Abstract

We investigate a novel implementation of hyperbolic metamaterial (HM) at far-infrared frequencies composed of stacked graphene sheets separated by thin dielectric layers. Using the surface conductivity model of graphene, we derive the homogenization formula for the multilayer structure by treating graphene sheets as lumped layers with complex admittances. Homogenization results and limits are investigated by comparison with a transfer matrix formulation for the HM constituent layers. We show that infrared iso-frequency wavevector dispersion characteristics of the proposed HM can be tuned by varying the chemical potential of the graphene sheets via electrostatic biasing. Accordingly, reflection and transmission properties for a film made of graphene-dielectric multilayer are tunable at terahertz frequencies, and we investigate the limits in using the homogenized model compared to the more accurate transfer matrix model. We also propose to use graphene-based HM as a super absorber for near-fields generated at its surface. The power emitted by a dipole near the surface of a graphene-based HM is increased dramatically (up to 5 × 102 at 2 THz), furthermore we show that most of the scattered power is directed into the HM. The validity and limits of the homogenized HM model are assessed also for near-fields and show that in certain conditions it overestimates the dipole radiated power into the HM.

© 2013 OSA

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  47. Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in graphene,” Phys. Rev. Lett.99, 246803 (2007).
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    [CrossRef]
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  52. F. Capolino and M. Albani, “Truncation effects in a semi-infinite periodic array of thin strips: A discrete wiener-hopf formulation,” Radio Sci.44, RS2S91 (2009).
    [CrossRef]
  53. P.-Y. Chen and A. Alu, “Atomically thin surface cloak using graphene monolayers,” ACS Nano5, 5855–5863 (2011).
    [CrossRef] [PubMed]
  54. Z. Jacob, J. Kim, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
    [CrossRef]

2013 (1)

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B87, 075416 (2013).
[CrossRef]

2012 (24)

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B86, 121108 (2012).
[CrossRef]

M. Tamagnone, J. Gomez-Diaz, J. Mosig, and J. Perruisseau-Carrier, “Analysis and design of terahertz antennas based on plasmonic resonant graphene sheets,” J. Appl. Phys.112, 114915 (2012).
[CrossRef]

B. Wang, X. Zhang, F. J. Garcia-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett.109, 073901 (2012).
[CrossRef] [PubMed]

L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbucken, “A graphene electron lens,” Appl. Phys. Lett.100, 153106 (2012).
[CrossRef]

C. S. R. Kaipa, G. W. P. Y. R. Yakovlev, Alexander Hanson, M. F. Medina, and F., “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B85, 245407 (2012).
[CrossRef]

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

A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B86, 195408 (2012).
[CrossRef]

D. Sounas and C. Caloz, “Gyrotropy and nonreciprocity of graphene for microwave applications,” IEEE Trans. Microw. Theory Techn.60, 901 –914 (2012).
[CrossRef]

G. Lovat, “Equivalent circuit for electromagnetic interaction and transmission through graphene sheets,” IEEE Trans. Electromagn. Compat.54, 101 –109 (2012).
[CrossRef]

C. Guclu, S. Campione, and F. Capolino, “Hyperbolic metamaterial as super absorber for scattered fields generated at its surface,” Phys. Rev. B86, 205130 (2012).
[CrossRef]

Y. Guo, W. Newman, C. Cortes, and Z. Jacob, “Applications of hyperbolic metamaterial substrates,” Adv. Opto-Electron.2012, 452502 (2012).

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett.101, 131106 (2012).
[CrossRef]

Z. Jacob, I. I. Smolyaninov, and E. E. Narimanov, “Broadband purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett.100, 181105 (2012).
[CrossRef]

T. U. Tumkur, J. K. Kitur, B. Chu, L. Gu, V. A. Podolskiy, E. E. Narimanov, and M. A. Noginov, “Control of reflectance and transmittance in scattering and curvilinear hyperbolic metamaterials,” Appl. Phys. Lett.101, 091105 (2012).
[CrossRef]

T. Tumkur, L. Gu, J. Kitur, E. Narimanov, and M. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett.100, 161103–161103 (2012).
[CrossRef]

A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B86, 035148 (2012).
[CrossRef]

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt.14, 063001 (2012).
[CrossRef]

G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of al:zno as a plasmonic component for near-infrared metamaterials,” PNAS109, 8834–8838 (2012).
[CrossRef] [PubMed]

J. Kim, V. Drachev, Z. Jacob, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express20, 8100–8116 (2012).
[CrossRef] [PubMed]

C. Rizza, A. Ciattoni, E. Spinozzi, and L. Columbo, “Terahertz active spatial filtering through optically tunable hyperbolic metamaterials,” Opt. Lett.37, 3345–3347 (2012).
[CrossRef]

A. Vakil and N. Engheta, “One-atom-thick reflectors for surface plasmon polariton surface waves on graphene,” Opt. Comm.285, 3428 – 3430 (2012).
[CrossRef]

C. S. R. Kaipa, A. B. Yakovlev, F. Medina, and F. Mesa, “Transmission through stacked 2d periodic distributions of square conducting patches,” J. Appl. Phys.112, 033101 (2012).
[CrossRef]

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic meta-materials: Strengths and limitations,” Phys. Rev. A85, 053842 (2012).
[CrossRef]

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science336, 205–209 (2012).
[CrossRef] [PubMed]

2011 (9)

S. Campione, S. Steshenko, M. Albani, and F. Capolino, “Complex modes and effective refractive index in 3d periodic arrays of plasmonic nanospheres,” Opt. Express19, 26027–26043 (2011).
[CrossRef]

X. Ni, G. Naik, A. Kildishev, Y. Barnakov, A. Boltasseva, and V. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B103, 553–558 (2011).
[CrossRef]

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

G. W. Hanson, A. B. Yakovlev, and A. Mafi, “Excitation of discrete and continuous spectrum for a surface conductivity model of graphene,” J. Appl. Phys.110, 114305 (2011).
[CrossRef]

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett.36, 2530–2532 (2011).
[CrossRef] [PubMed]

J. Sun, J. Zhou, B. Li, and F. Kang, “Indefinite permittivity and negative refraction in natural material: Graphite,” Appl. Phys. Lett.98, 101901 (2011).
[CrossRef]

Y. R. Padooru, A. B. Yakovlev, C. S. Kaipa, F. Medina, and F. Mesa, “Circuit modeling of multiband high-impedance surface absorbers in the microwave regime,” Phys. Rev. B84, 035108 (2011).
[CrossRef]

D. L. Sounas and C. Caloz, “Electromagnetic nonreciprocity and gyrotropy of graphene,” Appl. Phys. Lett.98, 021911 (2011).
[CrossRef]

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

2010 (4)

C. S. Kaipa, A. B. Yakovlev, F. Medina, F. Mesa, C. Butler, and A. P. Hibbins, “Circuit modeling of the transmissivity of stacked two-dimensional metallic meshes,” Opt. Express18, 13309–13320 (2010).
[CrossRef] [PubMed]

I. Smolyaninov and E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett.105, 67402 (2010).
[CrossRef]

G. Naik and A. Boltasseva, “Semiconductors for plasmonics and metamaterials,” Phys. Status Solidi Rapid Res. Lett.4, 295–297 (2010).
[CrossRef]

Z. Jacob, J. Kim, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

2009 (2)

F. Capolino and M. Albani, “Truncation effects in a semi-infinite periodic array of thin strips: A discrete wiener-hopf formulation,” Radio Sci.44, RS2S91 (2009).
[CrossRef]

C. Chen, S. Rosenblatt, K. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. Stormer, T. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nature Nanotech.4, 861–867 (2009).
[CrossRef]

2008 (4)

X. Wang, L. Zhi, and K. Mullen, “Transparent, conductive graphene electrodes for dye-sensitized solar cells,” Nano Lett.8, 323–327 (2008).
[CrossRef]

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett.100, 117401 (2008).
[CrossRef] [PubMed]

F. Rana, “Graphene terahertz plasmon oscillators,” IEEE Trans. Nanotechnol.7, 91–99 (2008).
[CrossRef]

G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys.103, 064302 (2008).
[CrossRef]

2007 (2)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and hall conductivity in graphene,” Phys. Rev. B75, 165407 (2007).
[CrossRef]

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in graphene,” Phys. Rev. Lett.99, 246803 (2007).
[CrossRef]

2006 (1)

2005 (1)

V. P. Gusynin and S. G. Sharapov, “Unconventional integer quantum hall effect in graphene,” Phys. Rev. Lett.95, 146801 (2005).
[CrossRef] [PubMed]

2004 (1)

K. Novoselov, A. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, and A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
[CrossRef] [PubMed]

2003 (2)

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett.90, 077405 (2003).
[CrossRef] [PubMed]

J. Pendry and S. Ramakrishna, “Refining the perfect lens,” Physica B: Condensed Matter338, 329 – 332 (2003).
[CrossRef]

1993 (1)

R. A. Jishi, M. S. Dresselhaus, and G. Dresselhaus, “Electron-phonon coupling and the electrical conductivity of fullerene nanotubules,” Phys. Rev. B48, 11385–11389 (1993).
[CrossRef]

Adam, S.

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in graphene,” Phys. Rev. Lett.99, 246803 (2007).
[CrossRef]

Albani, M.

S. Campione, S. Steshenko, M. Albani, and F. Capolino, “Complex modes and effective refractive index in 3d periodic arrays of plasmonic nanospheres,” Opt. Express19, 26027–26043 (2011).
[CrossRef]

F. Capolino and M. Albani, “Truncation effects in a semi-infinite periodic array of thin strips: A discrete wiener-hopf formulation,” Radio Sci.44, RS2S91 (2009).
[CrossRef]

Alu, A.

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

Andryieuski, A.

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B86, 121108 (2012).
[CrossRef]

Balashov, T.

L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbucken, “A graphene electron lens,” Appl. Phys. Lett.100, 153106 (2012).
[CrossRef]

Barnakov, Y.

X. Ni, G. Naik, A. Kildishev, Y. Barnakov, A. Boltasseva, and V. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B103, 553–558 (2011).
[CrossRef]

Belov, P. A.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B87, 075416 (2013).
[CrossRef]

A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B86, 035148 (2012).
[CrossRef]

Bolotin, K.

C. Chen, S. Rosenblatt, K. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. Stormer, T. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nature Nanotech.4, 861–867 (2009).
[CrossRef]

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in graphene,” Phys. Rev. Lett.99, 246803 (2007).
[CrossRef]

Boltasseva, A.

G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of al:zno as a plasmonic component for near-infrared metamaterials,” PNAS109, 8834–8838 (2012).
[CrossRef] [PubMed]

J. Kim, V. Drachev, Z. Jacob, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express20, 8100–8116 (2012).
[CrossRef] [PubMed]

X. Ni, G. Naik, A. Kildishev, Y. Barnakov, A. Boltasseva, and V. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B103, 553–558 (2011).
[CrossRef]

Z. Jacob, J. Kim, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

G. Naik and A. Boltasseva, “Semiconductors for plasmonics and metamaterials,” Phys. Status Solidi Rapid Res. Lett.4, 295–297 (2010).
[CrossRef]

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Y. Guo, W. Newman, C. Cortes, and Z. Jacob, “Applications of hyperbolic metamaterial substrates,” Adv. Opto-Electron.2012, 452502 (2012).

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J. Kim, V. Drachev, Z. Jacob, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express20, 8100–8116 (2012).
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Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett.101, 131106 (2012).
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Z. Jacob, I. I. Smolyaninov, and E. E. Narimanov, “Broadband purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett.100, 181105 (2012).
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Z. Jacob, J. Kim, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

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K. Novoselov, A. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, and A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
[CrossRef] [PubMed]

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R. A. Jishi, M. S. Dresselhaus, and G. Dresselhaus, “Electron-phonon coupling and the electrical conductivity of fullerene nanotubules,” Phys. Rev. B48, 11385–11389 (1993).
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Y. R. Padooru, A. B. Yakovlev, C. S. Kaipa, F. Medina, and F. Mesa, “Circuit modeling of multiband high-impedance surface absorbers in the microwave regime,” Phys. Rev. B84, 035108 (2011).
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C. S. Kaipa, A. B. Yakovlev, F. Medina, F. Mesa, C. Butler, and A. P. Hibbins, “Circuit modeling of the transmissivity of stacked two-dimensional metallic meshes,” Opt. Express18, 13309–13320 (2010).
[CrossRef] [PubMed]

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C. S. R. Kaipa, G. W. P. Y. R. Yakovlev, Alexander Hanson, M. F. Medina, and F., “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B85, 245407 (2012).
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C. Chen, S. Rosenblatt, K. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. Stormer, T. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nature Nanotech.4, 861–867 (2009).
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G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of al:zno as a plasmonic component for near-infrared metamaterials,” PNAS109, 8834–8838 (2012).
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J. Kim, V. Drachev, Z. Jacob, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express20, 8100–8116 (2012).
[CrossRef] [PubMed]

Z. Jacob, J. Kim, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

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C. Chen, S. Rosenblatt, K. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. Stormer, T. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nature Nanotech.4, 861–867 (2009).
[CrossRef]

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in graphene,” Phys. Rev. Lett.99, 246803 (2007).
[CrossRef]

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T. Tumkur, L. Gu, J. Kitur, E. Narimanov, and M. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett.100, 161103–161103 (2012).
[CrossRef]

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T. U. Tumkur, J. K. Kitur, B. Chu, L. Gu, V. A. Podolskiy, E. E. Narimanov, and M. A. Noginov, “Control of reflectance and transmittance in scattering and curvilinear hyperbolic metamaterials,” Appl. Phys. Lett.101, 091105 (2012).
[CrossRef]

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I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B87, 075416 (2013).
[CrossRef]

A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B86, 035148 (2012).
[CrossRef]

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

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H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science336, 205–209 (2012).
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H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science336, 205–209 (2012).
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A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett.100, 117401 (2008).
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C. Chen, S. Rosenblatt, K. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. Stormer, T. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nature Nanotech.4, 861–867 (2009).
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A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B86, 121108 (2012).
[CrossRef]

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J. Sun, J. Zhou, B. Li, and F. Kang, “Indefinite permittivity and negative refraction in natural material: Graphite,” Appl. Phys. Lett.98, 101901 (2011).
[CrossRef]

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G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of al:zno as a plasmonic component for near-infrared metamaterials,” PNAS109, 8834–8838 (2012).
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L. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, NJ, 1973).

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L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbucken, “A graphene electron lens,” Appl. Phys. Lett.100, 153106 (2012).
[CrossRef]

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C. S. R. Kaipa, A. B. Yakovlev, F. Medina, and F. Mesa, “Transmission through stacked 2d periodic distributions of square conducting patches,” J. Appl. Phys.112, 033101 (2012).
[CrossRef]

Y. R. Padooru, A. B. Yakovlev, C. S. Kaipa, F. Medina, and F. Mesa, “Circuit modeling of multiband high-impedance surface absorbers in the microwave regime,” Phys. Rev. B84, 035108 (2011).
[CrossRef]

C. S. Kaipa, A. B. Yakovlev, F. Medina, F. Mesa, C. Butler, and A. P. Hibbins, “Circuit modeling of the transmissivity of stacked two-dimensional metallic meshes,” Opt. Express18, 13309–13320 (2010).
[CrossRef] [PubMed]

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C. S. R. Kaipa, G. W. P. Y. R. Yakovlev, Alexander Hanson, M. F. Medina, and F., “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B85, 245407 (2012).
[CrossRef]

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H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science336, 205–209 (2012).
[CrossRef] [PubMed]

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C. S. R. Kaipa, A. B. Yakovlev, F. Medina, and F. Mesa, “Transmission through stacked 2d periodic distributions of square conducting patches,” J. Appl. Phys.112, 033101 (2012).
[CrossRef]

Y. R. Padooru, A. B. Yakovlev, C. S. Kaipa, F. Medina, and F. Mesa, “Circuit modeling of multiband high-impedance surface absorbers in the microwave regime,” Phys. Rev. B84, 035108 (2011).
[CrossRef]

C. S. Kaipa, A. B. Yakovlev, F. Medina, F. Mesa, C. Butler, and A. P. Hibbins, “Circuit modeling of the transmissivity of stacked two-dimensional metallic meshes,” Opt. Express18, 13309–13320 (2010).
[CrossRef] [PubMed]

Molesky, S.

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett.101, 131106 (2012).
[CrossRef]

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt.14, 063001 (2012).
[CrossRef]

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K. Novoselov, A. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, and A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
[CrossRef] [PubMed]

Mosig, J.

M. Tamagnone, J. Gomez-Diaz, J. Mosig, and J. Perruisseau-Carrier, “Analysis and design of terahertz antennas based on plasmonic resonant graphene sheets,” J. Appl. Phys.112, 114915 (2012).
[CrossRef]

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L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbucken, “A graphene electron lens,” Appl. Phys. Lett.100, 153106 (2012).
[CrossRef]

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I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B87, 075416 (2013).
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J. Kim, V. Drachev, Z. Jacob, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express20, 8100–8116 (2012).
[CrossRef] [PubMed]

X. Ni, G. Naik, A. Kildishev, Y. Barnakov, A. Boltasseva, and V. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B103, 553–558 (2011).
[CrossRef]

Z. Jacob, J. Kim, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

G. Naik and A. Boltasseva, “Semiconductors for plasmonics and metamaterials,” Phys. Status Solidi Rapid Res. Lett.4, 295–297 (2010).
[CrossRef]

Naik, G. V.

G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of al:zno as a plasmonic component for near-infrared metamaterials,” PNAS109, 8834–8838 (2012).
[CrossRef] [PubMed]

Narimanov, E.

J. Kim, V. Drachev, Z. Jacob, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express20, 8100–8116 (2012).
[CrossRef] [PubMed]

T. Tumkur, L. Gu, J. Kitur, E. Narimanov, and M. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett.100, 161103–161103 (2012).
[CrossRef]

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science336, 205–209 (2012).
[CrossRef] [PubMed]

Z. Jacob, J. Kim, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

I. Smolyaninov and E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett.105, 67402 (2010).
[CrossRef]

Narimanov, E. E.

T. U. Tumkur, J. K. Kitur, B. Chu, L. Gu, V. A. Podolskiy, E. E. Narimanov, and M. A. Noginov, “Control of reflectance and transmittance in scattering and curvilinear hyperbolic metamaterials,” Appl. Phys. Lett.101, 091105 (2012).
[CrossRef]

Z. Jacob, I. I. Smolyaninov, and E. E. Narimanov, “Broadband purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett.100, 181105 (2012).
[CrossRef]

Newman, W.

Y. Guo, W. Newman, C. Cortes, and Z. Jacob, “Applications of hyperbolic metamaterial substrates,” Adv. Opto-Electron.2012, 452502 (2012).

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt.14, 063001 (2012).
[CrossRef]

Ni, X.

X. Ni, G. Naik, A. Kildishev, Y. Barnakov, A. Boltasseva, and V. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B103, 553–558 (2011).
[CrossRef]

Noginov, M.

T. Tumkur, L. Gu, J. Kitur, E. Narimanov, and M. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett.100, 161103–161103 (2012).
[CrossRef]

Noginov, M. A.

T. U. Tumkur, J. K. Kitur, B. Chu, L. Gu, V. A. Podolskiy, E. E. Narimanov, and M. A. Noginov, “Control of reflectance and transmittance in scattering and curvilinear hyperbolic metamaterials,” Appl. Phys. Lett.101, 091105 (2012).
[CrossRef]

Novoselov, K.

K. Novoselov, A. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, and A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
[CrossRef] [PubMed]

Ozerov, I.

L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbucken, “A graphene electron lens,” Appl. Phys. Lett.100, 153106 (2012).
[CrossRef]

Padooru, Y. R.

Y. R. Padooru, A. B. Yakovlev, C. S. Kaipa, F. Medina, and F. Mesa, “Circuit modeling of multiband high-impedance surface absorbers in the microwave regime,” Phys. Rev. B84, 035108 (2011).
[CrossRef]

Pendry, J.

J. Pendry and S. Ramakrishna, “Refining the perfect lens,” Physica B: Condensed Matter338, 329 – 332 (2003).
[CrossRef]

Perruisseau-Carrier, J.

A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B86, 195408 (2012).
[CrossRef]

M. Tamagnone, J. Gomez-Diaz, J. Mosig, and J. Perruisseau-Carrier, “Analysis and design of terahertz antennas based on plasmonic resonant graphene sheets,” J. Appl. Phys.112, 114915 (2012).
[CrossRef]

Poddubny, A. N.

A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B86, 035148 (2012).
[CrossRef]

Podolskiy, V. A.

T. U. Tumkur, J. K. Kitur, B. Chu, L. Gu, V. A. Podolskiy, E. E. Narimanov, and M. A. Noginov, “Control of reflectance and transmittance in scattering and curvilinear hyperbolic metamaterials,” Appl. Phys. Lett.101, 091105 (2012).
[CrossRef]

Portail, M.

L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbucken, “A graphene electron lens,” Appl. Phys. Lett.100, 153106 (2012).
[CrossRef]

Pozar, D.

D. Pozar, Microwave engineering (John Wiley & Sons, 2009).

Ramakrishna, S.

J. Pendry and S. Ramakrishna, “Refining the perfect lens,” Physica B: Condensed Matter338, 329 – 332 (2003).
[CrossRef]

Rana, F.

F. Rana, “Graphene terahertz plasmon oscillators,” IEEE Trans. Nanotechnol.7, 91–99 (2008).
[CrossRef]

Rizza, C.

Rosenblatt, S.

C. Chen, S. Rosenblatt, K. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. Stormer, T. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nature Nanotech.4, 861–867 (2009).
[CrossRef]

Sahaf, H.

L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbucken, “A graphene electron lens,” Appl. Phys. Lett.100, 153106 (2012).
[CrossRef]

Schurig, D.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett.90, 077405 (2003).
[CrossRef] [PubMed]

Shadrivov, I. V.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B87, 075416 (2013).
[CrossRef]

Shalaev, V.

J. Kim, V. Drachev, Z. Jacob, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express20, 8100–8116 (2012).
[CrossRef] [PubMed]

X. Ni, G. Naik, A. Kildishev, Y. Barnakov, A. Boltasseva, and V. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B103, 553–558 (2011).
[CrossRef]

Z. Jacob, J. Kim, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

Shalaev, V. M.

G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of al:zno as a plasmonic component for near-infrared metamaterials,” PNAS109, 8834–8838 (2012).
[CrossRef] [PubMed]

Sharapov, S. G.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and hall conductivity in graphene,” Phys. Rev. B75, 165407 (2007).
[CrossRef]

V. P. Gusynin and S. G. Sharapov, “Unconventional integer quantum hall effect in graphene,” Phys. Rev. Lett.95, 146801 (2005).
[CrossRef] [PubMed]

Sipe, J. E.

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic meta-materials: Strengths and limitations,” Phys. Rev. A85, 053842 (2012).
[CrossRef]

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett.36, 2530–2532 (2011).
[CrossRef] [PubMed]

Smith, D. R.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett.90, 077405 (2003).
[CrossRef] [PubMed]

Smolyaninov, I.

I. Smolyaninov and E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett.105, 67402 (2010).
[CrossRef]

Smolyaninov, I. I.

Z. Jacob, I. I. Smolyaninov, and E. E. Narimanov, “Broadband purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett.100, 181105 (2012).
[CrossRef]

Sounas, D.

D. Sounas and C. Caloz, “Gyrotropy and nonreciprocity of graphene for microwave applications,” IEEE Trans. Microw. Theory Techn.60, 901 –914 (2012).
[CrossRef]

Sounas, D. L.

D. L. Sounas and C. Caloz, “Electromagnetic nonreciprocity and gyrotropy of graphene,” Appl. Phys. Lett.98, 021911 (2011).
[CrossRef]

Spinozzi, E.

Steshenko, S.

Stormer, H.

C. Chen, S. Rosenblatt, K. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. Stormer, T. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nature Nanotech.4, 861–867 (2009).
[CrossRef]

Stormer, H. L.

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in graphene,” Phys. Rev. Lett.99, 246803 (2007).
[CrossRef]

Sun, J.

J. Sun, J. Zhou, B. Li, and F. Kang, “Indefinite permittivity and negative refraction in natural material: Graphite,” Appl. Phys. Lett.98, 101901 (2011).
[CrossRef]

Tamagnone, M.

M. Tamagnone, J. Gomez-Diaz, J. Mosig, and J. Perruisseau-Carrier, “Analysis and design of terahertz antennas based on plasmonic resonant graphene sheets,” J. Appl. Phys.112, 114915 (2012).
[CrossRef]

Tan, Y.-W.

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in graphene,” Phys. Rev. Lett.99, 246803 (2007).
[CrossRef]

Teng, J.

B. Wang, X. Zhang, F. J. Garcia-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett.109, 073901 (2012).
[CrossRef] [PubMed]

Thongrattanasiri, S.

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

Tumkur, T.

T. Tumkur, L. Gu, J. Kitur, E. Narimanov, and M. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett.100, 161103–161103 (2012).
[CrossRef]

Tumkur, T. U.

T. U. Tumkur, J. K. Kitur, B. Chu, L. Gu, V. A. Podolskiy, E. E. Narimanov, and M. A. Noginov, “Control of reflectance and transmittance in scattering and curvilinear hyperbolic metamaterials,” Appl. Phys. Lett.101, 091105 (2012).
[CrossRef]

Vakil, A.

A. Vakil and N. Engheta, “One-atom-thick reflectors for surface plasmon polariton surface waves on graphene,” Opt. Comm.285, 3428 – 3430 (2012).
[CrossRef]

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

van der Marel, D.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett.100, 117401 (2008).
[CrossRef] [PubMed]

van Heumen, E.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett.100, 117401 (2008).
[CrossRef] [PubMed]

Wang, B.

B. Wang, X. Zhang, F. J. Garcia-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett.109, 073901 (2012).
[CrossRef] [PubMed]

Wang, X.

X. Wang, L. Zhi, and K. Mullen, “Transparent, conductive graphene electrodes for dye-sensitized solar cells,” Nano Lett.8, 323–327 (2008).
[CrossRef]

Webb, K. J.

Wulfhekel, W.

L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbucken, “A graphene electron lens,” Appl. Phys. Lett.100, 153106 (2012).
[CrossRef]

Yakovlev, A. B.

C. S. R. Kaipa, A. B. Yakovlev, F. Medina, and F. Mesa, “Transmission through stacked 2d periodic distributions of square conducting patches,” J. Appl. Phys.112, 033101 (2012).
[CrossRef]

Y. R. Padooru, A. B. Yakovlev, C. S. Kaipa, F. Medina, and F. Mesa, “Circuit modeling of multiband high-impedance surface absorbers in the microwave regime,” Phys. Rev. B84, 035108 (2011).
[CrossRef]

G. W. Hanson, A. B. Yakovlev, and A. Mafi, “Excitation of discrete and continuous spectrum for a surface conductivity model of graphene,” J. Appl. Phys.110, 114305 (2011).
[CrossRef]

C. S. Kaipa, A. B. Yakovlev, F. Medina, F. Mesa, C. Butler, and A. P. Hibbins, “Circuit modeling of the transmissivity of stacked two-dimensional metallic meshes,” Opt. Express18, 13309–13320 (2010).
[CrossRef] [PubMed]

Yakovlev, G. W. P. Y. R.

C. S. R. Kaipa, G. W. P. Y. R. Yakovlev, Alexander Hanson, M. F. Medina, and F., “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B85, 245407 (2012).
[CrossRef]

Yang, M.

Yuan, X.

B. Wang, X. Zhang, F. J. Garcia-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett.109, 073901 (2012).
[CrossRef] [PubMed]

Zayats, A. V.

A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B86, 035148 (2012).
[CrossRef]

Zhang, X.

B. Wang, X. Zhang, F. J. Garcia-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett.109, 073901 (2012).
[CrossRef] [PubMed]

Zhang, Y.

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in graphene,” Phys. Rev. Lett.99, 246803 (2007).
[CrossRef]

K. Novoselov, A. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, and A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
[CrossRef] [PubMed]

Zhao, Y.

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in graphene,” Phys. Rev. Lett.99, 246803 (2007).
[CrossRef]

Zhi, L.

X. Wang, L. Zhi, and K. Mullen, “Transparent, conductive graphene electrodes for dye-sensitized solar cells,” Nano Lett.8, 323–327 (2008).
[CrossRef]

Zhou, J.

J. Sun, J. Zhou, B. Li, and F. Kang, “Indefinite permittivity and negative refraction in natural material: Graphite,” Appl. Phys. Lett.98, 101901 (2011).
[CrossRef]

Zhukovsky, S. V.

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic meta-materials: Strengths and limitations,” Phys. Rev. A85, 053842 (2012).
[CrossRef]

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett.36, 2530–2532 (2011).
[CrossRef] [PubMed]

ACS Nano (1)

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

Adv. Opto-Electron. (1)

Y. Guo, W. Newman, C. Cortes, and Z. Jacob, “Applications of hyperbolic metamaterial substrates,” Adv. Opto-Electron.2012, 452502 (2012).

Appl. Phys. B (2)

Z. Jacob, J. Kim, G. Naik, A. Boltasseva, E. Narimanov, and V. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B100, 215–218 (2010).
[CrossRef]

X. Ni, G. Naik, A. Kildishev, Y. Barnakov, A. Boltasseva, and V. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B103, 553–558 (2011).
[CrossRef]

Appl. Phys. Lett. (7)

J. Sun, J. Zhou, B. Li, and F. Kang, “Indefinite permittivity and negative refraction in natural material: Graphite,” Appl. Phys. Lett.98, 101901 (2011).
[CrossRef]

D. L. Sounas and C. Caloz, “Electromagnetic nonreciprocity and gyrotropy of graphene,” Appl. Phys. Lett.98, 021911 (2011).
[CrossRef]

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett.101, 131106 (2012).
[CrossRef]

Z. Jacob, I. I. Smolyaninov, and E. E. Narimanov, “Broadband purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett.100, 181105 (2012).
[CrossRef]

T. U. Tumkur, J. K. Kitur, B. Chu, L. Gu, V. A. Podolskiy, E. E. Narimanov, and M. A. Noginov, “Control of reflectance and transmittance in scattering and curvilinear hyperbolic metamaterials,” Appl. Phys. Lett.101, 091105 (2012).
[CrossRef]

T. Tumkur, L. Gu, J. Kitur, E. Narimanov, and M. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett.100, 161103–161103 (2012).
[CrossRef]

L. Gerhard, E. Moyen, T. Balashov, I. Ozerov, M. Portail, H. Sahaf, L. Masson, W. Wulfhekel, and M. Hanbucken, “A graphene electron lens,” Appl. Phys. Lett.100, 153106 (2012).
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IEEE Trans. Electromagn. Compat. (1)

G. Lovat, “Equivalent circuit for electromagnetic interaction and transmission through graphene sheets,” IEEE Trans. Electromagn. Compat.54, 101 –109 (2012).
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IEEE Trans. Microw. Theory Techn. (1)

D. Sounas and C. Caloz, “Gyrotropy and nonreciprocity of graphene for microwave applications,” IEEE Trans. Microw. Theory Techn.60, 901 –914 (2012).
[CrossRef]

IEEE Trans. Nanotechnol. (1)

F. Rana, “Graphene terahertz plasmon oscillators,” IEEE Trans. Nanotechnol.7, 91–99 (2008).
[CrossRef]

J. Appl. Phys. (4)

G. W. Hanson, A. B. Yakovlev, and A. Mafi, “Excitation of discrete and continuous spectrum for a surface conductivity model of graphene,” J. Appl. Phys.110, 114305 (2011).
[CrossRef]

M. Tamagnone, J. Gomez-Diaz, J. Mosig, and J. Perruisseau-Carrier, “Analysis and design of terahertz antennas based on plasmonic resonant graphene sheets,” J. Appl. Phys.112, 114915 (2012).
[CrossRef]

G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys.103, 064302 (2008).
[CrossRef]

C. S. R. Kaipa, A. B. Yakovlev, F. Medina, and F. Mesa, “Transmission through stacked 2d periodic distributions of square conducting patches,” J. Appl. Phys.112, 033101 (2012).
[CrossRef]

J. Opt. (1)

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt.14, 063001 (2012).
[CrossRef]

Nano Lett. (1)

X. Wang, L. Zhi, and K. Mullen, “Transparent, conductive graphene electrodes for dye-sensitized solar cells,” Nano Lett.8, 323–327 (2008).
[CrossRef]

Nature Nanotech. (1)

C. Chen, S. Rosenblatt, K. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. Stormer, T. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nature Nanotech.4, 861–867 (2009).
[CrossRef]

Opt. Comm. (1)

A. Vakil and N. Engheta, “One-atom-thick reflectors for surface plasmon polariton surface waves on graphene,” Opt. Comm.285, 3428 – 3430 (2012).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. A (1)

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic meta-materials: Strengths and limitations,” Phys. Rev. A85, 053842 (2012).
[CrossRef]

Phys. Rev. B (9)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and hall conductivity in graphene,” Phys. Rev. B75, 165407 (2007).
[CrossRef]

R. A. Jishi, M. S. Dresselhaus, and G. Dresselhaus, “Electron-phonon coupling and the electrical conductivity of fullerene nanotubules,” Phys. Rev. B48, 11385–11389 (1993).
[CrossRef]

Y. R. Padooru, A. B. Yakovlev, C. S. Kaipa, F. Medina, and F. Mesa, “Circuit modeling of multiband high-impedance surface absorbers in the microwave regime,” Phys. Rev. B84, 035108 (2011).
[CrossRef]

A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B86, 195408 (2012).
[CrossRef]

C. S. R. Kaipa, G. W. P. Y. R. Yakovlev, Alexander Hanson, M. F. Medina, and F., “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B85, 245407 (2012).
[CrossRef]

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B87, 075416 (2013).
[CrossRef]

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B86, 121108 (2012).
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C. Guclu, S. Campione, and F. Capolino, “Hyperbolic metamaterial as super absorber for scattered fields generated at its surface,” Phys. Rev. B86, 205130 (2012).
[CrossRef]

A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar, “Microscopic model of purcell enhancement in hyperbolic metamaterials,” Phys. Rev. B86, 035148 (2012).
[CrossRef]

Phys. Rev. Lett. (7)

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett.90, 077405 (2003).
[CrossRef] [PubMed]

I. Smolyaninov and E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett.105, 67402 (2010).
[CrossRef]

V. P. Gusynin and S. G. Sharapov, “Unconventional integer quantum hall effect in graphene,” Phys. Rev. Lett.95, 146801 (2005).
[CrossRef] [PubMed]

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett.100, 117401 (2008).
[CrossRef] [PubMed]

B. Wang, X. Zhang, F. J. Garcia-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett.109, 073901 (2012).
[CrossRef] [PubMed]

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

Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in graphene,” Phys. Rev. Lett.99, 246803 (2007).
[CrossRef]

Phys. Status Solidi Rapid Res. Lett. (1)

G. Naik and A. Boltasseva, “Semiconductors for plasmonics and metamaterials,” Phys. Status Solidi Rapid Res. Lett.4, 295–297 (2010).
[CrossRef]

Physica B: Condensed Matter (1)

J. Pendry and S. Ramakrishna, “Refining the perfect lens,” Physica B: Condensed Matter338, 329 – 332 (2003).
[CrossRef]

PNAS (1)

G. V. Naik, J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, “Demonstration of al:zno as a plasmonic component for near-infrared metamaterials,” PNAS109, 8834–8838 (2012).
[CrossRef] [PubMed]

Radio Sci. (1)

F. Capolino and M. Albani, “Truncation effects in a semi-infinite periodic array of thin strips: A discrete wiener-hopf formulation,” Radio Sci.44, RS2S91 (2009).
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Science (3)

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science336, 205–209 (2012).
[CrossRef] [PubMed]

K. Novoselov, A. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, and A. Firsov, “Electric field effect in atomically thin carbon films,” Science306, 666–669 (2004).
[CrossRef] [PubMed]

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

Other (2)

L. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, NJ, 1973).

D. Pozar, Microwave engineering (John Wiley & Sons, 2009).

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Fig. 1
Fig. 1

Composite multilayer material made by stacking graphene sheets and dielectric layers. Under certain conditions it exhibits hyperbolic-like iso-frequency wavevector dispersion as depicted in the inset, where vg indicates the direction of the group velocity.

Fig. 2
Fig. 2

Effective medium complex relative permittivity term εt = εtt for biased and unbiased graphene multilayer configuration.

Fig. 3
Fig. 3

Relative effective medium complex permittivity term εt = εtt of graphene HM versus the graphene sheets’ chemical potential for various spacer thicknesses at 12 THz.

Fig. 4
Fig. 4

Iso-frequency wavevector dispersion (kz = βzz) versus kt computed by both Bloch theory (dashed-dotted lines) and EMA (solid lines), for different chemical potential levels at 2 THz (a,b), and at 12 THz (c,d).

Fig. 5
Fig. 5

Reflection and transmission versus frequency for a finite thickness graphene-silica multilayered HM, at normal, and oblique incidence for both TEz and TMz polarizations, calculated by transfer matrix method (solid lines) and EMA (circles) when graphene layers are unbiased, i.e., μc = 0 eV.

Fig. 6
Fig. 6

Reflection and transmission versus frequency, for the same set of parameters as Fig. 5, except that now graphene layers are biased with μc = 0.4 eV.

Fig. 7
Fig. 7

Reflection and transmission of a 30° TMz wave from a 10 layer graphene-dielectric stack at 10 THz with variable spacer d, based on transfer matrix (solid lines) and EMA (circles).

Fig. 8
Fig. 8

(a) Dipole near-field emission over a finite thickness multilayer graphene HM over of a substrate, and (b) the its transverse equivalent network (TEN) for every spectral wave (both TEz and TMz).

Fig. 9
Fig. 9

(a) Ratio between power emitted in the lower space with the one in the upper space, Pdown/Pup, and (b) the ratio Ptot/Pfree space related to the transverse dipole located near the interface of free space and graphene-based HM made by N graphene layers on top of Si substrate. Calculations done via multilayer transfer matrix method (lines) and via EMA (markers) when chemical potential is μc = 0 eV.

Fig. 10
Fig. 10

(a) Ratio Pdown/Pup and (b) ratio Ptot/Pfree space for the same set of parameters in Fig. 9, but when chemical potential is μc = 0.4 eV.

Fig. 11
Fig. 11

Emitted power spectrum p TM ( k t ) = p up TM ( k t ) + p down TM ( k t ) in Eq. (15), solid lines, versus normalized traverse wavenumber ktd/π at (a) 0.1 THz, and (b) 3 THz, for different number of graphene-dielectric layers:N = 1, 10, and N → ∞. For comparison we also show the power spectrum p TE ( k t ) = p up TE ( k t ) + p down TE ( k t ) for N =1 and N → ∞ (dashed lines). The points A, B, and C denote the spectrum points k0d/π, ε d k 0 d / π, and ε S i k 0 d / π, respectively. Left panel plots have a horizontal logarithmic scale whereas right panel plots have a horizontal linear scale.

Fig. 12
Fig. 12

(a) Ratio Pdown/Pup and (b) ratio Ptot/Pfree space related to the transverse dipole located near the interface of free space and a semi-infinite graphene-based HM at 2 THz plotted versus dipole distance h, for different chemical potential μc values obtained via transfer matrix method (lines) and EMA (markers).

Equations (20)

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σ ( ω , μ c ) = j 4 π e 2 k B T h 2 ( ω j 2 Γ ) ( μ c k B T + 2 ln ( e μ c / ( k B T ) + 1 ) ) j 4 π e 2 ( ω j 2 Γ ) h 2 0 f D ( ζ ) f D ( ζ ) ( ω j 2 Γ ) 2 16 ( π ζ / h ) 2 d ζ ,
ε _ eff = ε t ( x ^ x ^ + y ^ y ^ ) + ε z z ^ z ^ .
ε t = ε t ' j ε t = ε d j σ ( ω , μ c ) ω ε 0 d .
k z 2 + k t 2 = ε t k 0 2 , TE z
k z 2 ε t + k t 2 ε z = k 0 2 , TM z
cos ( k z d ) = cos ( κ d d ) + j 1 2 σ Z d sin ( κ d d ) ,
1 ( k z d ) 2 2 1 ( κ d d ) 2 2 + j σ 2 Z d κ d d .
k z 2 = κ d 2 j σ ω μ 0 d , TE z
k z 2 = κ d 2 j σ κ d 2 ω ε 0 ε d d , TM z .
k z 2 = [ ε d j σ ω ε 0 d ] k 0 2 k t 2 ,
k z 2 = [ ε d j σ ω ε 0 d ] k 0 2 [ ε d j σ ω ε 0 d ] 1 ε d k t 2 .
k z 2 = ε t k 0 2 k t 2 , TE z
k z 2 = ε t k 0 2 ε t ε z k t 2 , TM z
P up , down = ω 2 | p t | 2 8 π 0 ( p up , down TE + p up , down TM ) d k t ,
p up , down TE , TM ( k t ) = Re ( Y up , down TE , TM * ( k t ) ) | Y tot TE , TM ( k t ) | 2 k t .
Y down = Y 0 j Y 0 sin ( κ 0 h ) + cos ( κ 0 h ) Y HM , N Y 0 cos ( κ 0 h ) + j sin ( κ 0 h ) Y HM , N .
[ T unit ] = [ A unit B unit C unit D unit ] = [ 1 0 σ 1 ] [ cos ( κ d d ) j Z d sin ( κ d d ) j Z d sin ( κ d d ) cos ( κ d d ) ] = [ cos ( κ d d ) j Z d sin ( κ d d ) j Z d sin ( κ d d ) + σ cos ( κ d d ) j σ Z d sin ( κ d d ) + cos ( κ d d ) ] ,
[ T N ] = [ A N B N C N D N ] = [ T unit ] N .
Y HM , N = C N + D N Y subs A N + B N Y subs ,
Y Bloch = A unit D unit ± ( A unit + D unit ) 2 4 2 B unit .

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