Abstract

The interference between conventional multipoles (e.g., electric and magnetic dipole, electric quadrupole, etc.) is known as the cause of unidirectional backward and forward scattering of nanoparticles. However, an unconventional multipole moment, toroidal dipole moment is generally overlooked in the unidirectional scattering. In this work, we systematically investigate the unidirectional scattering in the system of plasmonic nanoparticles. It is found that the toroidal dipole moment can play a significant role in the unidirectional backward scattering. The structural tunability of the unidirectional scattering is also demonstrated. Our results can find applications in the design of nanoantennas.

© 2017 Optical Society of America

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2017 (1)

H. Xiang, L. Ge, L. Liu, T. Jiang, Z. Q. Zhang, C. T. Chan, and D. Han, “A minimal discrete model for toroidal moments and its experimental realization,” Phys. Rev. B 95(4), 045403 (2017).
[Crossref]

2016 (4)

F. Qin, Q. Zhang, and J. J. Xiao, “Sub-wavelength unidirectional antenna realized by stacked spoof localized surface plasmon resonators,” Sci. Rep. 6(1), 29773 (2016).
[Crossref] [PubMed]

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [PubMed]

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

T. Shibanuma, P. Albella, and S. A. Maier, “Unidirectional light scattering with high efficiency at optical frequencies based on low-loss dielectric nanoantennas,” Nanoscale 8(29), 14184–14192 (2016).
[Crossref] [PubMed]

2015 (7)

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus magneto-electric nanosphere dimers exhibiting unidirectional visible light scattering and strong electromagnetic field enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

A. Pors, S. K. Andersen, and S. I. Bozhevolnyi, “Unidirectional scattering by nanoparticles near substrates: generalized Kerker conditions,” Opt. Express 23(22), 28808–28828 (2015).
[Crossref] [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).
[Crossref]

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).
[Crossref]

Y. Li, M. Wan, W. Wu, Z. Chen, P. Zhan, and Z. Wang, “Broadband zero-backward and near-zero-forward scattering by metallo-dielectric core-shell nanoparticles,” Sci. Rep. 5(1), 12491 (2015).
[Crossref] [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).
[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]

2014 (2)

2013 (5)

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
[Crossref] [PubMed]

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (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(1), 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]

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

2012 (1)

2011 (3)

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011).
[Crossref] [PubMed]

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano 5(3), 2042–2050 (2011).
[Crossref] [PubMed]

2010 (5)

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (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]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (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)

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

2007 (1)

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]

1983 (1)

1972 (1)

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

Albella, P.

T. Shibanuma, P. Albella, and S. A. Maier, “Unidirectional light scattering with high efficiency at optical frequencies based on low-loss dielectric nanoantennas,” Nanoscale 8(29), 14184–14192 (2016).
[Crossref] [PubMed]

Albrektsen, O.

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref] [PubMed]

Andersen, S. K.

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

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, J.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

Bao, K.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

Bardhan, R.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (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]

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Bonod, N.

Bozhevolnyi, S. I.

A. Pors, S. K. Andersen, and S. I. Bozhevolnyi, “Unidirectional scattering by nanoparticles near substrates: generalized Kerker conditions,” Opt. Express 23(22), 28808–28828 (2015).
[Crossref] [PubMed]

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref] [PubMed]

Capasso, F.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

Chan, C. T.

H. Xiang, L. Ge, L. Liu, T. Jiang, Z. Q. Zhang, C. T. Chan, and D. Han, “A minimal discrete model for toroidal moments and its experimental realization,” Phys. Rev. B 95(4), 045403 (2017).
[Crossref]

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

K. H. Fung and C. T. Chan, “Plasmonic modes in periodic metal nanoparticle chains: a direct dynamic eigenmode analysis,” Opt. Lett. 32(8), 973–975 (2007).
[Crossref] [PubMed]

Chang, W. S.

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011).
[Crossref] [PubMed]

Chen, H.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus magneto-electric nanosphere dimers exhibiting unidirectional visible light scattering and strong electromagnetic field enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

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

Chen, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[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(1), 1237 (2013).
[Crossref] [PubMed]

Chen, Z.

Y. Li, M. Wan, W. Wu, Z. Chen, P. Zhan, and Z. Wang, “Broadband zero-backward and near-zero-forward scattering by metallo-dielectric core-shell nanoparticles,” Sci. Rep. 5(1), 12491 (2015).
[Crossref] [PubMed]

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.

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]

Deng, S.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus magneto-electric nanosphere dimers exhibiting unidirectional visible light scattering and strong electromagnetic field enhancement,” ACS Nano 9(1), 436–448 (2015).
[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]

Dregely, D.

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano 5(3), 2042–2050 (2011).
[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]

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]

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref] [PubMed]

Fan, J. A.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

Fan, Y.

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

Fedotov, V. A.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [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).
[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(1), 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]

Fu, Y. H.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
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Gao, L.

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).
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H. Xiang, L. Ge, L. Liu, T. Jiang, Z. Q. Zhang, C. T. Chan, and D. Han, “A minimal discrete model for toroidal moments and its experimental realization,” Phys. Rev. B 95(4), 045403 (2017).
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M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano 5(3), 2042–2050 (2011).
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Halas, N. J.

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011).
[Crossref] [PubMed]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

Han, D.

H. Xiang, L. Ge, L. Liu, T. Jiang, Z. Q. Zhang, C. T. Chan, and D. Han, “A minimal discrete model for toroidal moments and its experimental realization,” Phys. Rev. B 95(4), 045403 (2017).
[Crossref]

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).
[Crossref]

L. Ge, T. Zhan, D. Han, X. Liu, and J. Zi, “Unusual electromagnetic scattering by cylinders of topological insulator,” Opt. Express 22(25), 30833–30842 (2014).
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M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano 5(3), 2042–2050 (2011).
[Crossref] [PubMed]

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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Højlund-Nielsen, E.

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

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(1), 1237 (2013).
[Crossref] [PubMed]

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S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Jiang, T.

H. Xiang, L. Ge, L. Liu, T. Jiang, Z. Q. Zhang, C. T. Chan, and D. Han, “A minimal discrete model for toroidal moments and its experimental realization,” Phys. Rev. B 95(4), 045403 (2017).
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P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
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T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(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]

Ke, Y.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus magneto-electric nanosphere dimers exhibiting unidirectional visible light scattering and strong electromagnetic field enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

Kerker, M.

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).
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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]

Kristensen, A.

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[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]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
[Crossref] [PubMed]

Lal, S.

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011).
[Crossref] [PubMed]

Lapin, Z.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Lei, B.

Li, H.

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

Li, J. Q.

Z. G. Dong, J. Zhu, X. B. Yin, J. Q. Li, C. G. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87(24), 245429 (2013).
[Crossref]

Li, Y.

Y. Li, M. Wan, W. Wu, Z. Chen, P. Zhan, and Z. Wang, “Broadband zero-backward and near-zero-forward scattering by metallo-dielectric core-shell nanoparticles,” Sci. Rep. 5(1), 12491 (2015).
[Crossref] [PubMed]

Lin, Z.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

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N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011).
[Crossref] [PubMed]

Liu, L.

H. Xiang, L. Ge, L. Liu, T. Jiang, Z. Q. Zhang, C. T. Chan, and D. Han, “A minimal discrete model for toroidal moments and its experimental realization,” Phys. Rev. B 95(4), 045403 (2017).
[Crossref]

Liu, N.

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano 5(3), 2042–2050 (2011).
[Crossref] [PubMed]

Liu, P.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus magneto-electric nanosphere dimers exhibiting unidirectional visible light scattering and strong electromagnetic field enhancement,” ACS Nano 9(1), 436–448 (2015).
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W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015).
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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).
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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]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
[Crossref] [PubMed]

Ma, H.

Maier, S. A.

T. Shibanuma, P. Albella, and S. A. Maier, “Unidirectional light scattering with high efficiency at optical frequencies based on low-loss dielectric nanoantennas,” Nanoscale 8(29), 14184–14192 (2016).
[Crossref] [PubMed]

Manoharan, V. N.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

Miroshnichenko, A. E.

W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (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. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
[Crossref] [PubMed]

Mortensen, N. A.

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

Narimanov, E. E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Ng, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Nielsen, M. G.

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref] [PubMed]

Noginov, M. A.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Nordlander, P.

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011).
[Crossref] [PubMed]

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

Novotny, L.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Papasimakis, N.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[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]

Person, S.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

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H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
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Pors, A.

A. Pors, S. K. Andersen, and S. I. Bozhevolnyi, “Unidirectional scattering by nanoparticles near substrates: generalized Kerker conditions,” Opt. Express 23(22), 28808–28828 (2015).
[Crossref] [PubMed]

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref] [PubMed]

Qin, F.

F. Qin, Q. Zhang, and J. J. Xiao, “Sub-wavelength unidirectional antenna realized by stacked spoof localized surface plasmon resonators,” Sci. Rep. 6(1), 29773 (2016).
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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]

Radko, I. P.

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref] [PubMed]

Raybould, T. A.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [PubMed]

Rolly, B.

Sáenz, J. J.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Savinov, V.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [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).
[Crossref]

Shalaev, V. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Shibanuma, T.

T. Shibanuma, P. Albella, and S. A. Maier, “Unidirectional light scattering with high efficiency at optical frequencies based on low-loss dielectric nanoantennas,” Nanoscale 8(29), 14184–14192 (2016).
[Crossref] [PubMed]

Shvets, G.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

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]

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

Stout, B.

Stout, S.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Su, Y.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus magneto-electric nanosphere dimers exhibiting unidirectional visible light scattering and strong electromagnetic field enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

Suteewong, T.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

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]

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(1), 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]

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.

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]

Vannahme, C.

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

Vogelgesang, R.

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano 5(3), 2042–2050 (2011).
[Crossref] [PubMed]

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]

Wan, M.

Y. Li, M. Wan, W. Wu, Z. Chen, P. Zhan, and Z. Wang, “Broadband zero-backward and near-zero-forward scattering by metallo-dielectric core-shell nanoparticles,” Sci. Rep. 5(1), 12491 (2015).
[Crossref] [PubMed]

Wang, D.-S.

Wang, H.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus magneto-electric nanosphere dimers exhibiting unidirectional visible light scattering and strong electromagnetic field enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

Wang, Z.

Y. Li, M. Wan, W. Wu, Z. Chen, P. Zhan, and Z. Wang, “Broadband zero-backward and near-zero-forward scattering by metallo-dielectric core-shell nanoparticles,” Sci. Rep. 5(1), 12491 (2015).
[Crossref] [PubMed]

Wei, Z.

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

Wicks, G.

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

Wiesner, U.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Willatzen, M.

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref] [PubMed]

Wu, C.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[Crossref] [PubMed]

Wu, P. C.

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(1), 1237 (2013).
[Crossref] [PubMed]

Wu, W.

Y. Li, M. Wan, W. Wu, Z. Chen, P. Zhan, and Z. Wang, “Broadband zero-backward and near-zero-forward scattering by metallo-dielectric core-shell nanoparticles,” Sci. Rep. 5(1), 12491 (2015).
[Crossref] [PubMed]

Xiang, H.

H. Xiang, L. Ge, L. Liu, T. Jiang, Z. Q. Zhang, C. T. Chan, and D. Han, “A minimal discrete model for toroidal moments and its experimental realization,” Phys. Rev. B 95(4), 045403 (2017).
[Crossref]

Xiao, J. J.

F. Qin, Q. Zhang, and J. J. Xiao, “Sub-wavelength unidirectional antenna realized by stacked spoof localized surface plasmon resonators,” Sci. Rep. 6(1), 29773 (2016).
[Crossref] [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).
[Crossref]

Xie, W.

Xu, N.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus magneto-electric nanosphere dimers exhibiting unidirectional visible light scattering and strong electromagnetic field enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

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, 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).
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Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
[Crossref] [PubMed]

Zhan, P.

Y. Li, M. Wan, W. Wu, Z. Chen, P. Zhan, and Z. Wang, “Broadband zero-backward and near-zero-forward scattering by metallo-dielectric core-shell nanoparticles,” Sci. Rep. 5(1), 12491 (2015).
[Crossref] [PubMed]

Zhan, T.

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W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole induced transparency in core-shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015).
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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).
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H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus magneto-electric nanosphere dimers exhibiting unidirectional visible light scattering and strong electromagnetic field enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

Zhang, Q.

F. Qin, Q. Zhang, and J. J. Xiao, “Sub-wavelength unidirectional antenna realized by stacked spoof localized surface plasmon resonators,” Sci. Rep. 6(1), 29773 (2016).
[Crossref] [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).
[Crossref]

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]

Zhang, X. M.

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).
[Crossref]

Zhang, Z. Q.

H. Xiang, L. Ge, L. Liu, T. Jiang, Z. Q. Zhang, C. T. Chan, and D. Han, “A minimal discrete model for toroidal moments and its experimental realization,” Phys. Rev. B 95(4), 045403 (2017).
[Crossref]

Zheludev, N. I.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
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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]

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(1), 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]

Zhu, G.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

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]

Zhu, X.

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

Zi, J.

ACS Nano (2)

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano 5(3), 2042–2050 (2011).
[Crossref] [PubMed]

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus magneto-electric nanosphere dimers exhibiting unidirectional visible light scattering and strong electromagnetic field enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

ACS Photonics (1)

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).
[Crossref]

Chem. Rev. (1)

N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

Laser Photonics Rev. (1)

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

Nano Lett. (2)

S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13(4), 1806–1809 (2013).
[Crossref] [PubMed]

A. B. Evlyukhin, S. I. Bozhevolnyi, A. Pors, M. G. Nielsen, I. P. Radko, M. Willatzen, and O. Albrektsen, “Detuned electrical dipoles for plasmonic sensing,” Nano Lett. 10(11), 4571–4577 (2010).
[Crossref] [PubMed]

Nanoscale (1)

T. Shibanuma, P. Albella, and S. A. Maier, “Unidirectional light scattering with high efficiency at optical frequencies based on low-loss dielectric nanoantennas,” Nanoscale 8(29), 14184–14192 (2016).
[Crossref] [PubMed]

Nat. Commun. (2)

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. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
[Crossref] [PubMed]

Nat. Mater. (2)

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

X. Zhu, C. Vannahme, E. Højlund-Nielsen, N. A. Mortensen, and A. Kristensen, “Plasmonic colour laser printing,” Nat. Nanotechnol. 11(4), 325–329 (2016).
[Crossref] [PubMed]

Nat. Photonics (1)

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5(9), 531–534 (2011).
[Crossref]

Nature (1)

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (4)

Z. G. Dong, J. Zhu, X. B. Yin, J. Q. Li, C. G. Lu, and X. Zhang, “All-optical Hall effect by the dynamic toroidal moment in a cavity-based metamaterial,” Phys. Rev. B 87(24), 245429 (2013).
[Crossref]

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

H. Xiang, L. Ge, L. Liu, T. Jiang, Z. Q. Zhang, C. T. Chan, and D. Han, “A minimal discrete model for toroidal moments and its experimental realization,” Phys. Rev. B 95(4), 045403 (2017).
[Crossref]

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

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (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]

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. Li, M. Wan, W. Wu, Z. Chen, P. Zhan, and Z. Wang, “Broadband zero-backward and near-zero-forward scattering by metallo-dielectric core-shell nanoparticles,” Sci. Rep. 5(1), 12491 (2015).
[Crossref] [PubMed]

F. Qin, Q. Zhang, and J. J. Xiao, “Sub-wavelength unidirectional antenna realized by stacked spoof localized surface plasmon resonators,” Sci. Rep. 6(1), 29773 (2016).
[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(1), 1237 (2013).
[Crossref] [PubMed]

Science (3)

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
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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).
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T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330(6010), 1510–1512 (2010).
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Figures (6)

Fig. 1
Fig. 1 Schematic view of the system under study. The incident wave is polarized along the z axis. The radii of three plasmonic nanospheres are R1, R2 and R3, respectively, from left to right. The BS (backward scattering) and FS (forward scattering) are along the direction of - k i and k i, respectively.
Fig. 2
Fig. 2 (a) Scattering cross section for single plasmonic nanospheres with different radii, the solid lines represent the contribution from the dipolar term with n = 1. (b) Scattering intensity of BS and FS as functions of the frequency, calculated by the electric dipole approximation (solid lines) and COMSOL Multiphysics (dashed lines), respectively. (c) Ratio of BS to FS intensity. The blue solid line is calculated from the radiation of the multipole moments (P, T, M, Qe and Qm) of the tri-particle assembly, while the dashed line is the simulated result. The insets show the angular distribution of the scattering intensity in the far field for three different frequencies. Here we set R1 = R3 = 20 nm, R2 = 25 nm, and d = 60 nm.
Fig. 3
Fig. 3 (a) Radiation spectra of different multipole moments, including electric dipole (P), magnetic dipole (M), toroidal dipole (T), electric quadrupole (Qe) and magnetic quadrupole (Qm). (b) Spatial profile of the electric and magnetic field at the frequency of the maximum of BS/FS. For the forward scattering, the amplitude and phase of scattered electric waves for different multipole moments in the far field are shown in (c) and (d), respectively. The colors in (c) and (d) represent the same multipole moments as those in (a). The dashed gray line indicates the frequency of the maximum of BS/FS (marked by BS/FSmax in Fig. 2(c)). The geometric parameters are the same as those in Fig. 2(b).
Fig. 4
Fig. 4 (a) Ratio of BS intensity to FS intensity as a function of the radius R2 of the central nanosphere and incident frequency. Other parameters are kept the same as those in Fig. 2(b). The black curves represent the equal intensity of BS and FS. The ratio of BS/FS is very low (<0.02) in the black colored region. (b) Angular distribution of the scattering intensity in the far field for the point A and B marked in (a), where the red arrow indicates the direction of incident waves. In (c) and (d), the amplitude and phase of scattered electric fields radiated by different multipole moments in the forward direction are shown for R2 = 22 nm (corresponding to the dashed white line in (a)). In (c) and (d), the multipole moments are shown by the same color as those in Fig. 3.
Fig. 5
Fig. 5 (a) BS/ FS as a function of separation distance d. The maximal ratio increases as d decreases. (b) Ratio of scattering intensity in the –y direction to that in the y direction for different incident angle θi. d = 60 nm is fixed here. The black curves represent BS/FS = 1. The scattering pattern in the far field for different incident angles θi are shown for ω = 0.531 ωp (c) and ω = 0.538 ωp (d). The other parameters are the same as those in Fig. 2(b).
Fig. 6
Fig. 6 BS/FS for different permittivity of background medium εb (a) and radii of side nanospheres (b). In (b), the solid and dashed lines represents γ = 0 and γ = 0.003 ωp, respectively. The background is the free space. Other parameters in (a) and (b) are kept the same as those in Fig. 2(b). In (c), the ratio of BS/FS for the assembly of silver nanospheres embedded in TiO2 are shown by the black lines, where we set R1 = R3 = 15 nm, R2 = 25 nm and d = 45 nm. The corresponding radiation power for different multipoles are plotted in (d), where the gray dashed line represents the frequency of maximal BS/FS. In (a) and (c), the discrete triangles are calculated by COMSOL Multiphysics.

Equations (8)

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p i = α i ( ω ) [ j i g ( r i r j ) p j + E i ext ]
P = i p i ,
M = i k 0 2 i r i × p i ,
T = i k 0 10 i [ 2 r i 2 p i ( r i p i ) r i ] ,
Q α β ( e ) = 1 2 i [ r i , α p i , β + r i , β p i , α 2 3 ( r i p i ) δ α β ] ,
Q α β ( m ) = i k 0 3 i [ ( r i × p i ) α r β + ( r i × p i ) β r α ] .
I p = 2 ω 4 3 c 3 | P | 2 , I m = 2 ω 4 3 c 3 | M | 2 , I T = 2 ω 6 3 c 5 | T | 2 , I Q e = ω 6 5 c 5 | Q α β ( e ) | 2 , I Q m = ω 6 40 c 5 | Q α β ( m ) | 2 .
E s = R ( r ) [ F p ( θ , ϕ ) + F T ( θ , ϕ ) + F m ( θ , ϕ ) + F Q e ( θ , ϕ ) + F Q m ( θ , ϕ ) ] ,

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