Abstract

An analog of electromagnetically induced transparency (EIT) in an asymmetric E-shaped all-dielectric metasurface was proposed and numerically demonstrated in the near infrared spectral region. The E-shaped metasurface supports a strong toroidal dipolar resonance with high quality (Q) factor, which is verified by decomposed scattered powers for multipole moments using a Cartesian coordinate system. A high transmission EIT-like optical response was achieved, and clearly interpreted by the destructive interference between the dark toroidal dipolar moment and bright magnetic dipolar mode through the asymmetric metasurface. The bandwidth of the transparency window can be easily designed by changing the asymmetric parameter of the structure. The proposed E-shaped all-dielectric metasurface gives a new way to realize toroidal dipolar response and has potential applications in bio-chemical sensing, narrowband filters, optical modulations, and slow light based devices.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (3)

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

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] [PubMed]

Y. Fan, F. Zhang, N. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
[Crossref]

2017 (10)

Z. C. Wei, X. P. Li, N. F. Zhong, X. P. Tan, X. M. Zhang, H. Z. Liu, H. Y. Meng, and R. S. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12(3), 641–647 (2017).
[Crossref]

S. D. Liu, Z. X. Wang, W. J. Wang, J. D. Chen, 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] [PubMed]

N. A. Nemkov, I. V. Stenishchev, and A. A. Basharin, “Nontrivial nonradiating all-dielectric anapole,” Sci. Rep. 7(1), 1064 (2017).
[Crossref] [PubMed]

J. S. Totero Gongora, A. E. Miroshnichenko, Y. S. Kivshar, and A. Fratalocchi, “Anapole nanolasers for mode-locking and ultrafast pulse generation,” Nat. Commun. 8, 15535 (2017).
[Crossref] [PubMed]

L. Zhu, L. Dong, J. Guo, F. Y. Meng, X. J. He, C. H. Zhao, and Q. Wu, “A low-loss electromagnetically induced transparency (EIT) metamaterial based on coupling between electric and toroidal dipoles,” RSC Advances 7(88), 55897–55904 (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]

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] [PubMed]

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

Y. R. Sun, H. Chen, X. J. Li, and Z. Hong, “Electromagnetically induced transparency in planar metamaterials based on guided mode resonance,” Opt. Commun. 392, 142–146 (2017).
[Crossref]

2016 (6)

E. Petronijevic and C. Sibilia, “All-optical tuning of EIT-like dielectric metasurfaces by means of chalcogenide phase change materials,” Opt. Express 24(26), 30411–30420 (2016).
[Crossref] [PubMed]

S. Campione, S. Liu, L. I. Basilio, L. K. Warne, W. L. Langston, T. S. Luk, J. R. Wendt, J. L. Reno, G. A. Keeler, I. Brener, and M. B. Sinclair, “Broken symmetry dielectric resonators for high quality factor Fano metasurfaces,” ACS Photonics 3(12), 2362–2367 (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] [PubMed]

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
[Crossref] [PubMed]

G. Grinblat, Y. Li, M. P. Nielsen, R. F. Oulton, and S. A. Maier, “Enhanced third harmonic generation in single germanium nanodisks excited at the anapole mode,” Nano Lett. 16(7), 4635–4640 (2016).
[Crossref] [PubMed]

A. C. Tasolamprou, O. Tsilipakos, M. Kafesaki, C. M. Soukoulis, and E. N. Economou, “Toroidal eigenmodes in all-dielectric metamolecules,” Phys. Rev. B 94(20), 205433 (2016).
[Crossref]

2015 (7)

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] [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]

W. Liu, J. Zhang, B. Lei, H. Hu, and A. E. Miroshnichenko, “Invisible nanowires with interfering electric and toroidal dipoles,” Opt. Lett. 40(10), 2293–2296 (2015).
[Crossref] [PubMed]

H. M. Li, S. B. Liu, S. Y. Liu, S. Y. Wang, G. W. Ding, H. Yang, Z. Y. Yu, and H. F. Zhang, “Low-loss metamaterial electromagnetically induced transparency based on electric toroidal dipolar response,” Appl. Phys. Lett. 106(8), 083511 (2015).
[Crossref]

J. N. He, J. Q. Wang, P. Ding, C. Z. Fan, and E. J. Liang, “Gain-assisted plasmon induced transparency in T-shaped metamaterials for slow light,” J. Opt. 17(5), 055002 (2015).
[Crossref]

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear fano-resonant dielectric metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref] [PubMed]

M. Wan, Y. Song, L. Zhang, and F. Zhou, “Broadband plasmon-induced transparency in terahertz metamaterials via constructive interference of electric and magnetic couplings,” Opt. Express 23(21), 27361–27368 (2015).
[Crossref] [PubMed]

2014 (5)

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] [PubMed]

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
[Crossref] [PubMed]

J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Strong field enhancement and light-matter interactions with all-dielectric metamaterials based on split bar resonators,” Opt. Express 22(25), 30889–30898 (2014).
[Crossref] [PubMed]

H. M. Li, S. B. Liu, S. Y. Liu, and H. F. Zhang, “Electromagnetically induced transparency with large group index induced by simultaneously exciting the electric and the magnetic resonance,” Appl. Phys. Lett. 105(13), 133514 (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]

2013 (5)

2012 (3)

Z. G. Dong, P. Ni, J. Zhu, X. Yin, and X. Zhang, “Toroidal dipole response in a multifold double-ring metamaterial,” Opt. Express 20(12), 13065–13070 (2012).
[Crossref] [PubMed]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012).
[Crossref] [PubMed]

W. Cao, R. Singh, I. A. I. Al-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. 37(16), 3366–3368 (2012).
[Crossref] [PubMed]

2010 (4)

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing,” Nano Lett. 10(4), 1103–1107 (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]

L. Zhang, P. Tassin, T. Koschny, C. Kurter, S. M. Anlage, and C. M. Soukoulis, “Large group delay in a microwave metamaterial analog of electromagnetically induced transparency,” Appl. Phys. Lett. 97(24), 241904 (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] [PubMed]

2009 (3)

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009).
[Crossref]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref] [PubMed]

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2008 (2)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
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2007 (2)

K. Marinov, A. D. Boardman, V. A. Fedotov, and N. I. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007).
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2005 (2)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
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C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70(1), 37–41 (2002).
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1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
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1991 (1)

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L. Zhang, P. Tassin, T. Koschny, C. Kurter, S. M. Anlage, and C. M. Soukoulis, “Large group delay in a microwave metamaterial analog of electromagnetically induced transparency,” Appl. Phys. Lett. 97(24), 241904 (2010).
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J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012).
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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).
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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).
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K. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
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Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear fano-resonant dielectric metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
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S. Campione, S. Liu, L. I. Basilio, L. K. Warne, W. L. Langston, T. S. Luk, J. R. Wendt, J. L. Reno, G. A. Keeler, I. Brener, and M. B. Sinclair, “Broken symmetry dielectric resonators for high quality factor Fano metasurfaces,” ACS Photonics 3(12), 2362–2367 (2016).
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Briggs, D. P.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear fano-resonant dielectric metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
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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).
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M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
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J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99(10), 107401 (2007).
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Cao, W.

Chen, H.

Y. R. Sun, H. Chen, X. J. Li, and Z. Hong, “Electromagnetically induced transparency in planar metamaterials based on guided mode resonance,” Opt. Commun. 392, 142–146 (2017).
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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).
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J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012).
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Chen, J. D.

Chen, S.

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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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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Chen, X.

Chen, Y. H.

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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Chen, Z. H.

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(1), 8069 (2015).
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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).
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Chong, C. T.

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

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).
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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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Cong, L.

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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Cui, A.

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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Cui, Y.

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
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Dayal, G.

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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Ding, G. W.

H. M. Li, S. B. Liu, S. Y. Liu, S. Y. Wang, G. W. Ding, H. Yang, Z. Y. Yu, and H. F. Zhang, “Low-loss metamaterial electromagnetically induced transparency based on electric toroidal dipolar response,” Appl. Phys. Lett. 106(8), 083511 (2015).
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Ding, P.

J. N. He, J. Q. Wang, P. Ding, C. Z. Fan, and E. J. Liang, “Gain-assisted plasmon induced transparency in T-shaped metamaterials for slow light,” J. Opt. 17(5), 055002 (2015).
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Dong, L.

L. Zhu, L. Dong, J. Guo, F. Y. Meng, X. J. He, C. H. Zhao, and Q. Wu, “A low-loss electromagnetically induced transparency (EIT) metamaterial based on coupling between electric and toroidal dipoles,” RSC Advances 7(88), 55897–55904 (2017).
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Dong, Z. G.

Du, S.

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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Economou, E. 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).
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A. C. Tasolamprou, O. Tsilipakos, M. Kafesaki, C. M. Soukoulis, and E. N. Economou, “Toroidal eigenmodes in all-dielectric metamolecules,” Phys. Rev. B 94(20), 205433 (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).
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Eigenthaler, U.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing,” Nano Lett. 10(4), 1103–1107 (2010).
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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(1), 8069 (2015).
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Fan, C. Z.

J. N. He, J. Q. Wang, P. Ding, C. Z. Fan, and E. J. Liang, “Gain-assisted plasmon induced transparency in T-shaped metamaterials for slow light,” J. Opt. 17(5), 055002 (2015).
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Fan, S.

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
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Fan, S. H.

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

Fan, Y.

Y. Fan, F. Zhang, N. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
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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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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).
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Fedotov, V. A.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric metamaterials with toroidal dipolar response,” Phys. Rev. X 5(1), 011036 (2015).
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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).
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V. A. Fedotov, A. V. Rogacheva, V. Savinov, D. P. Tsai, and N. I. Zheludev, “Resonant transparency and non-trivial non-radiating excitations in toroidal metamaterials,” Sci. Rep. 3(1), 2967 (2013).
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N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101(25), 253903 (2008).
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K. Marinov, A. D. Boardman, V. A. Fedotov, and N. I. Zheludev, “Toroidal metamaterial,” New J. Phys. 9(9), 324 (2007).
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Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref] [PubMed]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
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J. S. Totero Gongora, A. E. Miroshnichenko, Y. S. Kivshar, and A. Fratalocchi, “Anapole nanolasers for mode-locking and ultrafast pulse generation,” Nat. Commun. 8, 15535 (2017).
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Y. Fan, F. Zhang, N. Shen, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Achieving a high-Q response in metamaterials by manipulating the toroidal excitations,” Phys. Rev. A 97(3), 033816 (2018).
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Garrido Alzar, C. L.

C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70(1), 37–41 (2002).
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Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
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Geohegan, D.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear fano-resonant dielectric metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref] [PubMed]

Giessen, H.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing,” Nano Lett. 10(4), 1103–1107 (2010).
[Crossref] [PubMed]

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

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
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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).
[Crossref] [PubMed]

Gu, J.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012).
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Guo, J.

L. Zhu, L. Dong, J. Guo, F. Y. Meng, X. J. He, C. H. Zhao, and Q. Wu, “A low-loss electromagnetically induced transparency (EIT) metamaterial based on coupling between electric and toroidal dipoles,” RSC Advances 7(88), 55897–55904 (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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Halas, N. J.

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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Han, J.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012).
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Harris, S. E.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[Crossref]

K. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
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J. N. He, J. Q. Wang, P. Ding, C. Z. Fan, and E. J. Liang, “Gain-assisted plasmon induced transparency in T-shaped metamaterials for slow light,” J. Opt. 17(5), 055002 (2015).
[Crossref]

He, M.

He, X. J.

L. Zhu, L. Dong, J. Guo, F. Y. Meng, X. J. He, C. H. Zhao, and Q. Wu, “A low-loss electromagnetically induced transparency (EIT) metamaterial based on coupling between electric and toroidal dipoles,” RSC Advances 7(88), 55897–55904 (2017).
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Hirscher, M.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing,” Nano Lett. 10(4), 1103–1107 (2010).
[Crossref] [PubMed]

Hong, Z.

Y. R. Sun, H. Chen, X. J. Li, and Z. Hong, “Electromagnetically induced transparency in planar metamaterials based on guided mode resonance,” Opt. Commun. 392, 142–146 (2017).
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Hu, H.

Huang, Y. W.

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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Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
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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).
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ACS Photonics (1)

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Adv. Mater. (3)

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Figures (8)

Fig. 1
Fig. 1 (a) Schematic of an E-shaped all-dielectric metasurface. (b) Unit cell of the metasurface.
Fig. 2
Fig. 2 (a) Transmission spectra of symmetric E-shaped metasurface (l2 = 750 nm) when electric field of the incidence is along the x-axis shown in the inset. (b),(c) Distributions of the electric and magnetic field in the x-y plane and y-z plane at λ = 1540 nm, respectively. (d) Schematic of T (toroidal dipole) excitation in the unit cell, M represents the head-to-tail magnetic moment.
Fig. 3
Fig. 3 The full multipole decomposition of the first contributing five multipole moments of the E-shaped metasurface: electric dipole (P), magnetic dipole (M), toroidal dipole (T), electric quadrupole (Qe) and magnetic quadrupoles (Qm). The log scale in the y axis is chosen so as to reveal more clearly the contribution of the multipole terms as well.
Fig. 4
Fig. 4 Q factor and wavelength dependences of toroidal resonance on the rod’s length l2 (w = 120 nm) (a) and width w (l2 = 730 nm) (b).
Fig. 5
Fig. 5 (a) Transmission spectra of symmetric E-shaped metasurface (Δg = 0, l2 = 730 nm) when the incident wave is polarized along the y-axis shown in the inset. (b), (c) Distributions of the electric and magnetic field in the x-y plane and y-z plane at λ = 1520 nm, respectively. (d) Multipole expansion results of the scattered power in the Cartesian coordinate system for broad magnetic resonance.
Fig. 6
Fig. 6 (a) Transmission of asymmetric E-shaped metasurface (Δg = 20 nm) when the electric field of the normal incidence is along the y-axis shown in the inset. (b)~(d): Electric field distributions in the x-y plane (e)~(g): Magnetic field distributions in the x-z plane bisecting the metasurface. (b),(e): dip I (λ = 1514 nm); (c),(f): peak II (λ = 1525 nm); and (d),(g): dip III (λ = 1528 nm), respectively.
Fig. 7
Fig. 7 (a) Transmissions of asymmetric metasurface with various Δg. (b) Q value dependence of the EIT-like window on Δg. (c) Transmissions of asymmetric metasurfaces (Δg = 20 nm) at different parameter of l1.
Fig. 8
Fig. 8 (a) The retrieved effective refractive index for the proposed structure when Δg = 100 nm. (b) The extracted group index at transparency wavelength of 1525 nm with respect to Δg.

Equations (2)

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I (Fγ+ω ω 0 ) 2 (ω ω 0 ) 2 + γ 2
n g = n e (ω)+ n e (ω) ω

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