Abstract

Integrating gate-tunable graphene with plasmonic nanostructures or metamaterials offers a great potential in achieving dynamic control of plasmonic response. While remarkable progress has been made in realizing efficient graphene-induced modulations of plasmon resonances, a full picture of graphene-plasmon interactions and the consequent deep understanding on graphene-enabled tuning mechanism remain largely unexplored. Here, we theoretically identify, for the first time, two distinct modulation effects that can coexist in graphene-based plasmonic nanostructure: graphene can influence the plasmon resonances by either acting as equivalent nanocircuit elements or effectively altering their excitation environment, leading to totally different tuning behaviors. A general dependency of tuning features on the graphene-induced impedance, irrespective of structure geometries, is established when graphene serves as nanocircuit elements. We demonstrate that these two modulation effects can be dynamically controlled by appropriately integrating graphene with plasmonic nanostructures, which provide an active window for efficient modulation of surface plasmons. Our findings may pave the way towards realizing dynamic control of plasmonic response, which holds great potential applications in graphene-based active nanoplasmonic devices.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

D. Li, W. Wang, H. Zhang, Y. Zhu, S. Zhang, Z. Zhang, X. Zhang, J. Yi, and W. Wei, “Graphene-induced modulation effects on magnetic plasmon in multilayer metal-dielectric-metal metamaterial,” Appl. Phys. Lett. 112, 131101 (2018).
[Crossref]

Y. Hajati, Z. Zanbouri, and M. Sabaeian, “Low-loss and high-performance mid-infrared plasmon-phonon in graphene-hexagonal boron nitride waveguide,” J. Opt. Soc. Am. B 35, 446–453 (2018).
[Crossref]

2017 (3)

P. Rodriguez-Lopez, W. J. M. Kort-Kamp, D. A. R. Dalvit, and L. M. Woods, “Casimir force phase transitions in the graphene family,” Nat. Commun. 8, 14699 (2017).
[Crossref] [PubMed]

M. Gurram, S. Omar, and B. J. van Wees, “Bias induced up to 100% spin-injection and detection polarizations in ferromagnet/bilayer-hbn/graphene/hbn heterostructures,” Nat. Commun. 8, 248 (2017).
[Crossref]

Z. Vafapour, Y. Hajati, M. Hajati, and H. Ghahraloud, “Graphene-based mid-infrared biosensor,” J. Opt. Soc. Am. B 34, 2586–2592 (2017).
[Crossref]

2016 (3)

2015 (5)

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]

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hbn system,” Nano Lett. 15, 3172–3180 (2015).
[Crossref] [PubMed]

M. M. Jadidi, A. B. Sushkov, R. L. Myers-Ward, A. K. Boyd, K. M. Daniels, D. K. Gaskill, M. S. Fuhrer, H. D. Drew, and T. E. Murphy, “Tunable terahertz hybrid metal-graphene plasmons,” Nano Lett. 15, 7099–7104 (2015).
[Crossref] [PubMed]

B. D. Thackray, P. A. Thomas, G. H. Auton, F. J. Rodriguez, O. P. Marshall, V. G. Kravets, and A. N. Grigorenko, “Super-narrow, extremely high quality collective plasmon resonances at telecom wavelengths and their application in a hybrid graphene-plasmonic modulator,” Nano Lett. 15, 3519–3523 (2015).
[Crossref] [PubMed]

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

2014 (4)

B. Zhao, J. M. Zhao, and Z. M. Zhang, “Enhancement of near-infrared absorption in graphene with metal gratings,” Appl. Phys. Lett. 105, 031905 (2014).
[Crossref]

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]

S. Tsoi, P. Dev, A. L. Friedman, R. Stine, J. T. Robinson, T. L. Reinecke, and P. E. Sheehan, “van der waals screening by single-layer graphene and molybdenum disulfide,” ACS Nano 8, 12410–12417 (2014).
[Crossref] [PubMed]

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref] [PubMed]

2013 (6)

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. Photon. 7, 394–399 (2013).
[Crossref]

F. Valmorra, G. Scalari, C. Maissen, W. Fu, C. Schoenenberger, J. W. Choi, H. G. Park, M. Beck, and J. Faist, “Low-bias active control of terahertz waves by coupling large-area cvd graphene to a terahertz metamaterial,” Nano Lett. 13, 3193–3198 (2013).
[Crossref] [PubMed]

L. Wang, I. Meric, P. Y. Huang, Q. Gao, Y. Gao, H. Tran, T. Taniguchi, K. Watanabe, L. M. Campos, D. A. Muller, J. Guo, P. Kim, J. Hone, K. L. Shepard, and C. R. Dean, “One-dimensional electrical contact to a two-dimensional material,” Science 342, 614–617 (2013).
[Crossref] [PubMed]

Y. Xiao, Y. Francescato, V. Giannini, M. Rahmani, T. R. Roschuk, A. M. Gilbertson, Y. Sonnefraud, C. Mattevi, M. Hong, L. F. Cohen, and S. A. Maier, “Probing the dielectric response of graphene via dual-band plasmonic nanoresonators,” Phys. Chem. Chem. Phys. 15, 5395–5399 (2013).
[Crossref] [PubMed]

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, 1257–1264 (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. Javier Garcia de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” Acs Nano 7, 2388–2395 (2013).
[Crossref] [PubMed]

2012 (5)

N. K. Emani, T.-F. Chung, X. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically tunable damping of plasmonic resonances with graphene,” Nano Lett. 12, 5202–5206 (2012).
[Crossref] [PubMed]

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12, 3808–3813 (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, 5598–5602 (2012).
[Crossref] [PubMed]

A. Ferreira and N. M. R. Peres, “Complete light absorption in graphene-metamaterial corrugated structures,” Phys. Rev. B 86, 205401 (2012).
[Crossref]

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12, 2773–2777 (2012).
[Crossref] [PubMed]

2011 (4)

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. Nanotech. 6, 630–634 (2011).
[Crossref]

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 106, 089901 (2011).
[Crossref]

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, 64–67 (2011).
[Crossref] [PubMed]

T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
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2010 (5)

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
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M. L. Brongersma and V. M. Shalaev, “The case for plasmonics,” Science 328, 440–441 (2010).
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D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
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N. Papasimakis, Z. Q. Luo, Z. X. Shen, F. De Angelis, E. Di Fabrizio, A. E. Nikolaenko, and N. I. Zheludev, “Graphene in a photonic metamaterial,” Opt. Express 18, 8353–8359 (2010).
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N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
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2009 (3)

E. G. Galkina, B. A. Ivanov, S. Savel’ev, V. A. Yampol’skii, and F. Nori, “Drastic change of the casimir force at the metal-insulator transition,” Phys. Rev. B 80, 125119 (2009).
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H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photon. 3, 148–151 (2009).
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2008 (10)

R. A. Pala, K. T. Shimizu, N. A. Melosh, and M. L. Brongersma, “A nonvolatile plasmonic switch employing photochromic molecules,” Nano Lett. 8, 1506–1510 (2008).
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F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320, 206–209 (2008).
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2007 (3)

N. Engheta, “Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
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2006 (2)

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
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H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
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2005 (3)

A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, “Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip au nanotriangles,” Phys. Rev. B 72, 165409 (2005).
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2004 (2)

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).
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2002 (1)

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2000 (1)

B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: Influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
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1997 (1)

M. Schubert, B. Rheinlander, E. Franke, H. Neumann, J. Hahn, M. Roder, and F. Richter, “Anisotropy of boron nitride thin-film reflectivity spectra by generalized ellipsometry,” Appl. Phys. Lett. 70, 1819–1821 (1997).
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1907 (1)

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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. Javier Garcia de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” Acs Nano 7, 2388–2395 (2013).
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Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12, 3808–3813 (2012).
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N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 106, 089901 (2011).
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M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12, 2773–2777 (2012).
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Atwater, H. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: A metal-oxide-si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
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B. Auguie and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902 (2008).
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B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: Influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
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H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photon. 3, 148–151 (2009).
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H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
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A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hbn system,” Nano Lett. 15, 3172–3180 (2015).
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H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photon. 3, 148–151 (2009).
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J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
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B. Auguie and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902 (2008).
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Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
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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. Nanotech. 6, 630–634 (2011).
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F. Valmorra, G. Scalari, C. Maissen, W. Fu, C. Schoenenberger, J. W. Choi, H. G. Park, M. Beck, and J. Faist, “Low-bias active control of terahertz waves by coupling large-area cvd graphene to a terahertz metamaterial,” Nano Lett. 13, 3193–3198 (2013).
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Bell, R. R.

Bell, S. E.

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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).
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N. K. Emani, T.-F. Chung, X. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically tunable damping of plasmonic resonances with graphene,” Nano Lett. 12, 5202–5206 (2012).
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M. M. Jadidi, A. B. Sushkov, R. L. Myers-Ward, A. K. Boyd, K. M. Daniels, D. K. Gaskill, M. S. Fuhrer, H. D. Drew, and T. E. Murphy, “Tunable terahertz hybrid metal-graphene plasmons,” Nano Lett. 15, 7099–7104 (2015).
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D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
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J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
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M. L. Brongersma and V. M. Shalaev, “The case for plasmonics,” Science 328, 440–441 (2010).
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R. A. Pala, K. T. Shimizu, N. A. Melosh, and M. L. Brongersma, “A nonvolatile plasmonic switch employing photochromic molecules,” Nano Lett. 8, 1506–1510 (2008).
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Brueck, S. R. J.

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94, 037402 (2005).
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S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95, 137404 (2005).
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J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
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L. Wang, I. Meric, P. Y. Huang, Q. Gao, Y. Gao, H. Tran, T. Taniguchi, K. Watanabe, L. M. Campos, D. A. Muller, J. Guo, P. Kim, J. Hone, K. L. Shepard, and C. R. Dean, “One-dimensional electrical contact to a two-dimensional material,” Science 342, 614–617 (2013).
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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, 1257–1264 (2013).
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A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97, 187401 (2006).
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H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photon. 3, 148–151 (2009).
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H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
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D. Wu, Y. Liu, R. Li, L. Chen, R. Ma, C. Liu, and H. Ye, “Infrared perfect ultra-narrow band absorber as plasmonic sensor,” Nanoscale Res. Lett. 11, 483 (2016).
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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).
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N. K. Emani, T.-F. Chung, X. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically tunable damping of plasmonic resonances with graphene,” Nano Lett. 12, 5202–5206 (2012).
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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).
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N. K. Emani, T.-F. Chung, X. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically tunable damping of plasmonic resonances with graphene,” Nano Lett. 12, 5202–5206 (2012).
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H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photon. 3, 148–151 (2009).
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F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320, 206–209 (2008).
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A. Sundaramurthy, K. B. Crozier, G. S. Kino, D. P. Fromm, P. J. Schuck, and W. E. Moerner, “Field enhancement and gap-dependent resonance in a system of two opposing tip-to-tip au nanotriangles,” Phys. Rev. B 72, 165409 (2005).
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L. Wang, I. Meric, P. Y. Huang, Q. Gao, Y. Gao, H. Tran, T. Taniguchi, K. Watanabe, L. M. Campos, D. A. Muller, J. Guo, P. Kim, J. Hone, K. L. Shepard, and C. R. Dean, “One-dimensional electrical contact to a two-dimensional material,” Science 342, 614–617 (2013).
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M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12, 2773–2777 (2012).
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J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: A metal-oxide-si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
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J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: A metal-oxide-si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
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B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: Influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000).
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M. M. Jadidi, A. B. Sushkov, R. L. Myers-Ward, A. K. Boyd, K. M. Daniels, D. K. Gaskill, M. S. Fuhrer, H. D. Drew, and T. E. Murphy, “Tunable terahertz hybrid metal-graphene plasmons,” Nano Lett. 15, 7099–7104 (2015).
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T. J. Echtermeyer, L. Britnell, P. K. Jasnos, A. Lombardo, R. V. Gorbachev, A. N. Grigorenko, A. K. Geim, A. C. Ferrari, and K. S. Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
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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).
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N. K. Emani, T.-F. Chung, X. Ni, A. V. Kildishev, Y. P. Chen, and A. Boltasseva, “Electrically tunable damping of plasmonic resonances with graphene,” Nano Lett. 12, 5202–5206 (2012).
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Figures (4)

Fig. 1
Fig. 1 (a) Schematic of a graphene sheet connecting to a nanostructure with length l and width d. It introduces an additional impedance ZG with a voltage UG across the graphene sheet. (b) Graphene-induced reactance XG (solid) and resistance RG (dash) as a function of graphene Fermi energy at LSP peak wavelength of 2400 nm.
Fig. 2
Fig. 2 (a) 3-dimentional schematic illustration of the test plasmonic nanostructure with a monolayer graphene embedded in the first layer of hBN. (b) The simulated absorptance spectrum for the test structure in absence of graphene with the bar-pair period p = 2400 nm, illustrating the first-order LSP centred at λ0 with a super narrow spectral width of 3 nm. (c) The simulated spatial distribution of the electric field amplitude |E| at the resonance wavelength of λ0.
Fig. 3
Fig. 3 (a) The LSP peak wavelength as a function of graphene Fermi energy obtained by numerical simulations (blue) and nanocircuit model (red). (b) The real part of the 2D graphene sheet conductivity with a vertical green line denoting the graphene Fermi energy of 2 |Ef| = ħω0 ≈ 0.52 eV. (c) The simulated (solid blue) and modelled (solid red) absorptance αR as a function of graphene Fermi energy obtained at the peak wavelength λR. The dashed blue line represents the simulated αR ≈ 0.84 in absence of graphene. (d) The simulated spectral widths Δλ (solid blue) of the absorptance spectra together with the graphene-induced resistance RG(Ef, λR) (red). The dashed blue line represents the simulated Δλ in absence of graphene. (e) Equivalent nanocircuit for the test hybrid nanostructure. (f) Illustration of three types of optical transition processes (I, II and III), corresponding to three modulating regions separated by the shaded area in (a–d).
Fig. 4
Fig. 4 (a) Schematic of the nanostructure with graphene on top, and the distribution of the electric field at LSP resonance. The simulated (blue) and fitted (red) results of graphene-induced LSP wavelength shift (b), the corresponding absorptance (c) at LSP peak wavelength and spectral width (d) as a function of 2|Ef|. The purple lines in (b) and (c) give λR and αR obtained by nanocircuit model. (e) The real (blue) and imaginary (red) part of graphene permittivity. The blue dashed lines in (c) and (d) represent the absorptance and spectral width of LSP resonances in the bare nanostructure.

Equations (10)

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× H = J T = σ G E i ω 0 E .
Z G = R G i X G = U G I T = t G | E | l d | J T | = t G l d ( σ G i ω 0 ) .
G = Gr + i Gi = 1 + i σ G ω 0 ,
Z G = ξ i ( Gr + i Gi ) .
λ m sup / sub = p m [ n ± sin ( θ ) ] .
σ Gs = σ intra + σ inter = σ 1 + i σ 2
σ intra = 2 i e 2 k B T π 2 ( ω + i τ 1 ) ln [ 2 cosh ( E f 2 k B T ) ]
σ inter = e 2 4 [ 1 2 + 1 π arctan ( ω 2 E f 2 k B T ) i 2 π ln ( ω + 2 E f ) 2 ( ω 2 E f ) 2 + ( 2 k B T ) 2 ] .
λ R = Ap f Gr ( E f , λ 0 ) + ( 1 f ) air .
α R = α 1 e β Gi h + ( 1 α 1 e β Gi h ) κ .

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