Abstract

General actively tunable near-field plasmon-induced transparency (PIT) systems based on couplings between localized plasmon resonances of graphene nanostructures not only suffer from interantenna separations of smaller than 20 nm, but also lack switchable effect about the transparency window. Here, the performance of an active PIT system based on graphene grating-sheet with near-field coupling distance of more than 100 nm is investigated in mid-infrared. The transparency window in spectrum is analyzed objectively and proved to be more likely stemmed from Aulter-Townes splitting. The proposed system exhibits flexible tunability in slow-light and electro-optical switches, promising for practical active photonic devices.

© 2016 Optical Society of America

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2015 (2)

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-Gonzaolez, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

B. Zhao and Z. M. Zhang, “Strong plasmonic coupling between graphene ribbon array and metal gratings,” ACS Photonics 2, 1611–1618 (2015).
[Crossref]

2014 (8)

A. Y. Nikitin, T. Low, and L. Martin-Moreno, “Anomalous reflection phase of graphene plasmons and its influence on resonators,” Phys. Rev. B 90, 041407 (2014).
[Crossref]

L. P. Du, D. Y. Tang, and X. C. Yuan, “Edge-reflection phase directed plasmonic resonances on graphene nano-structures,” Opt. Express 22, 22689–22698 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Ozdemir, 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]

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]

L. Wang, W. Cai, W. Luo, Z. Ma, C. Du, X. Zhang, and J. Xu, “Mid-infrared plasmon induced transparency in heterogeneous graphene ribbon pairs,” Opt. Express 22, 32450–32456 (2014).
[Crossref]

C. Zeng, J. Guo, and X. M. Liu, “High-contrast electro-optic modulation of spatial light induced by graphene-integrated fabry-perot microcavity,” Appl. Phys. Lett. 105, 121103 (2014).
[Crossref]

R. W. Yu, R. Alaee, F. Lederer, and C. Rockstuhl, “Manipulating the interaction between localized and delocalized surface plasmon-polaritons in graphene,” Phys. Rev. B 90, 085409 (2014).
[Crossref]

P. Alonso-Gonzalez, A. Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera, S. Velez, J. Chen, G. Navickaite, F. Kop-pens, A. Zurutuza, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns,” Science 344, 1369–1373 (2014).
[Crossref] [PubMed]

2013 (5)

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 2541–2547 (2013).
[Crossref] [PubMed]

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, 2388–2395 (2013).
[Crossref] [PubMed]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (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, 203112 (2013).
[Crossref]

X. Shi, D. Han, Y. Dai, Z. Yu, Y. Sun, H. Chen, X. Liu, and J. Zi, “Plasmonic analog of electromagnetically induced transparency in nanostructure graphene,” Opt. Express 21, 28438–43 (2013).
[Crossref]

2012 (5)

P. Tassin, L. Zhang, R. Zhao, A. Jain, T. Koschny, and C. M. Soukoulis, “Electromagnetically induced transparency and absorption in metamaterials: the radiating two-oscillator model and its experimental confirmation,” Phys. Rev. Lett. 109, 187401 (2012).
[Crossref] [PubMed]

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

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[Crossref]

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

2011 (3)

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, 630–634 (2011).
[Crossref] [PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11, 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, 163604 (2011).
[Crossref] [PubMed]

2010 (1)

R. D. Kekatpure, E. S. Barnard, W. Cai, and M. L. Brongersma, “Phase-coupled plasmon-induced transparency,” Phys. Rev. Lett. 104, 243902 (2010).
[Crossref] [PubMed]

2009 (2)

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

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

2008 (1)

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

2007 (1)

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
[Crossref]

2006 (1)

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. 8, 318 (2006).
[Crossref]

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

2003 (1)

E. J. Wagenmakers, “Model selection and multimodel inference: A practical information-theoretic approach,” J. Math. Psych. 47, 580–586 (2003).
[Crossref]

1991 (1)

K. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

1955 (1)

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100, 703–722 (1955).
[Crossref]

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, 2388–2395 (2013).
[Crossref] [PubMed]

Alaee, R.

R. W. Yu, R. Alaee, F. Lederer, and C. Rockstuhl, “Manipulating the interaction between localized and delocalized surface plasmon-polaritons in graphene,” Phys. Rev. B 90, 085409 (2014).
[Crossref]

Alonso-Gonzalez, P.

P. Alonso-Gonzalez, A. Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera, S. Velez, J. Chen, G. Navickaite, F. Kop-pens, A. Zurutuza, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns,” Science 344, 1369–1373 (2014).
[Crossref] [PubMed]

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

Alonso-Gonzaolez, P.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-Gonzaolez, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Anisimov, P. M.

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

Arigong, B.

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]

Atwater, H. A.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 2541–2547 (2013).
[Crossref] [PubMed]

Autler, S. H.

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100, 703–722 (1955).
[Crossref]

Avouris, P.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

Azad, A. K.

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

Badioli, M.

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

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Barnard, E. S.

R. D. Kekatpure, E. S. Barnard, W. Cai, and M. L. Brongersma, “Phase-coupled plasmon-induced transparency,” Phys. Rev. Lett. 104, 243902 (2010).
[Crossref] [PubMed]

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Bechtel, H. 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, 630–634 (2011).
[Crossref] [PubMed]

Boller, K.

K. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Brar, V. W.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 2541–2547 (2013).
[Crossref] [PubMed]

Brongersma, M. L.

R. D. Kekatpure, E. S. Barnard, W. Cai, and M. L. Brongersma, “Phase-coupled plasmon-induced transparency,” Phys. Rev. Lett. 104, 243902 (2010).
[Crossref] [PubMed]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

Cai, W.

L. Wang, W. Cai, W. Luo, Z. Ma, C. Du, X. Zhang, and J. Xu, “Mid-infrared plasmon induced transparency in heterogeneous graphene ribbon pairs,” Opt. Express 22, 32450–32456 (2014).
[Crossref]

R. D. Kekatpure, E. S. Barnard, W. Cai, and M. L. Brongersma, “Phase-coupled plasmon-induced transparency,” Phys. Rev. Lett. 104, 243902 (2010).
[Crossref] [PubMed]

Camara, N.

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Figures (8)

Fig. 1
Fig. 1 Scheme of the proposed graphene grating/sheet system. (a) 3D view shows a graphene grating consisted of ribbons, beneath which lies a layer of graphene. (b) Cross-section of the structure in x-z plane. The period of graphene grating is Λ, and the width of ribbons is W. A plane wave incidents normally on the grating, with the electric field polarized along x direction. The separation of the two graphene layers is D. Surrounding dielectric constants are ε 1, ε 2 and ε 3, respectively.
Fig. 2
Fig. 2 (a) Dispersion relation of a suspended graphene sheet. The Fermi energy is 0.3 eV. (b) Extinction spectra for graphene grating of period 300 nm and Fermi energy of 0.3 eV. The widths of ribbons are changed from 50 to 250 nm. The dipolar plasmon resonance arises at 31.7 THz for W of 104 nm, as indicated by the dashed line.
Fig. 3
Fig. 3 (a) Transmission spectrum for the graphene grating-sheet system when the width of the ribbons is 104 nm. Here, D=120 nm. ν 1,ν 2 denote the frequencies at the left and right dip respectively. ν 12 is the frequency at the PIT peak. (b) Simulated field distributions (|Ez |2) for a unit cell at frequency of ν 1(top left), ν 2(bottom left) and ν 12(top right), respectively. A and B mark the planes of graphene sheet and grating, respectively. The bottom right panel shows the electric field distributions(Ez ) at ν 12. (c) Normalized distributions of |E| along the vertical line indicated in (b) at ν 12.
Fig. 4
Fig. 4 Numerical (blue dots) and analytically fitted (red curves) transmission spectra for different separation of D.
Fig. 5
Fig. 5 (a) Upper panel: The parameters κ, γ 1 and γ 2 used in fitting. Lower panel: AIC weights of the EIT (blue curve) and ATS models (green curve). (b) The same as (a), except that µ 2=30000 cm2/(V s) here.
Fig. 6
Fig. 6 Tunability of the transparency window with the change of Fermi energies EF of graphene ribbons and sheet (EF 1 = EF 2 = EF ). D is 50 nm here. The white dashed line indicates the frequency of the LPR/FSP mode.
Fig. 7
Fig. 7 (a) Transmission spectra for graphene grating-sheet system at different Fermi energies EF (EF 1 = EF 2 = EF ). Width of graphene ribbons is 183 nm. Distance between grating and sheet is 150 nm. (b) Corresponding group delays with increased Fermi energies.
Fig. 8
Fig. 8 The performance in active electric-optical switches. EF 1 are (a) 0.5 eV, (b) 0.6 eV and (c) 0.7 eV, respectively. At ON states (black solid curves), EF 2 have the identical values as EF 1 in all three panels. While at OFF states (red dashed curves, EF 2 are (a) 0.3 eV, (b) 0.35 eV and (c) 0.4 eV, respectively. The distance D is 100 nm.

Equations (10)

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σ ( ω ) = 2 e 2 T π i ω + i τ 1 log [ 2 cosh ( E F 2 K B T ) ] + e 2 4 [ H ( ω / 2 ) + 4 i ω π 0 d ε H ( ε ) H ( ω / 2 ) ω 2 4 ε 2 ] ,
H ( ε ) = sinh ( ε / k B T ) cosh ( E F / k B T ) + cosh ( ε / k B T ) .
ε 2 k G P 2 ε 2 k 0 2 + ε 3 k G P 2 ε 3 k 0 2 = i σ ω ε 0 ,
k G P ( ω ) = 2 i ω ε 0 σ ( ω ) .
q Λ = m 2 π
x ¨ 1 + γ 1 x ˙ 1 + ω 1 2 x 1 + κ 2 x 2 = a 1 E 0 e i ω t , x ¨ 2 + γ 2 x ˙ 2 + ω 2 2 x 2 + κ 2 x 1 = 0 ,
χ ( ω ) = χ r + i χ i ω 2 2 ω 2 + i γ 2 ω ( ω 1 2 ω 2 + i γ 1 ω ) ( ω 2 2 ω 2 + i γ 2 ω ) κ 4 .
T E I T = 1 C 1 ( ω Ω 1 ) 2 + Γ 1 2 + C 2 ( ω Ω 2 ) 2 + Γ 2 2 ,
T A T S = 1 C 1 ( ω Ω 1 ) 2 + Γ 1 2 + C 2 ( ω Ω 2 ) 2 + Γ 2 2 ,
Δ φ + q W = n π ,

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