Abstract

We investigate ultrathin metasurfaces defined by anisotropic conductivity tensors using a Green’s function approach, focusing on their exciting plasmonic interactions and dramatic enhancement of light-matter interactions for hyperbolic dispersion. We apply our analytical formulation to explore several practical implementations at THz and near infrared frequencies, including electrically and magnetically-biased graphene sheets – a natural isotropic elliptic metasurface – and densely-packed arrays of graphene ribbons modelled through an effective medium approach. This latter configuration allows the electrical control of their band diagram topology – from elliptic to hyperbolic, going through the extremely anisotropic σ-near-zero case – providing unprecedented control over the confinement and direction of plasmon propagation while simultaneously boosting the local density of states. Finally, we study the influence of the strip granularity to delimit the accuracy of effective medium theory to model the electromagnetic interactions with hyperbolic metasurfaces. Our findings may lead to the development of ultrathin reconfigurable plasmonic devices able to provide extreme confinement and dynamic guidance of light while strongly interacting with their surroundings, with direct application in sensing, imaging, hyperlensing, on-chip networks, and communications.

© 2015 Optical Society of America

Full Article  |  PDF Article

Corrections

Alexandra Boltasseva and Jennifer Dionne, "Plasmonics feature issue: publisher’s note," Opt. Mater. Express 5, 2978-2978 (2015)
https://www.osapublishing.org/ome/abstract.cfm?uri=ome-5-12-2978

24 November 2015: A correction was made to the title.


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References

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    [Crossref]
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    [Crossref] [PubMed]
  44. D. Correas-Serrano, J. S. Gomez-Diaz, J. Perruisseau-Carrier, and A. Álvarez-Melcón, “Spatially Dispersive Graphene Single and Parallel Plate Waveguides: Analysis and Circuit Model,” IEEE Trans. Microw. Theory Tech. 61(12), 4333–4344 (2013).
    [Crossref]
  45. A. Ferreira, N. M. R. Peres, and A. H. Castro Neto, “Confined magneto-optical waves in graphene,” Phys. Rev. B 85(20), 205426 (2012).
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  46. J. S. Gómez-Díaz and J. Perruisseau-Carrier, “Propagation of hybrid transverse magnetic-transverse electric plasmons on magnetically biased graphene sheets,” J. Appl. Phys. 112(12), 124906 (2012).
    [Crossref]
  47. M. Tymchenko, A. Y. Nikitin, and L. Martín-Moreno, “Faraday Rotation Due to Excitation of Magnetoplasmons in Graphene Microribbons,” ACS Nano 7(11), 9780–9787 (2013).
    [Crossref] [PubMed]

2015 (4)

J. S. Gomez-Diaz, M. Tymchenko, and A. Alù, “Hyperbolic plasmons and topological transitions over uniaxial metasurfaces,” Phys. Rev. Lett. 114(23), 233901 (2015).
[Crossref] [PubMed]

O. Y. Yermakov, A. I. Ovcharenko, M. Song, A. A. Bogdanov, I. V. Iorsh, and Yu. S. Kivshar, “Hybrid waves localized at hyperbolic metasurfaces,” Phys. Rev. B 91(23), 235423 (2015).
[Crossref]

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref] [PubMed]

J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun. 6, 6334 (2015).
[Crossref] [PubMed]

2014 (6)

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014).
[Crossref] [PubMed]

M. Esquius-Morote, J. S. Gómez-Diaz, and J. Perruisseau-Carrier, “Sinusoidally Modulated Graphene Leaky-Wave Antenna for Electronic Beamscanning at THz,” IEEE Trans. Terahertz Sci. Technol. 4(1), 116–122 (2014).
[Crossref]

S. H. Mousavi, A. B. Khanikaev, J. Allen, M. Allen, and G. Shvets, “Gyromagnetically Induced Transparency of Metasurfaces,” Phys. Rev. Lett. 112(11), 117402 (2014).
[Crossref] [PubMed]

F. J. García de Abajo, “Graphene Plasmonics: Challenges and Opportunities,” ACS Photonics 1(3), 135–152 (2014).
[Crossref]

P. Chen, H. Huang, D. Akinwande, and A. Alu, “Graphene-Based Plasmonic Platform for Reconfigurable Terahertz Nanodevices,” ACS Photonics 1(8), 647–654 (2014).
[Crossref]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

2013 (16)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

F. Monticone, N. M. Estakhri, and A. Alù, “Full Control of Nanoscale Optical Transmission with a Composite Metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

D. L. Sounas, H. S. Skulason, H. V. Nguyen, A. Guermoune, M. Siaj, T. Szkopek, and C. Caloz, “Faraday rotation in magnetically biased graphene at microwave frequencies,” Appl. Phys. Lett. 102(19), 191901 (2013).
[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. B 87(7), 075416 (2013).
[Crossref]

A. M. Patel and A. Grbic, “Modeling and Analysis of Printed-Circuit Tensor Impedance Surfaces,” IEEE Trans. Antenn. Propag. 61(1), 211–220 (2013).
[Crossref]

R. Quarfoth and D. Sievenpiper, “Artificial Tensor Impedance Surface Waveguides,” IEEE Trans. Antenn. Propag. 61(7), 3597–3606 (2013).
[Crossref]

P. Tassin, T. Koschny, and C. M. Soukoulis, “Graphene for terahertz applications,” Science 341(6146), 620–621 (2013).
[Crossref] [PubMed]

M. Tymchenko, A. Y. Nikitin, and L. Martín-Moreno, “Faraday Rotation Due to Excitation of Magnetoplasmons in Graphene Microribbons,” ACS Nano 7(11), 9780–9787 (2013).
[Crossref] [PubMed]

D. Correas-Serrano, J. S. Gomez-Diaz, J. Perruisseau-Carrier, and A. Álvarez-Melcón, “Spatially Dispersive Graphene Single and Parallel Plate Waveguides: Analysis and Circuit Model,” IEEE Trans. Microw. Theory Tech. 61(12), 4333–4344 (2013).
[Crossref]

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013).
[Crossref] [PubMed]

C. Simovski, S. Maslovski, I. Nefedov, and S. Tretyakov, “Optimization of radiative heat transfer in hyperbolic metamaterials for thermophotovoltaic applications,” Opt. Express 21(12), 14988–15013 (2013).
[Crossref] [PubMed]

C. Argyropoulos, N. M. Estakhri, F. Monticone, and A. Alù, “Negative refraction, gain and nonlinear effects in hyperbolic metamaterials,” Opt. Express 21(12), 15037–15047 (2013).
[Crossref] [PubMed]

V. P. Drachev, V. A. Podolskiy, and A. V. Kildishev, “Hyperbolic metamaterials: new physics behind a classical problem,” Opt. Express 21(12), 15048–15064 (2013).
[Crossref] [PubMed]

J. S. Gómez-Díaz and J. Perruisseau-Carrier, “Graphene-based plasmonic switches at near infrared frequencies,” Opt. Express 21(13), 15490–15504 (2013).
[Crossref] [PubMed]

J. S. Gómez-Díaz, M. Esquius-Morote, and J. Perruisseau-Carrier, “Plane wave excitation-detection of non-resonant plasmons along finite-width graphene strips,” Opt. Express 21(21), 24856–24872 (2013).
[Crossref] [PubMed]

2012 (5)

A. Ferreira, N. M. R. Peres, and A. H. Castro Neto, “Confined magneto-optical waves in graphene,” Phys. Rev. B 85(20), 205426 (2012).
[Crossref]

J. S. Gómez-Díaz and J. Perruisseau-Carrier, “Propagation of hybrid transverse magnetic-transverse electric plasmons on magnetically biased graphene sheets,” J. Appl. Phys. 112(12), 124906 (2012).
[Crossref]

A. V. Chshelokova, P. V. Kapitanova, A. N. Poddubny, D. S. Filonov, A. P. Slobozhanyuk, Y. S. Kivshar, and P. A. Belov, “Hyperbolic transmission-line metamaterials,” J. Appl. Phys. 112(7), 073116 (2012).
[Crossref]

H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref] [PubMed]

S. H. Mousavi, A. B. Khanikaev, and G. Shvets, “Optical properties of Fano-resonant metallic metasurfaces on a substrate,” Phys. Rev. B 85(15), 155429 (2012).
[Crossref]

2011 (2)

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene Plasmonics: A Platform for Strong Light-Matter Interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 023807 (2011).
[Crossref]

2010 (1)

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

2009 (1)

A. Fang, T. Koschny, and C. M. Soukoulis, “Optical anisotropic metamaterials: negative refraction and focusing,” Phys. Rev. B 79(24), 245127 (2009).
[Crossref]

2008 (1)

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

2007 (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

2006 (3)

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[Crossref]

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73(11), 113110 (2006).
[Crossref]

2003 (2)

D. R. Smith and D. Schurig, “Electromagnetic Wave Propagation in Media with Indefinite Permittivity and Permeability Tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

H. J. Bilow, “Guided Waves on a Planar Tensor Impedance Surface,” IEEE Trans. Antenn. Propag. 51(10), 2788–2792 (2003).
[Crossref]

1992 (1)

A. Lakhtakia, “Green’s functions and Brewster condition for a halfspace bounded by an anisotropic impedance plane,” Int. J. Infrared Millim. Waves 13(2), 161–170 (1992).
[Crossref]

Akinwande, D.

P. Chen, H. Huang, D. Akinwande, and A. Alu, “Graphene-Based Plasmonic Platform for Reconfigurable Terahertz Nanodevices,” ACS Photonics 1(8), 647–654 (2014).
[Crossref]

Alekseyev, L. V.

Allen, J.

S. H. Mousavi, A. B. Khanikaev, J. Allen, M. Allen, and G. Shvets, “Gyromagnetically Induced Transparency of Metasurfaces,” Phys. Rev. Lett. 112(11), 117402 (2014).
[Crossref] [PubMed]

Allen, M.

S. H. Mousavi, A. B. Khanikaev, J. Allen, M. Allen, and G. Shvets, “Gyromagnetically Induced Transparency of Metasurfaces,” Phys. Rev. Lett. 112(11), 117402 (2014).
[Crossref] [PubMed]

Alu, A.

P. Chen, H. Huang, D. Akinwande, and A. Alu, “Graphene-Based Plasmonic Platform for Reconfigurable Terahertz Nanodevices,” ACS Photonics 1(8), 647–654 (2014).
[Crossref]

Alù, A.

J. S. Gomez-Diaz, M. Tymchenko, and A. Alù, “Hyperbolic plasmons and topological transitions over uniaxial metasurfaces,” Phys. Rev. Lett. 114(23), 233901 (2015).
[Crossref] [PubMed]

C. Argyropoulos, N. M. Estakhri, F. Monticone, and A. Alù, “Negative refraction, gain and nonlinear effects in hyperbolic metamaterials,” Opt. Express 21(12), 15037–15047 (2013).
[Crossref] [PubMed]

F. Monticone, N. M. Estakhri, and A. Alù, “Full Control of Nanoscale Optical Transmission with a Composite Metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

Álvarez-Melcón, A.

D. Correas-Serrano, J. S. Gomez-Diaz, J. Perruisseau-Carrier, and A. Álvarez-Melcón, “Spatially Dispersive Graphene Single and Parallel Plate Waveguides: Analysis and Circuit Model,” IEEE Trans. Microw. Theory Tech. 61(12), 4333–4344 (2013).
[Crossref]

Argyropoulos, C.

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[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. B 87(7), 075416 (2013).
[Crossref]

A. V. Chshelokova, P. V. Kapitanova, A. N. Poddubny, D. S. Filonov, A. P. Slobozhanyuk, Y. S. Kivshar, and P. A. Belov, “Hyperbolic transmission-line metamaterials,” J. Appl. Phys. 112(7), 073116 (2012).
[Crossref]

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 023807 (2011).
[Crossref]

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73(11), 113110 (2006).
[Crossref]

Bernard, L. S.

J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun. 6, 6334 (2015).
[Crossref] [PubMed]

Bilow, H. J.

H. J. Bilow, “Guided Waves on a Planar Tensor Impedance Surface,” IEEE Trans. Antenn. Propag. 51(10), 2788–2792 (2003).
[Crossref]

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S. H. Mousavi, A. B. Khanikaev, J. Allen, M. Allen, and G. Shvets, “Gyromagnetically Induced Transparency of Metasurfaces,” Phys. Rev. Lett. 112(11), 117402 (2014).
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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. B 87(7), 075416 (2013).
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M. Tymchenko, A. Y. Nikitin, and L. Martín-Moreno, “Faraday Rotation Due to Excitation of Magnetoplasmons in Graphene Microribbons,” ACS Nano 7(11), 9780–9787 (2013).
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Ovcharenko, A. I.

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A. M. Patel and A. Grbic, “Modeling and Analysis of Printed-Circuit Tensor Impedance Surfaces,” IEEE Trans. Antenn. Propag. 61(1), 211–220 (2013).
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A. Ferreira, N. M. R. Peres, and A. H. Castro Neto, “Confined magneto-optical waves in graphene,” Phys. Rev. B 85(20), 205426 (2012).
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J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun. 6, 6334 (2015).
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A. V. Chshelokova, P. V. Kapitanova, A. N. Poddubny, D. S. Filonov, A. P. Slobozhanyuk, Y. S. Kivshar, and P. A. Belov, “Hyperbolic transmission-line metamaterials,” J. Appl. Phys. 112(7), 073116 (2012).
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Polking, M.

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D. R. Smith and D. Schurig, “Electromagnetic Wave Propagation in Media with Indefinite Permittivity and Permeability Tensors,” Phys. Rev. Lett. 90(7), 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. B 87(7), 075416 (2013).
[Crossref]

Shalaev, V. M.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

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[Crossref] [PubMed]

Shvets, G.

S. H. Mousavi, A. B. Khanikaev, J. Allen, M. Allen, and G. Shvets, “Gyromagnetically Induced Transparency of Metasurfaces,” Phys. Rev. Lett. 112(11), 117402 (2014).
[Crossref] [PubMed]

S. H. Mousavi, A. B. Khanikaev, and G. Shvets, “Optical properties of Fano-resonant metallic metasurfaces on a substrate,” Phys. Rev. B 85(15), 155429 (2012).
[Crossref]

Siaj, M.

D. L. Sounas, H. S. Skulason, H. V. Nguyen, A. Guermoune, M. Siaj, T. Szkopek, and C. Caloz, “Faraday rotation in magnetically biased graphene at microwave frequencies,” Appl. Phys. Lett. 102(19), 191901 (2013).
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R. Quarfoth and D. Sievenpiper, “Artificial Tensor Impedance Surface Waveguides,” IEEE Trans. Antenn. Propag. 61(7), 3597–3606 (2013).
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Skulason, H. S.

D. L. Sounas, H. S. Skulason, H. V. Nguyen, A. Guermoune, M. Siaj, T. Szkopek, and C. Caloz, “Faraday rotation in magnetically biased graphene at microwave frequencies,” Appl. Phys. Lett. 102(19), 191901 (2013).
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A. V. Chshelokova, P. V. Kapitanova, A. N. Poddubny, D. S. Filonov, A. P. Slobozhanyuk, Y. S. Kivshar, and P. A. Belov, “Hyperbolic transmission-line metamaterials,” J. Appl. Phys. 112(7), 073116 (2012).
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D. R. Smith and D. Schurig, “Electromagnetic Wave Propagation in Media with Indefinite Permittivity and Permeability Tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

Song, M.

O. Y. Yermakov, A. I. Ovcharenko, M. Song, A. A. Bogdanov, I. V. Iorsh, and Yu. S. Kivshar, “Hybrid waves localized at hyperbolic metasurfaces,” Phys. Rev. B 91(23), 235423 (2015).
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C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
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P. Tassin, T. Koschny, and C. M. Soukoulis, “Graphene for terahertz applications,” Science 341(6146), 620–621 (2013).
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A. Fang, T. Koschny, and C. M. Soukoulis, “Optical anisotropic metamaterials: negative refraction and focusing,” Phys. Rev. B 79(24), 245127 (2009).
[Crossref]

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D. L. Sounas, H. S. Skulason, H. V. Nguyen, A. Guermoune, M. Siaj, T. Szkopek, and C. Caloz, “Faraday rotation in magnetically biased graphene at microwave frequencies,” Appl. Phys. Lett. 102(19), 191901 (2013).
[Crossref]

Szkopek, T.

D. L. Sounas, H. S. Skulason, H. V. Nguyen, A. Guermoune, M. Siaj, T. Szkopek, and C. Caloz, “Faraday rotation in magnetically biased graphene at microwave frequencies,” Appl. Phys. Lett. 102(19), 191901 (2013).
[Crossref]

Taniguchi, T.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
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P. Tassin, T. Koschny, and C. M. Soukoulis, “Graphene for terahertz applications,” Science 341(6146), 620–621 (2013).
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Tretyakov, S.

Tymchenko, M.

J. S. Gomez-Diaz, M. Tymchenko, and A. Alù, “Hyperbolic plasmons and topological transitions over uniaxial metasurfaces,” Phys. Rev. Lett. 114(23), 233901 (2015).
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C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
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C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
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A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
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O. Y. Yermakov, A. I. Ovcharenko, M. Song, A. A. Bogdanov, I. V. Iorsh, and Yu. S. Kivshar, “Hybrid waves localized at hyperbolic metasurfaces,” Phys. Rev. B 91(23), 235423 (2015).
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Young, A. F.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
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ACS Nano (1)

M. Tymchenko, A. Y. Nikitin, and L. Martín-Moreno, “Faraday Rotation Due to Excitation of Magnetoplasmons in Graphene Microribbons,” ACS Nano 7(11), 9780–9787 (2013).
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ACS Photonics (2)

F. J. García de Abajo, “Graphene Plasmonics: Challenges and Opportunities,” ACS Photonics 1(3), 135–152 (2014).
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P. Chen, H. Huang, D. Akinwande, and A. Alu, “Graphene-Based Plasmonic Platform for Reconfigurable Terahertz Nanodevices,” ACS Photonics 1(8), 647–654 (2014).
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Appl. Phys. Lett. (1)

D. L. Sounas, H. S. Skulason, H. V. Nguyen, A. Guermoune, M. Siaj, T. Szkopek, and C. Caloz, “Faraday rotation in magnetically biased graphene at microwave frequencies,” Appl. Phys. Lett. 102(19), 191901 (2013).
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IEEE Trans. Microw. Theory Tech. (1)

D. Correas-Serrano, J. S. Gomez-Diaz, J. Perruisseau-Carrier, and A. Álvarez-Melcón, “Spatially Dispersive Graphene Single and Parallel Plate Waveguides: Analysis and Circuit Model,” IEEE Trans. Microw. Theory Tech. 61(12), 4333–4344 (2013).
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M. Esquius-Morote, J. S. Gómez-Diaz, and J. Perruisseau-Carrier, “Sinusoidally Modulated Graphene Leaky-Wave Antenna for Electronic Beamscanning at THz,” IEEE Trans. Terahertz Sci. Technol. 4(1), 116–122 (2014).
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G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
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A. V. Chshelokova, P. V. Kapitanova, A. N. Poddubny, D. S. Filonov, A. P. Slobozhanyuk, Y. S. Kivshar, and P. A. Belov, “Hyperbolic transmission-line metamaterials,” J. Appl. Phys. 112(7), 073116 (2012).
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J. S. Gómez-Díaz and J. Perruisseau-Carrier, “Propagation of hybrid transverse magnetic-transverse electric plasmons on magnetically biased graphene sheets,” J. Appl. Phys. 112(12), 124906 (2012).
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V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
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Nano Lett. (1)

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene Plasmonics: A Platform for Strong Light-Matter Interactions,” Nano Lett. 11(8), 3370–3377 (2011).
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Nat. Commun. (1)

J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun. 6, 6334 (2015).
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Nat. Mater. (1)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
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Nat. Nanotechnol. (2)

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
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Nat. Photonics (1)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
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Nature (1)

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
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Opt. Express (7)

Phys. Rev. A (1)

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Spontaneous radiation of a finite-size dipole emitter in hyperbolic media,” Phys. Rev. A 84(2), 023807 (2011).
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Phys. Rev. B (7)

O. Y. Yermakov, A. I. Ovcharenko, M. Song, A. A. Bogdanov, I. V. Iorsh, and Yu. S. Kivshar, “Hybrid waves localized at hyperbolic metasurfaces,” Phys. Rev. B 91(23), 235423 (2015).
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P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73(11), 113110 (2006).
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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. B 87(7), 075416 (2013).
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S. H. Mousavi, A. B. Khanikaev, and G. Shvets, “Optical properties of Fano-resonant metallic metasurfaces on a substrate,” Phys. Rev. B 85(15), 155429 (2012).
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J. S. Gomez-Diaz, M. Tymchenko, and A. Alù, “Hyperbolic plasmons and topological transitions over uniaxial metasurfaces,” Phys. Rev. Lett. 114(23), 233901 (2015).
[Crossref] [PubMed]

D. R. Smith and D. Schurig, “Electromagnetic Wave Propagation in Media with Indefinite Permittivity and Permeability Tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

S. H. Mousavi, A. B. Khanikaev, J. Allen, M. Allen, and G. Shvets, “Gyromagnetically Induced Transparency of Metasurfaces,” Phys. Rev. Lett. 112(11), 117402 (2014).
[Crossref] [PubMed]

Science (3)

P. Tassin, T. Koschny, and C. M. Soukoulis, “Graphene for terahertz applications,” Science 341(6146), 620–621 (2013).
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A. Leviyev, B. Stein, T. Galfsky, H. Krishnamoorthy, I. L. Kuskovsky, V. Menon, and A. B. Khanikaev, “Nonreciprocity and One-Way Topological Transitions in Hyperbolic Metamaterials”, arXiv:1505.05438v1 [physics.optics].

N. Engheta and R. Ziolkowski, Metamaterials: Physics and Engineering Explorations (Wiley, New York, 2006).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C + + : the art of scientific computing, 3rd edition (Cambridge University Press, New York, 2007).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press Cambridge, England, 2006).

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Figures (7)

Fig. 1
Fig. 1   E z field component of surface plasmons excited by a z-oriented electric dipole located 10 nm above homogeneous metasurfaces defined by various conductivity tensors. (a) Isotropic elliptical metasurface with σ x x = σ y y = 0.05 + 0.3 i   mS . (b) Hyperbolic metasurface with σ x x = 0.05 0.3 i   mS and σ y y = 0.05 + 0.3 i   mS . (c) Hyperbolic metasurface with σ x x = 0.05 + 0.15 i   mS , σ y y = 0.05 0.15 i   mS , σ x y = σ y x = 0.26 i   mS . (d) σ -near zero metasurface with σ x x = 0.05 + 0.1 i   mS and   σ x x = 0.05 5 i   mS . The insets show possible realizations of the different metasurface topologies using pristine or nanostructured graphene layers.
Fig. 2
Fig. 2 Isofrequency contours of several lossless anisotropic metasurfaces. (a) Elliptic isotropic (red line) and anisotropic (blue line) configurations, with σ x x = σ y y = 0.5 i   mS and σ x x = 5 i   m S ,   σ y y = 0.37 i   mS , respectively. (b) Hyperbolic metasurface, with σ x x = 5 i   m S ,   σ y y = 5 i   mS . (c) Hyperbolic metasurface, with σ x x = 5 i   m S ,   σ y y = 5 i   mS ,   σ x y = σ y x = 15 i   m S . The green line is computed using the asymptotic expression of Eq. (10). The inset (top right) illustrates the procedure employed to accurately solve the dispersion relation of Eq. (8). Operation frequency is 10 THz.
Fig. 3
Fig. 3 Electrically and magnetically-biased graphene as a natural isotropic elliptic metasurface. Isofrequency contour of the supported plasmons at 10 THz versus (a) chemical potential, with B = 0   T , (b) magnetic field, with μ c = 0.2   eV . SER in logarithm scale of a z-oriented emitter versus its position d above graphene [see inset of Fig. 1(b)] as a function of: (c) chemical potential, with B = 0   T at 10 THz, (d) magnetic field, with μ c = 0.2  eV at 10 THz, (e) frequency, with B = 0   T and μ c = 0.05  eV , and (f) frequency, with B = 5   T and μ c = 0.05  eV . Other parameters are the graphene relaxation time τ = 0.1   ps , and temperature T = 300   K .
Fig. 4
Fig. 4 Effective conductivity tensor   σ ¯ ¯ e f f (in mS) of an array of densely packed graphene strips versus frequency and ribbon width W , computed using the effective medium approach (15). (a) Re [ σ y y e f f ] , (b) Im [ σ y y e f f ] , (c) Re [ σ x x e f f ] , (d) Im [ σ x x e f f ] . The periodicity is set to L = 50   n m , the temperature is T = 300   K , and the graphene relaxation time and chemical potential are τ = 0.1   p s and μ c = 0.2   e V , respectively.
Fig. 5
Fig. 5 Properties of the surface plasmons supported by an array of densely packed graphene strips. Normalized phase constant (a) and figure of merit (b) of the SPPs versus their angle of propagation φ within the metasurface, for different strip widths W. The graphene chemical potential is μ c = 0.2  eV . Panels (c) and (d) show similar data versus graphene chemical potential, keeping the strip width fix to W = 44   n m . Isofrequency contours (dispersion relation) of the metasurface versus (e) strip width W, fixing graphene chemical potential to μ c = 0.2  eV and (f) chemical potential, keeping the strip width fix to W = 44   nm . Other parameters are strip periodicity L = 50  nm , graphene relaxation time τ = 0.1   ps , operation frequency 10 THz and temperature T = 300   K .
Fig. 6
Fig. 6 SER in logarithmic scale for a z-oriented emitter located above an array of densely packed graphene strips versus the ribbon width W . The SER is computed using Eq. (2), modelling the structure using the effective conductivity tensor of Eq. (15). In the upper row, the SER of a dipole placed at d = 10 nm above the metasurface is shown versus frequency. Graphene’s chemical potential is set to (a) μ c = 0.2  eV and (b) μ c = 1.0  eV . The lower row depicts the SER of an emitter versus its distance d towards the metasurface. Graphene’s chemical potential is μ c = 0.2  eV , and frequency is set to (c) 10 THz and (d) 30 THz. Other parameters are strips periodicity L = 50   n m , graphene relaxation time τ = 0.1   ps and temperature   T = 300   K .
Fig. 7
Fig. 7 Influence of periodicity in the electromagnetic response of graphene-based hyperbolic metasurfaces. (a) SER in logarithm scale of x, y and z-oriented emitters located above an array of densely packed graphene strips versus their periodicity L . The SER is computed using Eq. (2), modelling the structure using the effective conductivity tensor of Eq. (15). Panels (b), (c) and (d) shows the dispersion relation of the structure, computed using a full-wave mode-matching approach [47] (colormaps) and the homogenous metasurface model of Eq. (15) (white dashed line). (b) L = 15   nm , (c) L = 50   nm , and (d) L = 85   nm , corresponding to points B, C and D of panel (a). The strip width is W = L / 2 , operation frequency is 10 THz, and graphene relaxation time, chemical potential and temperature are τ = 0.1  ps , μ c = 0.2   eV , and T = 300  K , respectively.

Equations (15)

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σ ¯ ¯ = ( σ x x σ x y σ y x σ y y ) ,
S E R = P P 0 = 1 + 6 π | μ p | k 0 μ p Im [ G ¯ ¯ S ( r 0 , r 0 , ω ) ] μ p ,
G ¯ ¯ S ( r 0 , r 0 , ω ) = i 8 π 2 ( Γ s s M ¯ ¯ s s + Γ s p M ¯ ¯ s p + Γ p s M ¯ ¯ p s + Γ p p M ¯ ¯ p p ) e i 2 k z z 0 d k x d k y ,
M ¯ ¯ s s = 1 k z k ρ 2 ( k y 2 k x k y 0 k x k y k x 2 0 0 0 0 ) , M ¯ ¯ p p = k z k 0 2 k ρ 2 ( k x 2 k x k y k x k ρ 2 / k z k x k y k y 2 k y k ρ 2 / k z k x k ρ 2 / k z k y k ρ 2 / k z k ρ 4 / k z 2 ) , M ¯ ¯ s p = 1 k 0 k ρ 2 ( k x k y k y 2 k y k ρ 2 / k z k x 2 k x k y k x k ρ 2 / k z 0 0 0 ) , M ¯ ¯ p s = 1 k 0 k ρ 2 ( k x k y k x 2 0 k y 2 k x k y 0 k y k ρ 2 / k z k x k ρ 2 / k z 0 ) ,
Γ ¯ ¯ = ( Γ s s Γ s p Γ p s Γ p p ) = ( η 0 σ y y ( 2 Z p + η 0 σ ' x x ) + η 0 2 σ x y σ y x ( 2 Z s + η 0 σ y y ) ( 2 Z p + η 0 σ x x ) η 0 2 σ x y σ y x 2 c p Z p η 0 σ x y [ ( 2 Z s + η 0 σ y y ) ( 2 Z p + η 0 σ x x ) η 0 2 σ x y σ y x ] 2 Z s η 0 σ y x c p [ ( 2 Z s + η 0 σ y y ) ( 2 Z p + η 0 σ x x ) η 0 2 σ x y σ y x ] η 0 σ x x ( 2 Z s + η 0 σ y y ) + η 0 2 σ x y σ y x ( 2 Z s + η 0 σ y y ) ( 2 Z p + η 0 σ x x ) η 0 2 σ x y σ y x ) ,
σ ¯ ¯ = ( σ x x σ x y σ y x σ y y ) = R ¯ ¯ T σ ¯ ¯ R ¯ ¯ = 1 k ρ 2 ( k x 2 σ x x + k y 2 σ y y + k x k y ( σ x y + σ y x ) k x 2 σ x y k y 2 σ y x + k x k y ( σ y y σ x x ) k x 2 σ y x k y 2 σ x y + k x k y ( σ y y σ x x ) k x 2 σ y y + k y 2 σ x x k x k y ( σ x y + σ y x ) ) ,
R ¯ ¯ = ( cos ( φ ) sin ( φ ) sin ( φ ) cos ( φ ) ) = 1 k ρ ( k x k y k y k x ) , R ¯ ¯ T = ( cos ( φ ) sin ( φ ) sin ( φ ) cos ( φ ) ) = 1 k ρ ( k x k y k y k x ) ,
( 2 Z s + η 0 σ ' y y ) ( 2 Z p + η 0 σ ' x x ) η 0 2 σ ' x y σ ' y x = 0.
k z ± ( φ ) = k 0 2 σ x x [ ( 2 η 0 + η 0 2 ( σ x x σ y y σ x y σ y x ) ) ± ( 2 η 0 + η 0 2 ( σ x x σ y y σ x y σ y x ) ) 2 4 σ x x σ y y ] .
k y = m k x ± b ,
m ( 1 , 2 ) = 1 2 σ y y [ ( σ x y + σ y x ) ± ( σ x y + σ y x ) 2 4 σ x x σ y y ] ,
b ( 1 , 2 ) = m ( 1 , 2 ) k 0 1 [ A 2 σ x x ] 2  and b ( 3 ) = k 0 1 [ A 2 σ y y ] 2 ,
m ( 1 , 2 ) = ± σ x x σ y y , b ( 1 , 2 ) = m ( 1 , 2 ) k 0 1 + ( 2 η 0 σ x x ) 2  and b ( 3 ) = k 0 1 + ( 2 η 0 σ y y ) 2 .
σ ¯ ¯ = ( σ d σ h σ h σ d ) ,
σ x x e f f = L σ σ C W σ C + G σ and σ y y e f f = σ W L ,

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