phys. Rev. E 65, 046609 (2002).
[CrossRef]

1999 (1)

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

1972 (1)

P. B. Johson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).

Akimov, Y. A.

Albrektsen, O.

Altug, H.

A. Artar, A. A. Yanik, and H. Altug, “Multispectral plasmon induced transparency in coupled meta-atoms,” Nano Lett. 11, 1685–1689 (2011).

Artar, A.

A. Artar, A. A. Yanik, and H. Altug, “Multispectral plasmon induced transparency in coupled meta-atoms,” Nano Lett. 11, 1685–1689 (2011).

Bai, P.

Bao, J.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[CrossRef]

Bao, K.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[CrossRef]

Bardhan, R.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[CrossRef]

Boltasseva, A.

Bozhevolnyi, S. I.

Cai, W.

Capasso, F.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[CrossRef]

Catchpole, K. R.

Chang, S. H.

L. J. Sherry, S. H. Chang, G. C. Schatz, and R. P. V. Duyne, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

Chau, Y. F.

Chen, C. J.

Chen, H.

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

Chen, W. T.

Chettiar, U. K.

Chilkoti, A.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
[CrossRef]

Christy, R. W.

P. B. Johson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).

Chu, H. S.

Ciracì, C.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
[CrossRef]

Dong, Z. G.

Z. G. Dong, J. Zhu, X. B. Yin, J. Q. Li, C. G. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87, 245429 (2013).

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101, 144015 (2012).

Drachev, V. P.

Duyne, R. P. V.

L. J. Sherry, S. H. Chang, G. C. Schatz, and R. P. V. Duyne, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Fan, J. A.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[CrossRef]

Fan, Y.

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

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, 1510–1512 (2010).
[CrossRef]

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Macroscopic electromagnetic response of metamaterials with toroidal resonances,” arXiv: 1310.0106v1.

Genov, D. A.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007).

Guo, G. Y.

Halas, N. J.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[CrossRef]

He, Q.

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11, 426–431 (2012).
[CrossRef]

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Hill, R. T.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
[CrossRef]

Ho, Y. Z.

Holden, A. J.

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

Hsiao, C. T.

Huang, Y. W.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Johson, P. B.

P. B. Johson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).

Kaelberer, T.

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

Kildishev, A. V.

Koschny, T.

Li, E. P.

Li, H.

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

Li, J. Q.

Z. G. Dong, J. Zhu, X. B. Yin, J. Q. Li, C. G. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87, 245429 (2013).

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101, 144015 (2012).

Li, X.

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11, 426–431 (2012).
[CrossRef]

Liu, H.

Q. Zhang, J. J. Xiao, X. M. Zhang, Y. Yao, and H. Liu, “Reversal of optical binding force by Fano resonance in plasmonic nanorod heterodimer,” Opt. Express 21, 6601–6608 (2013).
[CrossRef]

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007).

Liu, Y. M.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007).

Liu, Z. W.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007).

Lu, C.

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101, 144015 (2012).

Lu, C. G.

Z. G. Dong, J. Zhu, X. B. Yin, J. Q. Li, C. G. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87, 245429 (2013).

Manoharan, V. N.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[CrossRef]

Martin, O. J. F.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Mock, J. J.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
[CrossRef]

Moreau, A.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
[CrossRef]

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Noguez, C.

C. Noguez, “Surface plasmons on metal nanoparticles: the influence of shape and physical environment,” J. Phys. Chem. C 111, 3806–3819 (2007).
[CrossRef]

Nordlander, P.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

Papasimakis, N.

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

Pendry, J. B.

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

Pohl, D. W.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef]

Polman, A.

Pors, A.

Radescu, E. E.

E. E. Radescu and G. Vaman, “Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles,” Phys. Rev. E 65, 046609 (2002).
[CrossRef]

Rho, J.

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101, 144015 (2012).

Robbins, D. J.

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

Sarychev, A. K.

A. K. Sarychev, G. Shvets, and V. M. Shalaev, “Magnetic plasmon resonance,” Phys. Rev. E 73, 036609 (2006).
[CrossRef]

Savinov, V.

Schatz, G. C.

L. J. Sherry, S. H. Chang, G. C. Schatz, and R. P. V. Duyne, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

Shalaev, V. M.

Sherry, L. J.

L. J. Sherry, S. H. Chang, G. C. Schatz, and R. P. V. Duyne, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

Shvets, G.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[CrossRef]

A. K. Sarychev, G. Shvets, and V. M. Shalaev, “Magnetic plasmon resonance,” Phys. Rev. E 73, 036609 (2006).
[CrossRef]

Smith, D. R.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
[CrossRef]

Soukoulis, C. M.

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

R. K. Zhao, P. Tassin, T. Tassin, T. Koschny, and C. M. Soukoulis, “Optical forces in nanowire pairs and metamaterials,” Opt. Express 18, 25665–25676 (2010).
[CrossRef]

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

Sun, C.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007).

Sun, S.

Sun, S. L.

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11, 426–431 (2012).
[CrossRef]

Tassin, P.

Tassin, T.

Tsai, D. P.

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E. E. Radescu and G. Vaman, “Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles,” Phys. Rev. E 65, 046609 (2002).
[CrossRef]

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A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
[CrossRef]

Wei, Z.

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

Wiley, B. J.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
[CrossRef]

Willatzen, M.

Wu, C.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010).
[CrossRef]

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H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007).

Wu, P. C.

Xiao, J. J.

Xiao, S. Y.

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11, 426–431 (2012).
[CrossRef]

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S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11, 426–431 (2012).
[CrossRef]

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A. Artar, A. A. Yanik, and H. Altug, “Multispectral plasmon induced transparency in coupled meta-atoms,” Nano Lett. 11, 1685–1689 (2011).

Yao, Y.

Yin, X.

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101, 144015 (2012).

Yin, X. B.

Z. G. Dong, J. Zhu, X. B. Yin, J. Q. Li, C. G. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87, 245429 (2013).

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Zhang, Q.

Zhang, X.

Z. G. Dong, J. Zhu, X. B. Yin, J. Q. Li, C. G. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87, 245429 (2013).

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101, 144015 (2012).

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007).

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Zhou, L.

Zhu, J.

Z. G. Dong, J. Zhu, X. B. Yin, J. Q. Li, C. G. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87, 245429 (2013).

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101, 144015 (2012).

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H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007).

Appl. Phys. Lett. (1)

Z. G. Dong, J. Zhu, J. Rho, J. Q. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101, 144015 (2012).

IEEE Trans. Microwave Theory Tech. (1)

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

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Nat. Mater. (1)

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11, 426–431 (2012).
[CrossRef]

Nature (1)

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled colloidal nanoantennas,” Nature 492, 86–89 (2012).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. B (4)

Z. G. Dong, J. Zhu, X. B. Yin, J. Q. Li, C. G. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87, 245429 (2013).

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H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76, 073101 (2007).

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

Phys. Rev. E (2)

E. E. Radescu and G. Vaman, “Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles,” Phys. Rev. E 65, 046609 (2002).
[CrossRef]

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T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330, 1510–1512 (2010).
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V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Macroscopic electromagnetic response of metamaterials with toroidal resonances,” arXiv: 1310.0106v1.

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Figures (10)

Fig. 1.
Fig. 1.

Sketch of the SCSN pair. The global and the local coordinate origins are at the center of the gap and the disk, respectively. The position of the circular air holes with radii r is measured by the local coordinates, Px and Py.

Fig. 2.
Fig. 2.

(a) Optical cross sections of the SCSND without the holes (e.g., for r=0nm). The peaks in the spectrum all come from the magnetic resonance relevant modes. (b) Radiation power of the multipole moments. Despite the strong scattering power from the electric dipole moment in the z direction, the radial scattering power at the peak positions mainly comes from the corresponding magnetic modes.

Fig. 3.
Fig. 3.

Near-field features of the SCSND at the resonant frequencies of MD, MQ, T, and MH mode. (a) to (d) Surface charge distributions. (e) to (h) Amplitude of the induced currents (contour) and corresponding field vector (white cones). (i) to (l) Amplitude of the near magnetic field (contour) and corresponding field vector (white cones). (m) to (p) Schematic figure of equivalent MD pattern for the modes.

Fig. 4.
Fig. 4.

(a) Extinction cross-section spectra for disk pair with holes of different r. (b) Radiation power of the multipole moments for r=50nm.

Fig. 5.
Fig. 5.

Resonant frequencies of the first three magnetic resonances versus the radii of the air holes that are positioned at the center of the silver disks.

Fig. 6.
Fig. 6.

Resonant modes induced currents and the magnetic field of the SCSND when the air holes are at the center and of radii r=50nm. (a)–(c) Induced currents. (d)–(f) Magnetic field. (g)–(i) Equivalent MDs.

Fig. 7.
Fig. 7.

ECS and radiation power of the SCSND with offset air holes. (a) to (b) Air hole offset in the x direction. (c) to (d) Air hole offset in the y direction.

Fig. 8.
Fig. 8.

Resonant frequencies of the first three magnetic modes that are located at the off-center position of the silver disks. (a) Hole radii fixed at r=50nm for various Px and Py. (b) At a fixed position for various hole radii r.

Fig. 9.
Fig. 9.

Induced current density and the near magnetic field of the SCSND when air holes are at the position of Px=50nm and Py=0nm with r=50nm. (a) to (c) Induced currents. (d) to (f) Near magnetic field. (g) to (i) Equivalent schematic MDs.

Fig. 10.
Fig. 10.

Induced currents and the near magnetic field of the SCSND when air holes are at the position of Px=0nm and Px=50nm with r=50nm. (a) to (c) Induced currents. (d) to (f) Near magnetic field. (g) to (i) Equivalent schematic MDs.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

I=2ω43c3|P|2+2ω43c3|M|2+2ω63c5|T|2+ω65c5|Qαβ|2+ω640c5|Mαβ|2
P=1iωJd3r,
M=12c(r×J)d3r,
T=110c[(r·J)r2r2J]d3r,
Qαβ=1i2ω[rαJβ+rβJα23(r·J)δαβ]d3r,
Mαβ=13c[(r×J)αrβ+(r×J)βrα]d3r.

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