Abstract

Due to metal losses in plasmonic metamaterials, high-refractive-index dielectrics are promising to improve optical performances of their metallic counterparts. In this paper, a LiTaO3 microtube metamaterial is numerically investigated to explore the toroidal dipolar resonance based on the multipole expansion theory. The local field strength probed on the central axis of the microtube is greatly enhanced for the toroidal dipolar mode, forming a strong hot spot concentrated in the deep-subwavelength scale. Furthermore, we also show the influences of geometrical parameter on the quality (Q) factor of the toroidal mode. The high Q factor and strongly concentrated field strength in the toroidal microtube metamaterial offer application potentials such as sensing, energy havesting, particle trapping, and nonlinear optical effects.

© 2015 Optical Society of America

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  1. 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]
  2. C. Schwartz, “Theory of hyperfine structure,” Phys. Rev. 97(2), 380–395 (1955).
    [Crossref]
  3. 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(4), 046609 (2002).
    [Crossref] [PubMed]
  4. L. B. Zel’dovich, “The relation between decay asymmetry and dipole moment of elementary particles,” Sov. Phys. JETP 6, 1148 (1958).
  5. 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]
  6. K. Marinov, A. D. Boardman, V. A. Fedotov, and N. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007).
    [Crossref]
  7. 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]
  8. 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]
  9. J. Li, Y. Zhang, R. Jin, Q. Wang, Q. Chen, and Z. Dong, “Excitation of plasmon toroidal mode at optical frequencies by angle-resolved reflection,” Opt. Lett. 39(23), 6683–6686 (2014).
    [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. 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]
  12. N. V. Hud and I. D. Vilfan, “Toroidal DNA condensates: Unraveling the fine structure and the role of nucleation in determining size,” Annu. Rev. Biophys. Biomol. Struct. 34(1), 295–318 (2005).
    [Crossref] [PubMed]
  13. I. I. Naumov, L. Bellaiche, and H. Fu, “Unusual phase transitions in ferroelectric nanodisks and nanorods,” Nature 432(7018), 737–740 (2004).
    [Crossref] [PubMed]
  14. A. K. Zvezdin, V. V. Kostyuchenko, A. I. Popov, A. F. Popkov, and A. Ceulemans, “Toroidal moment in the molecular magnet V15,” Phys. Rev. B 80(17), 172404 (2009).
    [Crossref]
  15. A. Ceulemans, L. F. Chibotaru, and P. W. Fowler, “Molecular anapole moments,” Phys. Rev. Lett. 80(9), 1861–1864 (1998).
    [Crossref]
  16. 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]
  17. 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]
  18. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
    [Crossref] [PubMed]
  19. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
    [Crossref] [PubMed]
  20. R. Yahiaoui, U. C. Chung, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Towards left-handed metamaterials using single-size dielectric resonators: The case of TiO2-disks at millimeter wavelengths,” Appl. Phys. Lett. 101(4), 042909 (2012).
    [Crossref]
  21. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [Crossref] [PubMed]
  22. N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101(25), 253903 (2008).
    [Crossref] [PubMed]
  23. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref] [PubMed]
  24. B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
    [Crossref] [PubMed]
  25. 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]
  26. 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]
  27. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
    [Crossref] [PubMed]
  28. Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5, 5753 (2014).
    [Crossref] [PubMed]
  29. K. C. Huang, M. L. Povinelli, and J. D. Joannopoulos, “Negative effective permeability in polaritonic photonic crystals,” Appl. Phys. Lett. 85(4), 543 (2004).
    [Crossref]
  30. F. L. Zhang, X. C. Huang, Q. Zhao, L. Chen, Y. Wang, Q. Li, X. He, C. Li, and K. Chen, “Fano resonance of an asymmetric dielectric wire pair,” Appl. Phys. Lett. 105(17), 172901 (2014).
    [Crossref]
  31. Y. Bao, X. Zhu, and Z. Fang, “Plasmonic toroidal dipolar response under radially polarized excitation,” Sci. Rep. 5, 11793 (2015).
    [Crossref] [PubMed]
  32. 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]
  33. M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72(19), 193103 (2005).
    [Crossref]
  34. J. Li and A. Wood, “Finite element analysis for wave propagation in double negative metamaterials,” J. Sci. Comput. 32(2), 263–286 (2007).
    [Crossref]

2015 (4)

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]

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]

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]

2014 (3)

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5, 5753 (2014).
[Crossref] [PubMed]

F. L. Zhang, X. C. Huang, Q. Zhao, L. Chen, Y. Wang, Q. Li, X. He, C. Li, and K. Chen, “Fano resonance of an asymmetric dielectric wire pair,” Appl. Phys. Lett. 105(17), 172901 (2014).
[Crossref]

J. Li, Y. Zhang, R. Jin, Q. Wang, Q. Chen, and Z. Dong, “Excitation of plasmon toroidal mode at optical frequencies by angle-resolved reflection,” Opt. Lett. 39(23), 6683–6686 (2014).
[Crossref] [PubMed]

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]

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]

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]

2012 (5)

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]

R. Yahiaoui, U. C. Chung, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Towards left-handed metamaterials using single-size dielectric resonators: The case of TiO2-disks at millimeter wavelengths,” Appl. Phys. Lett. 101(4), 042909 (2012).
[Crossref]

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (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]

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]

2010 (2)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (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]

2009 (1)

A. K. Zvezdin, V. V. Kostyuchenko, A. I. Popov, A. F. Popkov, and A. Ceulemans, “Toroidal moment in the molecular magnet V15,” Phys. Rev. B 80(17), 172404 (2009).
[Crossref]

2008 (2)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101(25), 253903 (2008).
[Crossref] [PubMed]

2007 (2)

J. Li and A. Wood, “Finite element analysis for wave propagation in double negative metamaterials,” J. Sci. Comput. 32(2), 263–286 (2007).
[Crossref]

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

2006 (1)

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

2005 (3)

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72(19), 193103 (2005).
[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]

N. V. Hud and I. D. Vilfan, “Toroidal DNA condensates: Unraveling the fine structure and the role of nucleation in determining size,” Annu. Rev. Biophys. Biomol. Struct. 34(1), 295–318 (2005).
[Crossref] [PubMed]

2004 (3)

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

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

K. C. Huang, M. L. Povinelli, and J. D. Joannopoulos, “Negative effective permeability in polaritonic photonic crystals,” Appl. Phys. Lett. 85(4), 543 (2004).
[Crossref]

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(4), 046609 (2002).
[Crossref] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

1998 (1)

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

Aitchison, J. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72(19), 193103 (2005).
[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]

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]

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]

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]

Briggs, D. P.

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5, 5753 (2014).
[Crossref] [PubMed]

Ceulemans, A.

A. K. Zvezdin, V. V. Kostyuchenko, A. I. Popov, A. F. Popkov, and A. Ceulemans, “Toroidal moment in the molecular magnet V15,” Phys. Rev. B 80(17), 172404 (2009).
[Crossref]

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

Chau, Y. F.

Chen, K.

F. L. Zhang, X. C. Huang, Q. Zhao, L. Chen, Y. Wang, Q. Li, X. He, C. Li, and K. Chen, “Fano resonance of an asymmetric dielectric wire pair,” Appl. Phys. Lett. 105(17), 172901 (2014).
[Crossref]

Chen, L.

F. L. Zhang, X. C. Huang, Q. Zhao, L. Chen, Y. Wang, Q. Li, X. He, C. Li, and K. Chen, “Fano resonance of an asymmetric dielectric wire pair,” Appl. Phys. Lett. 105(17), 172901 (2014).
[Crossref]

Chen, Q.

Chen, W. T.

Chibotaru, L. F.

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

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]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Chung, U. C.

R. Yahiaoui, U. C. Chung, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Towards left-handed metamaterials using single-size dielectric resonators: The case of TiO2-disks at millimeter wavelengths,” Appl. Phys. Lett. 101(4), 042909 (2012).
[Crossref]

Dong, Z.

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]

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]

Elissalde, C.

R. Yahiaoui, U. C. Chung, C. Elissalde, M. Maglione, V. Vigneras, and P. Mounaix, “Towards left-handed metamaterials using single-size dielectric resonators: The case of TiO2-disks at millimeter wavelengths,” Appl. Phys. Lett. 101(4), 042909 (2012).
[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. 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]

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

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101(25), 253903 (2008).
[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]

Fowler, P. W.

A. Ceulemans, L. F. 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]

Giessen, H.

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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).
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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]

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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]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 The three-dimensional (a) and elemental top-view (b) illustrations of the infinitely-long dielectric microtube metamaterial. A probe was used to monitor the local-field enhancement at the supposed hot spot for the toroidal dipolar resonance (i.e., at the center of the microtube).
Fig. 2
Fig. 2 (a) The transmittance, reflectance, and absorbance spectra. (b) Decomposed scattered power in terms of multipoles.
Fig. 3
Fig. 3 The resonant local field distribution at 1.33 THz. (a) displacement current density J, (b) H field vector, (c) Ey field map and the probed magnitude along the x-direction diametral path, and (d) the enhanced local field Ey probed at the central axis of the microtube as a function of frequency of the excitation wave.
Fig. 4
Fig. 4 Influence of the inner radius (R1) of the microtube on the toroidal mode. (a) Toroidal-resonance transmission spectrum. (b) Q factor and the hot-spot intensity probed at the center of the microtube.

Equations (6)

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ε = ε ω 2 - ω L 2 + i ω γ ω 2 ω T 2 + i ω γ ,
electric dipole moment : P = 1 i ω J d 3 r,
magnetic dipole moment : M = 1 2 c ( r × J ) d 3 r,
toroidal dipole moment : T = 1 10 c [ ( r J ) r 2 r 2 J ] d 3 r,
electric quadrupole moment : Q α β = 1 i 2 ω [ r α J β + r β J α 2 3 ( r J ) δ α β ] d 3 r,
magnetic quadrupole moment : M α β = 1 3 c [ ( r × J ) α r β + ( r × J ) β r α ] d 3 r ,

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