Abstract

We experimentally investigate the terahertz (THz) response of conductively coupled asymmetric split ring resonator-based meta-molecules in the layout of reflection and rotational symmetry. In the reflectional symmetry case, the horizontally polarized THz excites a couple of trapped modes: the low-order one is a coupled Fano-resonance, and the high-order one is a decoupled dipole oscillator. The vertically polarized THz excites an inductive-capacitor resonance as a low-order trapped mode below the frequency of a high-order intrinsic mode. The quality factors (Q factors) of trapped modes decrease with the displacement of top-and-bottom gap increasing. In the rotational symmetry case, the horizontally polarized THz excites a single trapped mode owing to coupled Fano-resonance. The vertically polarized THz excites a high-order trapped mode of coupled multiple dipole oscillations beyond the frequency of intrinsic low-order dipole oscillation. The Q factors of trapped modes increase with the displacement of the top-and-bottom gap increase. For the first time, our results reveal the trapped modes’ evolution owing to the interaction of Fano-resonators conductively coupled under different symmetry.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (5)

L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
[Crossref]

A. Ahmadivand, B. Gerislioglu, and N. Pala, “Active control over the interplay between the dark and hidden sides of plasmonics using metallodielectric Au−Ge2Sb2Te5 unit cells,” J. Phys. Chem. C 121(36), 19966–19974 (2017).
[Crossref]

Z. Zhao, X. Zheng, W. Peng, J. Zhang, H. Zhao, Z. Luo, and W. Shi, “Localized terahertz electromagnetically-induced transparency-like phenomenon in a conductively coupled trimer metamolecule,” Opt. Express 25(20), 24410–24424 (2017).
[Crossref] [PubMed]

Z. Zhao, X. Zheng, W. Peng, H. Zhao, J. Zhang, Z. Luo, and W. Shi, “Localized slow light phenomenon in symmetry broken terahertz metamolecule made of conductively coupled dark resonators,” Opt. Mater. Express 7(6), 1950–1961 (2017).
[Crossref]

X. Zheng, Z. Zhao, W. Shi, and W. Peng, “Broadband terahertz plasmon-induced transparency via asymmetric coupling inside meta-molecules,” Opt. Mater. Express 7(3), 1035–1047 (2017).
[Crossref]

2016 (7)

A. Ahmadivand, R. Sinha, B. Gerislioglu, M. Karabiyik, N. Pala, and M. Shur, “Transition from capacitive coupling to direct charge transfer in asymmetric terahertz plasmonic assemblies,” Opt. Lett. 41(22), 5333–5336 (2016).
[Crossref] [PubMed]

Z. Zhao, Z. Song, W. Shi, and W. Peng, “Plasmon-induced transparency-like behavior at terahertz region via dipole oscillation detuning in a hybrid planar metamaterial,” Opt. Mater. Express 6(7), 2190–2200 (2016).
[Crossref]

Q. Xu, X. Su, C. Ouyang, N. Xu, W. Cao, Y. Zhang, Q. Li, C. Hu, J. Gu, Z. Tian, A. K. Azad, J. Han, and W. Zhang, “Frequency-agile electromagnetically induced transparency analogue in terahertz metamaterials,” Opt. Lett. 41(19), 4562–4565 (2016).
[Crossref] [PubMed]

N. Xu, M. Manjappa, R. Singh, and W. Zhang, “Tailoring the electromagnetically induced transparency and absorbance in coupled Fano–Lorentzian metasurfaces: A classical analog of a four-level tripod quantum system,” Adv. Opt. Mater. 4(8), 1179–1185 (2016).
[Crossref]

P. Pitchappa, M. Manjappa, C. P. Ho, R. Singh, N. Singh, and C. Lee, “Active control of electromagnetically induced transparency analog in terahertz MEMS metamaterial,” Adv. Opt. Mater. 4(4), 541–547 (2016).
[Crossref]

M. Manjappa, Y. K. Srivastava, and R. Singh, “Lattice-induced transparency in planar metamaterials,” Phys. Rev. B 94(16), 161103 (2016).
[Crossref]

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref] [PubMed]

2015 (6)

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Q. Guo, W. Gao, J. Chen, Y. Liu, and S. Zhang, “Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials,” Phys. Rev. Lett. 115(6), 067402 (2015).
[Crossref] [PubMed]

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual mode in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

X. Han, T. Wang, X. Li, S. Xiao, and Y. Zhu, “Dynamically tunable plasmon induced transparency in a graphene-based nanoribbon waveguide coupled with graphene rectangular resonators structure on sapphire substrate,” Opt. Express 23(25), 31945–31955 (2015).
[Crossref] [PubMed]

2014 (3)

R. Singh, I. Al-Naib, D. R. Chowdhury, L. Cong, C. Rockstuhl, and W. Zhang, “Probing the transition from an uncoupled to a strong near-field coupled regime between bright and dark mode resonators in metasurfaces,” Appl. Phys. Lett. 105(8), 081108 (2014).
[Crossref]

N. Born, I. Al-Naib, C. Jansen, T. Ozaki, R. Morandotti, and M. Koch, “Excitation of multiple trapped-eigenmodes in terahertz metamolecule lattices,” Appl. Phys. Lett. 104(10), 101107 (2014).
[Crossref]

L.D. Negro, “Electromagnetic metamaterials: Simplicity unlocks complexity,” Nat. Mater. 13(12), 1080–1081 (2014).
[Crossref] [PubMed]

2013 (2)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

S. D. Jenkins and J. Ruostekoski, “Metamaterial transparency induced by cooperative electromagnetic interactions,” Phys. Rev. Lett. 111(14), 147401 (2013).
[Crossref] [PubMed]

2012 (2)

W. Cao, R. Singh, I. A. 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]

I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(17), 171108 (2012).

2011 (3)

R. Singh, I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Y. Yang, R. Singh, and W. Zhang, “Anomalous terahertz transmission in bow-tie plasmonic antenna apertures,” Opt. Lett. 36(15), 2901–2903 (2011).
[Crossref] [PubMed]

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107(4), 043901 (2011).
[Crossref] [PubMed]

2010 (3)

J. Petschulat, A. Chipouline, A. Tünnermann, T. Pertsch, C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Simple and versatile analytical approach for planar metamaterials,” Phys. Rev. B 82(7), 075102 (2010).
[Crossref]

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. P. Lee, “Magnetic plasmon resonance: Underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).
[Crossref]

Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express 18(21), 22412–22417 (2010).
[Crossref] [PubMed]

2009 (2)

I. Al-Naib, C. Jansen, and M. Koch, “High Q-factor metasurfaces based on miniaturized asymmetric single split resonators,” Appl. Phys. Lett. 94(15), 153505 (2009).
[Crossref]

I. Al-Naib, C. Jansen, and M. Koch, “Thin-film sensing with planar asymmetric metamaterial resonators,” Appl. Phys. Lett. 93(8), 083507 (2009).
[Crossref]

2007 (1)

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref] [PubMed]

2005 (1)

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction of a combined double S-shaped metamaterial,” Appl. Phys. Lett. 86(15), 151909 (2005).
[Crossref]

2004 (3)

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

A. B. Movchan and S. Guenneau, “Split-ring resonators and localized modes,” Phys. Rev. B 70(12), 125116 (2004).
[Crossref]

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref] [PubMed]

Ahmadivand, A.

A. Ahmadivand, B. Gerislioglu, and N. Pala, “Active control over the interplay between the dark and hidden sides of plasmonics using metallodielectric Au−Ge2Sb2Te5 unit cells,” J. Phys. Chem. C 121(36), 19966–19974 (2017).
[Crossref]

A. Ahmadivand, R. Sinha, B. Gerislioglu, M. Karabiyik, N. Pala, and M. Shur, “Transition from capacitive coupling to direct charge transfer in asymmetric terahertz plasmonic assemblies,” Opt. Lett. 41(22), 5333–5336 (2016).
[Crossref] [PubMed]

Alapan, Y.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref] [PubMed]

Al-Naib, I.

N. Born, I. Al-Naib, C. Jansen, T. Ozaki, R. Morandotti, and M. Koch, “Excitation of multiple trapped-eigenmodes in terahertz metamolecule lattices,” Appl. Phys. Lett. 104(10), 101107 (2014).
[Crossref]

R. Singh, I. Al-Naib, D. R. Chowdhury, L. Cong, C. Rockstuhl, and W. Zhang, “Probing the transition from an uncoupled to a strong near-field coupled regime between bright and dark mode resonators in metasurfaces,” Appl. Phys. Lett. 105(8), 081108 (2014).
[Crossref]

I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(17), 171108 (2012).

R. Singh, I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

I. Al-Naib, C. Jansen, and M. Koch, “High Q-factor metasurfaces based on miniaturized asymmetric single split resonators,” Appl. Phys. Lett. 94(15), 153505 (2009).
[Crossref]

I. Al-Naib, C. Jansen, and M. Koch, “Thin-film sensing with planar asymmetric metamaterial resonators,” Appl. Phys. Lett. 93(8), 083507 (2009).
[Crossref]

Al-Naib, I. A.

Anlage, S. M.

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107(4), 043901 (2011).
[Crossref] [PubMed]

Azad, A. K.

Q. Xu, X. Su, C. Ouyang, N. Xu, W. Cao, Y. Zhang, Q. Li, C. Hu, J. Gu, Z. Tian, A. K. Azad, J. Han, and W. Zhang, “Frequency-agile electromagnetically induced transparency analogue in terahertz metamaterials,” Opt. Lett. 41(19), 4562–4565 (2016).
[Crossref] [PubMed]

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

Baena, J. D.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref] [PubMed]

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Beruete, M.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref] [PubMed]

Bonache, J.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref] [PubMed]

Born, N.

N. Born, I. Al-Naib, C. Jansen, T. Ozaki, R. Morandotti, and M. Koch, “Excitation of multiple trapped-eigenmodes in terahertz metamolecule lattices,” Appl. Phys. Lett. 104(10), 101107 (2014).
[Crossref]

Cao, J.-X.

Cao, W.

Chaker, M.

I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(17), 171108 (2012).

Chen, H.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction of a combined double S-shaped metamaterial,” Appl. Phys. Lett. 86(15), 151909 (2005).
[Crossref]

Chen, J.

Q. Guo, W. Gao, J. Chen, Y. Liu, and S. Zhang, “Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials,” Phys. Rev. Lett. 115(6), 067402 (2015).
[Crossref] [PubMed]

Chen, K.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction of a combined double S-shaped metamaterial,” Appl. Phys. Lett. 86(15), 151909 (2005).
[Crossref]

Chen, X.

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Chipouline, A.

J. Petschulat, A. Chipouline, A. Tünnermann, T. Pertsch, C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Simple and versatile analytical approach for planar metamaterials,” Phys. Rev. B 82(7), 075102 (2010).
[Crossref]

Chowdhury, D. R.

R. Singh, I. Al-Naib, D. R. Chowdhury, L. Cong, C. Rockstuhl, and W. Zhang, “Probing the transition from an uncoupled to a strong near-field coupled regime between bright and dark mode resonators in metasurfaces,” Appl. Phys. Lett. 105(8), 081108 (2014).
[Crossref]

Cong, L.

R. Singh, I. Al-Naib, D. R. Chowdhury, L. Cong, C. Rockstuhl, and W. Zhang, “Probing the transition from an uncoupled to a strong near-field coupled regime between bright and dark mode resonators in metasurfaces,” Appl. Phys. Lett. 105(8), 081108 (2014).
[Crossref]

Córdova-Castro, R. M.

L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
[Crossref]

De Luca, A.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref] [PubMed]

Delprat, S.

I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(17), 171108 (2012).

Dong, Z.-G.

ElKabbash, M.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref] [PubMed]

Falcone, F.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref] [PubMed]

Fedotov, V. A.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref] [PubMed]

Gao, W.

Q. Guo, W. Gao, J. Chen, Y. Liu, and S. Zhang, “Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials,” Phys. Rev. Lett. 115(6), 067402 (2015).
[Crossref] [PubMed]

Gerislioglu, B.

A. Ahmadivand, B. Gerislioglu, and N. Pala, “Active control over the interplay between the dark and hidden sides of plasmonics using metallodielectric Au−Ge2Sb2Te5 unit cells,” J. Phys. Chem. C 121(36), 19966–19974 (2017).
[Crossref]

A. Ahmadivand, R. Sinha, B. Gerislioglu, M. Karabiyik, N. Pala, and M. Shur, “Transition from capacitive coupling to direct charge transfer in asymmetric terahertz plasmonic assemblies,” Opt. Lett. 41(22), 5333–5336 (2016).
[Crossref] [PubMed]

Grzegorczyk, T. M.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction of a combined double S-shaped metamaterial,” Appl. Phys. Lett. 86(15), 151909 (2005).
[Crossref]

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Gu, J.

Guenneau, S.

A. B. Movchan and S. Guenneau, “Split-ring resonators and localized modes,” Phys. Rev. B 70(12), 125116 (2004).
[Crossref]

Guo, Q.

Q. Guo, W. Gao, J. Chen, Y. Liu, and S. Zhang, “Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials,” Phys. Rev. Lett. 115(6), 067402 (2015).
[Crossref] [PubMed]

Gurkan, U. A.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref] [PubMed]

Ham, B. S.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. P. Lee, “Magnetic plasmon resonance: Underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).
[Crossref]

Han, J.

Han, X.

He, M.

He, X.

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual mode in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

Hinczewski, M.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref] [PubMed]

Ho, C. P.

P. Pitchappa, M. Manjappa, C. P. Ho, R. Singh, N. Singh, and C. Lee, “Active control of electromagnetically induced transparency analog in terahertz MEMS metamaterial,” Adv. Opt. Mater. 4(4), 541–547 (2016).
[Crossref]

Hu, C.

Huang, X.

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

Huangfu, J.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction of a combined double S-shaped metamaterial,” Appl. Phys. Lett. 86(15), 151909 (2005).
[Crossref]

Ilker, E.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref] [PubMed]

Iorsh, I.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Jang, W. H.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. P. Lee, “Magnetic plasmon resonance: Underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).
[Crossref]

Jansen, C.

N. Born, I. Al-Naib, C. Jansen, T. Ozaki, R. Morandotti, and M. Koch, “Excitation of multiple trapped-eigenmodes in terahertz metamolecule lattices,” Appl. Phys. Lett. 104(10), 101107 (2014).
[Crossref]

I. Al-Naib, C. Jansen, and M. Koch, “Thin-film sensing with planar asymmetric metamaterial resonators,” Appl. Phys. Lett. 93(8), 083507 (2009).
[Crossref]

I. Al-Naib, C. Jansen, and M. Koch, “High Q-factor metasurfaces based on miniaturized asymmetric single split resonators,” Appl. Phys. Lett. 94(15), 153505 (2009).
[Crossref]

Jenkins, S. D.

S. D. Jenkins and J. Ruostekoski, “Metamaterial transparency induced by cooperative electromagnetic interactions,” Phys. Rev. Lett. 111(14), 147401 (2013).
[Crossref] [PubMed]

Kante, B.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Karabiyik, M.

Kita, S.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Kivshar, Y.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Koch, M.

N. Born, I. Al-Naib, C. Jansen, T. Ozaki, R. Morandotti, and M. Koch, “Excitation of multiple trapped-eigenmodes in terahertz metamolecule lattices,” Appl. Phys. Lett. 104(10), 101107 (2014).
[Crossref]

I. Al-Naib, C. Jansen, and M. Koch, “Thin-film sensing with planar asymmetric metamaterial resonators,” Appl. Phys. Lett. 93(8), 083507 (2009).
[Crossref]

I. Al-Naib, C. Jansen, and M. Koch, “High Q-factor metasurfaces based on miniaturized asymmetric single split resonators,” Appl. Phys. Lett. 94(15), 153505 (2009).
[Crossref]

Kong, J. A.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction of a combined double S-shaped metamaterial,” Appl. Phys. Lett. 86(15), 151909 (2005).
[Crossref]

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Koschny, T.

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107(4), 043901 (2011).
[Crossref] [PubMed]

Kurter, C.

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107(4), 043901 (2011).
[Crossref] [PubMed]

Laso, M. A. G.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref] [PubMed]

Lederer, F.

I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(17), 171108 (2012).

J. Petschulat, A. Chipouline, A. Tünnermann, T. Pertsch, C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Simple and versatile analytical approach for planar metamaterials,” Phys. Rev. B 82(7), 075102 (2010).
[Crossref]

Lee, C.

P. Pitchappa, M. Manjappa, C. P. Ho, R. Singh, N. Singh, and C. Lee, “Active control of electromagnetically induced transparency analog in terahertz MEMS metamaterial,” Adv. Opt. Mater. 4(4), 541–547 (2016).
[Crossref]

Lee, Y. P.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. P. Lee, “Magnetic plasmon resonance: Underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).
[Crossref]

Li, Q.

Li, T.

Li, X.

Li, Y.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Liu, H.

Liu, Y.

Q. Guo, W. Gao, J. Chen, Y. Liu, and S. Zhang, “Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials,” Phys. Rev. Lett. 115(6), 067402 (2015).
[Crossref] [PubMed]

Loncar, M.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Lopetegi, T.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref] [PubMed]

Lu, Y.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. P. Lee, “Magnetic plasmon resonance: Underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).
[Crossref]

Luo, Z.

Lv, H.

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

Manjappa, M.

N. Xu, M. Manjappa, R. Singh, and W. Zhang, “Tailoring the electromagnetically induced transparency and absorbance in coupled Fano–Lorentzian metasurfaces: A classical analog of a four-level tripod quantum system,” Adv. Opt. Mater. 4(8), 1179–1185 (2016).
[Crossref]

P. Pitchappa, M. Manjappa, C. P. Ho, R. Singh, N. Singh, and C. Lee, “Active control of electromagnetically induced transparency analog in terahertz MEMS metamaterial,” Adv. Opt. Mater. 4(4), 541–547 (2016).
[Crossref]

M. Manjappa, Y. K. Srivastava, and R. Singh, “Lattice-induced transparency in planar metamaterials,” Phys. Rev. B 94(16), 161103 (2016).
[Crossref]

Marqués, R.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref] [PubMed]

Martín, F.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
[Crossref] [PubMed]

Mazur, E.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Menzel, C.

J. Petschulat, A. Chipouline, A. Tünnermann, T. Pertsch, C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Simple and versatile analytical approach for planar metamaterials,” Phys. Rev. B 82(7), 075102 (2010).
[Crossref]

Morandotti, R.

N. Born, I. Al-Naib, C. Jansen, T. Ozaki, R. Morandotti, and M. Koch, “Excitation of multiple trapped-eigenmodes in terahertz metamolecule lattices,” Appl. Phys. Lett. 104(10), 101107 (2014).
[Crossref]

I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(17), 171108 (2012).

R. Singh, I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Movchan, A. B.

A. B. Movchan and S. Guenneau, “Split-ring resonators and localized modes,” Phys. Rev. B 70(12), 125116 (2004).
[Crossref]

Muñoz, P.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Nasir, M. E.

L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
[Crossref]

Negro, L.D.

L.D. Negro, “Electromagnetic metamaterials: Simplicity unlocks complexity,” Nat. Mater. 13(12), 1080–1081 (2014).
[Crossref] [PubMed]

Nicholls, L. H.

L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
[Crossref]

O’Brien, K.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Olivier, N.

L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
[Crossref]

Ouyang, C.

Ozaki, T.

N. Born, I. Al-Naib, C. Jansen, T. Ozaki, R. Morandotti, and M. Koch, “Excitation of multiple trapped-eigenmodes in terahertz metamolecule lattices,” Appl. Phys. Lett. 104(10), 101107 (2014).
[Crossref]

I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(17), 171108 (2012).

R. Singh, I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Pacheco, J.

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Pala, N.

A. Ahmadivand, B. Gerislioglu, and N. Pala, “Active control over the interplay between the dark and hidden sides of plasmonics using metallodielectric Au−Ge2Sb2Te5 unit cells,” J. Phys. Chem. C 121(36), 19966–19974 (2017).
[Crossref]

A. Ahmadivand, R. Sinha, B. Gerislioglu, M. Karabiyik, N. Pala, and M. Shur, “Transition from capacitive coupling to direct charge transfer in asymmetric terahertz plasmonic assemblies,” Opt. Lett. 41(22), 5333–5336 (2016).
[Crossref] [PubMed]

Papasimakis, N.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref] [PubMed]

Paul, T.

J. Petschulat, A. Chipouline, A. Tünnermann, T. Pertsch, C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Simple and versatile analytical approach for planar metamaterials,” Phys. Rev. B 82(7), 075102 (2010).
[Crossref]

Peng, W.

Pertsch, T.

J. Petschulat, A. Chipouline, A. Tünnermann, T. Pertsch, C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Simple and versatile analytical approach for planar metamaterials,” Phys. Rev. B 82(7), 075102 (2010).
[Crossref]

Petschulat, J.

J. Petschulat, A. Chipouline, A. Tünnermann, T. Pertsch, C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Simple and versatile analytical approach for planar metamaterials,” Phys. Rev. B 82(7), 075102 (2010).
[Crossref]

Pitchappa, P.

P. Pitchappa, M. Manjappa, C. P. Ho, R. Singh, N. Singh, and C. Lee, “Active control of electromagnetically induced transparency analog in terahertz MEMS metamaterial,” Adv. Opt. Mater. 4(4), 541–547 (2016).
[Crossref]

Poddubny, A.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Prosvirnin, S. L.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref] [PubMed]

Ran, L.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction of a combined double S-shaped metamaterial,” Appl. Phys. Lett. 86(15), 151909 (2005).
[Crossref]

Reshef, O.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Rhee, J. Y.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. P. Lee, “Magnetic plasmon resonance: Underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).
[Crossref]

Rho, J.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Rocheleau, D.

I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(17), 171108 (2012).

Rockstuhl, C.

R. Singh, I. Al-Naib, D. R. Chowdhury, L. Cong, C. Rockstuhl, and W. Zhang, “Probing the transition from an uncoupled to a strong near-field coupled regime between bright and dark mode resonators in metasurfaces,” Appl. Phys. Lett. 105(8), 081108 (2014).
[Crossref]

I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(17), 171108 (2012).

R. Singh, I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

J. Petschulat, A. Chipouline, A. Tünnermann, T. Pertsch, C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Simple and versatile analytical approach for planar metamaterials,” Phys. Rev. B 82(7), 075102 (2010).
[Crossref]

Rodríguez-Fortuño, F. J.

L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
[Crossref]

Rose, M.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref] [PubMed]

Roy Chowdhury, D.

R. Singh, I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Ruostekoski, J.

S. D. Jenkins and J. Ruostekoski, “Metamaterial transparency induced by cooperative electromagnetic interactions,” Phys. Rev. Lett. 111(14), 147401 (2013).
[Crossref] [PubMed]

Salandrino, A.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Shi, W.

Shur, M.

Singh, N.

P. Pitchappa, M. Manjappa, C. P. Ho, R. Singh, N. Singh, and C. Lee, “Active control of electromagnetically induced transparency analog in terahertz MEMS metamaterial,” Adv. Opt. Mater. 4(4), 541–547 (2016).
[Crossref]

Singh, R.

P. Pitchappa, M. Manjappa, C. P. Ho, R. Singh, N. Singh, and C. Lee, “Active control of electromagnetically induced transparency analog in terahertz MEMS metamaterial,” Adv. Opt. Mater. 4(4), 541–547 (2016).
[Crossref]

N. Xu, M. Manjappa, R. Singh, and W. Zhang, “Tailoring the electromagnetically induced transparency and absorbance in coupled Fano–Lorentzian metasurfaces: A classical analog of a four-level tripod quantum system,” Adv. Opt. Mater. 4(8), 1179–1185 (2016).
[Crossref]

M. Manjappa, Y. K. Srivastava, and R. Singh, “Lattice-induced transparency in planar metamaterials,” Phys. Rev. B 94(16), 161103 (2016).
[Crossref]

R. Singh, I. Al-Naib, D. R. Chowdhury, L. Cong, C. Rockstuhl, and W. Zhang, “Probing the transition from an uncoupled to a strong near-field coupled regime between bright and dark mode resonators in metasurfaces,” Appl. Phys. Lett. 105(8), 081108 (2014).
[Crossref]

I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(17), 171108 (2012).

W. Cao, R. Singh, I. A. 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]

Y. Yang, R. Singh, and W. Zhang, “Anomalous terahertz transmission in bow-tie plasmonic antenna apertures,” Opt. Lett. 36(15), 2901–2903 (2011).
[Crossref] [PubMed]

R. Singh, I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Sinha, R.

Song, Z.

Z. Zhao, Z. Song, W. Shi, and W. Peng, “Plasmon-induced transparency-like behavior at terahertz region via dipole oscillation detuning in a hybrid planar metamaterial,” Opt. Mater. Express 6(7), 2190–2200 (2016).
[Crossref]

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual mode in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

Sorolla, M.

F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004).
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Soukoulis, C. M.

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107(4), 043901 (2011).
[Crossref] [PubMed]

Sreekanth, K. V.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref] [PubMed]

Srivastava, Y. K.

M. Manjappa, Y. K. Srivastava, and R. Singh, “Lattice-induced transparency in planar metamaterials,” Phys. Rev. B 94(16), 161103 (2016).
[Crossref]

Strangi, G.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref] [PubMed]

Su, X.

Suchowski, H.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Tassin, P.

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107(4), 043901 (2011).
[Crossref] [PubMed]

Taylor, A. J.

Tian, Z.

Tünnermann, A.

J. Petschulat, A. Chipouline, A. Tünnermann, T. Pertsch, C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Simple and versatile analytical approach for planar metamaterials,” Phys. Rev. B 82(7), 075102 (2010).
[Crossref]

Ustinov, A. V.

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107(4), 043901 (2011).
[Crossref] [PubMed]

Vulis, D. I.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Wang, S.-M.

Wang, T.

Wu, B.-I.

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Wurtz, G. A.

L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
[Crossref]

Xiao, S.

Xu, H.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. P. Lee, “Magnetic plasmon resonance: Underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).
[Crossref]

Xu, M.-X.

Xu, N.

Q. Xu, X. Su, C. Ouyang, N. Xu, W. Cao, Y. Zhang, Q. Li, C. Hu, J. Gu, Z. Tian, A. K. Azad, J. Han, and W. Zhang, “Frequency-agile electromagnetically induced transparency analogue in terahertz metamaterials,” Opt. Lett. 41(19), 4562–4565 (2016).
[Crossref] [PubMed]

N. Xu, M. Manjappa, R. Singh, and W. Zhang, “Tailoring the electromagnetically induced transparency and absorbance in coupled Fano–Lorentzian metasurfaces: A classical analog of a four-level tripod quantum system,” Adv. Opt. Mater. 4(8), 1179–1185 (2016).
[Crossref]

Xu, Q.

Yang, Y.

Y. Yang, R. Singh, and W. Zhang, “Anomalous terahertz transmission in bow-tie plasmonic antenna apertures,” Opt. Lett. 36(15), 2901–2903 (2011).
[Crossref] [PubMed]

R. Singh, I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Yin, M.

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Yin, X.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Zayats, A. V.

L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
[Crossref]

Zeng, B.

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

Zhang, H.

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

Zhang, J.

Zhang, L.

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107(4), 043901 (2011).
[Crossref] [PubMed]

Zhang, S.

Q. Guo, W. Gao, J. Chen, Y. Liu, and S. Zhang, “Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials,” Phys. Rev. Lett. 115(6), 067402 (2015).
[Crossref] [PubMed]

Zhang, W.

N. Xu, M. Manjappa, R. Singh, and W. Zhang, “Tailoring the electromagnetically induced transparency and absorbance in coupled Fano–Lorentzian metasurfaces: A classical analog of a four-level tripod quantum system,” Adv. Opt. Mater. 4(8), 1179–1185 (2016).
[Crossref]

Q. Xu, X. Su, C. Ouyang, N. Xu, W. Cao, Y. Zhang, Q. Li, C. Hu, J. Gu, Z. Tian, A. K. Azad, J. Han, and W. Zhang, “Frequency-agile electromagnetically induced transparency analogue in terahertz metamaterials,” Opt. Lett. 41(19), 4562–4565 (2016).
[Crossref] [PubMed]

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

R. Singh, I. Al-Naib, D. R. Chowdhury, L. Cong, C. Rockstuhl, and W. Zhang, “Probing the transition from an uncoupled to a strong near-field coupled regime between bright and dark mode resonators in metasurfaces,” Appl. Phys. Lett. 105(8), 081108 (2014).
[Crossref]

W. Cao, R. Singh, I. A. 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]

Y. Yang, R. Singh, and W. Zhang, “Anomalous terahertz transmission in bow-tie plasmonic antenna apertures,” Opt. Lett. 36(15), 2901–2903 (2011).
[Crossref] [PubMed]

R. Singh, I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Zhang, X.

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express 18(21), 22412–22417 (2010).
[Crossref] [PubMed]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction of a combined double S-shaped metamaterial,” Appl. Phys. Lett. 86(15), 151909 (2005).
[Crossref]

Zhang, Y.

Q. Xu, X. Su, C. Ouyang, N. Xu, W. Cao, Y. Zhang, Q. Li, C. Hu, J. Gu, Z. Tian, A. K. Azad, J. Han, and W. Zhang, “Frequency-agile electromagnetically induced transparency analogue in terahertz metamaterials,” Opt. Lett. 41(19), 4562–4565 (2016).
[Crossref] [PubMed]

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

Zhao, H.

Zhao, Z.

Zheludev, N. I.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref] [PubMed]

Zheng, X.

Zhu, S.-N.

Zhu, Y.

Zhuravel, A. P.

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, “Classical analogue of electromagnetically induced transparency with a metal-superconductor hybrid metamaterial,” Phys. Rev. Lett. 107(4), 043901 (2011).
[Crossref] [PubMed]

Adv. Opt. Mater. (2)

N. Xu, M. Manjappa, R. Singh, and W. Zhang, “Tailoring the electromagnetically induced transparency and absorbance in coupled Fano–Lorentzian metasurfaces: A classical analog of a four-level tripod quantum system,” Adv. Opt. Mater. 4(8), 1179–1185 (2016).
[Crossref]

P. Pitchappa, M. Manjappa, C. P. Ho, R. Singh, N. Singh, and C. Lee, “Active control of electromagnetically induced transparency analog in terahertz MEMS metamaterial,” Adv. Opt. Mater. 4(4), 541–547 (2016).
[Crossref]

Appl. Phys. Lett. (7)

I. Al-Naib, C. Jansen, and M. Koch, “Thin-film sensing with planar asymmetric metamaterial resonators,” Appl. Phys. Lett. 93(8), 083507 (2009).
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R. Singh, I. Al-Naib, D. R. Chowdhury, L. Cong, C. Rockstuhl, and W. Zhang, “Probing the transition from an uncoupled to a strong near-field coupled regime between bright and dark mode resonators in metasurfaces,” Appl. Phys. Lett. 105(8), 081108 (2014).
[Crossref]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction of a combined double S-shaped metamaterial,” Appl. Phys. Lett. 86(15), 151909 (2005).
[Crossref]

R. Singh, I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high-Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phys. Lett. 101(17), 171108 (2012).

N. Born, I. Al-Naib, C. Jansen, T. Ozaki, R. Morandotti, and M. Koch, “Excitation of multiple trapped-eigenmodes in terahertz metamolecule lattices,” Appl. Phys. Lett. 104(10), 101107 (2014).
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I. Al-Naib, C. Jansen, and M. Koch, “High Q-factor metasurfaces based on miniaturized asymmetric single split resonators,” Appl. Phys. Lett. 94(15), 153505 (2009).
[Crossref]

J. Appl. Phys. (1)

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual mode in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

J. Phys. Chem. C (1)

A. Ahmadivand, B. Gerislioglu, and N. Pala, “Active control over the interplay between the dark and hidden sides of plasmonics using metallodielectric Au−Ge2Sb2Te5 unit cells,” J. Phys. Chem. C 121(36), 19966–19974 (2017).
[Crossref]

Nanoscale (1)

Y. Zhang, T. Li, B. Zeng, H. Zhang, H. Lv, X. Huang, W. Zhang, and A. K. Azad, “A graphene based tunable terahertz sensor with double Fano resonances,” Nanoscale 7(29), 12682–12688 (2015).
[Crossref] [PubMed]

Nat. Mater. (3)

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref] [PubMed]

L.D. Negro, “Electromagnetic metamaterials: Simplicity unlocks complexity,” Nat. Mater. 13(12), 1080–1081 (2014).
[Crossref] [PubMed]

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref] [PubMed]

Nat. Photonics (3)

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Opt. Mater. Express (3)

Phys. Rev. B (4)

J. Petschulat, A. Chipouline, A. Tünnermann, T. Pertsch, C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Simple and versatile analytical approach for planar metamaterials,” Phys. Rev. B 82(7), 075102 (2010).
[Crossref]

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. P. Lee, “Magnetic plasmon resonance: Underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).
[Crossref]

A. B. Movchan and S. Guenneau, “Split-ring resonators and localized modes,” Phys. Rev. B 70(12), 125116 (2004).
[Crossref]

M. Manjappa, Y. K. Srivastava, and R. Singh, “Lattice-induced transparency in planar metamaterials,” Phys. Rev. B 94(16), 161103 (2016).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Phys. Rev. Lett. (5)

S. D. Jenkins and J. Ruostekoski, “Metamaterial transparency induced by cooperative electromagnetic interactions,” Phys. Rev. Lett. 111(14), 147401 (2013).
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Figures (7)

Fig. 1
Fig. 1 (a): Schematic diagram of the MM in reflection and rotational symmetry. The length of lateral l is 33 μm, the gap is 3 μm, The width of lateral w is 3 μm, the arm of single ASRR is 12 μm, respectively. (b) Microscopic images of the MM in rotational symmetry with lattice periods L of 50 μm. (c): Illustration of the symmetry broken evolution of two types MMs. (d): The diagram of THz transmittance measurement. Kz is the wave-vector of THz pulse, Ex is the polarization of electric component, Hy is the polarization of electric component.
Fig. 2
Fig. 2 (a) THz transmittance of MM in reflectional symmetry excited by the horizontally polarized (EX) and vertically polarized (EY) THz pulse. I, II, III, IV, V refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively. (b) THz transmittance of MM in rotational symmetry excited by the horizontally polarized (EX) and vertically polarized (EY) THz pulse. VI, VII, VIII, IX, X refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively. Blue solid-line: simulation data. Red solid-line: measurement data.
Fig. 3
Fig. 3 Q factors of resonance mode as a function of δ. The δ is 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively. (a) MM in reflectional symmetry excited by the horizontally polarized (EX) THz pulse. Blue solid square: νL. Red solid circle:νH. (b) MM in reflectional symmetry excited by the vertically polarized (EY) THz pulse. Blue hollow square: νL. Red hollow circle: νH. (c) MM in rotational symmetry excited by the horizontally polarized (EX) THz pulse. Black solid triangle: νs. (d) MM in rotational symmetry excited by the vertically polarized (EY) THz pulse. Blue hollow pentagon: νL. Purple hollow star: νH.
Fig. 4
Fig. 4 Surface currents of resonance modes of MMs in reflectional and rotational symmetry excited by the horizontally polarized (EX) and vertically polarized (EY) THz pulse. I, II, III, IV, V refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively in reflectional symmetry. VI, VII, VIII, IX, X refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm in rotational symmetry, Color bars: The relative strength of currents.
Fig. 5
Fig. 5 Magnetic field distribution of resonance modes of MMs in reflectional and rotational symmetry excited by the horizontally polarized (EX) THz wave and vertically polarized (EY) THz pulse. I, II, III, IV, V refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively in reflectional symmetry. VI, VII, VIII, IX, X refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm in rotational symmetry, Color bars: The relative strength of currents. + : THz wavevector, -: opposite to the THz wavevector.
Fig. 6
Fig. 6 Retrieved dielectric function of resonance mode of MM in reflectional symmetry excited by the horizontally polarized (EX) and vertically polarized (EY) THz pulse. I, II, III, IV, V refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm, respectively in reflectional symmetry. Red solid-line: The real part of permittivity. Blue solid-line: The imaginary part of permittivity.
Fig. 7
Fig. 7 Retrieved dielectric function of resonance mode of MM in rotational symmetry excited by the horizontally polarized (EX) and vertically polarized (EY) THz pulse. VI, VII, VIII, IX, X refers to the δ of 0 μm, 3 μm, 6 μm, 9 μm, and 12 μm respectively in rotational symmetry. Red solid-line: The real part of permittivity. Blue solid-line: The imaginary part of permittivity.

Tables (4)

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Table 1 The ν and Δν of reflectional symmetry

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Table 2 The ν and Δν of rotational symmetry

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Table 3 Q factors of resonance mode of MMs in reflectional and rotational symmetry

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Table 4 Dephasing time of trapped modes of MMs in reflectional and rotational symmetry

Equations (6)

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T( v )=| E sample ( v )/ E ref ( v ) |,
Q=ν/ Δν ,
ε( v )= ε r ( v )+i ε i ( v ),
z=± ( 1+ S 11 ) 2 S 21 2 ( 1 S 11 ) 2 S 21 2 ,
exp( i k 0 d )=X±i 1 X 2 ,
X=1/ 2 S 21 ( 1 S 11 2 + S 21 2 ) .

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