Abstract

We have designed and numerically analyzed the theta-shaped dielectric arrays based on a single resonator per unit cell and generated non-radiative anapole resonance with an enhanced Q-factor. Relying on breaking the symmetry, it is shown that instead of leading to additional radiation losses, the Q-factor in theta-shaped Si arrays is enlarged about one order larger than that of the perfect disk arrays. And the magnetic near-field enhancements can be extended outside of the structures and are extremely enlarged. Further, the asymmetrirc magnetic field distributions can be observed by changing the nanorod position, providing a new way of indirectly manipulating the localized magnetic fields. The high Q-factor and strong magnetic near-field enhancements outside of the structures can be easily tailored by adjusting different geometric parameters and are achieved simultaneously, which furthermore provides a useful insight into their tuning behavior.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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2018 (4)

S. Q. Li and K. B. Crozier, “Origin of the anapole condition as revealed by a simple expansion beyond the toroidal multipole,” Phys. Rev. B 97(24), 245423 (2018).
[Crossref]

M. Timofeeva, L. Lang, A. Bouravleuv, and I. Shtrom, “Anapoles in Free-Standing III-V Nanodisks Enhancing Second-Harmonic Generation,” Nano Lett. 18(6), 3695–3702 (2018).
[Crossref]

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-Assisted Strong Field Enhancement in Individual All-Dielectric Nanostructures,” ACS Photon. 5(5), 1960–1966 (2018).
[Crossref]

Y. Zhang, W. Liu, Z. Li, Z. Li, and S. Chen, “High-quality-factor multiple Fano resonances for refractive index sensing,” Opt. Lett. 43(8), 1842–1845 (2018).
[Crossref]

2017 (6)

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient third harmonic generation from metal–dielectric hybrid nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
[Crossref]

S. D. Liu, Z. X. Wang, W. J. Wang, and Z. H. Chen, “High Q-factor with the excitation of anapole modes in dielectric split nanodisk arrays,” Opt. Express 25(19), 22375–22387 (2017).
[Crossref]

V. A. Zenin, A. B. Evlyukhin, S. M. Novikov, and A. V. Lavrinenko, “Direct Amplitude-Phase Near-Field Observation of Higher-Order Anapole States,” Nano Lett. 17(11), 7152–7159 (2017).
[Crossref]

I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
[Crossref]

M. Gupta, Y. K. Srivastava, and M. Manjappa, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017).
[Crossref]

G. D. Liu, X. Zhai, S. X. Xia, and L. L. Wang, “Toroidal resonance based optical modulator employing hybrid graphene-dielectric metasurface,” Opt. Express 25(21), 26045–26054 (2017).
[Crossref]

2016 (6)

2015 (7)

Y. Yang, W. Wang, I. I. Kravchenko, and A. Puretzky, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref]

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, and R. M. Bakker, “Nonradiating anapole modes in dielectric Nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref]

W. Liu, B. Lei, J. Shi, and A. E. Miroshnichenko, “Elusive Pure Anapole Excitation in Homogenous Spherical Nanoparticles with Radial Anisotropy,” J. Nanomater. 2015, 1–7 (2015).
[Crossref]

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

D. J. Cai, Y. H. Huang, W. J. Wang, and Z. H. Chen, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
[Crossref]

C. Argyropoulos, “Enhanced transmission modulation based on dielectric metasurfaces loaded with grapheme,” Opt. Express 23(18), 23787–23797 (2015).
[Crossref]

H. Li, Y. Huang, F. Liang, C. Guo, W. Hua, and Y. Fang, “Fano resonance assisting plasmonic circular dichroism from nanorice heterodimers for extrinsic chirality,” Sci. Rep. 5(1), 16069 (2015).
[Crossref]

2014 (1)

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

2013 (2)

J. Zhang and N. I. Zheludev, “Near-infrared trapped mode magnetic resonance in an all-dielectric metamaterial,” Opt. Express 21(22), 26721–26728 (2013).
[Crossref]

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(1), 1527 (2013).
[Crossref]

2012 (3)

J. M. Geffrin and C. Eyraud, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

J. C. Ginn, I. Brener, D. W. Peters, and P. F. Hines, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref]

A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in all-dielectric oligomers,” Nano Lett. 12(12), 6459–6463 (2012).
[Crossref]

2011 (2)

A. Garcíaetxarri, C. López, J. J. Sáenz, and L. Chantada, “Strong magnetic response of submicron Silicon particles in the infrared,” Opt. Express 19(6), 4815–4826 (2011).
[Crossref]

R. Gómezmedina, F. Moreno, and M. Nietovesperinas, “Electric and magnetic dipolar response of germanium nanospheres interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5(1), 053512 (2011).
[Crossref]

2010 (4)

C. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, and H. Giessen, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

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]

A. B. Evlyukhin, C. Reinhardt, A. Seidel, and B. N. Chichkov, “Optical response features of Si-nanoparticle arrays,” Phys. Rev. B 82(4), 045404 (2010).
[Crossref]

2008 (1)

J. N. Anker, W. P. Hall, O. Lyandres, and R. P. V. Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref]

1974 (1)

J. E. Sipe and J. V. Kranendonk, “Macroscopic electromagnetic theory of resonant dielectrics,” Phys. Rev. A 9(5), 1806–1822 (1974).
[Crossref]

Albella, P.

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient third harmonic generation from metal–dielectric hybrid nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
[Crossref]

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, and R. P. V. Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref]

Argyropoulos, C.

Bakker, R. M.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, and R. M. Bakker, “Nonradiating anapole modes in dielectric Nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref]

Basharin, A. A.

I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
[Crossref]

Bouravleuv, A.

M. Timofeeva, L. Lang, A. Bouravleuv, and I. Shtrom, “Anapoles in Free-Standing III-V Nanodisks Enhancing Second-Harmonic Generation,” Nano Lett. 18(6), 3695–3702 (2018).
[Crossref]

Bozhevolnyi, S. I.

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-Assisted Strong Field Enhancement in Individual All-Dielectric Nanostructures,” ACS Photon. 5(5), 1960–1966 (2018).
[Crossref]

Brener, I.

J. C. Ginn, I. Brener, D. W. Peters, and P. F. Hines, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref]

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(1), 5753 (2014).
[Crossref]

Cai, D. J.

D. J. Cai, Y. H. Huang, W. J. Wang, and Z. H. Chen, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
[Crossref]

Campione, S.

S. Campione, S. Liu, and T. S. Luk, “Broken Symmetry Dielectric Resonators for High Quality Factor Fano Metasurfaces,” ACS Photon. 3(12), 2362–2367 (2016).
[Crossref]

Chantada, L.

Chen, S.

Chen, Z. H.

S. D. Liu, Z. X. Wang, W. J. Wang, and Z. H. Chen, “High Q-factor with the excitation of anapole modes in dielectric split nanodisk arrays,” Opt. Express 25(19), 22375–22387 (2017).
[Crossref]

D. J. Cai, Y. H. Huang, W. J. Wang, and Z. H. Chen, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
[Crossref]

Chichkov, B. N.

A. B. Evlyukhin, C. Reinhardt, A. Seidel, and B. N. Chichkov, “Optical response features of Si-nanoparticle arrays,” Phys. Rev. B 82(4), 045404 (2010).
[Crossref]

Crozier, K. B.

S. Q. Li and K. B. Crozier, “Origin of the anapole condition as revealed by a simple expansion beyond the toroidal multipole,” Phys. Rev. B 97(24), 245423 (2018).
[Crossref]

Dal, N. L.

Duyne, R. P. V.

J. N. Anker, W. P. Hall, O. Lyandres, and R. P. V. Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref]

Evlyukhin, A. B.

V. A. Zenin, A. B. Evlyukhin, S. M. Novikov, and A. V. Lavrinenko, “Direct Amplitude-Phase Near-Field Observation of Higher-Order Anapole States,” Nano Lett. 17(11), 7152–7159 (2017).
[Crossref]

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, and R. M. Bakker, “Nonradiating anapole modes in dielectric Nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref]

A. B. Evlyukhin, C. Reinhardt, A. Seidel, and B. N. Chichkov, “Optical response features of Si-nanoparticle arrays,” Phys. Rev. B 82(4), 045404 (2010).
[Crossref]

Eyraud, C.

J. M. Geffrin and C. Eyraud, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

Fang, Y.

H. Li, Y. Huang, F. Liang, C. Guo, W. Hua, and Y. Fang, “Fano resonance assisting plasmonic circular dichroism from nanorice heterodimers for extrinsic chirality,” Sci. Rep. 5(1), 16069 (2015).
[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]

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]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

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(1), 1527 (2013).
[Crossref]

Garcíaetxarri, A.

Geffrin, J. M.

J. M. Geffrin and C. Eyraud, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

Giessen, H.

C. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, and H. Giessen, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref]

Ginn, J. C.

J. C. Ginn, I. Brener, D. W. Peters, and P. F. Hines, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref]

Gómezmedina, R.

R. Gómezmedina, F. Moreno, and M. Nietovesperinas, “Electric and magnetic dipolar response of germanium nanospheres interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5(1), 053512 (2011).
[Crossref]

Gong, C.

Grinblat, G.

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient third harmonic generation from metal–dielectric hybrid nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
[Crossref]

Guo, C.

H. Li, Y. Huang, F. Liang, C. Guo, W. Hua, and Y. Fang, “Fano resonance assisting plasmonic circular dichroism from nanorice heterodimers for extrinsic chirality,” Sci. Rep. 5(1), 16069 (2015).
[Crossref]

Gupta, M.

M. Gupta, Y. K. Srivastava, and M. Manjappa, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017).
[Crossref]

Halas, N. J.

C. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, and H. Giessen, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref]

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, and R. P. V. Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref]

Hines, P. F.

J. C. Ginn, I. Brener, D. W. Peters, and P. F. Hines, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref]

Hua, W.

H. Li, Y. Huang, F. Liang, C. Guo, W. Hua, and Y. Fang, “Fano resonance assisting plasmonic circular dichroism from nanorice heterodimers for extrinsic chirality,” Sci. Rep. 5(1), 16069 (2015).
[Crossref]

Huang, Q.

Huang, Y.

H. Li, Y. Huang, F. Liang, C. Guo, W. Hua, and Y. Fang, “Fano resonance assisting plasmonic circular dichroism from nanorice heterodimers for extrinsic chirality,” Sci. Rep. 5(1), 16069 (2015).
[Crossref]

Huang, Y. H.

D. J. Cai, Y. H. Huang, W. J. Wang, and Z. H. Chen, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
[Crossref]

Ishitobi, H.

Kaelberer, T.

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

Kivshar, Y. S.

A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in all-dielectric oligomers,” Nano Lett. 12(12), 6459–6463 (2012).
[Crossref]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

Kranendonk, J. V.

J. E. Sipe and J. V. Kranendonk, “Macroscopic electromagnetic theory of resonant dielectrics,” Phys. Rev. A 9(5), 1806–1822 (1974).
[Crossref]

Kravchenko, I. I.

Y. Yang, W. Wang, I. I. Kravchenko, and A. Puretzky, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref]

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

Kuznetsov, A. I.

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(1), 1527 (2013).
[Crossref]

Lang, L.

M. Timofeeva, L. Lang, A. Bouravleuv, and I. Shtrom, “Anapoles in Free-Standing III-V Nanodisks Enhancing Second-Harmonic Generation,” Nano Lett. 18(6), 3695–3702 (2018).
[Crossref]

Lavrinenko, A. V.

V. A. Zenin, A. B. Evlyukhin, S. M. Novikov, and A. V. Lavrinenko, “Direct Amplitude-Phase Near-Field Observation of Higher-Order Anapole States,” Nano Lett. 17(11), 7152–7159 (2017).
[Crossref]

Lei, B.

W. Liu, B. Lei, J. Shi, and A. E. Miroshnichenko, “Elusive Pure Anapole Excitation in Homogenous Spherical Nanoparticles with Radial Anisotropy,” J. Nanomater. 2015, 1–7 (2015).
[Crossref]

Li, H.

H. Li, Y. Huang, F. Liang, C. Guo, W. Hua, and Y. Fang, “Fano resonance assisting plasmonic circular dichroism from nanorice heterodimers for extrinsic chirality,” Sci. Rep. 5(1), 16069 (2015).
[Crossref]

Li, S. Q.

S. Q. Li and K. B. Crozier, “Origin of the anapole condition as revealed by a simple expansion beyond the toroidal multipole,” Phys. Rev. B 97(24), 245423 (2018).
[Crossref]

Li, Z.

Liang, F.

H. Li, Y. Huang, F. Liang, C. Guo, W. Hua, and Y. Fang, “Fano resonance assisting plasmonic circular dichroism from nanorice heterodimers for extrinsic chirality,” Sci. Rep. 5(1), 16069 (2015).
[Crossref]

Liu, G. D.

Liu, S.

S. Campione, S. Liu, and T. S. Luk, “Broken Symmetry Dielectric Resonators for High Quality Factor Fano Metasurfaces,” ACS Photon. 3(12), 2362–2367 (2016).
[Crossref]

Liu, S. D.

Liu, W.

López, C.

Luk, T. S.

S. Campione, S. Liu, and T. S. Luk, “Broken Symmetry Dielectric Resonators for High Quality Factor Fano Metasurfaces,” ACS Photon. 3(12), 2362–2367 (2016).
[Crossref]

Luk’Yanchuk, B.

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(1), 1527 (2013).
[Crossref]

Luk’yanchuk, C. B.

C. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, and H. Giessen, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref]

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, and R. P. V. Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref]

Maier, S. A.

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient third harmonic generation from metal–dielectric hybrid nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
[Crossref]

C. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, and H. Giessen, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref]

Manjappa, M.

M. Gupta, Y. K. Srivastava, and M. Manjappa, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017).
[Crossref]

Miroshnichenko, A. E.

W. Liu, B. Lei, J. Shi, and A. E. Miroshnichenko, “Elusive Pure Anapole Excitation in Homogenous Spherical Nanoparticles with Radial Anisotropy,” J. Nanomater. 2015, 1–7 (2015).
[Crossref]

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, and R. M. Bakker, “Nonradiating anapole modes in dielectric Nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref]

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

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(1), 1527 (2013).
[Crossref]

A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in all-dielectric oligomers,” Nano Lett. 12(12), 6459–6463 (2012).
[Crossref]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

Moreno, F.

R. Gómezmedina, F. Moreno, and M. Nietovesperinas, “Electric and magnetic dipolar response of germanium nanospheres interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5(1), 053512 (2011).
[Crossref]

Nietovesperinas, M.

R. Gómezmedina, F. Moreno, and M. Nietovesperinas, “Electric and magnetic dipolar response of germanium nanospheres interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5(1), 053512 (2011).
[Crossref]

Nordlander, P.

C. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, and H. Giessen, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref]

Novikov, S. M.

V. A. Zenin, A. B. Evlyukhin, S. M. Novikov, and A. V. Lavrinenko, “Direct Amplitude-Phase Near-Field Observation of Higher-Order Anapole States,” Nano Lett. 17(11), 7152–7159 (2017).
[Crossref]

Palik, E. D.

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

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]

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]

Peters, D. W.

J. C. Ginn, I. Brener, D. W. Peters, and P. F. Hines, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref]

Puretzky, A.

Y. Yang, W. Wang, I. I. Kravchenko, and A. Puretzky, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref]

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]

Reinhardt, C.

A. B. Evlyukhin, C. Reinhardt, A. Seidel, and B. N. Chichkov, “Optical response features of Si-nanoparticle arrays,” Phys. Rev. B 82(4), 045404 (2010).
[Crossref]

Sáenz, J. J.

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]

Seidel, A.

A. B. Evlyukhin, C. Reinhardt, A. Seidel, and B. N. Chichkov, “Optical response features of Si-nanoparticle arrays,” Phys. Rev. B 82(4), 045404 (2010).
[Crossref]

Sekkat, Z.

Shi, J.

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

W. Liu, B. Lei, J. Shi, and A. E. Miroshnichenko, “Elusive Pure Anapole Excitation in Homogenous Spherical Nanoparticles with Radial Anisotropy,” J. Nanomater. 2015, 1–7 (2015).
[Crossref]

Shibanuma, T.

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient third harmonic generation from metal–dielectric hybrid nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
[Crossref]

Shtrom, I.

M. Timofeeva, L. Lang, A. Bouravleuv, and I. Shtrom, “Anapoles in Free-Standing III-V Nanodisks Enhancing Second-Harmonic Generation,” Nano Lett. 18(6), 3695–3702 (2018).
[Crossref]

Sipe, J. E.

J. E. Sipe and J. V. Kranendonk, “Macroscopic electromagnetic theory of resonant dielectrics,” Phys. Rev. A 9(5), 1806–1822 (1974).
[Crossref]

Srivastava, Y. K.

M. Gupta, Y. K. Srivastava, and M. Manjappa, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017).
[Crossref]

Stenishchev, I. V.

I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
[Crossref]

Timofeeva, M.

M. Timofeeva, L. Lang, A. Bouravleuv, and I. Shtrom, “Anapoles in Free-Standing III-V Nanodisks Enhancing Second-Harmonic Generation,” Nano Lett. 18(6), 3695–3702 (2018).
[Crossref]

Tong, W.

Tretyakov, S.

S. Tretyakov, Analytical Modeling in Applied Electromagnetics, (Artech House, 2003).

Tsai, D. P.

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]

Valentine, J.

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

Wang, L. L.

Wang, R.

Wang, W.

Y. Yang, W. Wang, I. I. Kravchenko, and A. Puretzky, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref]

Wang, W. J.

S. D. Liu, Z. X. Wang, W. J. Wang, and Z. H. Chen, “High Q-factor with the excitation of anapole modes in dielectric split nanodisk arrays,” Opt. Express 25(19), 22375–22387 (2017).
[Crossref]

D. J. Cai, Y. H. Huang, W. J. Wang, and Z. H. Chen, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
[Crossref]

Wang, Z. X.

Xia, J.

Xia, S. X.

Yang, Y.

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-Assisted Strong Field Enhancement in Individual All-Dielectric Nanostructures,” ACS Photon. 5(5), 1960–1966 (2018).
[Crossref]

Y. Yang, W. Wang, I. I. Kravchenko, and A. Puretzky, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref]

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

Yu, Y. F.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, and R. M. Bakker, “Nonradiating anapole modes in dielectric Nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref]

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(1), 1527 (2013).
[Crossref]

Zenin, V. A.

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-Assisted Strong Field Enhancement in Individual All-Dielectric Nanostructures,” ACS Photon. 5(5), 1960–1966 (2018).
[Crossref]

V. A. Zenin, A. B. Evlyukhin, S. M. Novikov, and A. V. Lavrinenko, “Direct Amplitude-Phase Near-Field Observation of Higher-Order Anapole States,” Nano Lett. 17(11), 7152–7159 (2017).
[Crossref]

Zhai, X.

Zhang, J.

Zhang, Y.

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).
[Crossref]

J. Zhang and N. I. Zheludev, “Near-infrared trapped mode magnetic resonance in an all-dielectric metamaterial,” Opt. Express 21(22), 26721–26728 (2013).
[Crossref]

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]

C. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, and H. Giessen, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref]

ACS Photon. (2)

Y. Yang, V. A. Zenin, and S. I. Bozhevolnyi, “Anapole-Assisted Strong Field Enhancement in Individual All-Dielectric Nanostructures,” ACS Photon. 5(5), 1960–1966 (2018).
[Crossref]

S. Campione, S. Liu, and T. S. Luk, “Broken Symmetry Dielectric Resonators for High Quality Factor Fano Metasurfaces,” ACS Photon. 3(12), 2362–2367 (2016).
[Crossref]

Appl. Phys. Lett. (1)

M. Gupta, Y. K. Srivastava, and M. Manjappa, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017).
[Crossref]

J. Nanomater. (1)

W. Liu, B. Lei, J. Shi, and A. E. Miroshnichenko, “Elusive Pure Anapole Excitation in Homogenous Spherical Nanoparticles with Radial Anisotropy,” J. Nanomater. 2015, 1–7 (2015).
[Crossref]

J. Nanophoton. (1)

R. Gómezmedina, F. Moreno, and M. Nietovesperinas, “Electric and magnetic dipolar response of germanium nanospheres interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. 5(1), 053512 (2011).
[Crossref]

J. Phys. Chem. C (1)

D. J. Cai, Y. H. Huang, W. J. Wang, and Z. H. Chen, “Fano Resonances Generated in a Single Dielectric Homogeneous Nanoparticle with High Structural Symmetry,” J. Phys. Chem. C 119(8), 4252–4260 (2015).
[Crossref]

Nano Lett. (5)

A. E. Miroshnichenko and Y. S. Kivshar, “Fano resonances in all-dielectric oligomers,” Nano Lett. 12(12), 6459–6463 (2012).
[Crossref]

M. Timofeeva, L. Lang, A. Bouravleuv, and I. Shtrom, “Anapoles in Free-Standing III-V Nanodisks Enhancing Second-Harmonic Generation,” Nano Lett. 18(6), 3695–3702 (2018).
[Crossref]

V. A. Zenin, A. B. Evlyukhin, S. M. Novikov, and A. V. Lavrinenko, “Direct Amplitude-Phase Near-Field Observation of Higher-Order Anapole States,” Nano Lett. 17(11), 7152–7159 (2017).
[Crossref]

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient third harmonic generation from metal–dielectric hybrid nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
[Crossref]

Y. Yang, W. Wang, I. I. Kravchenko, and A. Puretzky, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref]

Nat. Commun. (4)

A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, and R. M. Bakker, “Nonradiating anapole modes in dielectric Nanoparticles,” Nat. Commun. 6(1), 8069 (2015).
[Crossref]

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

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(1), 1527 (2013).
[Crossref]

J. M. Geffrin and C. Eyraud, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

Nat. Mater. (3)

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]

J. N. Anker, W. P. Hall, O. Lyandres, and R. P. V. Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008).
[Crossref]

C. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, and H. Giessen, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref]

Opt. Express (10)

G. D. Liu, X. Zhai, S. X. Xia, and L. L. Wang, “Toroidal resonance based optical modulator employing hybrid graphene-dielectric metasurface,” Opt. Express 25(21), 26045–26054 (2017).
[Crossref]

C. Argyropoulos, “Enhanced transmission modulation based on dielectric metasurfaces loaded with grapheme,” Opt. Express 23(18), 23787–23797 (2015).
[Crossref]

W. Tong, C. Gong, Q. Huang, and J. Xia, “Enhanced third harmonic generation in a silicon metasurface using trapped mode,” Opt. Express 24(17), 19661–19670 (2016).
[Crossref]

A. Garcíaetxarri, C. López, J. J. Sáenz, and L. Chantada, “Strong magnetic response of submicron Silicon particles in the infrared,” Opt. Express 19(6), 4815–4826 (2011).
[Crossref]

W. Tong, C. Gong, Q. Huang, and J. Xia, “Enhanced third harmonic generation in a silicon metasurface using trapped mode,” Opt. Express 24(17), 19661–19670 (2016).
[Crossref]

S. D. Liu, Z. X. Wang, W. J. Wang, and Z. H. Chen, “High Q-factor with the excitation of anapole modes in dielectric split nanodisk arrays,” Opt. Express 25(19), 22375–22387 (2017).
[Crossref]

J. Zhang and N. I. Zheludev, “Near-infrared trapped mode magnetic resonance in an all-dielectric metamaterial,” Opt. Express 21(22), 26721–26728 (2013).
[Crossref]

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

R. Wang and N. L. Dal, “Engineering non-radiative anapole modes for broadband absorption enhancement of light,” Opt. Express 24(17), 19048–19062 (2016).
[Crossref]

Z. Sekkat and H. Ishitobi, “Plasmonic coupled modes in metal-dielectric multilayer structures: Fano resonance and giant field enhancement,” Opt. Express 24(18), 20080–20088 (2016).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (1)

J. E. Sipe and J. V. Kranendonk, “Macroscopic electromagnetic theory of resonant dielectrics,” Phys. Rev. A 9(5), 1806–1822 (1974).
[Crossref]

Phys. Rev. B (2)

A. B. Evlyukhin, C. Reinhardt, A. Seidel, and B. N. Chichkov, “Optical response features of Si-nanoparticle arrays,” Phys. Rev. B 82(4), 045404 (2010).
[Crossref]

S. Q. Li and K. B. Crozier, “Origin of the anapole condition as revealed by a simple expansion beyond the toroidal multipole,” Phys. Rev. B 97(24), 245423 (2018).
[Crossref]

Phys. Rev. Lett. (1)

J. C. Ginn, I. Brener, D. W. Peters, and P. F. Hines, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref]

Rev. Mod. Phys. (1)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

Sci. Rep. (2)

H. Li, Y. Huang, F. Liang, C. Guo, W. Hua, and Y. Fang, “Fano resonance assisting plasmonic circular dichroism from nanorice heterodimers for extrinsic chirality,” Sci. Rep. 5(1), 16069 (2015).
[Crossref]

I. V. Stenishchev and A. A. Basharin, “Toroidal response in all-dielectric metamaterials based on water,” Sci. Rep. 7(1), 9468 (2017).
[Crossref]

Science (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]

Other (2)

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

S. Tretyakov, Analytical Modeling in Applied Electromagnetics, (Artech House, 2003).

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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic illustration of the theta-shaped Si arrays. (b) Top view and geometric parameters of a unit cell in the Si arrays. The polarization (E) and propagation (k) directions of incident wave are denoted.
Fig. 2.
Fig. 2. (a) Calculated spectra (1-Transmission) of the arrays (solid lines), where the W = 55 nm (red line) and W = 350 nm (blue line), R = 230 nm, r = 175 nm, T = 125 nm, P = 600 nm for the array with δ = 0 nm, and the dashed lines represent the fitted spectra with the oscillator model. (b) The extracted Q-factors and resonance positions as a function of the W.
Fig. 3.
Fig. 3. (a) Amplitude of the Cartesian ED moment |P|, MD moment |M|, and TD moment |ikT| around the TD resonance for W = 55 nm. (b) The phases and their difference of P and ikT. The other geometry parameters are identical as that of Fig. 2(a).
Fig. 4.
Fig. 4. (a) Transmission spectra of the arrays at different δ. (b) Amplitudes of the ED moment |P|, MD moment |M| and TD moment |ikT|. (c) The phases and the difference of P and ikT. (d) The extracted Q-factors of the arrays as a function of δ. The other geometry parameters are identical as that of Fig. 3.
Fig. 5.
Fig. 5. a) Normalized magnetic field (Hz) distributions at different resonances in the xy plane at the δ = 0 nm and 60 nm. The black cones represent electric field vector distributions. (b) Normalized magnetic near-field distributions |H/H0| and magnetic field vector distributions (white cones) at different resonances for the W = 55 nm at different δ.
Fig. 6.
Fig. 6. Dependence of transmission spectra of the arrays with δ = 60 nm on the different (a) P, (b) W, (c) T, (d) R. Other parameters are the same as the parameters used in Fig. 1(a) except the parameter shown in each Fig. 6.

Equations (1)

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T F a n o = | a 1 + a 2 + b ω ω 0 + i γ | 2

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