Abstract

In metamaterial systems, toroidal dipole (TD) plays an important role in determining their optical properties. Here, we proposed an all-dielectric metasurface consisting of two silicon split-ring resonators (SRRs) that can support strong TD resonance. The TD resonance is excited by TD moments both inside the unit cell and between the neighboring unit cells, and can be easily manipulated by altering the gap size or distance of the SRRs, leading to powerful electric and magnetic near-field enhancement. In addition, symmetric unprotected TD bound state in the continuum (TD-BIC) was achieved in closed-ring-resonator (CRR) metasurface, and transformed into leaky resonances with ultrahigh Q factors by adjusting the distance of CRRs. The proposed structure provides a good platform for us to better understand the coupling of SRRs, which is useful for the design and application of TD metasurfaces in biological sensors, nonlinear interactions and other photonic devices.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  2. G. Thorner, J. Kiat, C. Bogicevic, and I. Kornev, “Axial hypertoroidal moment in a ferroelectric nanotorus: A way to switch local polarization,” Phys. Rev. B 89(22), 220103 (2014).
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    [Crossref]
  6. 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).
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    [Crossref]
  29. X. Chen and W. Fan, “Study of the interaction between graphene and planar terahertz metamaterial with toroidal dipolar resonance,” Opt. Lett. 42(10), 2034–2037 (2017).
    [Crossref]
  30. S. Yang, Z. Liu, L. Jin, W. Li, S. Zhang, J. Li, and C. Gu, “Surface plasmon polariton mediated multiple toroidal resonances in 3D folding metamaterials,” ACS Photonics 4(11), 2650–2658 (2017).
    [Crossref]
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    [Crossref]
  32. X. Li, J. Yin, Z. Liu, Y. Wang, and Z. Hong, “Tailoring the excitation of two kinds of toroidal dipoles in all-dielectric metasurfaces,” Optik 201, 163502 (2020).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  38. F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112(21), 213903 (2014).
    [Crossref]
  39. C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1(9), 16048 (2016).
    [Crossref]
  40. A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, “Lasing action from photonic bound states in continuum,” Nature 541(7636), 196–199 (2017).
    [Crossref]
  41. M. A. Belyakov, M. A. Balezin, Z. F. Sadrieva, P. V. Kapitanova, E. A. Nenasheva, A. F. Sadreev, and A. A. Bogdanov, “Experimental observation of symmetry protected bound state in the continuum in a chain of dielectric disks,” Phys. Rev. A 99(5), 053804 (2019).
    [Crossref]
  42. Z. F. Sadrieva, I. S. Sinev, K. L. Koshelev, A. Samusev, I. V. Iorsh, O. Takayama, R. Malureanu, A. A. Bogdanov, and A. V. Lavrinenko, “Transition from optical bound states in the continuum to leaky resonances: Role of substrate and roughness,” ACS Photonics 4(4), 723–727 (2017).
    [Crossref]
  43. A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
    [Crossref]
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    [Crossref]
  45. 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 65(4), 046609 (2002).
    [Crossref]
  46. V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
    [Crossref]
  47. 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]
  48. S. H. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
    [Crossref]
  49. B. Luk’Yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
    [Crossref]
  50. Z. F. Sadrieva, I. S. Sinev, K. L. Koshelev, A. Samusev, I. V. Iorsh, O. Takayama, R. Malureanu, A. A. Bogdanov, and A. V. Lavrinenko, “Transition from Optical Bound States in the Continuum to Leaky Resonances: Role of Substrate and Roughness,” ACS Photonics 4(4), 723–727 (2017).
    [Crossref]
  51. K. Fan, I. V. Shadrivov, and W. J. Padilla, “Dynamic bound states in the continuum,” Optica 6(2), 169–173 (2019).
    [Crossref]
  52. 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]

2020 (1)

X. Li, J. Yin, Z. Liu, Y. Wang, and Z. Hong, “Tailoring the excitation of two kinds of toroidal dipoles in all-dielectric metasurfaces,” Optik 201, 163502 (2020).
[Crossref]

2019 (6)

B. Oeguet, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal dipole-enhanced third harmonic generation of deep ultraviolet light using plasmonic meta-atoms,” Nano Lett. 19(1), 605–611 (2019).
[Crossref]

J. F. Algorri, D. C. Zografopoulos, A. Ferraro, B. García-Cámara, R. Beccherelli, and J. M. Sánchez-Pena, “Ultrahigh-quality factor resonant dielectricmetasurfaces based on hollow nanocuboids,” Opt. Express 27(5), 6320–6330 (2019).
[Crossref]

Z. Li, T. Wu, and X. Zhang, “Tailoring toroidal and magnetic dipole excitations with the same dielectric structure,” Opt. Lett. 44(1), 57–62 (2019).
[Crossref]

M. A. Belyakov, M. A. Balezin, Z. F. Sadrieva, P. V. Kapitanova, E. A. Nenasheva, A. F. Sadreev, and A. A. Bogdanov, “Experimental observation of symmetry protected bound state in the continuum in a chain of dielectric disks,” Phys. Rev. A 99(5), 053804 (2019).
[Crossref]

F. Yesilkoy, E. R. Arvelo, Y. Jahani, M. Liu, A. Tittl, V. Cevher, Y. Kivshar, and H. Altug, “Ultrasensitive hyperspectral imaging and biodetection enabled by dielectric metasurfaces,” Nat. Photonics 13(6), 390–396 (2019).
[Crossref]

K. Fan, I. V. Shadrivov, and W. J. Padilla, “Dynamic bound states in the continuum,” Optica 6(2), 169–173 (2019).
[Crossref]

2018 (8)

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref]

A. Sayanskiy, M. Danaeifar, P. Kapitanova, and A. E. Miroshnichenko, “All-Dielectric Metalattice with Enhanced Toroidal Dipole Response,” Adv. Opt. Mater. 6(19), 1800302 (2018).
[Crossref]

B. Oeguet, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Low-loss and high- Q planar metamaterial with toroidal moment,” Phys. Rev. B 87, 115417 (2018).

B. Han, X. Li, C. Sui, J. Diao, X. Jing, and Z. Hong, “Analog of electromagnetically induced transparency in an E-shaped all-dielectric metasurface based on toroidal dipolar response,” Opt. Mater. Express 8(8), 2197–2207 (2018).
[Crossref]

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y. W. Huang, P. R. Wu, Y. H. Chen, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

M. Gupta, Y. K. Srivastava, and R. Singh, “A toroidal metamaterial switch,” Adv. Mater. 30(4), 1704845 (2018).
[Crossref]

Y. He, G. Guo, T. Feng, Y. Xu, and A. E. Miroshnichenko, “Toroidal dipole bound states in the continuum,” Phys. Rev. B 98(16), 161112 (2018).
[Crossref]

S. Xu, A. Sayanskiy, A. S. Kupriianov, V. R. Tuz, P. Kapitanova, H. Sun, W. Han, and Y. S. Kivshar, “Experimental Observation of Toroidal Dipole Modes in All-Dielectric Metasurfaces,” Adv. Opt. Mater. 7, 1801166 (2018).
[Crossref]

2017 (11)

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

X. Chen and W. Fan, “Study of the interaction between graphene and planar terahertz metamaterial with toroidal dipolar resonance,” Opt. Lett. 42(10), 2034–2037 (2017).
[Crossref]

S. Yang, Z. Liu, L. Jin, W. Li, S. Zhang, J. Li, and C. Gu, “Surface plasmon polariton mediated multiple toroidal resonances in 3D folding metamaterials,” ACS Photonics 4(11), 2650–2658 (2017).
[Crossref]

L. Cong, Y. K. Srivastava, and R. Singh, “Tailoring the multipoles in THz toroidal metamaterials,” Appl. Phys. Lett. 111(8), 081108 (2017).
[Crossref]

A. A. Basharin, V. Chuguevsky, N. Volsky, M. Kafesaki, and E. N. Economou, “Extremely high Q-factor metamaterials due to anapole excitation,” Phys. Rev. B 95(3), 035104 (2017).
[Crossref]

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

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

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).
[Crossref]

A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, “Lasing action from photonic bound states in continuum,” Nature 541(7636), 196–199 (2017).
[Crossref]

Z. F. Sadrieva, I. S. Sinev, K. L. Koshelev, A. Samusev, I. V. Iorsh, O. Takayama, R. Malureanu, A. A. Bogdanov, and A. V. Lavrinenko, “Transition from optical bound states in the continuum to leaky resonances: Role of substrate and roughness,” ACS Photonics 4(4), 723–727 (2017).
[Crossref]

Z. F. Sadrieva, I. S. Sinev, K. L. Koshelev, A. Samusev, I. V. Iorsh, O. Takayama, R. Malureanu, A. A. Bogdanov, and A. V. Lavrinenko, “Transition from Optical Bound States in the Continuum to Leaky Resonances: Role of Substrate and Roughness,” ACS Photonics 4(4), 723–727 (2017).
[Crossref]

2016 (4)

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1(9), 16048 (2016).
[Crossref]

M. Gupta and R. Singh, “Toroidal versus Fano Resonances in High Q planar THz Metamaterials,” Adv. Opt. Mater. 4(12), 2119–2125 (2016).
[Crossref]

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref]

L. Wei, Z. Xi, N. Bhattacharya, and H. P. Urbach, “Excitation of the radiationless anapole mode,” Optica 3(8), 799 (2016).
[Crossref]

2015 (3)

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(1), 8069 (2015).
[Crossref]

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, 011036 (2015).
[Crossref]

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]

2014 (6)

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]

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

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112(21), 213903 (2014).
[Crossref]

L. Guo, M. Li, X. Huang, and H. Yang, “Electric toroidal metamaterial for resonant transparency and circular cross-polarization conversion,” Appl. Phys. Lett. 105(3), 033507 (2014).
[Crossref]

M. Li, L. Guo, J. Dong, and H. Yang, “Resonant transparency in planar metamaterial with toroidal moment,” Appl. Phys. Express 7(8), 082201 (2014).
[Crossref]

G. Thorner, J. Kiat, C. Bogicevic, and I. Kornev, “Axial hypertoroidal moment in a ferroelectric nanotorus: A way to switch local polarization,” Phys. Rev. B 89(22), 220103 (2014).
[Crossref]

2013 (1)

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499(7457), 188–191 (2013).
[Crossref]

2012 (2)

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

Y. Huang, W. Chen, P. Wu, V. Fedotov, V. Savinov, Y. Ho, Y. Chau, N. I. Zheludev, and D. P. Tsai, “Design of plasmonic toroidal metamaterials at optical frequencies,” Opt. Express 20(2), 1760–1768 (2012).
[Crossref]

2010 (3)

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]

R. F. Ndangali and S. V. Shabanov, “Electromagnetic bound states in the radiation continuum for periodic double arrays of subwavelength dielectric cylinders,” J. Math. Phys. 51(10), 102901 (2010).
[Crossref]

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

2007 (1)

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

2002 (2)

S. H. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
[Crossref]

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 65(4), 046609 (2002).
[Crossref]

1986 (1)

V. M. Dubovik, L. A. Tosunian, and V. V. Tugushev, “Axial toroidal moments in electrodynamics and solid-state physics,” Zh. Eksp. Teor. Fiz. 90(2), 590–605 (1986).

1985 (1)

H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum,” Phys. Rev. A 32(6), 3231–3242 (1985).
[Crossref]

1975 (1)

F. H. Stillinger and D. R. Herrick, “Bound states in the continuum,” Phys. Rev. A 11(2), 446–454 (1975).
[Crossref]

1958 (1)

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

Algorri, J. F.

Altug, H.

F. Yesilkoy, E. R. Arvelo, Y. Jahani, M. Liu, A. Tittl, V. Cevher, Y. Kivshar, and H. Altug, “Ultrasensitive hyperspectral imaging and biodetection enabled by dielectric metasurfaces,” Nat. Photonics 13(6), 390–396 (2019).
[Crossref]

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S. Xu, A. Sayanskiy, A. S. Kupriianov, V. R. Tuz, P. Kapitanova, H. Sun, W. Han, and Y. S. Kivshar, “Experimental Observation of Toroidal Dipole Modes in All-Dielectric Metasurfaces,” Adv. Opt. Mater. 7, 1801166 (2018).
[Crossref]

Urbach, H. P.

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]

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 65(4), 046609 (2002).
[Crossref]

van Aken, P. A.

B. Oeguet, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal dipole-enhanced third harmonic generation of deep ultraviolet light using plasmonic meta-atoms,” Nano Lett. 19(1), 605–611 (2019).
[Crossref]

B. Oeguet, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Low-loss and high- Q planar metamaterial with toroidal moment,” Phys. Rev. B 87, 115417 (2018).

Vogelgesang, R.

B. Oeguet, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal dipole-enhanced third harmonic generation of deep ultraviolet light using plasmonic meta-atoms,” Nano Lett. 19(1), 605–611 (2019).
[Crossref]

B. Oeguet, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Low-loss and high- Q planar metamaterial with toroidal moment,” Phys. Rev. B 87, 115417 (2018).

Volsky, N.

A. A. Basharin, V. Chuguevsky, N. Volsky, M. Kafesaki, and E. N. Economou, “Extremely high Q-factor metamaterials due to anapole excitation,” Phys. Rev. B 95(3), 035104 (2017).
[Crossref]

Wang, L.

Wang, S.

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref]

Wang, W.

Wang, Y.

X. Li, J. Yin, Z. Liu, Y. Wang, and Z. Hong, “Tailoring the excitation of two kinds of toroidal dipoles in all-dielectric metasurfaces,” Optik 201, 163502 (2020).
[Crossref]

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P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y. W. Huang, P. R. Wu, Y. H. Chen, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
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Xi, Z.

Xia, S.

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M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
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S. Xu, A. Sayanskiy, A. S. Kupriianov, V. R. Tuz, P. Kapitanova, H. Sun, W. Han, and Y. S. Kivshar, “Experimental Observation of Toroidal Dipole Modes in All-Dielectric Metasurfaces,” Adv. Opt. Mater. 7, 1801166 (2018).
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M. Li, L. Guo, J. Dong, and H. Yang, “Resonant transparency in planar metamaterial with toroidal moment,” Appl. Phys. Express 7(8), 082201 (2014).
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S. Yang, Z. Liu, L. Jin, W. Li, S. Zhang, J. Li, and C. Gu, “Surface plasmon polariton mediated multiple toroidal resonances in 3D folding metamaterials,” ACS Photonics 4(11), 2650–2658 (2017).
[Crossref]

Yang, Y.

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]

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F. Yesilkoy, E. R. Arvelo, Y. Jahani, M. Liu, A. Tittl, V. Cevher, Y. Kivshar, and H. Altug, “Ultrasensitive hyperspectral imaging and biodetection enabled by dielectric metasurfaces,” Nat. Photonics 13(6), 390–396 (2019).
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A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
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I. B. Zel’Dovich, “The relation between decay asymmetry and dipole moment of elementary particles,” Sov. Phys. JETP 6(6), 1148 (1958).

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Zhang, S.

S. Yang, Z. Liu, L. Jin, W. Li, S. Zhang, J. Li, and C. Gu, “Surface plasmon polariton mediated multiple toroidal resonances in 3D folding metamaterials,” ACS Photonics 4(11), 2650–2658 (2017).
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Zhang, W.

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
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Z. Li, T. Wu, and X. Zhang, “Tailoring toroidal and magnetic dipole excitations with the same dielectric structure,” Opt. Lett. 44(1), 57–62 (2019).
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B. Luk’Yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
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C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499(7457), 188–191 (2013).
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Zhu, J.

Z. Dong, J. Zhu, J. Rho, J. Li, C. Lu, X. Yin, and X. Zhang, “Optical toroidal dipolar response by an asymmetric double-bar metamaterial,” Appl. Phys. Lett. 101(14), 144105 (2012).
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ACS Nano (1)

P. C. Wu, C. Y. Liao, V. Savinov, T. L. Chung, W. T. Chen, Y. W. Huang, P. R. Wu, Y. H. Chen, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Optical anapole metamaterial,” ACS Nano 12(2), 1920–1927 (2018).
[Crossref]

ACS Photonics (3)

S. Yang, Z. Liu, L. Jin, W. Li, S. Zhang, J. Li, and C. Gu, “Surface plasmon polariton mediated multiple toroidal resonances in 3D folding metamaterials,” ACS Photonics 4(11), 2650–2658 (2017).
[Crossref]

Z. F. Sadrieva, I. S. Sinev, K. L. Koshelev, A. Samusev, I. V. Iorsh, O. Takayama, R. Malureanu, A. A. Bogdanov, and A. V. Lavrinenko, “Transition from optical bound states in the continuum to leaky resonances: Role of substrate and roughness,” ACS Photonics 4(4), 723–727 (2017).
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Z. F. Sadrieva, I. S. Sinev, K. L. Koshelev, A. Samusev, I. V. Iorsh, O. Takayama, R. Malureanu, A. A. Bogdanov, and A. V. Lavrinenko, “Transition from Optical Bound States in the Continuum to Leaky Resonances: Role of Substrate and Roughness,” ACS Photonics 4(4), 723–727 (2017).
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Adv. Mater. (3)

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp toroidal resonances in planar terahertz metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
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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).
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M. Gupta, Y. K. Srivastava, and R. Singh, “A toroidal metamaterial switch,” Adv. Mater. 30(4), 1704845 (2018).
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Adv. Opt. Mater. (3)

M. Gupta and R. Singh, “Toroidal versus Fano Resonances in High Q planar THz Metamaterials,” Adv. Opt. Mater. 4(12), 2119–2125 (2016).
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A. Sayanskiy, M. Danaeifar, P. Kapitanova, and A. E. Miroshnichenko, “All-Dielectric Metalattice with Enhanced Toroidal Dipole Response,” Adv. Opt. Mater. 6(19), 1800302 (2018).
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S. Xu, A. Sayanskiy, A. S. Kupriianov, V. R. Tuz, P. Kapitanova, H. Sun, W. Han, and Y. S. Kivshar, “Experimental Observation of Toroidal Dipole Modes in All-Dielectric Metasurfaces,” Adv. Opt. Mater. 7, 1801166 (2018).
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Appl. Phys. Express (1)

M. Li, L. Guo, J. Dong, and H. Yang, “Resonant transparency in planar metamaterial with toroidal moment,” Appl. Phys. Express 7(8), 082201 (2014).
[Crossref]

Appl. Phys. Lett. (5)

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

L. Guo, M. Li, X. Huang, and H. Yang, “Electric toroidal metamaterial for resonant transparency and circular cross-polarization conversion,” Appl. Phys. Lett. 105(3), 033507 (2014).
[Crossref]

M. Gupta, Y. K. Srivastava, M. Manjappa, and R. Singh, “Sensing with toroidal metamaterial,” Appl. Phys. Lett. 110(12), 121108 (2017).
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Nano Lett. (1)

B. Oeguet, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal dipole-enhanced third harmonic generation of deep ultraviolet light using plasmonic meta-atoms,” Nano Lett. 19(1), 605–611 (2019).
[Crossref]

Nat. Commun. (2)

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]

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(1), 8069 (2015).
[Crossref]

Nat. Mater. (1)

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

Nat. Photonics (1)

F. Yesilkoy, E. R. Arvelo, Y. Jahani, M. Liu, A. Tittl, V. Cevher, Y. Kivshar, and H. Altug, “Ultrasensitive hyperspectral imaging and biodetection enabled by dielectric metasurfaces,” Nat. Photonics 13(6), 390–396 (2019).
[Crossref]

Nat. Rev. Mater. (1)

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1(9), 16048 (2016).
[Crossref]

Nature (2)

A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, “Lasing action from photonic bound states in continuum,” Nature 541(7636), 196–199 (2017).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499(7457), 188–191 (2013).
[Crossref]

New J. Phys. (1)

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

Opt. Express (4)

Opt. Lett. (2)

Opt. Mater. Express (1)

Optica (2)

Optik (1)

X. Li, J. Yin, Z. Liu, Y. Wang, and Z. Hong, “Tailoring the excitation of two kinds of toroidal dipoles in all-dielectric metasurfaces,” Optik 201, 163502 (2020).
[Crossref]

Phys. Rev. A (3)

F. H. Stillinger and D. R. Herrick, “Bound states in the continuum,” Phys. Rev. A 11(2), 446–454 (1975).
[Crossref]

H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum,” Phys. Rev. A 32(6), 3231–3242 (1985).
[Crossref]

M. A. Belyakov, M. A. Balezin, Z. F. Sadrieva, P. V. Kapitanova, E. A. Nenasheva, A. F. Sadreev, and A. A. Bogdanov, “Experimental observation of symmetry protected bound state in the continuum in a chain of dielectric disks,” Phys. Rev. A 99(5), 053804 (2019).
[Crossref]

Phys. Rev. B (5)

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

A. A. Basharin, V. Chuguevsky, N. Volsky, M. Kafesaki, and E. N. Economou, “Extremely high Q-factor metamaterials due to anapole excitation,” Phys. Rev. B 95(3), 035104 (2017).
[Crossref]

Y. He, G. Guo, T. Feng, Y. Xu, and A. E. Miroshnichenko, “Toroidal dipole bound states in the continuum,” Phys. Rev. B 98(16), 161112 (2018).
[Crossref]

B. Oeguet, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Low-loss and high- Q planar metamaterial with toroidal moment,” Phys. Rev. B 87, 115417 (2018).

G. Thorner, J. Kiat, C. Bogicevic, and I. Kornev, “Axial hypertoroidal moment in a ferroelectric nanotorus: A way to switch local polarization,” Phys. Rev. B 89(22), 220103 (2014).
[Crossref]

Phys. Rev. E (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 65(4), 046609 (2002).
[Crossref]

Phys. Rev. Lett. (1)

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112(21), 213903 (2014).
[Crossref]

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]

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, 011036 (2015).
[Crossref]

Science (2)

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

A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D. Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, “Imaging-based molecular barcoding with pixelated dielectric metasurfaces,” Science 360(6393), 1105–1109 (2018).
[Crossref]

Sov. Phys. JETP (1)

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

Zh. Eksp. Teor. Fiz. (1)

V. M. Dubovik, L. A. Tosunian, and V. V. Tugushev, “Axial toroidal moments in electrodynamics and solid-state physics,” Zh. Eksp. Teor. Fiz. 90(2), 590–605 (1986).

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Figures (7)

Fig. 1.
Fig. 1. Five scattering powers of multipoles decomposition for a pair of SRR at three different gap sizes: (a) g = 0 nm, (b) g = 100 nm, (c) g = 160 nm, where Py, Mx, Ty, Qe, Qm are ED, MD, TD, electric quadrupole, and magnetic quadrupole, respectively. IPT corresponds to the combined contribution of destructive interference between ED and TD. The inset in Fig. 1(b) represents the schematic of dual-SRR, and the inset in Fig. 1(c) shows the phase difference between the ED and TD moments.
Fig. 2.
Fig. 2. (a) Schematic of dual-SRR all-dielectric metasurface. (b) Unit cells of the metasurface. Here, Λx = Λy = 900 nm, l1 = 600 nm, l2 = 360 nm, w = 100 nm, thickness of the silicon SRR h = 200 nm. s and s’ represent the distances of SRRs inside the unit cell and between the neighboring unit cells, respectively, and s’ = Λx-2×l2-s.
Fig. 3.
Fig. 3. (a) Simulated and Fano fitted transmission spectrum of the metasurface (g = 50 nm), when Λx= Λy = 900 nm, s = 100 nm, and s’ = 80 nm. (b) Five scattering powers of multipoles decomposition for the metasurface, where Py, Mx, Ty, Qe and Qm are the ED, MD, TD, electric quadrupole and magnetic quadrupole, respectively. (c), (d) Distributions of the electric and magnetic near-fields in the x-y plane and x-z plane at λ = 1445 nm, respectively. T1 and T2 represent the intra- and inter-TD moments, respectively.
Fig. 4.
Fig. 4. (a) Transmission spectra of the metasurface at different gap g, when Λx= Λy = 900 nm, s = 100 nm, and s’ = 80 nm. (b) Q factor of the TD resonance with respect to gap g. (c) Dependences of scattering powers of ED (Py) and TD (Ty) of TD resonance on gap g. (d) Magnetic near-field distributions in the x-z plane at the resonance when g = 0 and 150 nm, respectively.
Fig. 5.
Fig. 5. (a) Transmissions of the metasurface (g = 50 nm) at different lattice periods Λx, when Λy = 900 nm, s = 100 nm, and s’ = 80 nm. (b) Q factor of the TD resonance with respect to Λx. (c) The scattering powers of the ED (Py) and TD (Ty) dependences on the lattice period in x-direction. (d) Magnetic near-field distributions at the resonance wavelengths when Λx = 850 and 1000 nm, respectively.
Fig. 6.
Fig. 6. (a) Transmissions of the dual-CRR metasurface at different s, when Λx =Λy = 900 nm. (b) Q factor of the TD resonance with respect to s for lossless and lossy CRRs.
Fig. 7.
Fig. 7. (a), (b): Electric and magnetic near-field enhancements in the x-y plane and x-z plane at the resonance wavelength when s = 90 nm. (c), (d): The maximum electric and magnetic near-field enhancement factor with respect to distance s. The lattice periods Λx, Λy are fixed of 900 nm.

Equations (1)

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I ( F γ + ω ω 0 ) 2 ( ω ω 0 ) 2 + γ 2

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