Abstract

We demonstrate the possibility of cloaking three-dimensional objects at multi-frequencies in the far-infrared part of the spectrum. The proposed cloaking mechanism exploits graphene layers wrapped around the object to be concealed. Graphene layers are doped via a variable external voltage difference permitting continuous tuning of the cloaking frequencies. Particularly, two configurations are investigated: (i) Only one graphene layer is used to suppress the scattering from a dielectric sphere. (ii) Several of these layers biased at different gate voltages are used to achieve a multi-frequency cloak. These frequencies can be set independently. The proposed cloak’s functionality is verified by near- and far-field computations. By considering geometry and material parameters that are realizable by practical experiments, we contribute to the development of graphene based plasmonic applications that may find use in disruptive photonic technologies.

© 2013 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
  6. I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett.102(21), 213901 (2009).
    [CrossRef] [PubMed]
  7. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  8. A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.72(1), 016623 (2005).
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    [CrossRef] [PubMed]
  14. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81(1), 109–162 (2009).
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  15. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308–1308 (2008).
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    [CrossRef] [PubMed]
  27. P.-Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano5(7), 5855–5863 (2011).
    [CrossRef] [PubMed]
  28. S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett.108(4), 047401 (2012).
    [CrossRef] [PubMed]
  29. A. Yu. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84(19), 195446 (2011).
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  33. A. Alù and N. Engheta, “Cloaked near-field scanning optical microscope tip for noninvasive near-field imaging,” Phys. Rev. Lett.105(26), 263906 (2010).
    [CrossRef] [PubMed]
  34. G. W. Hanson, “Dyadic Green’s functions and guided surface waves on graphene,” J. Appl. Phys.103, 064302 (2006).
    [CrossRef]
  35. P. Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater.24(44), OP281–OP304 (2012).
    [CrossRef] [PubMed]
  36. P. Y. Chen and A. Alù, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B84(20), 205110 (2011).
    [CrossRef]
  37. A. Alù, “Mantle cloak: Invisibility induced by a surface,” Phys. Rev. B80(24), 245115 (2009).
    [CrossRef]
  38. F. Monticone, C. Argyropoulos, and A. Alù, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci Rep2, 912–918 (2012).
    [CrossRef] [PubMed]

2012 (11)

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alù, “Experimental verification of three dimensional plasmonic cloaking in free-space,” New J. Phys.14(1), 013054 (2012).
[CrossRef]

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature490(7419), 192–200 (2012).
[CrossRef] [PubMed]

J. W. Ko, S.-W. Kim, J. Hong, K. Kang, and C. B. Park, “Synthesis of graphene-wrapped CuO hybrid materials by CO2 mineralization,” Green Chem.14(9), 2391–2394 (2012).
[CrossRef]

J. S. Lee, K. H. You, and C. B. Park, “Highly photoactive, low bandgap TiO2 nanoparticles wrapped by graphene,” Adv. Mater.24(8), 1084–1088 (2012).
[CrossRef] [PubMed]

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater.24(44), OP281–OP304 (2012).
[CrossRef] [PubMed]

F. Monticone, C. Argyropoulos, and A. Alù, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci Rep2, 912–918 (2012).
[CrossRef] [PubMed]

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett.108(4), 047401 (2012).
[CrossRef] [PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6(1), 431–440 (2012).
[CrossRef] [PubMed]

M. Farhat, S. Mühlig, C. Rockstuhl, and F. Lederer, “Scattering cancellation of the magnetic dipole field from macroscopic spheres,” Opt. Express20(13), 13896–13906 (2012).
[CrossRef] [PubMed]

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett.37(13), 2730–2732 (2012).
[CrossRef] [PubMed]

R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express20(27), 28017–28024 (2012).
[CrossRef] [PubMed]

2011 (9)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

P.-Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano5(7), 5855–5863 (2011).
[CrossRef] [PubMed]

A. Yu. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84(19), 195446 (2011).
[CrossRef]

S. Mühlig, M. Farhat, C. Rockstuhl, and F. Lederer, “Cloaking dielectric spherical objects by a shell of metallic nanoparticles,” Phys. Rev. B83(19), 195116 (2011).
[CrossRef]

K. Y. Shin, J.-Y. Hong, and J. Jang, “Micropatterning of graphene sheets by inkjet printing and its wideband dipole-antenna application,” Adv. Mater.23(18), 2113–2118 (2011).
[CrossRef] [PubMed]

P. Y. Chen and A. Alù, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B84(20), 205110 (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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

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

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

2010 (3)

T. Mueller, F. N. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics4(5), 297–301 (2010).
[CrossRef]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Cloaked near-field scanning optical microscope tip for noninvasive near-field imaging,” Phys. Rev. Lett.105(26), 263906 (2010).
[CrossRef] [PubMed]

2009 (4)

A. Alù, “Mantle cloak: Invisibility induced by a surface,” Phys. Rev. B80(24), 245115 (2009).
[CrossRef]

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80(24), 245435 (2009).
[CrossRef]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett.102(21), 213901 (2009).
[CrossRef] [PubMed]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81(1), 109–162 (2009).
[CrossRef]

2008 (2)

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308–1308 (2008).
[CrossRef] [PubMed]

M. Farhat, S. Guenneau, A. B. Movchan, and S. Enoch, “Achieving invisibility over a finite range of frequencies,” Opt. Express16(8), 5656–5661 (2008).
[CrossRef] [PubMed]

2007 (3)

A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: Mechanism, robustness, and physical insights,” Opt. Express15(6), 3318–3332 (2007).
[CrossRef] [PubMed]

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75(20), 205418 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007).
[CrossRef]

2006 (4)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

G. W. Hanson, “Dyadic Green’s functions and guided surface waves on graphene,” J. Appl. Phys.103, 064302 (2006).
[CrossRef]

2005 (1)

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.72(1), 016623 (2005).
[CrossRef] [PubMed]

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,” Science306(5696), 666–669 (2004).
[CrossRef] [PubMed]

Alaee, R.

Alù, A.

F. Monticone, C. Argyropoulos, and A. Alù, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci Rep2, 912–918 (2012).
[CrossRef] [PubMed]

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater.24(44), OP281–OP304 (2012).
[CrossRef] [PubMed]

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alù, “Experimental verification of three dimensional plasmonic cloaking in free-space,” New J. Phys.14(1), 013054 (2012).
[CrossRef]

P. Y. Chen and A. Alù, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B84(20), 205110 (2011).
[CrossRef]

P.-Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano5(7), 5855–5863 (2011).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Cloaked near-field scanning optical microscope tip for noninvasive near-field imaging,” Phys. Rev. Lett.105(26), 263906 (2010).
[CrossRef] [PubMed]

A. Alù, “Mantle cloak: Invisibility induced by a surface,” Phys. Rev. B80(24), 245115 (2009).
[CrossRef]

A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: Mechanism, robustness, and physical insights,” Opt. Express15(6), 3318–3332 (2007).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.72(1), 016623 (2005).
[CrossRef] [PubMed]

Argyropoulos, C.

F. Monticone, C. Argyropoulos, and A. Alù, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci Rep2, 912–918 (2012).
[CrossRef] [PubMed]

Avouris, P.

T. Mueller, F. N. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics4(5), 297–301 (2010).
[CrossRef]

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(10), 630–634 (2011).
[CrossRef] [PubMed]

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308–1308 (2008).
[CrossRef] [PubMed]

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308–1308 (2008).
[CrossRef] [PubMed]

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80(24), 245435 (2009).
[CrossRef]

Cai, W.

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett.37(13), 2730–2732 (2012).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007).
[CrossRef]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81(1), 109–162 (2009).
[CrossRef]

Chang, D. E.

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(8), 3370–3377 (2011).
[CrossRef] [PubMed]

Chen, P. Y.

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater.24(44), OP281–OP304 (2012).
[CrossRef] [PubMed]

P. Y. Chen and A. Alù, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B84(20), 205110 (2011).
[CrossRef]

Chen, P.-Y.

P.-Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano5(7), 5855–5863 (2011).
[CrossRef] [PubMed]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007).
[CrossRef]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6(1), 431–440 (2012).
[CrossRef] [PubMed]

Colombo, L.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature490(7419), 192–200 (2012).
[CrossRef] [PubMed]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Das Sarma, S.

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75(20), 205418 (2007).
[CrossRef]

Dubonos, S. V.

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,” Science306(5696), 666–669 (2004).
[CrossRef] [PubMed]

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Cloaked near-field scanning optical microscope tip for noninvasive near-field imaging,” Phys. Rev. Lett.105(26), 263906 (2010).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: Mechanism, robustness, and physical insights,” Opt. Express15(6), 3318–3332 (2007).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.72(1), 016623 (2005).
[CrossRef] [PubMed]

Enoch, S.

Ergin, T.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Fal’ko, V. I.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature490(7419), 192–200 (2012).
[CrossRef] [PubMed]

Farhat, M.

Firsov, A. A.

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,” Science306(5696), 666–669 (2004).
[CrossRef] [PubMed]

García de Abajo, F. J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6(1), 431–440 (2012).
[CrossRef] [PubMed]

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett.108(4), 047401 (2012).
[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(8), 3370–3377 (2011).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

A. Yu. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84(19), 195446 (2011).
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Geim, A. K.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81(1), 109–162 (2009).
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R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308–1308 (2008).
[CrossRef] [PubMed]

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,” Science306(5696), 666–669 (2004).
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Gellert, P. R.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature490(7419), 192–200 (2012).
[CrossRef] [PubMed]

Geng, B.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature474(7349), 64–67 (2011).
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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. Nanotechnol.6(10), 630–634 (2011).
[CrossRef] [PubMed]

Girit, C.

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

Grigorenko, A. N.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308–1308 (2008).
[CrossRef] [PubMed]

Grigorieva, I. V.

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,” Science306(5696), 666–669 (2004).
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Guenneau, S.

Guinea, F.

A. Yu. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84(19), 195446 (2011).
[CrossRef]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81(1), 109–162 (2009).
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Hanson, G. W.

G. W. Hanson, “Dyadic Green’s functions and guided surface waves on graphene,” J. Appl. Phys.103, 064302 (2006).
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Hao, Z.

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

J. W. Ko, S.-W. Kim, J. Hong, K. Kang, and C. B. Park, “Synthesis of graphene-wrapped CuO hybrid materials by CO2 mineralization,” Green Chem.14(9), 2391–2394 (2012).
[CrossRef]

Hong, J.-Y.

K. Y. Shin, J.-Y. Hong, and J. Jang, “Micropatterning of graphene sheets by inkjet printing and its wideband dipole-antenna application,” Adv. Mater.23(18), 2113–2118 (2011).
[CrossRef] [PubMed]

Horng, J.

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

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75(20), 205418 (2007).
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Jablan, M.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80(24), 245435 (2009).
[CrossRef]

Jang, J.

K. Y. Shin, J.-Y. Hong, and J. Jang, “Micropatterning of graphene sheets by inkjet printing and its wideband dipole-antenna application,” Adv. Mater.23(18), 2113–2118 (2011).
[CrossRef] [PubMed]

Jiang, D.

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,” Science306(5696), 666–669 (2004).
[CrossRef] [PubMed]

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

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

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
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Kang, K.

J. W. Ko, S.-W. Kim, J. Hong, K. Kang, and C. B. Park, “Synthesis of graphene-wrapped CuO hybrid materials by CO2 mineralization,” Green Chem.14(9), 2391–2394 (2012).
[CrossRef]

Kerkhoff, A.

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alù, “Experimental verification of three dimensional plasmonic cloaking in free-space,” New J. Phys.14(1), 013054 (2012).
[CrossRef]

Kildishev, A. V.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett.102(21), 213901 (2009).
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W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007).
[CrossRef]

Kim, K.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature490(7419), 192–200 (2012).
[CrossRef] [PubMed]

Kim, S.-W.

J. W. Ko, S.-W. Kim, J. Hong, K. Kang, and C. B. Park, “Synthesis of graphene-wrapped CuO hybrid materials by CO2 mineralization,” Green Chem.14(9), 2391–2394 (2012).
[CrossRef]

Ko, J. W.

J. W. Ko, S.-W. Kim, J. Hong, K. Kang, and C. B. Park, “Synthesis of graphene-wrapped CuO hybrid materials by CO2 mineralization,” Green Chem.14(9), 2391–2394 (2012).
[CrossRef]

Koppens, F. H. L.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6(1), 431–440 (2012).
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S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett.108(4), 047401 (2012).
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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(8), 3370–3377 (2011).
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Lederer, F.

Lee, J. S.

J. S. Lee, K. H. You, and C. B. Park, “Highly photoactive, low bandgap TiO2 nanoparticles wrapped by graphene,” Adv. Mater.24(8), 1084–1088 (2012).
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U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
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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. Nanotechnol.6(10), 630–634 (2011).
[CrossRef] [PubMed]

Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Manjavacas, A.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6(1), 431–440 (2012).
[CrossRef] [PubMed]

Martin, M.

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

Martin-Moreno, L.

A. Yu. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84(19), 195446 (2011).
[CrossRef]

Melin, K.

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alù, “Experimental verification of three dimensional plasmonic cloaking in free-space,” New J. Phys.14(1), 013054 (2012).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Monticone, F.

F. Monticone, C. Argyropoulos, and A. Alù, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci Rep2, 912–918 (2012).
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Moreno, G.

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alù, “Experimental verification of three dimensional plasmonic cloaking in free-space,” New J. Phys.14(1), 013054 (2012).
[CrossRef]

Morozov, S. V.

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,” Science306(5696), 666–669 (2004).
[CrossRef] [PubMed]

Movchan, A. B.

Mueller, T.

T. Mueller, F. N. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics4(5), 297–301 (2010).
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Mühlig, S.

M. Farhat, S. Mühlig, C. Rockstuhl, and F. Lederer, “Scattering cancellation of the magnetic dipole field from macroscopic spheres,” Opt. Express20(13), 13896–13906 (2012).
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S. Mühlig, M. Farhat, C. Rockstuhl, and F. Lederer, “Cloaking dielectric spherical objects by a shell of metallic nanoparticles,” Phys. Rev. B83(19), 195116 (2011).
[CrossRef]

Nair, R. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308–1308 (2008).
[CrossRef] [PubMed]

Nikitin, A. Yu.

A. Yu. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B84(19), 195446 (2011).
[CrossRef]

Novoselov, K. S.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature490(7419), 192–200 (2012).
[CrossRef] [PubMed]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81(1), 109–162 (2009).
[CrossRef]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308–1308 (2008).
[CrossRef] [PubMed]

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,” Science306(5696), 666–669 (2004).
[CrossRef] [PubMed]

Park, C. B.

J. S. Lee, K. H. You, and C. B. Park, “Highly photoactive, low bandgap TiO2 nanoparticles wrapped by graphene,” Adv. Mater.24(8), 1084–1088 (2012).
[CrossRef] [PubMed]

J. W. Ko, S.-W. Kim, J. Hong, K. Kang, and C. B. Park, “Synthesis of graphene-wrapped CuO hybrid materials by CO2 mineralization,” Green Chem.14(9), 2391–2394 (2012).
[CrossRef]

Pendry, J. B.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Peres, N. M. R.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81(1), 109–162 (2009).
[CrossRef]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308–1308 (2008).
[CrossRef] [PubMed]

Rainwater, D.

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alù, “Experimental verification of three dimensional plasmonic cloaking in free-space,” New J. Phys.14(1), 013054 (2012).
[CrossRef]

Rockstuhl, C.

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Schwab, M. G.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature490(7419), 192–200 (2012).
[CrossRef] [PubMed]

Shalaev, V. M.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett.102(21), 213901 (2009).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007).
[CrossRef]

Shen, Y. R.

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

Shin, K. Y.

K. Y. Shin, J.-Y. Hong, and J. Jang, “Micropatterning of graphene sheets by inkjet printing and its wideband dipole-antenna application,” Adv. Mater.23(18), 2113–2118 (2011).
[CrossRef] [PubMed]

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Smolyaninov, I. I.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett.102(21), 213901 (2009).
[CrossRef] [PubMed]

Smolyaninova, V. N.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett.102(21), 213901 (2009).
[CrossRef] [PubMed]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80(24), 245435 (2009).
[CrossRef]

Soric, J.

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater.24(44), OP281–OP304 (2012).
[CrossRef] [PubMed]

Soric, J. C.

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alù, “Experimental verification of three dimensional plasmonic cloaking in free-space,” New J. Phys.14(1), 013054 (2012).
[CrossRef]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Stauber, T.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science320(5881), 1308–1308 (2008).
[CrossRef] [PubMed]

Stenger, N.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Thongrattanasiri, S.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett.108(4), 047401 (2012).
[CrossRef] [PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6(1), 431–440 (2012).
[CrossRef] [PubMed]

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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

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

Wang, L.

Wegener, M.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Xia, F. N.

T. Mueller, F. N. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics4(5), 297–301 (2010).
[CrossRef]

Xu, J.

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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

You, K. H.

J. S. Lee, K. H. You, and C. B. Park, “Highly photoactive, low bandgap TiO2 nanoparticles wrapped by graphene,” Adv. Mater.24(8), 1084–1088 (2012).
[CrossRef] [PubMed]

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Zettl, A.

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

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett.37(13), 2730–2732 (2012).
[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,” Nature474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Zhang, Y.

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,” Science306(5696), 666–669 (2004).
[CrossRef] [PubMed]

ACS Nano (2)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano6(1), 431–440 (2012).
[CrossRef] [PubMed]

P.-Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano5(7), 5855–5863 (2011).
[CrossRef] [PubMed]

Adv. Mater. (3)

J. S. Lee, K. H. You, and C. B. Park, “Highly photoactive, low bandgap TiO2 nanoparticles wrapped by graphene,” Adv. Mater.24(8), 1084–1088 (2012).
[CrossRef] [PubMed]

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater.24(44), OP281–OP304 (2012).
[CrossRef] [PubMed]

K. Y. Shin, J.-Y. Hong, and J. Jang, “Micropatterning of graphene sheets by inkjet printing and its wideband dipole-antenna application,” Adv. Mater.23(18), 2113–2118 (2011).
[CrossRef] [PubMed]

Green Chem. (1)

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Figures (4)

Fig. 1
Fig. 1

(a) Sketch of a graphene sheet on top of dielectric substrate. (b) SPP dispersion relation with chemical potential set to 1000 meV. (c) Real and (d) imaginary parts of the bulk permittivity of graphene layer given by Eqs. (1)-(4) for various values of chemical potential ranging from 100 to 1000 meV and frequency ranging from 100 to 750 THz. The inset shows the energy bands of the graphene. (c) Effect of damping frequency ( Γ c ) on graphene permittivity ε V,G : solid lines represent the real part whereas dotted-dashed lines represent imaginary part.

Fig. 2
Fig. 2

(a) Scattering efficiency ( σ S,N ) of the dielectric sphere cloaked with the graphene shell with complex permittivity ε V,G (negative solution). σ S,N has dips at various frequencies corresponding to different effective plasma frequencies. (b) Same as in (a) but for the graphene shell with complex permittivity ε V,G 0 (near positive solution). (c) Graphene cloaks with different intrinsic losses for chemical potential 1000 meV. (d) Comparison between graphene plasmonic cloaks and mantle cloaks approximation.

Fig. 3
Fig. 3

Norm of the total electric field in V/m in linear scale in the presence of (a) the bare dielectric sphere and (b) cloaked sphere, both illuminated by a plane wave with unit amplitude (1 V/m) electric field in the x-direction and propagating in the y-direction. The excitation frequency is 58 THz . Scattering cross section σ S normalized by the geometrical cross section π a 2 in linear scale for (c) the bare dielectric sphere and (d) the cloaked sphere on the xy-plane. The scattering form the cloaked sphere is approximately 40 times smaller than the scattering from the bare sphere. Note that the polar axis scales in (c) and (d) are different.

Fig. 4
Fig. 4

(a) Scattering efficiency ( σ S,N ) for the dielectric sphere of Fig. 2 (dotted-dashed red line) covered by one graphene layer (dotted-red line), two layers (dashed-blue line), and three layers (solid-green line). (b) Scattering efficiency as function of frequency and radius of the third layer in logarithmic scale (in dB).

Equations (8)

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σ S,G (ω)= σ S,G (ω)j σ S,G (ω)= σ intra (ω)+ σ inter (ω).
σ intra (ω)=j q 2 π(ω+j Γ c ) [ μ c +2 k B Tln( e μ c / k B T +1 ) ],
σ inter (ω)=j q 2 4π ln[ 2| μ c |(ω+j Γ c ) 2| μ c |+(ω+j Γ c ) ],
ε V,G (ω)=1+j σ V,G (ω) / ε 0 ω .
c n TE,TM (ω)= U n TE,TM (ω) U n TE,TM (ω)+j V n TE,TM (ω) .
U n TM (ω)=| j n (ka) j n ( k c a) y n ( k c a) 0 j n (ka)/ε j n ( k c a)/ ε V,G (ω) y n ( k c a)/ ε V,G (ω) 0 0 j n ( k c a c ) y n ( k c a c ) j n ( k 0 a c ) 0 j n ( k c a c )/ ε V,G (ω) y n ( k c a c )/ ε V,G (ω) j n ( k 0 a c )/ ε 0 |.
σ S = 2π | k 0 | 2 n=1 (2n+1)[ | c n TE | 2 + | c n TM | 2 ] .
γ 3 = [ ε V,G (ω) ε 0 ][ 2 ε V,G (ω)+ε ] [ ε V,G (ω)ε ][ 2 ε V,G (ω)+ ε 0 ] .

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