Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).

[PubMed]

Z.-J. Yang, R. B. Jiang, X. L. Zhuo, Y.-M. Xie, J. F. Wang, and H.-Q. Lin, “Dielectric nanoresonators for light manipulation,” Phys. Rep. 701, 1–50 (2017).

S. Guo, X. Li, J. Zhu, T. Tong, and B. Wei, “Au NPs@MoS2 sub-micrometer sphere-ZnO nanorod hybrid structures for efficient photocatalytic hydrogen evolution with excellent stability,” Small 12(41), 5692–5701 (2016).

[PubMed]

X. H. Li, S. H. Guo, C. X. Kan, J. M. Zhu, T. T. Tong, S. L. Ke, W. C. H. Choy, and B. Q. Wei, “Au multimer@MoS2 hybrid structures for efficient photocatalytical hydrogen production via strongly plasmonic coupling effect,” Nano Energy 30, 549–558 (2016).

S. Zhang, R. Jiang, Y.-M. Xie, Q. Ruan, B. Yang, J. Wang, and H.-Q. Lin, “Colloidal moderate-refractive-index Cu2O nanospheres as visible-region nanoantennas with electromagnetic resonance and directional light-scattering properties,” Adv. Mater. 27(45), 7432–7439 (2015).

[PubMed]

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).

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (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).

[PubMed]

W. Liu, J. 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).

[PubMed]

W. Liu, J. Shi, B. Lei, H. Hu, and A. E. Miroshnichenko, “Efficient excitation and tuning of toroidal dipoles within individual homogenous nanoparticles,” Opt. Express 23(19), 24738–24747 (2015).

[PubMed]

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).

L. Ungur, S. K. Langley, T. N. Hooper, B. Moubaraki, E. K. Brechin, K. S. Murray, and L. F. Chibotaru, “Net toroidal magnetic moment in the ground state of a {Dy6}-triethanolamine ring,” J. Am. Chem. Soc. 134(45), 18554–18557 (2012).

[PubMed]

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).

[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).

[PubMed]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).

[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).

[PubMed]

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).

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

[PubMed]

K. Sawada and N. Nagaosa, “Optical magnetoelectric effect in multiferroic materials: evidence for a Lorentz force acting on a ray of light,” Phys. Rev. Lett. 95(23), 237402 (2005).

[PubMed]

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 Pt 2), 036603 (2005).

[PubMed]

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

[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(4 Pt 2B), 046609 (2002).

[PubMed]

G. N. Afanasiev, “Simplest sources of electromagnetic fields as a tool for testing the reciprocity-like theorems,” J. Phys. D 34(4), 539–559 (2001).

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

G. N. Afanasiev and V. M. Dubovik, “Some remarkable charge-current configurations,” Phys. Part. Nucl. 29(4), 366–391 (1998).

J. Sinzig and M. Quinten, “Scattering and absorption by spherical multilayer particles,” Appl. Phys. A Mater. Sci. Process. 58(2), 157–162 (1994).

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

V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, “Axial toroidal moments in electrodynamics and solid-state physics,” Sov. Phys. JETP 63(2), 344–351 (1986).

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

I. B. Zel’dovich, “Electromagnetic interaction with parity violation,” J. Exp. Theor. Phys. 33, 1531–1533 (1957).

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).

[PubMed]

G. N. Afanasiev, “Simplest sources of electromagnetic fields as a tool for testing the reciprocity-like theorems,” J. Phys. D 34(4), 539–559 (2001).

G. N. Afanasiev and V. M. Dubovik, “Some remarkable charge-current configurations,” Phys. Part. Nucl. 29(4), 366–391 (1998).

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

[PubMed]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).

[PubMed]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).

[PubMed]

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).

[PubMed]

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).

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

[PubMed]

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 Pt 2), 036603 (2005).

[PubMed]

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).

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

[PubMed]

L. Ungur, S. K. Langley, T. N. Hooper, B. Moubaraki, E. K. Brechin, K. S. Murray, and L. F. Chibotaru, “Net toroidal magnetic moment in the ground state of a {Dy6}-triethanolamine ring,” J. Am. Chem. Soc. 134(45), 18554–18557 (2012).

[PubMed]

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

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).

[PubMed]

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).

[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).

[PubMed]

L. Ungur, S. K. Langley, T. N. Hooper, B. Moubaraki, E. K. Brechin, K. S. Murray, and L. F. Chibotaru, “Net toroidal magnetic moment in the ground state of a {Dy6}-triethanolamine ring,” J. Am. Chem. Soc. 134(45), 18554–18557 (2012).

[PubMed]

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

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).

[PubMed]

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).

[PubMed]

X. H. Li, S. H. Guo, C. X. Kan, J. M. Zhu, T. T. Tong, S. L. Ke, W. C. H. Choy, and B. Q. Wei, “Au multimer@MoS2 hybrid structures for efficient photocatalytical hydrogen production via strongly plasmonic coupling effect,” Nano Energy 30, 549–558 (2016).

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

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).

[PubMed]

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).

[PubMed]

G. N. Afanasiev and V. M. Dubovik, “Some remarkable charge-current configurations,” Phys. Part. Nucl. 29(4), 366–391 (1998).

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

V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, “Axial toroidal moments in electrodynamics and solid-state physics,” Sov. Phys. JETP 63(2), 344–351 (1986).

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

[PubMed]

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).

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).

[PubMed]

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).

[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).

[PubMed]

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).

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).

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).

[PubMed]

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 Pt 2), 036603 (2005).

[PubMed]

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

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

[PubMed]

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).

[PubMed]

S. Guo, X. Li, J. Zhu, T. Tong, and B. Wei, “Au NPs@MoS2 sub-micrometer sphere-ZnO nanorod hybrid structures for efficient photocatalytic hydrogen evolution with excellent stability,” Small 12(41), 5692–5701 (2016).

[PubMed]

X. H. Li, S. H. Guo, C. X. Kan, J. M. Zhu, T. T. Tong, S. L. Ke, W. C. H. Choy, and B. Q. Wei, “Au multimer@MoS2 hybrid structures for efficient photocatalytical hydrogen production via strongly plasmonic coupling effect,” Nano Energy 30, 549–558 (2016).

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).

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).

[PubMed]

L. Ungur, S. K. Langley, T. N. Hooper, B. Moubaraki, E. K. Brechin, K. S. Murray, and L. F. Chibotaru, “Net toroidal magnetic moment in the ground state of a {Dy6}-triethanolamine ring,” J. Am. Chem. Soc. 134(45), 18554–18557 (2012).

[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).

[PubMed]

W. Liu, J. Shi, B. Lei, H. Hu, and A. E. Miroshnichenko, “Efficient excitation and tuning of toroidal dipoles within individual homogenous nanoparticles,” Opt. Express 23(19), 24738–24747 (2015).

[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).

[PubMed]

S. Zhang, R. Jiang, Y.-M. Xie, Q. Ruan, B. Yang, J. Wang, and H.-Q. Lin, “Colloidal moderate-refractive-index Cu2O nanospheres as visible-region nanoantennas with electromagnetic resonance and directional light-scattering properties,” Adv. Mater. 27(45), 7432–7439 (2015).

[PubMed]

Z.-J. Yang, R. B. Jiang, X. L. Zhuo, Y.-M. Xie, J. F. Wang, and H.-Q. Lin, “Dielectric nanoresonators for light manipulation,” Phys. Rep. 701, 1–50 (2017).

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

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).

[PubMed]

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).

X. H. Li, S. H. Guo, C. X. Kan, J. M. Zhu, T. T. Tong, S. L. Ke, W. C. H. Choy, and B. Q. Wei, “Au multimer@MoS2 hybrid structures for efficient photocatalytical hydrogen production via strongly plasmonic coupling effect,” Nano Energy 30, 549–558 (2016).

X. H. Li, S. H. Guo, C. X. Kan, J. M. Zhu, T. T. Tong, S. L. Ke, W. C. H. Choy, and B. Q. Wei, “Au multimer@MoS2 hybrid structures for efficient photocatalytical hydrogen production via strongly plasmonic coupling effect,” Nano Energy 30, 549–558 (2016).

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).

[PubMed]

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).

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).

[PubMed]

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).

[PubMed]

L. Ungur, S. K. Langley, T. N. Hooper, B. Moubaraki, E. K. Brechin, K. S. Murray, and L. F. Chibotaru, “Net toroidal magnetic moment in the ground state of a {Dy6}-triethanolamine ring,” J. Am. Chem. Soc. 134(45), 18554–18557 (2012).

[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).

[PubMed]

W. Liu, J. Shi, B. Lei, H. Hu, and A. E. Miroshnichenko, “Efficient excitation and tuning of toroidal dipoles within individual homogenous nanoparticles,” Opt. Express 23(19), 24738–24747 (2015).

[PubMed]

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).

[PubMed]

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).

[PubMed]

S. Guo, X. Li, J. Zhu, T. Tong, and B. Wei, “Au NPs@MoS2 sub-micrometer sphere-ZnO nanorod hybrid structures for efficient photocatalytic hydrogen evolution with excellent stability,” Small 12(41), 5692–5701 (2016).

[PubMed]

X. H. Li, S. H. Guo, C. X. Kan, J. M. Zhu, T. T. Tong, S. L. Ke, W. C. H. Choy, and B. Q. Wei, “Au multimer@MoS2 hybrid structures for efficient photocatalytical hydrogen production via strongly plasmonic coupling effect,” Nano Energy 30, 549–558 (2016).

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).

[PubMed]

Z.-J. Yang, R. B. Jiang, X. L. Zhuo, Y.-M. Xie, J. F. Wang, and H.-Q. Lin, “Dielectric nanoresonators for light manipulation,” Phys. Rep. 701, 1–50 (2017).

S. Zhang, R. Jiang, Y.-M. Xie, Q. Ruan, B. Yang, J. Wang, and H.-Q. Lin, “Colloidal moderate-refractive-index Cu2O nanospheres as visible-region nanoantennas with electromagnetic resonance and directional light-scattering properties,” Adv. Mater. 27(45), 7432–7439 (2015).

[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).

[PubMed]

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

W. Liu, J. Shi, B. Lei, H. Hu, and A. E. Miroshnichenko, “Efficient excitation and tuning of toroidal dipoles within individual homogenous nanoparticles,” Opt. Express 23(19), 24738–24747 (2015).

[PubMed]

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).

[PubMed]

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).

[PubMed]

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).

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 Pt 2), 036603 (2005).

[PubMed]

W. Liu, J. 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).

[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).

[PubMed]

W. Liu, J. Shi, B. Lei, H. Hu, and A. E. Miroshnichenko, “Efficient excitation and tuning of toroidal dipoles within individual homogenous nanoparticles,” Opt. Express 23(19), 24738–24747 (2015).

[PubMed]

L. Ungur, S. K. Langley, T. N. Hooper, B. Moubaraki, E. K. Brechin, K. S. Murray, and L. F. Chibotaru, “Net toroidal magnetic moment in the ground state of a {Dy6}-triethanolamine ring,” J. Am. Chem. Soc. 134(45), 18554–18557 (2012).

[PubMed]

L. Ungur, S. K. Langley, T. N. Hooper, B. Moubaraki, E. K. Brechin, K. S. Murray, and L. F. Chibotaru, “Net toroidal magnetic moment in the ground state of a {Dy6}-triethanolamine ring,” J. Am. Chem. Soc. 134(45), 18554–18557 (2012).

[PubMed]

K. Sawada and N. Nagaosa, “Optical magnetoelectric effect in multiferroic materials: evidence for a Lorentz force acting on a ray of light,” Phys. Rev. Lett. 95(23), 237402 (2005).

[PubMed]

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

[PubMed]

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

[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).

[PubMed]

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

[PubMed]

J. Sinzig and M. Quinten, “Scattering and absorption by spherical multilayer particles,” Appl. Phys. A Mater. Sci. Process. 58(2), 157–162 (1994).

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 Pt 2B), 046609 (2002).

[PubMed]

S. Zhang, R. Jiang, Y.-M. Xie, Q. Ruan, B. Yang, J. Wang, and H.-Q. Lin, “Colloidal moderate-refractive-index Cu2O nanospheres as visible-region nanoantennas with electromagnetic resonance and directional light-scattering properties,” Adv. Mater. 27(45), 7432–7439 (2015).

[PubMed]

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).

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).

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).

[PubMed]

K. Sawada and N. Nagaosa, “Optical magnetoelectric effect in multiferroic materials: evidence for a Lorentz force acting on a ray of light,” Phys. Rev. Lett. 95(23), 237402 (2005).

[PubMed]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).

[PubMed]

J. Sinzig and M. Quinten, “Scattering and absorption by spherical multilayer particles,” Appl. Phys. A Mater. Sci. Process. 58(2), 157–162 (1994).

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).

S. Guo, X. Li, J. Zhu, T. Tong, and B. Wei, “Au NPs@MoS2 sub-micrometer sphere-ZnO nanorod hybrid structures for efficient photocatalytic hydrogen evolution with excellent stability,” Small 12(41), 5692–5701 (2016).

[PubMed]

X. H. Li, S. H. Guo, C. X. Kan, J. M. Zhu, T. T. Tong, S. L. Ke, W. C. H. Choy, and B. Q. Wei, “Au multimer@MoS2 hybrid structures for efficient photocatalytical hydrogen production via strongly plasmonic coupling effect,” Nano Energy 30, 549–558 (2016).

V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, “Axial toroidal moments in electrodynamics and solid-state physics,” Sov. Phys. JETP 63(2), 344–351 (1986).

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).

[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).

[PubMed]

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

V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, “Axial toroidal moments in electrodynamics and solid-state physics,” Sov. Phys. JETP 63(2), 344–351 (1986).

L. Ungur, S. K. Langley, T. N. Hooper, B. Moubaraki, E. K. Brechin, K. S. Murray, and L. F. Chibotaru, “Net toroidal magnetic moment in the ground state of a {Dy6}-triethanolamine ring,” J. Am. Chem. Soc. 134(45), 18554–18557 (2012).

[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(4 Pt 2B), 046609 (2002).

[PubMed]

S. Zhang, R. Jiang, Y.-M. Xie, Q. Ruan, B. Yang, J. Wang, and H.-Q. Lin, “Colloidal moderate-refractive-index Cu2O nanospheres as visible-region nanoantennas with electromagnetic resonance and directional light-scattering properties,” Adv. Mater. 27(45), 7432–7439 (2015).

[PubMed]

Z.-J. Yang, R. B. Jiang, X. L. Zhuo, Y.-M. Xie, J. F. Wang, and H.-Q. Lin, “Dielectric nanoresonators for light manipulation,” Phys. Rep. 701, 1–50 (2017).

S. Guo, X. Li, J. Zhu, T. Tong, and B. Wei, “Au NPs@MoS2 sub-micrometer sphere-ZnO nanorod hybrid structures for efficient photocatalytic hydrogen evolution with excellent stability,” Small 12(41), 5692–5701 (2016).

[PubMed]

X. H. Li, S. H. Guo, C. X. Kan, J. M. Zhu, T. T. Tong, S. L. Ke, W. C. H. Choy, and B. Q. Wei, “Au multimer@MoS2 hybrid structures for efficient photocatalytical hydrogen production via strongly plasmonic coupling effect,” Nano Energy 30, 549–558 (2016).

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).

[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).

[PubMed]

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).

Z.-J. Yang, R. B. Jiang, X. L. Zhuo, Y.-M. Xie, J. F. Wang, and H.-Q. Lin, “Dielectric nanoresonators for light manipulation,” Phys. Rep. 701, 1–50 (2017).

S. Zhang, R. Jiang, Y.-M. Xie, Q. Ruan, B. Yang, J. Wang, and H.-Q. Lin, “Colloidal moderate-refractive-index Cu2O nanospheres as visible-region nanoantennas with electromagnetic resonance and directional light-scattering properties,” Adv. Mater. 27(45), 7432–7439 (2015).

[PubMed]

S. Zhang, R. Jiang, Y.-M. Xie, Q. Ruan, B. Yang, J. Wang, and H.-Q. Lin, “Colloidal moderate-refractive-index Cu2O nanospheres as visible-region nanoantennas with electromagnetic resonance and directional light-scattering properties,” Adv. Mater. 27(45), 7432–7439 (2015).

[PubMed]

Z.-J. Yang, R. B. Jiang, X. L. Zhuo, Y.-M. Xie, J. F. Wang, and H.-Q. Lin, “Dielectric nanoresonators for light manipulation,” Phys. Rep. 701, 1–50 (2017).

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).

[PubMed]

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).

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).

[PubMed]

I. B. Zel’dovich, “Electromagnetic interaction with parity violation,” J. Exp. Theor. Phys. 33, 1531–1533 (1957).

W. Liu, J. 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).

[PubMed]

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).

S. Zhang, R. Jiang, Y.-M. Xie, Q. Ruan, B. Yang, J. Wang, and H.-Q. Lin, “Colloidal moderate-refractive-index Cu2O nanospheres as visible-region nanoantennas with electromagnetic resonance and directional light-scattering properties,” Adv. Mater. 27(45), 7432–7439 (2015).

[PubMed]

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).

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 Pt 2), 036603 (2005).

[PubMed]

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).

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).

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).

[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).

[PubMed]

S. Guo, X. Li, J. Zhu, T. Tong, and B. Wei, “Au NPs@MoS2 sub-micrometer sphere-ZnO nanorod hybrid structures for efficient photocatalytic hydrogen evolution with excellent stability,” Small 12(41), 5692–5701 (2016).

[PubMed]

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).

[PubMed]

X. H. Li, S. H. Guo, C. X. Kan, J. M. Zhu, T. T. Tong, S. L. Ke, W. C. H. Choy, and B. Q. Wei, “Au multimer@MoS2 hybrid structures for efficient photocatalytical hydrogen production via strongly plasmonic coupling effect,” Nano Energy 30, 549–558 (2016).

Z.-J. Yang, R. B. Jiang, X. L. Zhuo, Y.-M. Xie, J. F. Wang, and H.-Q. Lin, “Dielectric nanoresonators for light manipulation,” Phys. Rep. 701, 1–50 (2017).

Q. Zhang, J. J. Xiao, X. M. Zhang, D. Han, and L. Gao, “Core–shell-structured dielectric–metal circular nanodisk antenna: gap plasmon assisted magnetic toroid-like cavity modes,” ACS Photonics 2(1), 60–65 (2015).

Z. Liu, S. Du, A. Cui, Z. Li, Y. Fan, S. Chen, W. Li, J. Li, and C. Gu, “High-quality-factor mid-infrared toroidal excitation in folded 3D metamaterials,” Adv. Mater. 29(17), 1606298 (2017).

[PubMed]

S. Zhang, R. Jiang, Y.-M. Xie, Q. Ruan, B. Yang, J. Wang, and H.-Q. Lin, “Colloidal moderate-refractive-index Cu2O nanospheres as visible-region nanoantennas with electromagnetic resonance and directional light-scattering properties,” Adv. Mater. 27(45), 7432–7439 (2015).

[PubMed]

J. Sinzig and M. Quinten, “Scattering and absorption by spherical multilayer particles,” Appl. Phys. A Mater. Sci. Process. 58(2), 157–162 (1994).

L. Ungur, S. K. Langley, T. N. Hooper, B. Moubaraki, E. K. Brechin, K. S. Murray, and L. F. Chibotaru, “Net toroidal magnetic moment in the ground state of a {Dy6}-triethanolamine ring,” J. Am. Chem. Soc. 134(45), 18554–18557 (2012).

[PubMed]

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

[PubMed]

I. B. Zel’dovich, “Electromagnetic interaction with parity violation,” J. Exp. Theor. Phys. 33, 1531–1533 (1957).

G. N. Afanasiev, “Simplest sources of electromagnetic fields as a tool for testing the reciprocity-like theorems,” J. Phys. D 34(4), 539–559 (2001).

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

X. H. Li, S. H. Guo, C. X. Kan, J. M. Zhu, T. T. Tong, S. L. Ke, W. C. H. Choy, and B. Q. Wei, “Au multimer@MoS2 hybrid structures for efficient photocatalytical hydrogen production via strongly plasmonic coupling effect,” Nano Energy 30, 549–558 (2016).

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).

[PubMed]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2011).

[PubMed]

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

[PubMed]

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).

[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).

[PubMed]

W. Liu, J. Shi, B. Lei, H. Hu, and A. E. Miroshnichenko, “Efficient excitation and tuning of toroidal dipoles within individual homogenous nanoparticles,” Opt. Express 23(19), 24738–24747 (2015).

[PubMed]

B. M. Ross and L. P. Lee, “Comparison of near- and far-field measures for plasmon resonance of metallic nanoparticles,” Opt. Lett. 34(7), 896–898 (2009).

[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).

[PubMed]

G. N. Afanasiev and V. M. Dubovik, “Some remarkable charge-current configurations,” Phys. Part. Nucl. 29(4), 366–391 (1998).

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

Z.-J. Yang, R. B. Jiang, X. L. Zhuo, Y.-M. Xie, J. F. Wang, and H.-Q. Lin, “Dielectric nanoresonators for light manipulation,” Phys. Rep. 701, 1–50 (2017).

B. N. Khlebtsov, V. A. Khanadeyev, J. Ye, D. W. Mackowski, G. Borghs, and N. G. Khlebtsov, “Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells,” Phys. Rev. B 77(3), 035440 (2008).

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

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).

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 Pt 2B), 046609 (2002).

[PubMed]

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 Pt 2), 036603 (2005).

[PubMed]

K. Sawada and N. Nagaosa, “Optical magnetoelectric effect in multiferroic materials: evidence for a Lorentz force acting on a ray of light,” Phys. Rev. Lett. 95(23), 237402 (2005).

[PubMed]

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

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).

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).

[PubMed]

S. Guo, X. Li, J. Zhu, T. Tong, and B. Wei, “Au NPs@MoS2 sub-micrometer sphere-ZnO nanorod hybrid structures for efficient photocatalytic hydrogen evolution with excellent stability,” Small 12(41), 5692–5701 (2016).

[PubMed]

V. M. Dubovik, L. A. Tosunyan, and V. V. Tugushev, “Axial toroidal moments in electrodynamics and solid-state physics,” Sov. Phys. JETP 63(2), 344–351 (1986).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, Inc., 1983).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).