Abstract

Toroidal dipolar response in a metallic metastructure, composed of double flat rings, is utilized to manipulate the radiation pattern of a single dipolar emitter (e.g., florescent molecule/atom or quantum dot). Strong Fano-type radiation spectrum can be obtained when these two coupling dipoles are spatially overlapped, leading to significant radiation suppression (so-called nonradiating source) attributed to the dipolar destructive interference. Moreover, this nonradiating configuration will become a directionally super-radiating nanoantenna after a radial displacement of the emitter with respect to the toroidal flat-ring geometry, which emits linearly polarized radiation with orders of power enhancement in a particular orientation. The demonstrated radiation characteristics from a toroidal-dipole-mediated dipolar emitter indicate a promising manipulation capability of the dipolar emission source by intriguing toroidal dipolar response.

© 2015 Optical Society of America

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  1. L. B. Zel’dovich, “The relation between decay asymmetry and dipole moment of elementary particles,” Sov. Phys. JETP 6, 1148 (1958).
  2. 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]
  3. C. Schwartz, “Theory of hyperfine structure,” Phys. Rev. 97(2), 380–395 (1955).
    [Crossref]
  4. 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 Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 046609 (2002).
    [Crossref] [PubMed]
  5. 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]
  6. Z. G. Dong, P. Ni, J. Zhu, X. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012).
    [Crossref] [PubMed]
  7. V. Savinov, V. A. Fedotov, W. T. Chen, Y. W. Huang, D. P. Tsai, D. B. Burckel, I. Brener, and N. I. Zheludev, “Toroidal photonic metamaterial,” in Conference on Lasers and Electro-Optics (IEEE, 2012), pp. 1–2.
  8. K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007).
    [Crossref]
  9. 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(14), 144105 (2012).
    [Crossref]
  10. 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]
  11. 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]
  12. A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
    [Crossref]
  13. Y. Bao, X. Zhu, and Z. Fang, “Plasmonic toroidal dipolar response under radially polarized excitation,” Sci. Rep. 5, 11793 (2015).
    [Crossref] [PubMed]
  14. V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
    [Crossref]
  15. G. N. Afanasiev and Y. P. Stepanovsky, “The electromagnetic-field of elementary time-dependent toroidal sources,” J. Phys. A 28(16), 4565–4580 (1995).
    [Crossref]
  16. W. Liu, J. Zhang, B. Lei, H. Hu, and A. E. Miroshnichenko, “Invisible nanowires with interfering electric and toroidal dipoles,” Opt. Lett. 40(10), 2293–2296 (2015).
    [Crossref] [PubMed]
  17. W. Liu, J. F. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564-570 (2015).
  18. A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
    [Crossref] [PubMed]
  19. A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Dispersion properties of nonradiating configurations: Finite-difference time-domain modeling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036603 (2005).
    [Crossref] [PubMed]
  20. 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(24), 245429 (2013).
    [Crossref]
  21. J. Li, J. Shao, J. Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, “Optical responses of magnetic-vortex resonance in double-disk metamaterial variations,” Phys. Lett. A 378(26-27), 1871–1875 (2014).
    [Crossref]
  22. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  23. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
    [Crossref] [PubMed]
  24. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  25. I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
    [Crossref] [PubMed]
  26. T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. Vanhulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2(4), 234–237 (2008).
    [Crossref]
  27. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
    [Crossref] [PubMed]
  28. W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
    [Crossref] [PubMed]
  29. W. Liu, J. Zhang, B. Lei, H. Ma, W. Xie, and H. Hu, “Ultra-directional forward scattering by individual core-shell nanoparticles,” Opt. Express 22(13), 16178–16187 (2014).
    [Crossref] [PubMed]
  30. W. Liu, A. E. Miroshnichenko, and Y. S. Kivshar, “Control of light scattering by nanoparticles with optically-induced magnetic responses,” Chin. Phys. B 23(4), 047806 (2014).
    [Crossref]

2015 (5)

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Y. Bao, X. Zhu, and Z. Fang, “Plasmonic toroidal dipolar response under radially polarized excitation,” Sci. Rep. 5, 11793 (2015).
[Crossref] [PubMed]

W. Liu, J. Zhang, B. Lei, H. Hu, and A. E. Miroshnichenko, “Invisible nanowires with interfering electric and toroidal dipoles,” Opt. Lett. 40(10), 2293–2296 (2015).
[Crossref] [PubMed]

W. Liu, J. F. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564-570 (2015).

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

2014 (5)

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
[Crossref]

J. Li, J. Shao, J. Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, “Optical responses of magnetic-vortex resonance in double-disk metamaterial variations,” Phys. Lett. A 378(26-27), 1871–1875 (2014).
[Crossref]

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

W. Liu, J. Zhang, B. Lei, H. Ma, W. Xie, and H. Hu, “Ultra-directional forward scattering by individual core-shell nanoparticles,” Opt. Express 22(13), 16178–16187 (2014).
[Crossref] [PubMed]

W. Liu, A. E. Miroshnichenko, and Y. S. Kivshar, “Control of light scattering by nanoparticles with optically-induced magnetic responses,” Chin. Phys. B 23(4), 047806 (2014).
[Crossref]

2013 (3)

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]

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(24), 245429 (2013).
[Crossref]

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)

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

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]

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

2010 (3)

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[Crossref] [PubMed]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
[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]

2008 (1)

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. Vanhulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2(4), 234–237 (2008).
[Crossref]

2007 (1)

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

2005 (1)

A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Dispersion properties of nonradiating configurations: Finite-difference time-domain modeling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036603 (2005).
[Crossref] [PubMed]

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 Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 046609 (2002).
[Crossref] [PubMed]

1995 (1)

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

1972 (1)

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

1958 (1)

L. B. Zel’dovich, “The relation between decay asymmetry and dipole moment of elementary particles,” Sov. Phys. JETP 6, 1148 (1958).

1955 (1)

C. Schwartz, “Theory of hyperfine structure,” Phys. Rev. 97(2), 380–395 (1955).
[Crossref]

Afanasiev, G. N.

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

Bakker, R. M.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Bao, Y.

Y. Bao, X. Zhu, and Z. Fang, “Plasmonic toroidal dipolar response under radially polarized excitation,” Sci. Rep. 5, 11793 (2015).
[Crossref] [PubMed]

Bartal, G.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[Crossref] [PubMed]

Basharin, A. A.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Boardman, A. D.

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

A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Dispersion properties of nonradiating configurations: Finite-difference time-domain modeling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036603 (2005).
[Crossref] [PubMed]

Brener, I.

V. Savinov, V. A. Fedotov, W. T. Chen, Y. W. Huang, D. P. Tsai, D. B. Burckel, I. Brener, and N. I. Zheludev, “Toroidal photonic metamaterial,” in Conference on Lasers and Electro-Optics (IEEE, 2012), pp. 1–2.

Burckel, D. B.

V. Savinov, V. A. Fedotov, W. T. Chen, Y. W. Huang, D. P. Tsai, D. B. Burckel, I. Brener, and N. I. Zheludev, “Toroidal photonic metamaterial,” in Conference on Lasers and Electro-Optics (IEEE, 2012), pp. 1–2.

Castro-López, M.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

Chau, Y. F.

Chen, Q.

J. Li, J. Shao, J. Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, “Optical responses of magnetic-vortex resonance in double-disk metamaterial variations,” Phys. Lett. A 378(26-27), 1871–1875 (2014).
[Crossref]

Chen, W. T.

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. Savinov, V. A. Fedotov, W. T. Chen, Y. W. Huang, D. P. Tsai, D. B. Burckel, I. Brener, and N. I. Zheludev, “Toroidal photonic metamaterial,” in Conference on Lasers and Electro-Optics (IEEE, 2012), pp. 1–2.

Chichkov, B. N.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Chipouline, A.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Christy, R. W.

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

Curto, A. G.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
[Crossref] [PubMed]

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(24), 245429 (2013).
[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(14), 144105 (2012).
[Crossref]

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

Dong, Z.-G.

J. Li, J. Shao, J. Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, “Optical responses of magnetic-vortex resonance in double-disk metamaterial variations,” Phys. Lett. A 378(26-27), 1871–1875 (2014).
[Crossref]

Economou, E. N.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Evlyukhin, A. B.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Fang, Z.

Y. Bao, X. Zhu, and Z. Fang, “Plasmonic toroidal dipolar response under radially polarized excitation,” Sci. Rep. 5, 11793 (2015).
[Crossref] [PubMed]

Fedotov, V.

Fedotov, V. A.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
[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]

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]

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

A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Dispersion properties of nonradiating configurations: Finite-difference time-domain modeling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036603 (2005).
[Crossref] [PubMed]

V. Savinov, V. A. Fedotov, W. T. Chen, Y. W. Huang, D. P. Tsai, D. B. Burckel, I. Brener, and N. I. Zheludev, “Toroidal photonic metamaterial,” in Conference on Lasers and Electro-Optics (IEEE, 2012), pp. 1–2.

Hancu, I. M.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

Ho, Y. Z.

Hu, H.

Huang, Y. W.

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. Savinov, V. A. Fedotov, W. T. Chen, Y. W. Huang, D. P. Tsai, D. B. Burckel, I. Brener, and N. I. Zheludev, “Toroidal photonic metamaterial,” in Conference on Lasers and Electro-Optics (IEEE, 2012), pp. 1–2.

Johnson, P. B.

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

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Kivshar, Y. S.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

W. Liu, A. E. Miroshnichenko, and Y. S. Kivshar, “Control of light scattering by nanoparticles with optically-induced magnetic responses,” Chin. Phys. B 23(4), 047806 (2014).
[Crossref]

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

Kreuzer, M. P.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
[Crossref] [PubMed]

Kuttge, M.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

Kuznetsov, A. I.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Lei, B.

Li, J.

J. Li, J. Shao, J. Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, “Optical responses of magnetic-vortex resonance in double-disk metamaterial variations,” Phys. Lett. A 378(26-27), 1871–1875 (2014).
[Crossref]

Li, J. Q.

J. Li, J. Shao, J. Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, “Optical responses of magnetic-vortex resonance in double-disk metamaterial variations,” Phys. Lett. A 378(26-27), 1871–1875 (2014).
[Crossref]

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(24), 245429 (2013).
[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(14), 144105 (2012).
[Crossref]

Liu, W.

W. Liu, J. F. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564-570 (2015).

W. Liu, J. Zhang, B. Lei, H. Hu, and A. E. Miroshnichenko, “Invisible nanowires with interfering electric and toroidal dipoles,” Opt. Lett. 40(10), 2293–2296 (2015).
[Crossref] [PubMed]

W. Liu, J. Zhang, B. Lei, H. Ma, W. Xie, and H. Hu, “Ultra-directional forward scattering by individual core-shell nanoparticles,” Opt. Express 22(13), 16178–16187 (2014).
[Crossref] [PubMed]

W. Liu, A. E. Miroshnichenko, and Y. S. Kivshar, “Control of light scattering by nanoparticles with optically-induced magnetic responses,” Chin. Phys. B 23(4), 047806 (2014).
[Crossref]

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

Liu, Y.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[Crossref] [PubMed]

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(14), 144105 (2012).
[Crossref]

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(24), 245429 (2013).
[Crossref]

Luk’yanchuk, B.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Ma, H.

Marinov, K.

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

A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Dispersion properties of nonradiating configurations: Finite-difference time-domain modeling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036603 (2005).
[Crossref] [PubMed]

Miroshnichenko, A. E.

W. Liu, J. F. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564-570 (2015).

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

W. Liu, J. Zhang, B. Lei, H. Hu, and A. E. Miroshnichenko, “Invisible nanowires with interfering electric and toroidal dipoles,” Opt. Lett. 40(10), 2293–2296 (2015).
[Crossref] [PubMed]

W. Liu, A. E. Miroshnichenko, and Y. S. Kivshar, “Control of light scattering by nanoparticles with optically-induced magnetic responses,” Chin. Phys. B 23(4), 047806 (2014).
[Crossref]

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

Neshev, D. N.

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

Ni, P.

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]

Quidant, R.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
[Crossref] [PubMed]

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 Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 046609 (2002).
[Crossref] [PubMed]

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(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]

Savinov, V.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
[Crossref]

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]

V. Savinov, V. A. Fedotov, W. T. Chen, Y. W. Huang, D. P. Tsai, D. B. Burckel, I. Brener, and N. I. Zheludev, “Toroidal photonic metamaterial,” in Conference on Lasers and Electro-Optics (IEEE, 2012), pp. 1–2.

Schwartz, C.

C. Schwartz, “Theory of hyperfine structure,” Phys. Rev. 97(2), 380–395 (1955).
[Crossref]

Segerink, F. B.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. Vanhulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2(4), 234–237 (2008).
[Crossref]

Shao, J.

J. Li, J. Shao, J. Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, “Optical responses of magnetic-vortex resonance in double-disk metamaterial variations,” Phys. Lett. A 378(26-27), 1871–1875 (2014).
[Crossref]

Soukoulis, C. M.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Stefani, F. D.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. Vanhulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2(4), 234–237 (2008).
[Crossref]

Stepanovsky, Y. P.

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

Taminiau, T. H.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
[Crossref] [PubMed]

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. Vanhulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2(4), 234–237 (2008).
[Crossref]

Tsai, D. P.

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]

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]

V. Savinov, V. A. Fedotov, W. T. Chen, Y. W. Huang, D. P. Tsai, D. B. Burckel, I. Brener, and N. I. Zheludev, “Toroidal photonic metamaterial,” in Conference on Lasers and Electro-Optics (IEEE, 2012), pp. 1–2.

Vaman, G.

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 Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 046609 (2002).
[Crossref] [PubMed]

van Hulst, N. F.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
[Crossref] [PubMed]

Vanhulst, N. F.

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. Vanhulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2(4), 234–237 (2008).
[Crossref]

Volpe, G.

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
[Crossref] [PubMed]

Wu, P. C.

Xie, W.

Yin, X.

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

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(24), 245429 (2013).
[Crossref]

Yu, X. Q.

J. Li, J. Shao, J. Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, “Optical responses of magnetic-vortex resonance in double-disk metamaterial variations,” Phys. Lett. A 378(26-27), 1871–1875 (2014).
[Crossref]

Yu, Y. F.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Zel’dovich, L. B.

L. B. Zel’dovich, “The relation between decay asymmetry and dipole moment of elementary particles,” Sov. Phys. JETP 6, 1148 (1958).

Zentgraf, T.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[Crossref] [PubMed]

Zhai, Y.

J. Li, J. Shao, J. Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, “Optical responses of magnetic-vortex resonance in double-disk metamaterial variations,” Phys. Lett. A 378(26-27), 1871–1875 (2014).
[Crossref]

Zhang, J.

Zhang, J. F.

W. Liu, J. F. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564-570 (2015).

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(24), 245429 (2013).
[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(14), 144105 (2012).
[Crossref]

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

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[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]

A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Dispersion properties of nonradiating configurations: Finite-difference time-domain modeling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036603 (2005).
[Crossref] [PubMed]

Zheludev, N. I.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
[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]

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]

V. Savinov, V. A. Fedotov, W. T. Chen, Y. W. Huang, D. P. Tsai, D. B. Burckel, I. Brener, and N. I. Zheludev, “Toroidal photonic metamaterial,” in Conference on Lasers and Electro-Optics (IEEE, 2012), pp. 1–2.

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(24), 245429 (2013).
[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(14), 144105 (2012).
[Crossref]

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

Zhu, X.

Y. Bao, X. Zhu, and Z. Fang, “Plasmonic toroidal dipolar response under radially polarized excitation,” Sci. Rep. 5, 11793 (2015).
[Crossref] [PubMed]

ACS Nano (1)

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

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(14), 144105 (2012).
[Crossref]

Chin. Phys. B (1)

W. Liu, A. E. Miroshnichenko, and Y. S. Kivshar, “Control of light scattering by nanoparticles with optically-induced magnetic responses,” Chin. Phys. B 23(4), 047806 (2014).
[Crossref]

J. Phys. A (1)

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

Laser Photonics Rev. (1)

W. Liu, J. F. Zhang, and A. E. Miroshnichenko, “Toroidal dipole-induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564-570 (2015).

Nano Lett. (2)

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010).
[Crossref] [PubMed]

Nat. Commun. (1)

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6, 8069 (2015).
[Crossref] [PubMed]

Nat. Photonics (1)

T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. Vanhulst, “Optical antennas direct single-molecule emission,” Nat. Photonics 2(4), 234–237 (2008).
[Crossref]

New J. Phys. (1)

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

Opt. Express (3)

Opt. Lett. (1)

Phys. Lett. A (1)

J. Li, J. Shao, J. Q. Li, X. Q. Yu, Z.-G. Dong, Q. Chen, and Y. Zhai, “Optical responses of magnetic-vortex resonance in double-disk metamaterial variations,” Phys. Lett. A 378(26-27), 1871–1875 (2014).
[Crossref]

Phys. Rev. (1)

C. Schwartz, “Theory of hyperfine structure,” Phys. Rev. 97(2), 380–395 (1955).
[Crossref]

Phys. Rev. B (3)

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
[Crossref]

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

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(24), 245429 (2013).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

A. D. Boardman, K. Marinov, N. Zheludev, and V. A. Fedotov, “Dispersion properties of nonradiating configurations: Finite-difference time-domain modeling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(3), 036603 (2005).
[Crossref] [PubMed]

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 Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 046609 (2002).
[Crossref] [PubMed]

Phys. Rev. X (1)

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Sci. Rep. (3)

Y. Bao, X. Zhu, and Z. Fang, “Plasmonic toroidal dipolar response under radially polarized excitation,” Sci. Rep. 5, 11793 (2015).
[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]

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]

Science (2)

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]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional emission of a quantum dot coupled to a nanoantenna,” Science 329(5994), 930–933 (2010).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

L. B. Zel’dovich, “The relation between decay asymmetry and dipole moment of elementary particles,” Sov. Phys. JETP 6, 1148 (1958).

Other (2)

V. Savinov, V. A. Fedotov, W. T. Chen, Y. W. Huang, D. P. Tsai, D. B. Burckel, I. Brener, and N. I. Zheludev, “Toroidal photonic metamaterial,” in Conference on Lasers and Electro-Optics (IEEE, 2012), pp. 1–2.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

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Figures (5)

Fig. 1
Fig. 1 Schematic of the metastructure composed of double metallic flat-rings with a silicon-oxide gap spacer. Note that the origin “O” of the coordinate system is located at the center of metastructure.
Fig. 2
Fig. 2 (a) Far-field radiating power for different axial displacements Δ y . The nonradiating dips and super-radiative peaks in the Fano-type resonant spectra indicate destructive and instructive interferences between toroidal and electric dipoles, respectively. (b) Destructively induced toroidal mode at the 945-nm wavelength, with out-of-phase magnetic circulating distribution against that of the dipolar emitting source ( Δ y = 0 nm ). (c) Constructively induced toroidal mode at the 1050-nm wavelength, with in-phase magnetic circulating distribution to the dipolar source ( Δ y = 0 nm ). (d) The scattered powers in terms of multipoles when Δ y = 0 nm .
Fig. 3
Fig. 3 Far-field radiating power for the radial displacement Δ x = 60 nm . The reference data are recorded by probe A/C for Δ x = 0 nm .
Fig. 4
Fig. 4 (a) Donut-like radiation pattern at 1050-nm wavelength for Δ x = 0 nm . (b) Modulated radiation pattern at 1050-nm radiative wavelength for Δ x = 60 nm . (c) Directional radiation pattern at 945-nm radiative wavelength for Δ x = 60 nm . (d)-(f) Two-dimensional radiation in dependence of the polar angle θ under an azimuthal angle ϕ = 90 degree, corresponding to (a)-(c), respectively. Note the 1-meter reference distance is used to set the radius of the virtual sphere for calculating field values of radiation pattern in Fig. 4.
Fig. 5
Fig. 5 Far-field radiation powers monitored by probe A (a), probe B (b), and probe C (c), under different radial displacements Δ x .

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