Abstract

To achieve plasmonically induced transparency (PIT), general near-field plasmonic systems based on couplings between localized plasmon resonances of nanostructures rely heavily on the well-designed interantenna separations. However, the implementation of such devices and techniques encounters great difficulties mainly to due to very small sized dimensions of the nanostructures and gaps between them. Here, we propose and numerically demonstrate that PIT can be achieved by using two graphene layers that are composed of a upper sinusoidally curved layer and a lower planar layer, avoiding any pattern of the graphene sheets. Both the analytical fitting and the Akaike Information Criterion (AIC) method are employed efficiently to distinguish the induced window, which is found to be more likely caused by Autler-Townes splitting (ATS) instead of electromagnetically induced transparency (EIT). Besides, our results show that the resonant modes cannot only be tuned dramatically by geometrically changing the grating amplitude and the interlayer spacing, but also by dynamically varying the Fermi energy of the graphene sheets. Potential applications of the proposed system could be expected on various photonic functional devices, including optical switches, plasmonic sensors.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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2016 (7)

J. Liu, H. Yang, C. Wang, K. Xu, and J. Xiao, “Experimental distinction of Autler-Townes splitting from electromagnetically induced transparency using coupled mechanical oscillators system,” Sci. Rep. 6, 19040 (2016).
[Crossref] [PubMed]

Z. Bai and G. Huang, “Plasmon dromions in a metamaterial via plasmon-induced transparency,” Phys. Rev. A 93(1), 013818 (2016).
[Crossref]

H. J. Li, L. L. Wang, and X. Zhai, “Plasmonically induced absorption and transparency based on MIM waveguides with concentric nanorings,” IEEE Photonics Technol. Lett. 28(13), 1454–1457 (2016).
[Crossref]

P. A. Huidobro, M. Kraft, S. A. Maier, and J. B. Pendry, “Graphene as a Tunable Anisotropic or Isotropic Plasmonic Metasurface,” ACS Nano 10(5), 5499–5506 (2016).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons,” Opt. Express 24(1), 427–436 (2016).
[Crossref] [PubMed]

S. Balci, O. Balci, N. Kakenov, F. B. Atar, and C. Kocabas, “Dynamic tuning of plasmon resonance in the visible using graphene,” Opt. Lett. 41(6), 1241–1244 (2016).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Localized plasmonic field enhancement in shaped graphene nanoribbons,” Opt. Express 24(15), 16336–16348 (2016).
[Crossref]

2015 (7)

Y. P. Chen, W. E. I. Sha, L. Jiang, and J. Hu, “Graphene plasmonics for tuning photon decay rate near metallic split-ring resonator in a multilayered substrate,” Opt. Express 23(3), 2798–2807 (2015).
[Crossref] [PubMed]

J. Q. Liu, Y. X. Zhou, L. Li, P. Wang, and A. V. Zayats, “Controlling plasmon-induced transparency of graphene metamolecules with external magnetic field,” Opt. Express 23(10), 12524–12532 (2015).
[Crossref] [PubMed]

L. Y. He, T. J. Wang, Y. P. Gao, C. Cao, and C. Wang, “Discerning electromagnetically induced transparency from Autler-Townes splitting in plasmonic waveguide and coupled resonators system,” Opt. Express 23(18), 23817–23826 (2015).
[Crossref] [PubMed]

T. H. Qiu, “Electromagnetically induced holographic imaging in hybrid artificial molecule,” Opt. Express 23(19), 24537–24546 (2015).
[Crossref] [PubMed]

L. Martín-Moreno, F. J. de Abajo, and F. J. García-Vidal, “Ultra-efficient coupling of a quantum emitter to the tunable guided plasmons of a carbon nanotube,” Phys. Rev. Lett. 115(17), 173601 (2015).
[Crossref] [PubMed]

J. P. Liu, X. Zhai, L. L. Wang, H. J. Li, F. Xie, Q. Lin, and S. X. Xia, “Analysis of mid-infrared surface plasmon modes in a graphene-based cylindrical hybrid waveguide,” Plasmonics 95, 1–9 (2015).

Q. Lin, X. Zhai, L. Wang, B. Wang, G. Liu, and S. Xia, “Combined theoretical analysis for plasmon-induced transparency in integrated graphene waveguides with direct and indirect couplings,” EPL-Europhys. Lett. 111(3), 34004 (2015).
[Crossref]

2014 (5)

J. Ding, B. Arigong, H. Ren, M. Zhou, J. Shao, M. Lu, Y. Chai, Y. Lin, and H. Zhang, “Tuneable complementary metamaterial structures based on graphene for single and multiple transparency windows,” Sci. Rep. 4, 6128 (2014).
[Crossref] [PubMed]

T. Cao, C. Wei, R. E. Simpson, L. Zhang, and M. J. Cryan, “Fast tuning of double Fano resonance using a phase-change metamaterial under low power intensity,” Sci. Rep. 4, 4463 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

F. J. Garcia de Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photonics 1(3), 135–152 (2014).
[Crossref]

H. C. Sun, Y. X. Liu, H. Ian, J. Q. You, E. Il’ichev, and F. Nori, “Electromagnetically induced transparency and Autler-Townes splitting in superconducting flux quantum circuits,” Phys. Rev. A 89(6), 063822 (2014).
[Crossref]

2013 (7)

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

N. Papasimakis, S. Thongrattanasiri, N. I. Zheludev, and F. J. García de Abajo, “The magnetic response of graphene split-ring metamaterials,” Light Sci. Appl. 2(7), e78 (2013).
[Crossref]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
[Crossref] [PubMed]

T. M. Slipchenko, M. L. Nesterov, L. Martin-Moreno, and A. Y. Nikitin, “Analytical solution for the diffraction of an electromagnetic wave by a graphene grating,” J. Opt. 15(11), 114008 (2013).
[Crossref]

L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler-Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87(1), 013823 (2013).
[Crossref]

H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

2012 (6)

W. S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A plasmonic Fano switch,” Nano Lett. 12(9), 4977–4982 (2012).
[Crossref] [PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbücken, “A graphene electron lens,” Appl. Phys. Lett. 100(15), 153106 (2012).
[Crossref]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Y. Guo, L. Yan, W. Pan, B. Luo, K. Wen, Z. Guo, and X. Luo, “Electromagnetically induced transparency (EIT)-like transmission in side-coupled complementary split-ring resonators,” Opt. Express 20(22), 24348–24355 (2012).
[Crossref] [PubMed]

2011 (7)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

P. M. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107(16), 163604 (2011).
[Crossref] [PubMed]

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum Fano resonance,” Phys. Rev. Lett. 106(10), 107403 (2011).
[Crossref] [PubMed]

E. H. Ahmed, S. Ingram, T. Kirova, O. Salihoglu, J. Huennekens, J. Qi, Y. Guan, and A. M. Lyyra, “Quantum control of the spin-orbit interaction using the Autler-Townes effect,” Phys. Rev. Lett. 107(16), 163601 (2011).
[Crossref] [PubMed]

M. J. Piotrowicz, C. MacCormick, A. Kowalczyk, S. Bergamini, I. I. Beterov, and E. A. Yakshina, “Measurement of the electric dipole moments for transitions to rubidium Rydberg states via Autler–Townes splitting,” New J. Phys. 13(9), 093012 (2011).
[Crossref]

2010 (2)

T. Y. Abi-Salloum, “Electromagnetically induced transparency and Autler-Townes splitting: two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81(5), 053836 (2010).
[Crossref]

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
[Crossref] [PubMed]

2008 (1)

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

2007 (1)

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007).
[Crossref] [PubMed]

2005 (1)

J. Dostalek, J. Homola, and M. Miler, “Rich information format surface plasmon resonance biosensor based on array of diffraction gratings,” Sens. Actuators B Chem. 107(1), 154–161 (2005).
[Crossref]

2003 (1)

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91(3), 037401 (2003).
[Crossref] [PubMed]

2001 (1)

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001).
[Crossref] [PubMed]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref] [PubMed]

Abi-Salloum, T. Y.

T. Y. Abi-Salloum, “Electromagnetically induced transparency and Autler-Townes splitting: two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81(5), 053836 (2010).
[Crossref]

Ahmed, E. H.

E. H. Ahmed, S. Ingram, T. Kirova, O. Salihoglu, J. Huennekens, J. Qi, Y. Guan, and A. M. Lyyra, “Quantum control of the spin-orbit interaction using the Autler-Townes effect,” Phys. Rev. Lett. 107(16), 163601 (2011).
[Crossref] [PubMed]

Ajayan, P. M.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

Alonso-González, P.

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L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler-Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87(1), 013823 (2013).
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J. Ding, B. Arigong, H. Ren, M. Zhou, J. Shao, M. Lu, Y. Chai, Y. Lin, and H. Zhang, “Tuneable complementary metamaterial structures based on graphene for single and multiple transparency windows,” Sci. Rep. 4, 6128 (2014).
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H. C. Sun, Y. X. Liu, H. Ian, J. Q. You, E. Il’ichev, and F. Nori, “Electromagnetically induced transparency and Autler-Townes splitting in superconducting flux quantum circuits,” Phys. Rev. A 89(6), 063822 (2014).
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P. A. Huidobro, M. Kraft, S. A. Maier, and J. B. Pendry, “Graphene as a Tunable Anisotropic or Isotropic Plasmonic Metasurface,” ACS Nano 10(5), 5499–5506 (2016).
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D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001).
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Ren, H.

J. Ding, B. Arigong, H. Ren, M. Zhou, J. Shao, M. Lu, Y. Chai, Y. Lin, and H. Zhang, “Tuneable complementary metamaterial structures based on graphene for single and multiple transparency windows,” Sci. Rep. 4, 6128 (2014).
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L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbücken, “A graphene electron lens,” Appl. Phys. Lett. 100(15), 153106 (2012).
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T. M. Slipchenko, M. L. Nesterov, L. Martin-Moreno, and A. Y. Nikitin, “Analytical solution for the diffraction of an electromagnetic wave by a graphene grating,” J. Opt. 15(11), 114008 (2013).
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W. S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A plasmonic Fano switch,” Nano Lett. 12(9), 4977–4982 (2012).
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H. C. Sun, Y. X. Liu, H. Ian, J. Q. You, E. Il’ichev, and F. Nori, “Electromagnetically induced transparency and Autler-Townes splitting in superconducting flux quantum circuits,” Phys. Rev. A 89(6), 063822 (2014).
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W. S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A plasmonic Fano switch,” Nano Lett. 12(9), 4977–4982 (2012).
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Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
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N. Papasimakis, S. Thongrattanasiri, N. I. Zheludev, and F. J. García de Abajo, “The magnetic response of graphene split-ring metamaterials,” Light Sci. Appl. 2(7), e78 (2013).
[Crossref]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001).
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Q. Lin, X. Zhai, L. Wang, B. Wang, G. Liu, and S. Xia, “Combined theoretical analysis for plasmon-induced transparency in integrated graphene waveguides with direct and indirect couplings,” EPL-Europhys. Lett. 111(3), 34004 (2015).
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Wang, C.

J. Liu, H. Yang, C. Wang, K. Xu, and J. Xiao, “Experimental distinction of Autler-Townes splitting from electromagnetically induced transparency using coupled mechanical oscillators system,” Sci. Rep. 6, 19040 (2016).
[Crossref] [PubMed]

L. Y. He, T. J. Wang, Y. P. Gao, C. Cao, and C. Wang, “Discerning electromagnetically induced transparency from Autler-Townes splitting in plasmonic waveguide and coupled resonators system,” Opt. Express 23(18), 23817–23826 (2015).
[Crossref] [PubMed]

Wang, F.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Wang, L.

Q. Lin, X. Zhai, L. Wang, B. Wang, G. Liu, and S. Xia, “Combined theoretical analysis for plasmon-induced transparency in integrated graphene waveguides with direct and indirect couplings,” EPL-Europhys. Lett. 111(3), 34004 (2015).
[Crossref]

Wang, L. L.

H. J. Li, L. L. Wang, and X. Zhai, “Plasmonically induced absorption and transparency based on MIM waveguides with concentric nanorings,” IEEE Photonics Technol. Lett. 28(13), 1454–1457 (2016).
[Crossref]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons,” Opt. Express 24(1), 427–436 (2016).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Localized plasmonic field enhancement in shaped graphene nanoribbons,” Opt. Express 24(15), 16336–16348 (2016).
[Crossref]

J. P. Liu, X. Zhai, L. L. Wang, H. J. Li, F. Xie, Q. Lin, and S. X. Xia, “Analysis of mid-infrared surface plasmon modes in a graphene-based cylindrical hybrid waveguide,” Plasmonics 95, 1–9 (2015).

Wang, P.

Wang, T. J.

Wang, Y.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

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

Wei, C.

T. Cao, C. Wei, R. E. Simpson, L. Zhang, and M. J. Cryan, “Fast tuning of double Fano resonance using a phase-change metamaterial under low power intensity,” Sci. Rep. 4, 4463 (2014).
[Crossref] [PubMed]

Wen, K.

Wen, S. C.

Wu, C.

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum Fano resonance,” Phys. Rev. Lett. 106(10), 107403 (2011).
[Crossref] [PubMed]

Wulfhekel, W.

L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbücken, “A graphene electron lens,” Appl. Phys. Lett. 100(15), 153106 (2012).
[Crossref]

Xia, S.

Q. Lin, X. Zhai, L. Wang, B. Wang, G. Liu, and S. Xia, “Combined theoretical analysis for plasmon-induced transparency in integrated graphene waveguides with direct and indirect couplings,” EPL-Europhys. Lett. 111(3), 34004 (2015).
[Crossref]

Xia, S. X.

Xiao, J.

J. Liu, H. Yang, C. Wang, K. Xu, and J. Xiao, “Experimental distinction of Autler-Townes splitting from electromagnetically induced transparency using coupled mechanical oscillators system,” Sci. Rep. 6, 19040 (2016).
[Crossref] [PubMed]

Xie, B. Y.

H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

Xie, F.

J. P. Liu, X. Zhai, L. L. Wang, H. J. Li, F. Xie, Q. Lin, and S. X. Xia, “Analysis of mid-infrared surface plasmon modes in a graphene-based cylindrical hybrid waveguide,” Plasmonics 95, 1–9 (2015).

Xu, K.

J. Liu, H. Yang, C. Wang, K. Xu, and J. Xiao, “Experimental distinction of Autler-Townes splitting from electromagnetically induced transparency using coupled mechanical oscillators system,” Sci. Rep. 6, 19040 (2016).
[Crossref] [PubMed]

Xu, Q.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Yakshina, E. A.

M. J. Piotrowicz, C. MacCormick, A. Kowalczyk, S. Bergamini, I. I. Beterov, and E. A. Yakshina, “Measurement of the electric dipole moments for transitions to rubidium Rydberg states via Autler–Townes splitting,” New J. Phys. 13(9), 093012 (2011).
[Crossref]

Yan, L.

Yang, H.

J. Liu, H. Yang, C. Wang, K. Xu, and J. Xiao, “Experimental distinction of Autler-Townes splitting from electromagnetically induced transparency using coupled mechanical oscillators system,” Sci. Rep. 6, 19040 (2016).
[Crossref] [PubMed]

Yang, L.

B. Peng, S. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

Yao, Y.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

You, J. Q.

H. C. Sun, Y. X. Liu, H. Ian, J. Q. You, E. Il’ichev, and F. Nori, “Electromagnetically induced transparency and Autler-Townes splitting in superconducting flux quantum circuits,” Phys. Rev. A 89(6), 063822 (2014).
[Crossref]

Yu, N.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Yu, P.

H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

Zayats, A. V.

Zettl, A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Zhai, X.

H. J. Li, L. L. Wang, and X. Zhai, “Plasmonically induced absorption and transparency based on MIM waveguides with concentric nanorings,” IEEE Photonics Technol. Lett. 28(13), 1454–1457 (2016).
[Crossref]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons,” Opt. Express 24(1), 427–436 (2016).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Localized plasmonic field enhancement in shaped graphene nanoribbons,” Opt. Express 24(15), 16336–16348 (2016).
[Crossref]

Q. Lin, X. Zhai, L. Wang, B. Wang, G. Liu, and S. Xia, “Combined theoretical analysis for plasmon-induced transparency in integrated graphene waveguides with direct and indirect couplings,” EPL-Europhys. Lett. 111(3), 34004 (2015).
[Crossref]

J. P. Liu, X. Zhai, L. L. Wang, H. J. Li, F. Xie, Q. Lin, and S. X. Xia, “Analysis of mid-infrared surface plasmon modes in a graphene-based cylindrical hybrid waveguide,” Plasmonics 95, 1–9 (2015).

Zhang, H.

J. Ding, B. Arigong, H. Ren, M. Zhou, J. Shao, M. Lu, Y. Chai, Y. Lin, and H. Zhang, “Tuneable complementary metamaterial structures based on graphene for single and multiple transparency windows,” Sci. Rep. 4, 6128 (2014).
[Crossref] [PubMed]

Zhang, L.

T. Cao, C. Wei, R. E. Simpson, L. Zhang, and M. J. Cryan, “Fast tuning of double Fano resonance using a phase-change metamaterial under low power intensity,” Sci. Rep. 4, 4463 (2014).
[Crossref] [PubMed]

Zhang, S.

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

Zhang, X.

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

Zharov, A. A.

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91(3), 037401 (2003).
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Zheludev, N. I.

N. Papasimakis, S. Thongrattanasiri, N. I. Zheludev, and F. J. García de Abajo, “The magnetic response of graphene split-ring metamaterials,” Light Sci. Appl. 2(7), e78 (2013).
[Crossref]

Zhou, M.

J. Ding, B. Arigong, H. Ren, M. Zhou, J. Shao, M. Lu, Y. Chai, Y. Lin, and H. Zhang, “Tuneable complementary metamaterial structures based on graphene for single and multiple transparency windows,” Sci. Rep. 4, 6128 (2014).
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S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007).
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ACS Nano (4)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
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Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[Crossref] [PubMed]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

P. A. Huidobro, M. Kraft, S. A. Maier, and J. B. Pendry, “Graphene as a Tunable Anisotropic or Isotropic Plasmonic Metasurface,” ACS Nano 10(5), 5499–5506 (2016).
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ACS Photonics (1)

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Appl. Phys. Lett. (2)

L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbücken, “A graphene electron lens,” Appl. Phys. Lett. 100(15), 153106 (2012).
[Crossref]

H. Cheng, S. Q. Chen, P. Yu, X. Y. Duan, B. Y. Xie, and J. G. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

EPL-Europhys. Lett. (1)

Q. Lin, X. Zhai, L. Wang, B. Wang, G. Liu, and S. Xia, “Combined theoretical analysis for plasmon-induced transparency in integrated graphene waveguides with direct and indirect couplings,” EPL-Europhys. Lett. 111(3), 34004 (2015).
[Crossref]

IEEE Photonics Technol. Lett. (1)

H. J. Li, L. L. Wang, and X. Zhai, “Plasmonically induced absorption and transparency based on MIM waveguides with concentric nanorings,” IEEE Photonics Technol. Lett. 28(13), 1454–1457 (2016).
[Crossref]

J. Opt. (1)

T. M. Slipchenko, M. L. Nesterov, L. Martin-Moreno, and A. Y. Nikitin, “Analytical solution for the diffraction of an electromagnetic wave by a graphene grating,” J. Opt. 15(11), 114008 (2013).
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Light Sci. Appl. (1)

N. Papasimakis, S. Thongrattanasiri, N. I. Zheludev, and F. J. García de Abajo, “The magnetic response of graphene split-ring metamaterials,” Light Sci. Appl. 2(7), e78 (2013).
[Crossref]

Nano Lett. (3)

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
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W. S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A plasmonic Fano switch,” Nano Lett. 12(9), 4977–4982 (2012).
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Nat. Commun. (1)

B. Peng, S. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Nature (1)

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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New J. Phys. (1)

M. J. Piotrowicz, C. MacCormick, A. Kowalczyk, S. Bergamini, I. I. Beterov, and E. A. Yakshina, “Measurement of the electric dipole moments for transitions to rubidium Rydberg states via Autler–Townes splitting,” New J. Phys. 13(9), 093012 (2011).
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Opt. Express (7)

T. H. Qiu, “Electromagnetically induced holographic imaging in hybrid artificial molecule,” Opt. Express 23(19), 24537–24546 (2015).
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Y. Guo, L. Yan, W. Pan, B. Luo, K. Wen, Z. Guo, and X. Luo, “Electromagnetically induced transparency (EIT)-like transmission in side-coupled complementary split-ring resonators,” Opt. Express 20(22), 24348–24355 (2012).
[Crossref] [PubMed]

L. Y. He, T. J. Wang, Y. P. Gao, C. Cao, and C. Wang, “Discerning electromagnetically induced transparency from Autler-Townes splitting in plasmonic waveguide and coupled resonators system,” Opt. Express 23(18), 23817–23826 (2015).
[Crossref] [PubMed]

J. Q. Liu, Y. X. Zhou, L. Li, P. Wang, and A. V. Zayats, “Controlling plasmon-induced transparency of graphene metamolecules with external magnetic field,” Opt. Express 23(10), 12524–12532 (2015).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons,” Opt. Express 24(1), 427–436 (2016).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, L. L. Wang, Q. Lin, and S. C. Wen, “Localized plasmonic field enhancement in shaped graphene nanoribbons,” Opt. Express 24(15), 16336–16348 (2016).
[Crossref]

Y. P. Chen, W. E. I. Sha, L. Jiang, and J. Hu, “Graphene plasmonics for tuning photon decay rate near metallic split-ring resonator in a multilayered substrate,” Opt. Express 23(3), 2798–2807 (2015).
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Opt. Lett. (1)

Phys. Rev. A (4)

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Z. Bai and G. Huang, “Plasmon dromions in a metamaterial via plasmon-induced transparency,” Phys. Rev. A 93(1), 013818 (2016).
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H. C. Sun, Y. X. Liu, H. Ian, J. Q. You, E. Il’ichev, and F. Nori, “Electromagnetically induced transparency and Autler-Townes splitting in superconducting flux quantum circuits,” Phys. Rev. A 89(6), 063822 (2014).
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A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91(3), 037401 (2003).
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Plasmonics (1)

J. P. Liu, X. Zhai, L. L. Wang, H. J. Li, F. Xie, Q. Lin, and S. X. Xia, “Analysis of mid-infrared surface plasmon modes in a graphene-based cylindrical hybrid waveguide,” Plasmonics 95, 1–9 (2015).

Sci. Rep. (3)

J. Ding, B. Arigong, H. Ren, M. Zhou, J. Shao, M. Lu, Y. Chai, Y. Lin, and H. Zhang, “Tuneable complementary metamaterial structures based on graphene for single and multiple transparency windows,” Sci. Rep. 4, 6128 (2014).
[Crossref] [PubMed]

T. Cao, C. Wei, R. E. Simpson, L. Zhang, and M. J. Cryan, “Fast tuning of double Fano resonance using a phase-change metamaterial under low power intensity,” Sci. Rep. 4, 4463 (2014).
[Crossref] [PubMed]

J. Liu, H. Yang, C. Wang, K. Xu, and J. Xiao, “Experimental distinction of Autler-Townes splitting from electromagnetically induced transparency using coupled mechanical oscillators system,” Sci. Rep. 6, 19040 (2016).
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Figures (5)

Fig. 1
Fig. 1 Scheme of the PIT system in our study: A plane layer (PL) of graphene sheet is placed on the xoz plane, below which is a substrate with permittivity ε3. The planar sheet is further covered by a media with permittivity ε2 and a sine shaped upper surface. The other layer of graphene sheet is perfectly placed onto the patterned surface, forming period sinusoidal gratings along x-direction (grating layer-GL). An x-polarized incident transverse magnetic (TM) laser light with wave number β0 and an angle θ strikes the surface of the periodically structured graphene system. The insert shows the front view of one period.
Fig. 2
Fig. 2 (a) Simulated normal-incidence transmission (Tr), reflection (Re), and absorption (Ab) properties of the proposed system without the PL of graphene. The magnetic field Hz components demonstrate the resonances associated with the M = 1 mode (b) and the M = 2 mode (c), respectively. (d) Simulated normal-incidence transmission, reflection, and absorption properties of the proposed PIT system with the PL of graphene. The magnetic field Hz components demonstrate the resonances associated with the QSM1 (e), the QAM1 (f), the QSM2 (g), and the QAM2 (h), respectively. The parameters are set as θ = 0, EF = 1.0 eV, A = 40 nm, and d = 20 nm.
Fig. 3
Fig. 3 (a) Simulated (Sim., dots-line in pink) and analytically fitted (green curves) absorption spectra for different values of grating amplitudes A with d = 20 nm. (b) Simulated (Sim., dots-line in blue) and analytically fitted (red curves) absorption spectra for different separation d between the two graphene layers with A = 40 nm. All of the fitted curves are obtained by using the ATS model from Eq. (6). The left absorption peaks in the curves are caused by the QSM1, while the right peaks are corresponding to QAM1.
Fig. 4
Fig. 4 (a) Absorption profile is presented together with the best fits of functions AEIT(C+, C, γ+, γ) (blue line) and AATS(C1, C2, δ1, δ2, γ1, γ2) (red line) when A = 40 nm, d = 20 nm. In this case, AATS(0.3613, 3.4602, 0.1739, 0.3372, 4.1670, 0.1590) fits the simulated data much better than AEIT(3.6028, 9.9132, 3.6287, 9.5157). (b) AIC weights as a function of grating amplitude for ATS model (red dots/curve) and for EIT model (green dots/curve) with d = 20 nm. (c) AIC weights as a function of distance between the two graphene layers for ATS model (pink dots/curve) and for EIT model (blue dots/curve) with A = 40 nm.
Fig. 5
Fig. 5 (a) Simulated normal-incidence absorption spectra of the two fundamental modes of the proposed PIT system with different Fermi energy level in graphene. The dash-dotted lines represent QSM1 while the solid lines represent QAM1. (b) Transmission amplitude vs EF at wavelength 10 μm. (c) Simulated normal-incidence transmission spectra with different refractive indexes outside of the graphene layers (that is ε1 = ε3 = n2) when ε2 = 2.25 and EF = 1.0 eV. (d) Scaling rule of resonant wavelengths of QSM1 and QSM2 with respect to refractive index n. The dots are simulated results from COMSOL, and the lines are linear fittings. (e) Absorption spectra of the two graphene sheets for various values of incident angle θ when EF = 1.0 eV. (f) Resonant wavelengths of QSM1 (red-dotted line, left radial axis) and QAM1 (green-dotted line, right radial axis) as a function of incident angle θ. The other parameters of this figure are A = 40 nm and d = 20 nm.

Equations (7)

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σ ( ω ) = i e 2 π 2 E F ω + i τ 1 i e 2 4 π 2 l n [ 2 E F + ( ω + i τ 1 ) 2 E F ( ω + i τ 1 ) ] ,
( δ 1 + i η 1 / 2 ) Φ 1 κ Φ 2 = i η c Φ i n ,
( δ 2 + i η 2 / 2 ) Φ 2 κ Φ 1 = 0 ,
χ = χ r + i χ i = ( ω ω 2 + i η 2 / 2 ) κ 2 ( ω ω 1 + i η 1 / 2 ) ( ω ω 2 + i η 2 / 2 ) ,
A E I T = 2 η c χ i = 2 η c ( ω + i χ + r ω + i 2 + δ 2 + ω - i χ r ω i 2 + δ 2 ) = C + 1 + δ 2 / ( γ + 2 / 4 ) C 1 + δ 2 / ( γ 2 / 4 ) ,
A A T S = 2 η c χ i = 2 η c ( ω + i χ + r ω + i 2 + ( δ ω + r ) 2 + ω - i χ r ω i 2 + ( δ ω - r ) 2 ) = C 1 1 + ( δ + δ 1 ) 2 / ( γ 1 2 / 4 ) + C 2 1 + ( δ δ 2 ) 2 / ( γ 2 2 / 4 ) ,
w A T S = e I A T S / 2 e I A T S / 2 + e I E I T / 2 , w E I T = 1 w A T S .

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