Abstract

We numerically demonstrate dynamically tuneable plasmon-induced transparency in a π-shaped metamolecules made of graphene nanostrips by applying external static magnetic field. It is shown that for graphene nanostrips with appropriate Fermi energy, the resonant wavelength, line-shape, and the polarization of transmitted light in the mid-infrared can be effectively controlled by magnetic field. In particular, giant polarization rotation exceeding 20° has been observed in asymmetric graphene metamolecules, which is further enhanced to almost 40° due the Faraday effect in the applied magnetic field, at around 9 μm wavelength, much higher frequency than the Faraday rotation observed in a semi-infinite graphene microribbons. The results offer a flexible approach for the development of compact, tunable graphene-based photonic devices.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
  24. A. Yu. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).
    [Crossref]
  25. I. V. Fialkovsky and D. V. Vassilevich, “Parity-odd effects and polarization rotation in graphene,” J. Phys. A: Math. Theor. 42, 442001 (2009).
    [Crossref]
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    [Crossref] [PubMed]

2014 (3)

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14, 78–82 (2014).
[Crossref]

L. Z. Yang, T. Hu, A. Shen, C. Y. Pei, B. Yang, T. G. Dai, H. Yu, Y. B. Li, X. Q. Jiang, and J. Y. Yang, “Ultra-compact optical modulator based on graphene-silica metamaterial,” Opt. Lett. 39, 1909–1912 (2014).
[Crossref] [PubMed]

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

2013 (4)

H. J. Li, L. L. Wang, J. Q. Liu, Z. R. Huang, B. Sun, and X. Zhai, “Investigation of the graphene based planar plasmonic filters,” Appl. Phys. Lett. 103, 211104 (2013).
[Crossref]

X. Shi, D. Z. Han, Y. Y. Dai, Z. F. Yu, Y. Sun, H. Chen, X. H. Liu, and J. Zi, “Plasmonic analog of electromagnetically induced transparency in nanostructure graphene,” Opt. Express 21, 28438–28443 (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]

M. Tymchenko, A. Y. Nikitin, and L. Martín-Moreno, “Faraday rotation due to excitation of magnetoplasmons in graphene microribbons,” ACS Nano 7, 9780–9787 (2013).
[Crossref] [PubMed]

2012 (6)

W. H. Wang, S. P. Apell, and J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86, 125450 (2012).
[Crossref]

M. Rahmani, D. YuanLei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12, 2101–2106 (2012).
[Crossref] [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. CastroNeto, 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]

P. Ginzburg, F. J. Rodríguez-Fortuno, A. Martinez, and A. V. Zayats, “Analogue of the quantum Hanle effect and polarization conversion in non-Hermitian plasmonic metamaterials,” Nano Lett. 12, 6309–6314 (2012).
[Crossref] [PubMed]

H. Yan, F. N. Xia, Z. Q Li, and P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[Crossref]

H. Yan, Z.Q. Li, X. S. Li, W. J. Zhu, P. Avouris, and F. N. Xia, “Infrared spectroscopy of tunable Dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012).
[Crossref] [PubMed]

2011 (2)

A. Yu. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).
[Crossref]

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday Effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011).
[Crossref]

2010 (2)

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

Z. G. Dong, H. Liu, M. X. Xu, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Plasmonically induced transparent magnetic resonance in a metallic metamaterial composed of asymmetric double bars,” Opt. Express 18, 18229–18234 (2010).
[Crossref] [PubMed]

2009 (3)

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

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

I. V. Fialkovsky and D. V. Vassilevich, “Parity-odd effects and polarization rotation in graphene,” J. Phys. A: Math. Theor. 42, 442001 (2009).
[Crossref]

2008 (2)

G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den Brink, and P. J. Kelly, “Doping graphene with metal contacts,” Phys. Rev. Lett. 101, 026803 (2008).
[Crossref] [PubMed]

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 (2)

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 86, 016803 (2007).
[Crossref]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2007).
[Crossref]

1997 (1)

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

Apell, S. P.

W. H. Wang, S. P. Apell, and J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86, 125450 (2012).
[Crossref]

Avouris, P.

H. Yan, Z.Q. Li, X. S. Li, W. J. Zhu, P. Avouris, and F. N. Xia, “Infrared spectroscopy of tunable Dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012).
[Crossref] [PubMed]

H. Yan, F. N. Xia, Z. Q Li, and P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[Crossref]

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. CastroNeto, 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]

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. CastroNeto, 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]

Bludov, Y. V.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday Effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011).
[Crossref]

Boltasseva, A.

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14, 78–82 (2014).
[Crossref]

Brocks, G.

G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den Brink, and P. J. Kelly, “Doping graphene with metal contacts,” Phys. Rev. Lett. 101, 026803 (2008).
[Crossref] [PubMed]

Castro Neto, A. H.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday Effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011).
[Crossref]

CastroNeto, A. H.

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. CastroNeto, 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]

Chen, H.

Chen, S. Q.

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]

Chen, Y. P.

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14, 78–82 (2014).
[Crossref]

Cheng, H.

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]

Chung, T. F.

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14, 78–82 (2014).
[Crossref]

Dai, T. G.

Dai, Y. Y.

Dominguez, G.

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. CastroNeto, 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]

Dong, Z. G.

Dorpe, P. V.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Duan, X. 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, 203112 (2013).
[Crossref]

Eigenthaler, U.

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

Emani, N. K.

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14, 78–82 (2014).
[Crossref]

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2007).
[Crossref]

Fei, Z.

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. CastroNeto, 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]

Ferreira, A.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday Effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011).
[Crossref]

Fialkovsky, I. V.

I. V. Fialkovsky and D. V. Vassilevich, “Parity-odd effects and polarization rotation in graphene,” J. Phys. A: Math. Theor. 42, 442001 (2009).
[Crossref]

Fleischhauer, M.

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

Fogler, M. M.

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. CastroNeto, 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]

García de Abajo, F. J.

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

García-Vidal, F. J.

A. Yu. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).
[Crossref]

Genov, D. A.

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]

Giannini, V.

M. Rahmani, D. YuanLei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12, 2101–2106 (2012).
[Crossref] [PubMed]

Giessen, H.

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

Giessen, Ha.

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

Ginzburg, P.

P. Ginzburg, F. J. Rodríguez-Fortuno, A. Martinez, and A. V. Zayats, “Analogue of the quantum Hanle effect and polarization conversion in non-Hermitian plasmonic metamaterials,” Nano Lett. 12, 6309–6314 (2012).
[Crossref] [PubMed]

Giovannetti, G.

G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den Brink, and P. J. Kelly, “Doping graphene with metal contacts,” Phys. Rev. Lett. 101, 026803 (2008).
[Crossref] [PubMed]

Guinea, F.

A. Yu. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).
[Crossref]

Han, D. Z.

Hao, F.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Harris, S. E.

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

Hirscher, M.

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

Hong, M.

M. Rahmani, D. YuanLei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12, 2101–2106 (2012).
[Crossref] [PubMed]

Hu, T.

Huang, Z. R.

H. J. Li, L. L. Wang, J. Q. Liu, Z. R. Huang, B. Sun, and X. Zhai, “Investigation of the graphene based planar plasmonic filters,” Appl. Phys. Lett. 103, 211104 (2013).
[Crossref]

Jiang, X. Q.

Karpan, V. M.

G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den Brink, and P. J. Kelly, “Doping graphene with metal contacts,” Phys. Rev. Lett. 101, 026803 (2008).
[Crossref] [PubMed]

Kästel, J.

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

Keilmann, F.

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. CastroNeto, 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]

Kelly, P. J.

G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den Brink, and P. J. Kelly, “Doping graphene with metal contacts,” Phys. Rev. Lett. 101, 026803 (2008).
[Crossref] [PubMed]

Khomyakov, P. A.

G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den Brink, and P. J. Kelly, “Doping graphene with metal contacts,” Phys. Rev. Lett. 101, 026803 (2008).
[Crossref] [PubMed]

Kildishev, A. V.

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14, 78–82 (2014).
[Crossref]

Kinaret, J. M.

W. H. Wang, S. P. Apell, and J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86, 125450 (2012).
[Crossref]

Langguth, L.

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

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

Lau, C. 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. CastroNeto, 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]

Li, H. J.

H. J. Li, L. L. Wang, J. Q. Liu, Z. R. Huang, B. Sun, and X. Zhai, “Investigation of the graphene based planar plasmonic filters,” Appl. Phys. Lett. 103, 211104 (2013).
[Crossref]

Li, T.

Li, X. S.

H. Yan, Z.Q. Li, X. S. Li, W. J. Zhu, P. Avouris, and F. N. Xia, “Infrared spectroscopy of tunable Dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012).
[Crossref] [PubMed]

Li, Y. B.

Li, Z. Q

H. Yan, F. N. Xia, Z. Q Li, and P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[Crossref]

Li, Z.Q.

H. Yan, Z.Q. Li, X. S. Li, W. J. Zhu, P. Avouris, and F. N. Xia, “Infrared spectroscopy of tunable Dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012).
[Crossref] [PubMed]

Liew, T. Y. F.

M. Rahmani, D. YuanLei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12, 2101–2106 (2012).
[Crossref] [PubMed]

Liu, H.

Liu, J. Q.

H. J. Li, L. L. Wang, J. Q. Liu, Z. R. Huang, B. Sun, and X. Zhai, “Investigation of the graphene based planar plasmonic filters,” Appl. Phys. Lett. 103, 211104 (2013).
[Crossref]

Liu, M.

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]

Liu, N.

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

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

Liu, X. H.

Lukiyanchuk, B.

M. Rahmani, D. YuanLei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12, 2101–2106 (2012).
[Crossref] [PubMed]

Maier, S. A.

M. Rahmani, D. YuanLei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12, 2101–2106 (2012).
[Crossref] [PubMed]

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Martinez, A.

P. Ginzburg, F. J. Rodríguez-Fortuno, A. Martinez, and A. V. Zayats, “Analogue of the quantum Hanle effect and polarization conversion in non-Hermitian plasmonic metamaterials,” Nano Lett. 12, 6309–6314 (2012).
[Crossref] [PubMed]

Martín-Moreno, L.

M. Tymchenko, A. Y. Nikitin, and L. Martín-Moreno, “Faraday rotation due to excitation of magnetoplasmons in graphene microribbons,” ACS Nano 7, 9780–9787 (2013).
[Crossref] [PubMed]

A. Yu. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).
[Crossref]

McLeod, A. S.

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. CastroNeto, 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]

Mesch, M.

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

Mikhailov, S. A.

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 86, 016803 (2007).
[Crossref]

Moshchalkov, V. V.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Nikitin, A. Y.

M. Tymchenko, A. Y. Nikitin, and L. Martín-Moreno, “Faraday rotation due to excitation of magnetoplasmons in graphene microribbons,” ACS Nano 7, 9780–9787 (2013).
[Crossref] [PubMed]

Nikitin, A. Yu.

A. Yu. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).
[Crossref]

Nordlander, P.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Pei, C. Y.

Pereira, V.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday Effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011).
[Crossref]

Peres, N. M. R.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday Effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011).
[Crossref]

Pfau, T.

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

Rahmani, M.

M. Rahmani, D. YuanLei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12, 2101–2106 (2012).
[Crossref] [PubMed]

Ranjbar, M.

M. Rahmani, D. YuanLei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12, 2101–2106 (2012).
[Crossref] [PubMed]

Rodin, A. S.

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. CastroNeto, 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]

Rodríguez-Fortuno, F. J.

P. Ginzburg, F. J. Rodríguez-Fortuno, A. Martinez, and A. V. Zayats, “Analogue of the quantum Hanle effect and polarization conversion in non-Hermitian plasmonic metamaterials,” Nano Lett. 12, 6309–6314 (2012).
[Crossref] [PubMed]

Shalaev, V. M.

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14, 78–82 (2014).
[Crossref]

Shen, A.

Shi, X.

Sobhani, H.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Sonnefraud, Y.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Sönnichsen, C.

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

Sun, B.

H. J. Li, L. L. Wang, J. Q. Liu, Z. R. Huang, B. Sun, and X. Zhai, “Investigation of the graphene based planar plasmonic filters,” Appl. Phys. Lett. 103, 211104 (2013).
[Crossref]

Sun, Y.

Thiemens, M.

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. CastroNeto, 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]

Tian, J. G.

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]

Tymchenko, M.

M. Tymchenko, A. Y. Nikitin, and L. Martín-Moreno, “Faraday rotation due to excitation of magnetoplasmons in graphene microribbons,” ACS Nano 7, 9780–9787 (2013).
[Crossref] [PubMed]

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2007).
[Crossref]

van den Brink, J.

G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den Brink, and P. J. Kelly, “Doping graphene with metal contacts,” Phys. Rev. Lett. 101, 026803 (2008).
[Crossref] [PubMed]

Vassilevich, D. V.

I. V. Fialkovsky and D. V. Vassilevich, “Parity-odd effects and polarization rotation in graphene,” J. Phys. A: Math. Theor. 42, 442001 (2009).
[Crossref]

Verellen, N.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

Viana-Gomes, J.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday Effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011).
[Crossref]

Wagner, M.

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. CastroNeto, 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]

Wang, L. L.

H. J. Li, L. L. Wang, J. Q. Liu, Z. R. Huang, B. Sun, and X. Zhai, “Investigation of the graphene based planar plasmonic filters,” Appl. Phys. Lett. 103, 211104 (2013).
[Crossref]

Wang, S. M.

Wang, W. H.

W. H. Wang, S. P. Apell, and J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86, 125450 (2012).
[Crossref]

Wang, Y.

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]

Weiss, T.

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

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

Xia, F. N.

H. Yan, Z.Q. Li, X. S. Li, W. J. Zhu, P. Avouris, and F. N. Xia, “Infrared spectroscopy of tunable Dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012).
[Crossref] [PubMed]

H. Yan, F. N. Xia, Z. Q Li, and P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[Crossref]

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, 203112 (2013).
[Crossref]

Xu, M. X.

Yan, H.

H. Yan, Z.Q. Li, X. S. Li, W. J. Zhu, P. Avouris, and F. N. Xia, “Infrared spectroscopy of tunable Dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012).
[Crossref] [PubMed]

H. Yan, F. N. Xia, Z. Q Li, and P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[Crossref]

Yang, B.

Yang, J. Y.

Yang, L. Z.

Yu, H.

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, 203112 (2013).
[Crossref]

Yu, Z. F.

YuanLei, D.

M. Rahmani, D. YuanLei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12, 2101–2106 (2012).
[Crossref] [PubMed]

Zayats, A. V.

P. Ginzburg, F. J. Rodríguez-Fortuno, A. Martinez, and A. V. Zayats, “Analogue of the quantum Hanle effect and polarization conversion in non-Hermitian plasmonic metamaterials,” Nano Lett. 12, 6309–6314 (2012).
[Crossref] [PubMed]

Zhai, X.

H. J. Li, L. L. Wang, J. Q. Liu, Z. R. Huang, B. Sun, and X. Zhai, “Investigation of the graphene based planar plasmonic filters,” Appl. Phys. Lett. 103, 211104 (2013).
[Crossref]

Zhang, L. M.

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. CastroNeto, 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]

Zhang, S.

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]

Zhang, X.

Zhao, Z.

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. CastroNeto, 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]

Zhu, S. N.

Zhu, W. J.

H. Yan, Z.Q. Li, X. S. Li, W. J. Zhu, P. Avouris, and F. N. Xia, “Infrared spectroscopy of tunable Dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012).
[Crossref] [PubMed]

Zi, J.

Ziegler, K.

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 86, 016803 (2007).
[Crossref]

ACS Nano (1)

M. Tymchenko, A. Y. Nikitin, and L. Martín-Moreno, “Faraday rotation due to excitation of magnetoplasmons in graphene microribbons,” ACS Nano 7, 9780–9787 (2013).
[Crossref] [PubMed]

ACS Photonics (1)

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

Appl. Phys. Lett. (2)

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]

H. J. Li, L. L. Wang, J. Q. Liu, Z. R. Huang, B. Sun, and X. Zhai, “Investigation of the graphene based planar plasmonic filters,” Appl. Phys. Lett. 103, 211104 (2013).
[Crossref]

J. Phys. A: Math. Theor. (1)

I. V. Fialkovsky and D. V. Vassilevich, “Parity-odd effects and polarization rotation in graphene,” J. Phys. A: Math. Theor. 42, 442001 (2009).
[Crossref]

Nano Lett. (6)

P. Ginzburg, F. J. Rodríguez-Fortuno, A. Martinez, and A. V. Zayats, “Analogue of the quantum Hanle effect and polarization conversion in non-Hermitian plasmonic metamaterials,” Nano Lett. 12, 6309–6314 (2012).
[Crossref] [PubMed]

M. Rahmani, D. YuanLei, V. Giannini, B. Lukiyanchuk, M. Ranjbar, T. Y. F. Liew, M. Hong, and S. A. Maier, “Subgroup decomposition of plasmonic resonances in hybrid oligomers: modeling the resonance lineshape,” Nano Lett. 12, 2101–2106 (2012).
[Crossref] [PubMed]

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

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. V. Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009).
[Crossref] [PubMed]

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of Fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14, 78–82 (2014).
[Crossref]

H. Yan, Z.Q. Li, X. S. Li, W. J. Zhu, P. Avouris, and F. N. Xia, “Infrared spectroscopy of tunable Dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012).
[Crossref] [PubMed]

Nat. Materials (1)

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

Nature (1)

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. CastroNeto, 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]

New J. Phys. (1)

H. Yan, F. N. Xia, Z. Q Li, and P. Avouris, “Plasmonics of coupled graphene micro-structures,” New J. Phys. 14, 125001 (2012).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (3)

A. Yu. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).
[Crossref]

W. H. Wang, S. P. Apell, and J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86, 125450 (2012).
[Crossref]

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday Effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011).
[Crossref]

Phys. Rev. Lett. (3)

G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den Brink, and P. J. Kelly, “Doping graphene with metal contacts,” Phys. Rev. Lett. 101, 026803 (2008).
[Crossref] [PubMed]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 86, 016803 (2007).
[Crossref]

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]

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[Crossref]

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[Crossref]

Other (1)

COMSOL 4.4, http://www.comsol.com/

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Figures (6)

Fig. 1
Fig. 1

Schematic of the metamolecule unit cell composed of graphene nanostrips on a glass substrate: the strip lengths are L1=64 nm and L2=48 nm, the widths are w1=20 nm and w2=12 nm, the separation between the nanostrips in x and y directions are s = 15 nm and d = 8 nm, respectively. The periodicity in x and y directions are px=py=120 nm. The electric field of incident light is along y direction. The static magnetic field B is perpendicular to the graphene plane (xy plane).

Fig. 2
Fig. 2

Spectra of the real part of permittivity components ((a),(c)) εxx and ((b),(d)) εxy of graphene in external magnetic field B= 0, 4, 8, and 10 T for ((a),(b)) Ef = 0.1 eV and ((c),(d)) 0.3 eV.

Fig. 3
Fig. 3

Transmission spectra of the array of graphene metamolecules for different external magnetic fields. The Fermi energy is Ef = 0.1 eV. The dips labeled as A0,4,8 and C0,4,8 and the peaks B0,4,8 are the wavelengths related to the Fano line-shape in the external magnetic field B=0, 4, 8 T, respectively. All other parameters are as in Fig. 1.

Fig. 4
Fig. 4

Electric field Ez distributions at 4 nm distance from graphene layer corresponding to the transmission spectral features labelled in Fig. 3 for the external magnetic field B =0, 4 and 8 T: (a)–(c) A0, B0, C0; (d)–(f) A4, B4, C4, (g)–(i) A8, B8, C8.

Fig. 5
Fig. 5

(a) Transmission spectra of graphene metamolecules for Ef = 0.3 eV. (b)–(c) The dependence of the PIT wavelength on the applied magnetic field for different Fermi energies. All other parameters are as in Fig. 1.

Fig. 6
Fig. 6

Transmission and Faraday rotation spectra for different magnetic fields, Fermi energies, and metamolecule parameters: (a) transmission and Faraday rotation spectra of symmetric metamolecules as in (d) for B=10 T and Ef = 0.2 eV; (b)–(c) Polarization rotation spectra for asymmetric metamolecules as in (e) and (f) with (b) Ef = 0.2 eV and (c) Ef = 0.6 eV, respectively. The separations between the nanostrips in x and y directions are s = 10 nm. (d)–(f) Electric field Ez distributions at the resonant wavelengths λ1, λ2, and λ3, respectively, marked in (a)–(c). The sign “+” and “−” denotes the charge distributions.

Equations (2)

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ε g = 1 + i ω t ε 0 ( σ x x σ x y 0 σ x y σ y y 0 0 0 σ d )
σ x x = σ y y = e 2 | E f | π 2 i ( ω + i / τ ) ( ω + i / τ ) 2 ω c 2 σ x y = σ y x = e 2 | E f | π 2 ω c ( ω + i / τ ) 2 ω c 2

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