Enhanced transmission modulation based on dielectric metasurfaces loaded with graphene

Christos Argyropoulos

doi:10.1364/OE.23.023787

Enhanced transmission modulation based on dielectric metasurfaces loaded with graphene

Christos Argyropoulos

Optics Express
Vol. 23,
Issue 18,
pp. 23787-23797
(2015)
•https://doi.org/10.1364/OE.23.023787

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Christos Argyropoulos, "Enhanced transmission modulation based on dielectric metasurfaces loaded with graphene," Opt. Express 23, 23787-23797 (2015)

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Related Topics
Table of Contents Category
- Metamaterials
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Metamaterials (160.3918)
- Modulators (230.4110)
- Nanophotonics and photonic crystals (350.4238)
- Subwavelength structures, nanostructures (310.6628)

About this Article
History
- Original Manuscript: June 30, 2015
- Revised Manuscript: August 13, 2015
- Manuscript Accepted: August 29, 2015
- Published: September 2, 2015

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Open Access

Abstract

We present a hybrid graphene/dielectric metasurface design to achieve strong tunable and modulated transmission at near-infrared (near-IR) frequencies. The proposed device is constituted by periodic pairs of asymmetric silicon nanobars placed over a silica substrate. An one-atom-thick graphene sheet is positioned over the all-dielectric metasurface. The in-plane electromagnetic fields are highly localized and enhanced with this metasurface due to its very low Ohmic losses at near-IR wavelengths. They strongly interact with graphene. Sharp Fano-type transmission spectrum is obtained at the resonant frequency of this hybrid configuration due to the cancelation of the electric and magnetic dipole responses at this frequency point. The properties of the graphene monolayer flake can be adjusted by tuning its Fermi energy or chemical potential, leading to different doping levels and, equivalently, material parameters. As a result, the Q-factor and the Fano-type resonant transmission spectrum of the proposed hybrid system can be efficiently tuned and controlled due to the strong light–graphene interaction. Higher than 60% modulation in the transmission coefficient is reported at near-IR frequencies. The proposed hybrid graphene/dielectric nanodevice has compact footprint, fast speed, and can be easily integrated to the current CMOS technology. These features would have promising applications to near-IR tunable filters, faster optical interconnects, efficient sensors, switches, and amplitude modulators.

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2015 (6)

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2014 (10)

L. Yang, T. Hu, A. Shen, C. Pei, B. Yang, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Ultracompact optical modulator based on graphene-silica metamaterial,” Opt. Lett. 39(7), 1909–1912 (2014).
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J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Strong field enhancement and light-matter interactions with all-dielectric metamaterials based on split bar resonators,” Opt. Express 22(25), 30889–30898 (2014).
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C. Qiu, W. Gao, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14(12), 6811–6815 (2014).
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[Crossref]

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[Crossref]

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Y. Yao, R. Shankar, P. Rauter, Y. Song, J. Kong, M. Loncar, and F. Capasso, “High-responsivity mid-infrared graphene detectors with antenna-enhanced photocarrier generation and collection,” Nano Lett. 14(7), 3749–3754 (2014).
[Crossref] [PubMed]

2013 (10)

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(6), 2541–2547 (2013).
[Crossref] [PubMed]

S. H. Mousavi, I. Kholmanov, K. B. Alici, D. Purtseladze, N. Arju, K. Tatar, D. Y. Fozdar, J. W. Suk, Y. Hao, A. B. Khanikaev, R. S. Ruoff, and G. Shvets, “Inductive tuning of Fano-resonant metasurfaces using plasmonic response of graphene in the mid-infrared,” Nano Lett. 13(3), 1111–1117 (2013).
[Crossref] [PubMed]

B. Gholipour, J. Zhang, K. F. MacDonald, D. W. Hewak, and N. I. Zheludev, “An all-optical, non-volatile, bidirectional, phase-change meta-switch,” Adv. Mater. 25(22), 3050–3054 (2013).
[Crossref] [PubMed]

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[Crossref] [PubMed]

M. Gullans, D. E. Chang, F. H. L. Koppens, F. J. G. de Abajo, and M. D. Lukin, “Single-photon nonlinear optics with graphene plasmons,” Phys. Rev. Lett. 111(24), 247401 (2013).
[Crossref] [PubMed]

J. Gosciniak and D. T. H. Tan, “Theoretical investigation of graphene-based photonic modulators,” Sci. Rep. 3, 1897 (2013).
[Crossref] [PubMed]

A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21(7), 9144–9155 (2013).
[Crossref] [PubMed]

T. Cao, C. Wei, R. Simpson, L. Zhang, and M. Cryan, “Rapid phase transition of a phase-change metamaterial perfect absorber,” Opt. Mater. Express 3(8), 1101–1110 (2013).
[Crossref]

B. Z. Xu, C. Q. Gu, Z. Li, and Z. Y. Niu, “A novel structure for tunable terahertz absorber based on graphene,” Opt. Express 21(20), 23803–23811 (2013).
[Crossref] [PubMed]

J. Zhang, K. F. MacDonald, and N. I. Zheludev, “Near-infrared trapped mode magnetic resonance in an all-dielectric metamaterial,” Opt. Express 21(22), 26721–26728 (2013).
[Crossref] [PubMed]

2012 (14)

R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012).
[Crossref] [PubMed]

J. Kim, H. Son, D. J. Cho, B. Geng, W. Regan, S. Shi, K. Kim, A. Zettl, Y.-R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
[Crossref] [PubMed]

V. V. Khardikov, E. O. Iarko, and S. L. Prosvirnin, “A giant red shift and enhancement of the light confinement in a planar array of dielectric bars,” J. Opt. 14(3), 035103 (2012).
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V. V. Khardikov, E. O. Iarko, and S. L. Prosvirnin, “A giant red shift and enhancement of the light confinement in a planar array of dielectric bars,” J. Opt. 14(3), 035103 (2012).
[Crossref]

Pruneri, V.

R. Yu, V. Pruneri, and F. J. G. de Abajo, “Resonant visible light modulation with graphene,” ACS Photonics 2(4), 550–558 (2015).
[Crossref]

Purtseladze, D.

Qin, S.

Qing, Q.

Qiu, C.

Rana, F.

Rauter, P.

Regan, W.

Rockstuhl, C.

R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012).
[Crossref] [PubMed]

Rodin, A. S.

Romagnoli, M.

V. Sorianello, M. Midrio, and M. Romagnoli, “Design optimization of single and double layer Graphene phase modulators in SOI,” Opt. Express 23(5), 6478–6490 (2015).
[Crossref] [PubMed]

Ruoff, R. S.

Sagade, A. A.

Salzberg, C. D.

C. D. Salzberg and J. J. Villa, “Infrared refractive indexes of silicon, germanium and modified selenium glass,” J. Opt. Soc. Am. 47(3), 244–246 (1957).
[Crossref]

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Savchenko, A. K.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
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Schlather, A.

Segalman, R. A.

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M. Lapine, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Magnetoelastic metamaterials,” Nat. Mater. 11(1), 30–33 (2012).
[Crossref] [PubMed]

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Shankar, R.

Shen, A.

Shen, Y. R.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

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Shen, Z. X.

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Shvets, G.

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T. Cao, C. Wei, R. Simpson, L. Zhang, and M. Cryan, “Rapid phase transition of a phase-change metamaterial perfect absorber,” Opt. Mater. Express 3(8), 1101–1110 (2013).
[Crossref]

Smith, D. R.

C. Argyropoulos, C. Ciracì, and D. R. Smith, “Enhanced optical bistability with film-coupled plasmonic nanocubes,” Appl. Phys. Lett. 104(6), 063108 (2014).
[Crossref]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Son, H.

Song, Y.

Sorianello, V.

V. Sorianello, M. Midrio, and M. Romagnoli, “Design optimization of single and double layer Graphene phase modulators in SOI,” Opt. Express 23(5), 6478–6490 (2015).
[Crossref] [PubMed]

Spasenovic, M.

Spencer, M. G.

Stauber, T.

Stormer, H. L.

Strait, J.

Strikwerda, A. C.

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

Suk, J. W.

Swan, A. K.

Tan, D. T. H.

J. Gosciniak and D. T. H. Tan, “Theoretical investigation of graphene-based photonic modulators,” Sci. Rep. 3, 1897 (2013).
[Crossref] [PubMed]

Tao, H.

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

Tao, N.

Tatar, K.

Thiemens, M.

Thongrattanasiri, S.

Tian, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Town, G. E.

A. Locatelli, G. E. Town, and C. De Angelis, “Graphene-based terahertz waveguide modulators,” IEEE Trans. THz Sci. Tech. 5(3), 351–357 (2015).
[Crossref]

Tulevski, G.

Tutuc, E.

Tymchenko, M.

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Vajtai, R.

Valdes-Garcia, A.

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[Crossref] [PubMed]

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Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5, 5753 (2014).
[Crossref] [PubMed]

Veksler, D.

Villa, J. J.

C. D. Salzberg and J. J. Villa, “Infrared refractive indexes of silicon, germanium and modified selenium glass,” J. Opt. Soc. Am. 47(3), 244–246 (1957).
[Crossref]

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A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[Crossref] [PubMed]

Wagner, M.

Wang, F.

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Wang, Q.-J.

W. Huang, X.-G. Yin, C.-P. Huang, Q.-J. Wang, T.-F. Miao, and Y.-Y. Zhu, “Optical switching of a metamaterial by temperature controlling,” Appl. Phys. Lett. 96(26), 261908 (2010).
[Crossref]

Wang, X.

Wang, Y.

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

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T. Cao, C. Wei, R. Simpson, L. Zhang, and M. Cryan, “Rapid phase transition of a phase-change metamaterial perfect absorber,” Opt. Mater. Express 3(8), 1101–1110 (2013).
[Crossref]

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Wu, C.

Wu, Y.

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F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[Crossref] [PubMed]

Xia, J.

Xiao, S.

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B. Z. Xu, C. Q. Gu, Z. Li, and Z. Y. Niu, “A novel structure for tunable terahertz absorber based on graphene,” Opt. Express 21(20), 23803–23811 (2013).
[Crossref] [PubMed]

Xu, Q.

Yan, H.

Yang, B.

Yang, J.

Yang, L.

Yang, Y.

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5, 5753 (2014).
[Crossref] [PubMed]

Yao, Y.

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Yin, X.-G.

W. Huang, X.-G. Yin, C.-P. Huang, Q.-J. Wang, T.-F. Miao, and Y.-Y. Zhu, “Optical switching of a metamaterial by temperature controlling,” Appl. Phys. Lett. 96(26), 261908 (2010).
[Crossref]

Yu, H.

Yu, L.

J. Zheng, L. Yu, S. He, and D. Dai, “Tunable pattern-free graphene nanoplasmonic waveguides on trenched silicon substrate,” Sci. Rep. 5, 7987 (2015).
[Crossref] [PubMed]

Yu, R.

R. Yu, V. Pruneri, and F. J. G. de Abajo, “Resonant visible light modulation with graphene,” ACS Photonics 2(4), 550–558 (2015).
[Crossref]

Yuan, X.

Yvind, K.

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zettl, A.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Zhang, J.

J. Zhang, K. F. MacDonald, and N. I. Zheludev, “Near-infrared trapped mode magnetic resonance in an all-dielectric metamaterial,” Opt. Express 21(22), 26721–26728 (2013).
[Crossref] [PubMed]

Zhang, L.

T. Cao, C. Wei, R. Simpson, L. Zhang, and M. Cryan, “Rapid phase transition of a phase-change metamaterial perfect absorber,” Opt. Mater. Express 3(8), 1101–1110 (2013).
[Crossref]

Zhang, L. M.

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

Zhang, Y.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Zhao, Z.

Zheludev, N. I.

J. Zhang, K. F. MacDonald, and N. I. Zheludev, “Near-infrared trapped mode magnetic resonance in an all-dielectric metamaterial,” Opt. Express 21(22), 26721–26728 (2013).
[Crossref] [PubMed]

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012).
[Crossref] [PubMed]

Zheng, J.

J. Zheng, L. Yu, S. He, and D. Dai, “Tunable pattern-free graphene nanoplasmonic waveguides on trenched silicon substrate,” Sci. Rep. 5, 7987 (2015).
[Crossref] [PubMed]

Zhu, W.

Zhu, X.

Zhu, Y.-Y.

W. Huang, X.-G. Yin, C.-P. Huang, Q.-J. Wang, T.-F. Miao, and Y.-Y. Zhu, “Optical switching of a metamaterial by temperature controlling,” Appl. Phys. Lett. 96(26), 261908 (2010).
[Crossref]

Zhu, Z.

ACS Nano (2)

ACS Photonics (1)

R. Yu, V. Pruneri, and F. J. G. de Abajo, “Resonant visible light modulation with graphene,” ACS Photonics 2(4), 550–558 (2015).
[Crossref]

Adv. Mater. (1)

Appl. Phys. Lett. (5)

C. Argyropoulos, C. Ciracì, and D. R. Smith, “Enhanced optical bistability with film-coupled plasmonic nanocubes,” Appl. Phys. Lett. 104(6), 063108 (2014).
[Crossref]

W. Huang, X.-G. Yin, C.-P. Huang, Q.-J. Wang, T.-F. Miao, and Y.-Y. Zhu, “Optical switching of a metamaterial by temperature controlling,” Appl. Phys. Lett. 96(26), 261908 (2010).
[Crossref]

IEEE Trans. THz Sci. Tech. (1)

A. Locatelli, G. E. Town, and C. De Angelis, “Graphene-based terahertz waveguide modulators,” IEEE Trans. THz Sci. Tech. 5(3), 351–357 (2015).
[Crossref]

J. Am. Chem. Soc. (1)

J. Opt. (1)

V. V. Khardikov, E. O. Iarko, and S. L. Prosvirnin, “A giant red shift and enhancement of the light confinement in a planar array of dielectric bars,” J. Opt. 14(3), 035103 (2012).
[Crossref]

J. Opt. Soc. Am. (2)

C. D. Salzberg and J. J. Villa, “Infrared refractive indexes of silicon, germanium and modified selenium glass,” J. Opt. Soc. Am. 47(3), 244–246 (1957).
[Crossref]

I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205–1208 (1965).
[Crossref]

Nano Lett. (10)

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[Crossref] [PubMed]

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Nat. Commun. (2)

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5, 5753 (2014).
[Crossref] [PubMed]

Nat. Mater. (3)

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012).
[Crossref] [PubMed]

M. Lapine, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Magnetoelastic metamaterials,” Nat. Mater. 11(1), 30–33 (2012).
[Crossref] [PubMed]

Nat. Nanotechnol. (3)

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[Crossref] [PubMed]

Nat. Photonics (1)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Nat. Phys. (1)

Nature (6)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Opt. Express (7)

V. Sorianello, M. Midrio, and M. Romagnoli, “Design optimization of single and double layer Graphene phase modulators in SOI,” Opt. Express 23(5), 6478–6490 (2015).
[Crossref] [PubMed]

J. Zhang, K. F. MacDonald, and N. I. Zheludev, “Near-infrared trapped mode magnetic resonance in an all-dielectric metamaterial,” Opt. Express 21(22), 26721–26728 (2013).
[Crossref] [PubMed]

R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012).
[Crossref] [PubMed]

B. Z. Xu, C. Q. Gu, Z. Li, and Z. Y. Niu, “A novel structure for tunable terahertz absorber based on graphene,” Opt. Express 21(20), 23803–23811 (2013).
[Crossref] [PubMed]

Opt. Lett. (1)

Opt. Mater. Express (1)

T. Cao, C. Wei, R. Simpson, L. Zhang, and M. Cryan, “Rapid phase transition of a phase-change metamaterial perfect absorber,” Opt. Mater. Express 3(8), 1101–1110 (2013).
[Crossref]

Phys. Rev. B (2)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Phys. Rev. Lett. (4)

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009).
[Crossref] [PubMed]

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref] [PubMed]

Sci. Rep. (3)

J. Gosciniak and D. T. H. Tan, “Theoretical investigation of graphene-based photonic modulators,” Sci. Rep. 3, 1897 (2013).
[Crossref] [PubMed]

J. Zheng, L. Yu, S. He, and D. Dai, “Tunable pattern-free graphene nanoplasmonic waveguides on trenched silicon substrate,” Sci. Rep. 5, 7987 (2015).
[Crossref] [PubMed]

Science (4)

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Other (1)

CST design studio2015, [ www.cst.com ].

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Fig. 1 Schematics of (a) the all-dielectric periodic metasurface and (b) the hybrid graphene/dielectric metasurface. The proposed structures are composed of a periodically arranged pair of asymmetric silicon nanobars placed over a silica substrate. Graphene is placed over the silicon nanobars.

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Fig. 2 (a) Fano resonance obtained in the transmission coefficient of the proposed all-dielectric metasurface shown in Fig. 1(a). (b) Corresponding simulated in-plane electric field (E_x) distribution monitored at the dip of transmission coefficient

(λ = 1.59 μ m)

. Enhanced in-plane electric fields are obtained and their antiparallel formation along the two asymmetric nanobars leads to the magnetic Fano resonance shown in caption (a).

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Fig. 3 (a) Real and (b) imaginary part of the complex permittivity of graphene as a function of the impinging radiation’s wavelength and the Fermi energy. As the Fermi energy or doping level increases, the loss in graphene [imaginary part of permittivity/caption (b)] rapidly decreases.

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Fig. 4 (a) Transmission coefficient versus incident radiation’s wavelength of the proposed hybrid graphene/dielectric metasurface shown in Fig. 1(b). The transmission excursion and Q-factor of the Fano resonance is increased and strongly modified for higher doping levels of graphene. (b) Computed percentage of the absolute value of the transmission coefficient difference versus the incident radiation’s wavelength. The properties of the proposed hybrid system change from heavily doped

(E_{F} = 0.75 e V)

to undoped

(E_{F} = 0 e V)

graphene. The amplitude of the transmission coefficient can be modulated by more than 60% at

λ = 1.59 μ m

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Equations (2)

Equations on this page are rendered with MathJax. Learn more.

ε_{g}^{r e a l} (E) = 1 + \frac{e^{2}}{8 π E ε_{0} g} \ln \frac{{(E + 2 | E_{F} |)}^{2} + Γ^{2}}{{(E - 2 | E_{F} |)}^{2} + Γ^{2}} - \frac{e^{2} | E_{F} |}{π ε_{0} g [E^{2} + {(1 / τ)}^{2}]},

ε_{g}^{i m a g} (E) = \frac{e^{2}}{4 E ε_{0} g} [1 + \frac{1}{π} (\tan^{- 1} \frac{E - 2 | E_{F} |}{Γ} - \tan^{- 1} \frac{E + 2 | E_{F} |}{Γ})] + \frac{e^{2} | E_{F} |}{π τ E ε_{0} g [E^{2} + {(1 / τ)}^{2}]},