Abstract

We present a wavelength tunable absorber composed of periodically patterned cross-shaped graphene arrays in the far-infrared and THz regions. The absorption of the single-layer array can essentially exceed the continuous graphene sheet by increasing the cross-arm width, even for small graphene filling ratio. As chemical potential and relaxation time increase, the absorption can be significantly enhanced. The complementary structure shows higher absorption compared to the original graphene array. Moreover, the wavelength of absorption maximum is angle-insensitive for both TE and TM polarizations. The absorption efficiency can be further improved with double layers of the cross-shaped graphene arrays, which are helpful to design dual-band and broadband absorbers.

© 2015 Optical Society of America

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  1. C. Watts, X. Liu, and W. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. Weinheim 24(23), OP98–OP120 (2012).
    [PubMed]
  2. Y. Li, H. Yan, D. Farmer, X. Meng, W. Zhu, R. Osgood, T. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
    [Crossref] [PubMed]
  3. S. Thongrattanasiri, F. Koppens, and F. Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
    [Crossref] [PubMed]
  4. A. Grigorenko, M. Polini, and K. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
    [Crossref]
  5. F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
    [Crossref]
  6. P. Avouris and M. Freitag, “Graphene photonics, plasmonics, and optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20(1), 6000112 (2014).
    [Crossref]
  7. F. Javier and G. Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photon. 1(3), 135–152 (2014).
    [Crossref]
  8. B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
    [Crossref]
  9. B. Wang, H. Huang, K. Wang, H. Long, and P. Lu, “Plasmonic routing in aperiodic graphene sheet arrays,” Opt. Lett. 39(16), 4867–4870 (2014).
    [Crossref] [PubMed]
  10. K. Novoselov, V. Falko, L. Colombo, P. Gellert, M. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
    [Crossref] [PubMed]
  11. D. Wang, X. Liu, L. He, Y. Yin, D. Wu, and J. Shi, “Manipulating graphene mobility and charge neutral point with ligand-bound nanoparticles as charge reservoir,” Nano Lett. 10(12), 4989–4993 (2010).
    [Crossref] [PubMed]
  12. G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7(6), 4810–4817 (2013).
    [Crossref] [PubMed]
  13. Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. Ajayan, F. Abajo, P. Nordlander, X. Zhu, and N. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
    [Crossref]
  14. K. Mak, M. Sfeir, Y. Wu, C. Lui, J. Misewich, and T. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
    [Crossref] [PubMed]
  15. A. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
    [Crossref]
  16. A. Ferreira, N. Peres, R. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
    [Crossref]
  17. T. Zhan, F. Zhao, X. Hu, X. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86(16), 165416 (2012).
    [Crossref]
  18. J. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photon. 1(4), 347–353 (2014).
    [Crossref]
  19. J.-T. Liu, N.-H. Liu, J. Li, X. Li, and J.-H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101(5), 052104 (2012).
    [Crossref]
  20. C. Qin, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Low-loss plasmonic supermodes in graphene multi-layers,” Opt. Express 22(21), 25324–25332 (2014).
    [Crossref] [PubMed]
  21. X. Meng, R. Grote, J. Dadap, N. Panoiu, and R. Osgood, “Engineering metal-nanoantennae/dye complexes for maximum fluorescence enhancement,” Opt. Express 22(18), 22018–22030 (2014).
    [Crossref] [PubMed]
  22. J. Luo, Y. Li, Z. Wang, Q. Zhang, and P. Lu, “Ultra-short isolated attosecond emission in mid-infrared inhomogeneous fields without CEP stabilization,” J. Phys. B 46, 145602 (2013).
    [Crossref]
  23. A. Nikitin, F. Guinea, F. Garcła-Vidal, and L. Martłn-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011).
    [Crossref]
  24. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. Bechtel, X. Liang, A. Zettl, Y. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
    [Crossref] [PubMed]
  25. A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
    [Crossref]
  26. A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B 86(19), 195408 (2012).
    [Crossref]
  27. A. Andryieuski and A. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21(7), 9144–9155 (2013).
    [Crossref] [PubMed]
  28. R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon meta-material,” Opt. Express 20(27), 28017–28024 (2012).
    [Crossref] [PubMed]
  29. Y. Zhang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Graphene based tunable metamaterial absorber and polarization modulation in terahertz frequency,” Opt. Express 22(19), 22743–22752, (2014).
    [Crossref] [PubMed]
  30. H. Tao, N. Landy, C. Bingham, X. Zhang, R. Averitt, and W. Padilla, “A metamaterial absorber for the terahertz regime: design, fabrication and characterization,” Opt. Express,  16(10), 7181–7188 (2008).
    [Crossref] [PubMed]
  31. X. Liu, T. Starr, A. Starr, and W. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104(20), 207403 (2010).
    [Crossref] [PubMed]
  32. C. Helgert, C. Menzel, C. Rockstuhl, E. Pshenay-Severin, E. Kley, A. Chipouline, A. Tnnermann, F. Lederer, and T. Pertsch, “Polarization-independent negative-index metamaterial in the near infrared,” Opt. Lett. 34(5), 704–706 (2009).
    [Crossref] [PubMed]
  33. D. Shchegolkov, A. Azad, J. OHara, and E. Simakov, “Perfect subwavelength fishnetlike metamaterial-based film terahertz absorbers,” Phys. Rev. B 82(20), 205117 (2010).
    [Crossref]
  34. P. Y. Chen and A. Al, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
    [Crossref] [PubMed]
  35. X.-H. Deng, J.-T. Liu, J. Yuan, T.-B. Wang, and N.-H. Liu, “Tunable THz absorption in graphene-based heterostructures,” Opt. Express 22(24), 30177–30183 (2014).
    [Crossref]
  36. G.W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide,” J. Appl. Phys 104(8), 084314 (2008).
    [Crossref]
  37. B. Wang, X. Zhang, K. Loh, and J. Teng, “Tunable broadband transmission and phase modulation of light through graphene multilayers,” J. Appl. Phys. 115(21), 213102 (2014).
    [Crossref]
  38. Y. Ye, Y. Jin, and S. He, “Omnidirectional, polarization-insensitive and broadband thin absorber in the terahertz regime,” J. Opt. Soc. Am. B 27(3), 498–504 (2010).
    [Crossref]
  39. H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
    [Crossref] [PubMed]
  40. Y. Cui, K. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
    [Crossref] [PubMed]

2014 (12)

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
[Crossref]

P. Avouris and M. Freitag, “Graphene photonics, plasmonics, and optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20(1), 6000112 (2014).
[Crossref]

F. Javier and G. Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photon. 1(3), 135–152 (2014).
[Crossref]

Y. Li, H. Yan, D. Farmer, X. Meng, W. Zhu, R. Osgood, T. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

B. Wang, H. Huang, K. Wang, H. Long, and P. Lu, “Plasmonic routing in aperiodic graphene sheet arrays,” Opt. Lett. 39(16), 4867–4870 (2014).
[Crossref] [PubMed]

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. Ajayan, F. Abajo, P. Nordlander, X. Zhu, and N. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

J. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photon. 1(4), 347–353 (2014).
[Crossref]

C. Qin, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Low-loss plasmonic supermodes in graphene multi-layers,” Opt. Express 22(21), 25324–25332 (2014).
[Crossref] [PubMed]

X. Meng, R. Grote, J. Dadap, N. Panoiu, and R. Osgood, “Engineering metal-nanoantennae/dye complexes for maximum fluorescence enhancement,” Opt. Express 22(18), 22018–22030 (2014).
[Crossref] [PubMed]

Y. Zhang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Graphene based tunable metamaterial absorber and polarization modulation in terahertz frequency,” Opt. Express 22(19), 22743–22752, (2014).
[Crossref] [PubMed]

X.-H. Deng, J.-T. Liu, J. Yuan, T.-B. Wang, and N.-H. Liu, “Tunable THz absorption in graphene-based heterostructures,” Opt. Express 22(24), 30177–30183 (2014).
[Crossref]

B. Wang, X. Zhang, K. Loh, and J. Teng, “Tunable broadband transmission and phase modulation of light through graphene multilayers,” J. Appl. Phys. 115(21), 213102 (2014).
[Crossref]

2013 (3)

J. Luo, Y. Li, Z. Wang, Q. Zhang, and P. Lu, “Ultra-short isolated attosecond emission in mid-infrared inhomogeneous fields without CEP stabilization,” J. Phys. B 46, 145602 (2013).
[Crossref]

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

G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7(6), 4810–4817 (2013).
[Crossref] [PubMed]

2012 (14)

C. Watts, X. Liu, and W. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. Weinheim 24(23), OP98–OP120 (2012).
[PubMed]

J.-T. Liu, N.-H. Liu, J. Li, X. Li, and J.-H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101(5), 052104 (2012).
[Crossref]

A. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[Crossref]

A. Ferreira, N. Peres, R. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[Crossref]

T. Zhan, F. Zhao, X. Hu, X. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86(16), 165416 (2012).
[Crossref]

K. Novoselov, V. Falko, L. Colombo, P. Gellert, M. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[Crossref] [PubMed]

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

A. Grigorenko, M. Polini, and K. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

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

A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
[Crossref]

A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B 86(19), 195408 (2012).
[Crossref]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

Y. Cui, K. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[Crossref] [PubMed]

2011 (3)

A. Nikitin, F. Guinea, F. Garcła-Vidal, and L. Martłn-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011).
[Crossref]

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

P. Y. Chen and A. Al, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

2010 (4)

D. Shchegolkov, A. Azad, J. OHara, and E. Simakov, “Perfect subwavelength fishnetlike metamaterial-based film terahertz absorbers,” Phys. Rev. B 82(20), 205117 (2010).
[Crossref]

X. Liu, T. Starr, A. Starr, and W. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104(20), 207403 (2010).
[Crossref] [PubMed]

D. Wang, X. Liu, L. He, Y. Yin, D. Wu, and J. Shi, “Manipulating graphene mobility and charge neutral point with ligand-bound nanoparticles as charge reservoir,” Nano Lett. 10(12), 4989–4993 (2010).
[Crossref] [PubMed]

Y. Ye, Y. Jin, and S. He, “Omnidirectional, polarization-insensitive and broadband thin absorber in the terahertz regime,” J. Opt. Soc. Am. B 27(3), 498–504 (2010).
[Crossref]

2009 (1)

2008 (3)

H. Tao, N. Landy, C. Bingham, X. Zhang, R. Averitt, and W. Padilla, “A metamaterial absorber for the terahertz regime: design, fabrication and characterization,” Opt. Express,  16(10), 7181–7188 (2008).
[Crossref] [PubMed]

G.W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide,” J. Appl. Phys 104(8), 084314 (2008).
[Crossref]

K. Mak, M. Sfeir, Y. Wu, C. Lui, J. Misewich, and T. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Abajo, F.

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. Ajayan, F. Abajo, P. Nordlander, X. Zhu, and N. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

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

Abajo, G.

F. Javier and G. Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photon. 1(3), 135–152 (2014).
[Crossref]

Ajayan, P.

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. Ajayan, F. Abajo, P. Nordlander, X. Zhu, and N. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

Al, A.

P. Y. Chen and A. Al, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Alaee, R.

Andryieuski, A.

Averitt, R.

Avouris, P.

P. Avouris and M. Freitag, “Graphene photonics, plasmonics, and optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20(1), 6000112 (2014).
[Crossref]

Y. Li, H. Yan, D. Farmer, X. Meng, W. Zhu, R. Osgood, T. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

Azad, A.

D. Shchegolkov, A. Azad, J. OHara, and E. Simakov, “Perfect subwavelength fishnetlike metamaterial-based film terahertz absorbers,” Phys. Rev. B 82(20), 205117 (2010).
[Crossref]

Bechtel, H.

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

Bingham, C.

Chandra, B.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

Chen, P. Y.

P. Y. Chen and A. Al, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Chipouline, A.

Colombo, L.

K. Novoselov, V. Falko, L. Colombo, P. Gellert, M. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[Crossref] [PubMed]

Cui, Y.

Y. Cui, K. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[Crossref] [PubMed]

Dadap, J.

Deng, X.-H.

Dubey, M.

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
[Crossref]

Falko, V.

K. Novoselov, V. Falko, L. Colombo, P. Gellert, M. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[Crossref] [PubMed]

Fallahi, A.

A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B 86(19), 195408 (2012).
[Crossref]

Fan, S.

J. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photon. 1(4), 347–353 (2014).
[Crossref]

Fang, N.

Y. Cui, K. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[Crossref] [PubMed]

Fang, Z.

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. Ajayan, F. Abajo, P. Nordlander, X. Zhu, and N. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

Farhat, M.

Farmer, D.

Y. Li, H. Yan, D. Farmer, X. Meng, W. Zhu, R. Osgood, T. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

Feng, Y.

Ferreira, A.

A. Ferreira, N. Peres, R. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[Crossref]

Freitag, M.

P. Avouris and M. Freitag, “Graphene photonics, plasmonics, and optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20(1), 6000112 (2014).
[Crossref]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[Crossref] [PubMed]

Fung, K.

Y. Cui, K. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[Crossref] [PubMed]

Garcia-Vidal, F.

A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
[Crossref]

Garcla-Vidal, F.

A. Nikitin, F. Guinea, F. Garcła-Vidal, and L. Martłn-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011).
[Crossref]

Gellert, P.

K. Novoselov, V. Falko, L. Colombo, P. Gellert, M. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[Crossref] [PubMed]

Geng, B.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. Bechtel, X. Liang, A. Zettl, Y. 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. Bechtel, X. Liang, A. Zettl, Y. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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A. Grigorenko, M. Polini, and K. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
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Guinea, F.

A. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
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A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
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A. Nikitin, F. Guinea, F. Garcła-Vidal, and L. Martłn-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011).
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Halas, N.

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. Ajayan, F. Abajo, P. Nordlander, X. Zhu, and N. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
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G.W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide,” J. Appl. Phys 104(8), 084314 (2008).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. Bechtel, X. Liang, A. Zettl, Y. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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He, L.

D. Wang, X. Liu, L. He, Y. Yin, D. Wu, and J. Shi, “Manipulating graphene mobility and charge neutral point with ligand-bound nanoparticles as charge reservoir,” Nano Lett. 10(12), 4989–4993 (2010).
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He, S.

Y. Cui, K. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
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Y. Ye, Y. Jin, and S. He, “Omnidirectional, polarization-insensitive and broadband thin absorber in the terahertz regime,” J. Opt. Soc. Am. B 27(3), 498–504 (2010).
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Y. Li, H. Yan, D. Farmer, X. Meng, W. Zhu, R. Osgood, T. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
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K. Mak, M. Sfeir, Y. Wu, C. Lui, J. Misewich, and T. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
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Horng, J.

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

J.-T. Liu, N.-H. Liu, J. Li, X. Li, and J.-H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101(5), 052104 (2012).
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Y. Cui, K. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
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Y. Ye, Y. Jin, and S. He, “Omnidirectional, polarization-insensitive and broadband thin absorber in the terahertz regime,” J. Opt. Soc. Am. B 27(3), 498–504 (2010).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. Bechtel, X. Liang, A. Zettl, Y. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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K. Novoselov, V. Falko, L. Colombo, P. Gellert, M. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
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Koppens, F.

S. Thongrattanasiri, F. Koppens, and F. Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
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Lavrinenko, A.

Lederer, F.

Li, J.

J.-T. Liu, N.-H. Liu, J. Li, X. Li, and J.-H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101(5), 052104 (2012).
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J.-T. Liu, N.-H. Liu, J. Li, X. Li, and J.-H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101(5), 052104 (2012).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
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Y. Li, H. Yan, D. Farmer, X. Meng, W. Zhu, R. Osgood, T. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
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J. Luo, Y. Li, Z. Wang, Q. Zhang, and P. Lu, “Ultra-short isolated attosecond emission in mid-infrared inhomogeneous fields without CEP stabilization,” J. Phys. B 46, 145602 (2013).
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Liang, X.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. Bechtel, X. Liang, A. Zettl, Y. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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X.-H. Deng, J.-T. Liu, J. Yuan, T.-B. Wang, and N.-H. Liu, “Tunable THz absorption in graphene-based heterostructures,” Opt. Express 22(24), 30177–30183 (2014).
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J.-T. Liu, N.-H. Liu, J. Li, X. Li, and J.-H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101(5), 052104 (2012).
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J.-T. Liu, N.-H. Liu, J. Li, X. Li, and J.-H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101(5), 052104 (2012).
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C. Watts, X. Liu, and W. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. Weinheim 24(23), OP98–OP120 (2012).
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T. Zhan, F. Zhao, X. Hu, X. Liu, and J. Zi, “Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies,” Phys. Rev. B 86(16), 165416 (2012).
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D. Wang, X. Liu, L. He, Y. Yin, D. Wu, and J. Shi, “Manipulating graphene mobility and charge neutral point with ligand-bound nanoparticles as charge reservoir,” Nano Lett. 10(12), 4989–4993 (2010).
[Crossref] [PubMed]

X. Liu, T. Starr, A. Starr, and W. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104(20), 207403 (2010).
[Crossref] [PubMed]

Liu, Z.

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. Ajayan, F. Abajo, P. Nordlander, X. Zhu, and N. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
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B. Wang, X. Zhang, K. Loh, and J. Teng, “Tunable broadband transmission and phase modulation of light through graphene multilayers,” J. Appl. Phys. 115(21), 213102 (2014).
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Lozano, G.

G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7(6), 4810–4817 (2013).
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Lui, C.

K. Mak, M. Sfeir, Y. Wu, C. Lui, J. Misewich, and T. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
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J. Luo, Y. Li, Z. Wang, Q. Zhang, and P. Lu, “Ultra-short isolated attosecond emission in mid-infrared inhomogeneous fields without CEP stabilization,” J. Phys. B 46, 145602 (2013).
[Crossref]

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Y. Cui, K. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[Crossref] [PubMed]

Mak, K.

K. Mak, M. Sfeir, Y. Wu, C. Lui, J. Misewich, and T. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. Bechtel, X. Liang, A. Zettl, Y. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
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A. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
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A. Nikitin, F. Guinea, F. Garcła-Vidal, and L. Martłn-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011).
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Y. Li, H. Yan, D. Farmer, X. Meng, W. Zhu, R. Osgood, T. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
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Misewich, J.

K. Mak, M. Sfeir, Y. Wu, C. Lui, J. Misewich, and T. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
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G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7(6), 4810–4817 (2013).
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A. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
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A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
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A. Nikitin, F. Guinea, F. Garcła-Vidal, and L. Martłn-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84(16), 161407 (2011).
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Nordlander, P.

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. Ajayan, F. Abajo, P. Nordlander, X. Zhu, and N. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
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A. Grigorenko, M. Polini, and K. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
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K. Novoselov, V. Falko, L. Colombo, P. Gellert, M. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
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OHara, J.

D. Shchegolkov, A. Azad, J. OHara, and E. Simakov, “Perfect subwavelength fishnetlike metamaterial-based film terahertz absorbers,” Phys. Rev. B 82(20), 205117 (2010).
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Osgood, R.

Y. Li, H. Yan, D. Farmer, X. Meng, W. Zhu, R. Osgood, T. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
[Crossref] [PubMed]

X. Meng, R. Grote, J. Dadap, N. Panoiu, and R. Osgood, “Engineering metal-nanoantennae/dye complexes for maximum fluorescence enhancement,” Opt. Express 22(18), 22018–22030 (2014).
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C. Watts, X. Liu, and W. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. Weinheim 24(23), OP98–OP120 (2012).
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X. Liu, T. Starr, A. Starr, and W. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104(20), 207403 (2010).
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Peres, N.

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G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7(6), 4810–4817 (2013).
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Polini, M.

A. Grigorenko, M. Polini, and K. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
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Qin, C.

Ramasubramaniam, A.

F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
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A. Ferreira, N. Peres, R. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
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G. Pirruccio, L. Moreno, G. Lozano, and J. Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7(6), 4810–4817 (2013).
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Rockstuhl, C.

Schlather, A.

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. Ajayan, F. Abajo, P. Nordlander, X. Zhu, and N. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

Schwab, M.

K. Novoselov, V. Falko, L. Colombo, P. Gellert, M. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
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K. Mak, M. Sfeir, Y. Wu, C. Lui, J. Misewich, and T. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

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D. Shchegolkov, A. Azad, J. OHara, and E. Simakov, “Perfect subwavelength fishnetlike metamaterial-based film terahertz absorbers,” Phys. Rev. B 82(20), 205117 (2010).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. Bechtel, X. Liang, A. Zettl, Y. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Shi, J.

D. Wang, X. Liu, L. He, Y. Yin, D. Wu, and J. Shi, “Manipulating graphene mobility and charge neutral point with ligand-bound nanoparticles as charge reservoir,” Nano Lett. 10(12), 4989–4993 (2010).
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D. Shchegolkov, A. Azad, J. OHara, and E. Simakov, “Perfect subwavelength fishnetlike metamaterial-based film terahertz absorbers,” Phys. Rev. B 82(20), 205117 (2010).
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X. Liu, T. Starr, A. Starr, and W. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104(20), 207403 (2010).
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X. Liu, T. Starr, A. Starr, and W. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104(20), 207403 (2010).
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A. Ferreira, N. Peres, R. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
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Tao, H.

Teng, J.

B. Wang, X. Zhang, K. Loh, and J. Teng, “Tunable broadband transmission and phase modulation of light through graphene multilayers,” J. Appl. Phys. 115(21), 213102 (2014).
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B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
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S. Thongrattanasiri, F. Koppens, and F. Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
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Tulevski, G.

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B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
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D. Wang, X. Liu, L. He, Y. Yin, D. Wu, and J. Shi, “Manipulating graphene mobility and charge neutral point with ligand-bound nanoparticles as charge reservoir,” Nano Lett. 10(12), 4989–4993 (2010).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. Bechtel, X. Liang, A. Zettl, Y. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
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Wang, T.-B.

Wang, Y.

Z. Fang, Y. Wang, A. Schlather, Z. Liu, P. Ajayan, F. Abajo, P. Nordlander, X. Zhu, and N. Halas, “Active tunable absorption enhancement with graphene nanodisk arrays,” Nano Lett. 14(1), 299–304 (2014).
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J. Luo, Y. Li, Z. Wang, Q. Zhang, and P. Lu, “Ultra-short isolated attosecond emission in mid-infrared inhomogeneous fields without CEP stabilization,” J. Phys. B 46, 145602 (2013).
[Crossref]

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C. Watts, X. Liu, and W. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. Weinheim 24(23), OP98–OP120 (2012).
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D. Wang, X. Liu, L. He, Y. Yin, D. Wu, and J. Shi, “Manipulating graphene mobility and charge neutral point with ligand-bound nanoparticles as charge reservoir,” Nano Lett. 10(12), 4989–4993 (2010).
[Crossref] [PubMed]

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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
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K. Mak, M. Sfeir, Y. Wu, C. Lui, J. Misewich, and T. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
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F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
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F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
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Y. Cui, K. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
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Y. Li, H. Yan, D. Farmer, X. Meng, W. Zhu, R. Osgood, T. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14(3), 1573–1577 (2014).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
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Yin, Y.

D. Wang, X. Liu, L. He, Y. Yin, D. Wu, and J. Shi, “Manipulating graphene mobility and charge neutral point with ligand-bound nanoparticles as charge reservoir,” Nano Lett. 10(12), 4989–4993 (2010).
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Yuan, X.

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
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Figures (10)

Fig. 1
Fig. 1 Schematic of the geometry under consideration: the periodic cross-shaped graphene arrays with width w, length L and period a. The arrays are supported on a Si substrate coated by a thin SiO2 layer with thickness d. The incident electromagnetic wave is TE polarized with the electric fields along the y axis. The angle of incidence is θ.

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Fig. 2
Fig. 2 (a) The absorption spectra for different widths as L = 1.25 μm. (b)The electric field distributions (|E|) at the absorption peak for w/L = 0.3, 0.5, 0.7, and 0.9. (c) The absorption spectra for different lengths as w = 0.25 μm. (d) The electric field distributions at the absorption peak for L/a = 0.3, 0.5, 0.7, and 0.9. a = 2.5 μm and d = 0.3 μm.

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Fig. 3
Fig. 3 The resonant wavelength λm and the absorption maximum Am as a function of L/a and w/L for different periods. The resonant wavelength for (a) a = 2.5 μm and (c) a = 1.0 μm. The absorption maximum for (b) a = 2.5 μm and (d) a = 1.0 μm. In all panels, d = 0.3 μm.

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Fig. 4
Fig. 4 (a) The absorption spectra for different periods. (b) Dependence of the resonant wavelength and absorption maximum on the period. In (a) and (b), L = 1 μm, w = 0.25 μm, and d = 0.3 μm. (c) The absorption spectra for different thicknesses. (d) Dependence of the resonant wavelength and absorption maximum on thickness. In (c) and (d), L = 1.25 μm, w = 0.25 μm, and a = 2.5 μm. The insert shows electric field distributions (|E|) for (a) L/a = 0.1 and (c) d = 0.1 μm.

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Fig. 5
Fig. 5 The absorption spectra at various incident angles for (a) TE and (b) TM polarizations. The resonant wavelength and absorption maximum at various incident angles for (c) TE and (d) TM polarizations. The insert shows the electric field distributions (|E|) at θ = 0°.

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Fig. 6
Fig. 6 (a) The absorption spectra for different chemical potentials. (b) and (c) The electric field distributions (|E|) at the absorption peak for μc = 0.2 eV and 0.8 eV. (d) The resonant wavelength λm as a function of μc.

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Fig. 7
Fig. 7 (a) The absorption spectra for different relaxation times. The insert shows the electric field distributions (|E|) for τ = 0.5 ps at the absorption peaks labeled with A and B. (b) The electric field distributions at the absorption peaks of C for τ = 0.02 ps, 0.1 ps, 0.5 ps, and 2.5 ps.

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Fig. 8
Fig. 8 The complementary structure of Fig. 1.

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Fig. 9
Fig. 9 The absorption spectra at various incident angles for (a) TE and (c) TM polarizations. (b) and (d) The electric field distributions (|E|) at the absorption peak.

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Fig. 10
Fig. 10 (a) The structure consisting of double layers of periodic cross-shaped graphene arrays. (b) The absorption spectra for different h. (c) and (d) The electric field distributions (|E|) of y-z plane across the center as h = 0.3 μm. (c) λ = 62.75 μm. (d) λ = 86.75 μm. (e) The absorption spectra by applying different chemical potentials for graphene layers as h = 1.6 μm. μc = 0.4 eV for up layer and μc = 0.6 eV for down layer. The relaxation time for down layer is τ1 and up layer is 1.0 ps.

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