Abstract

In the present article we numerically investigated the magneto-optical behaviour of a sub-wavelength structure composed by a monolayer graphene and a metallic metasurface of optical resonators. Using this hybrid graphene-metal structure, a large increase of the non-reciprocal polarization rotation of graphene can be achieved over a broad range of terahertz frequencies. We demonstrate that the symmetry of the resonator geometry plays a key role for the performance of the system: in particular, increasing the symmetry of the resonator the non-reciprocal properties can be progressively enhanced. Moreover, the possibility to exploit the metallic metasurface as a voltage gate to vary the graphene Fermi energy allows the system working point to be tuned to the desired frequency range. Another peculiar result is the achievement of a structure able to operate both in transmission and reflection with almost the same performance, but in a different frequency range of operation. The described system is hence a sub-wavelength, tunable, multifunctional, effective non-reciprocal element in the terahertz region.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. A. Tredicucci and M. S. Vitiello, “Device concepts for graphene-based terahertz photonics,” IEEE J. Sel. Topics Quantum Electron. 20(1), 130–138 (2014).
    [Crossref]
  2. M. Shalaby, M. Peccianti, Y. Ozturk, and R. Morandotti, “A magnetic non-reciprocal isolator for broadband terahertz operation,” Nat. Commun. 4, 1558 (2013).
    [Crossref] [PubMed]
  3. O. Morikawa, A. Quema, S. Nashima, H. Sumikura, T. Nagashima, and M. Hangyo, “Faraday ellipticity and faraday rotation of a doped-silicon wafer studied by terahertz time-domain spectroscopy,” J. Appl. Phys. 100(3), 033105 (2006).
    [Crossref]
  4. A. Shuvaev, G. Astakhov, A. Pimenov, C. Brüne, H. Buhmann, and L. Molenkamp, “Giant magneto-optical faraday effect in hgte thin films in the terahertz spectral range,” Phys. Rev. Lett. 106(10), 107404 (2011).
    [Crossref] [PubMed]
  5. M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
    [Crossref]
  6. A. C. Neto, F. Guinea, N. M. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109 (2009).
    [Crossref]
  7. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
    [Crossref]
  8. I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
    [Crossref] [PubMed]
  9. N. Ubrig, I. Crassee, J. Levallois, I. O. Nedoliuk, F. Fromm, M. Kaiser, T. Seyller, and A. B. Kuzmenko, “Fabry-Pérot enhanced faraday rotation in graphene,” Opt. Express 21(21), 24736–24741 (2013).
    [Crossref] [PubMed]
  10. M. Tamagnone, C. Moldovan, J.-M. Poumirol, A. B. Kuzmenko, A. M. Ionescu, J. R. Mosig, and J. Perruisseau-Carrier, “Near optimal graphene terahertz non-reciprocal isolator,” Nat. Commun. 7, 11216 (2016).
    [Crossref] [PubMed]
  11. H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett. 98(26), 261915 (2011).
    [Crossref]
  12. H. Da, Q. Bao, R. Sanaei, J. Teng, K. P. Loh, F. J. Garcia-Vidal, and C.-W. Qiu, “Monolayer graphene photonic metastructures: Giant faraday rotation and nearly perfect transmission,” Phys. Rev. B 88(20), 205405 (2013).
    [Crossref]
  13. A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett. 101(23), 231605 (2012).
    [Crossref]
  14. Y. Hadad, A. R. Davoyan, N. Engheta, and B. Z. Steinberg, “Extreme and quantized magneto-optics with graphene meta-atoms and metasurfaces,” ACS Photonics 1(10), 1068–1073 (2014).
    [Crossref]
  15. J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
    [Crossref]
  16. S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
    [Crossref]
  17. A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
    [Crossref]
  18. M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
    [Crossref]
  19. M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95(8), 1658–1665 (2007).
    [Crossref]
  20. J. F. O’Hara, E. Smirnova, A. K. Azad, H.-T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).
  21. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
    [Crossref] [PubMed]
  22. W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009).
    [Crossref]
  23. M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photon. 8(7), 556–563 (2014).
    [Crossref]
  24. A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
    [Crossref]

2016 (1)

M. Tamagnone, C. Moldovan, J.-M. Poumirol, A. B. Kuzmenko, A. M. Ionescu, J. R. Mosig, and J. Perruisseau-Carrier, “Near optimal graphene terahertz non-reciprocal isolator,” Nat. Commun. 7, 11216 (2016).
[Crossref] [PubMed]

2015 (2)

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

2014 (4)

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photon. 8(7), 556–563 (2014).
[Crossref]

Y. Hadad, A. R. Davoyan, N. Engheta, and B. Z. Steinberg, “Extreme and quantized magneto-optics with graphene meta-atoms and metasurfaces,” ACS Photonics 1(10), 1068–1073 (2014).
[Crossref]

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

A. Tredicucci and M. S. Vitiello, “Device concepts for graphene-based terahertz photonics,” IEEE J. Sel. Topics Quantum Electron. 20(1), 130–138 (2014).
[Crossref]

2013 (3)

M. Shalaby, M. Peccianti, Y. Ozturk, and R. Morandotti, “A magnetic non-reciprocal isolator for broadband terahertz operation,” Nat. Commun. 4, 1558 (2013).
[Crossref] [PubMed]

N. Ubrig, I. Crassee, J. Levallois, I. O. Nedoliuk, F. Fromm, M. Kaiser, T. Seyller, and A. B. Kuzmenko, “Fabry-Pérot enhanced faraday rotation in graphene,” Opt. Express 21(21), 24736–24741 (2013).
[Crossref] [PubMed]

H. Da, Q. Bao, R. Sanaei, J. Teng, K. P. Loh, F. J. Garcia-Vidal, and C.-W. Qiu, “Monolayer graphene photonic metastructures: Giant faraday rotation and nearly perfect transmission,” Phys. Rev. B 88(20), 205405 (2013).
[Crossref]

2012 (4)

A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett. 101(23), 231605 (2012).
[Crossref]

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

2011 (3)

A. Shuvaev, G. Astakhov, A. Pimenov, C. Brüne, H. Buhmann, and L. Molenkamp, “Giant magneto-optical faraday effect in hgte thin films in the terahertz spectral range,” Phys. Rev. Lett. 106(10), 107404 (2011).
[Crossref] [PubMed]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
[Crossref]

H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett. 98(26), 261915 (2011).
[Crossref]

2010 (1)

A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
[Crossref]

2009 (2)

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

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009).
[Crossref]

2007 (2)

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95(8), 1658–1665 (2007).
[Crossref]

J. F. O’Hara, E. Smirnova, A. K. Azad, H.-T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

2006 (2)

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

O. Morikawa, A. Quema, S. Nashima, H. Sumikura, T. Nagashima, and M. Hangyo, “Faraday ellipticity and faraday rotation of a doped-silicon wafer studied by terahertz time-domain spectroscopy,” J. Appl. Phys. 100(3), 033105 (2006).
[Crossref]

Abbott, D.

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009).
[Crossref]

Al-Naib, I.

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

Alonso-González, P.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Astakhov, G.

A. Shuvaev, G. Astakhov, A. Pimenov, C. Brüne, H. Buhmann, and L. Molenkamp, “Giant magneto-optical faraday effect in hgte thin films in the terahertz spectral range,” Phys. Rev. Lett. 106(10), 107404 (2011).
[Crossref] [PubMed]

Averitt, R. D.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

Azad, A. K.

J. F. O’Hara, E. Smirnova, A. K. Azad, H.-T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

Bai, J.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

Baldacci, L.

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

Bao, Q.

H. Da, Q. Bao, R. Sanaei, J. Teng, K. P. Loh, F. J. Garcia-Vidal, and C.-W. Qiu, “Monolayer graphene photonic metastructures: Giant faraday rotation and nearly perfect transmission,” Phys. Rev. B 88(20), 205405 (2013).
[Crossref]

Baranowski, J.

A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
[Crossref]

Bostwick, A.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
[Crossref]

Brüne, C.

A. Shuvaev, G. Astakhov, A. Pimenov, C. Brüne, H. Buhmann, and L. Molenkamp, “Giant magneto-optical faraday effect in hgte thin films in the terahertz spectral range,” Phys. Rev. Lett. 106(10), 107404 (2011).
[Crossref] [PubMed]

Buhmann, H.

A. Shuvaev, G. Astakhov, A. Pimenov, C. Brüne, H. Buhmann, and L. Molenkamp, “Giant magneto-optical faraday effect in hgte thin films in the terahertz spectral range,” Phys. Rev. Lett. 106(10), 107404 (2011).
[Crossref] [PubMed]

Carrega, M.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Chen, H.-T.

J. F. O’Hara, E. Smirnova, A. K. Azad, H.-T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

Chen, J.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

Clerici, M.

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

Coletti, C.

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

Crassee, I.

N. Ubrig, I. Crassee, J. Levallois, I. O. Nedoliuk, F. Fromm, M. Kaiser, T. Seyller, and A. B. Kuzmenko, “Fabry-Pérot enhanced faraday rotation in graphene,” Opt. Express 21(21), 24736–24741 (2013).
[Crossref] [PubMed]

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
[Crossref]

Da, H.

H. Da, Q. Bao, R. Sanaei, J. Teng, K. P. Loh, F. J. Garcia-Vidal, and C.-W. Qiu, “Monolayer graphene photonic metastructures: Giant faraday rotation and nearly perfect transmission,” Phys. Rev. B 88(20), 205405 (2013).
[Crossref]

H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett. 98(26), 261915 (2011).
[Crossref]

Davoyan, A. R.

Y. Hadad, A. R. Davoyan, N. Engheta, and B. Z. Steinberg, “Extreme and quantized magneto-optics with graphene meta-atoms and metasurfaces,” ACS Photonics 1(10), 1068–1073 (2014).
[Crossref]

Degl’Innocenti, R.

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

Engheta, N.

Y. Hadad, A. R. Davoyan, N. Engheta, and B. Z. Steinberg, “Extreme and quantized magneto-optics with graphene meta-atoms and metasurfaces,” ACS Photonics 1(10), 1068–1073 (2014).
[Crossref]

Fallahi, A.

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photon. 8(7), 556–563 (2014).
[Crossref]

A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett. 101(23), 231605 (2012).
[Crossref]

Fan, H.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

Faugeras, C.

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
[Crossref]

Fromm, F.

N. Ubrig, I. Crassee, J. Levallois, I. O. Nedoliuk, F. Fromm, M. Kaiser, T. Seyller, and A. B. Kuzmenko, “Fabry-Pérot enhanced faraday rotation in graphene,” Opt. Express 21(21), 24736–24741 (2013).
[Crossref] [PubMed]

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

Gao, Y.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Gaponenko, I.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

Garcia-Vidal, F. J.

H. Da, Q. Bao, R. Sanaei, J. Teng, K. P. Loh, F. J. Garcia-Vidal, and C.-W. Qiu, “Monolayer graphene photonic metastructures: Giant faraday rotation and nearly perfect transmission,” Phys. Rev. B 88(20), 205405 (2013).
[Crossref]

Geim, A. K.

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

Gu, C.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

Guinea, F.

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

Hadad, Y.

Y. Hadad, A. R. Davoyan, N. Engheta, and B. Z. Steinberg, “Extreme and quantized magneto-optics with graphene meta-atoms and metasurfaces,” ACS Photonics 1(10), 1068–1073 (2014).
[Crossref]

Hangyo, M.

O. Morikawa, A. Quema, S. Nashima, H. Sumikura, T. Nagashima, and M. Hangyo, “Faraday ellipticity and faraday rotation of a doped-silicon wafer studied by terahertz time-domain spectroscopy,” J. Appl. Phys. 100(3), 033105 (2006).
[Crossref]

Highstrete, C.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

Hillenbrand, R.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Hone, J.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Hu, F.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

Huber, R.

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

Ionescu, A. M.

M. Tamagnone, C. Moldovan, J.-M. Poumirol, A. B. Kuzmenko, A. M. Ionescu, J. R. Mosig, and J. Perruisseau-Carrier, “Near optimal graphene terahertz non-reciprocal isolator,” Nat. Commun. 7, 11216 (2016).
[Crossref] [PubMed]

Kaiser, M.

Koppens, F. H. L.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Kuzmenko, A.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

Kuzmenko, A. B.

M. Tamagnone, C. Moldovan, J.-M. Poumirol, A. B. Kuzmenko, A. M. Ionescu, J. R. Mosig, and J. Perruisseau-Carrier, “Near optimal graphene terahertz non-reciprocal isolator,” Nat. Commun. 7, 11216 (2016).
[Crossref] [PubMed]

N. Ubrig, I. Crassee, J. Levallois, I. O. Nedoliuk, F. Fromm, M. Kaiser, T. Seyller, and A. B. Kuzmenko, “Fabry-Pérot enhanced faraday rotation in graphene,” Opt. Express 21(21), 24736–24741 (2013).
[Crossref] [PubMed]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
[Crossref]

Lange, C.

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

Lee, M.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

Levallois, J.

N. Ubrig, I. Crassee, J. Levallois, I. O. Nedoliuk, F. Fromm, M. Kaiser, T. Seyller, and A. B. Kuzmenko, “Fabry-Pérot enhanced faraday rotation in graphene,” Opt. Express 21(21), 24736–24741 (2013).
[Crossref] [PubMed]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
[Crossref]

Li, J.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

Liang, G.

H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett. 98(26), 261915 (2011).
[Crossref]

Loh, K. P.

H. Da, Q. Bao, R. Sanaei, J. Teng, K. P. Loh, F. J. Garcia-Vidal, and C.-W. Qiu, “Monolayer graphene photonic metastructures: Giant faraday rotation and nearly perfect transmission,” Phys. Rev. B 88(20), 205405 (2013).
[Crossref]

Lundeberg, M. B.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Maag, T.

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

Martinez, G.

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
[Crossref]

Mazhorova, A.

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

Miles, R. E.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95(8), 1658–1665 (2007).
[Crossref]

Miseikis, V.

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

Moldovan, C.

M. Tamagnone, C. Moldovan, J.-M. Poumirol, A. B. Kuzmenko, A. M. Ionescu, J. R. Mosig, and J. Perruisseau-Carrier, “Near optimal graphene terahertz non-reciprocal isolator,” Nat. Commun. 7, 11216 (2016).
[Crossref] [PubMed]

Molenkamp, L.

A. Shuvaev, G. Astakhov, A. Pimenov, C. Brüne, H. Buhmann, and L. Molenkamp, “Giant magneto-optical faraday effect in hgte thin films in the terahertz spectral range,” Phys. Rev. Lett. 106(10), 107404 (2011).
[Crossref] [PubMed]

Morandotti, R.

M. Shalaby, M. Peccianti, Y. Ozturk, and R. Morandotti, “A magnetic non-reciprocal isolator for broadband terahertz operation,” Nat. Commun. 4, 1558 (2013).
[Crossref] [PubMed]

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

Morikawa, O.

O. Morikawa, A. Quema, S. Nashima, H. Sumikura, T. Nagashima, and M. Hangyo, “Faraday ellipticity and faraday rotation of a doped-silicon wafer studied by terahertz time-domain spectroscopy,” J. Appl. Phys. 100(3), 033105 (2006).
[Crossref]

Mosig, J. R.

M. Tamagnone, C. Moldovan, J.-M. Poumirol, A. B. Kuzmenko, A. M. Ionescu, J. R. Mosig, and J. Perruisseau-Carrier, “Near optimal graphene terahertz non-reciprocal isolator,” Nat. Commun. 7, 11216 (2016).
[Crossref] [PubMed]

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photon. 8(7), 556–563 (2014).
[Crossref]

Naftaly, M.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95(8), 1658–1665 (2007).
[Crossref]

Nagashima, T.

O. Morikawa, A. Quema, S. Nashima, H. Sumikura, T. Nagashima, and M. Hangyo, “Faraday ellipticity and faraday rotation of a doped-silicon wafer studied by terahertz time-domain spectroscopy,” J. Appl. Phys. 100(3), 033105 (2006).
[Crossref]

Nashima, S.

O. Morikawa, A. Quema, S. Nashima, H. Sumikura, T. Nagashima, and M. Hangyo, “Faraday ellipticity and faraday rotation of a doped-silicon wafer studied by terahertz time-domain spectroscopy,” J. Appl. Phys. 100(3), 033105 (2006).
[Crossref]

Nedoliuk, I. O.

Neto, A. C.

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

Novoselov, K. S.

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

O’Hara, J. F.

J. F. O’Hara, E. Smirnova, A. K. Azad, H.-T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

Orlita, M.

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
[Crossref]

Ostler, M.

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
[Crossref]

Ozaki, T.

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

Ozturk, Y.

M. Shalaby, M. Peccianti, Y. Ozturk, and R. Morandotti, “A magnetic non-reciprocal isolator for broadband terahertz operation,” Nat. Commun. 4, 1558 (2013).
[Crossref] [PubMed]

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

Padilla, W. J.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

Pan, X.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

Peccianti, M.

M. Shalaby, M. Peccianti, Y. Ozturk, and R. Morandotti, “A magnetic non-reciprocal isolator for broadband terahertz operation,” Nat. Commun. 4, 1558 (2013).
[Crossref] [PubMed]

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

Peres, N. M.

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

Perruisseau-Carrier, J.

M. Tamagnone, C. Moldovan, J.-M. Poumirol, A. B. Kuzmenko, A. M. Ionescu, J. R. Mosig, and J. Perruisseau-Carrier, “Near optimal graphene terahertz non-reciprocal isolator,” Nat. Commun. 7, 11216 (2016).
[Crossref] [PubMed]

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photon. 8(7), 556–563 (2014).
[Crossref]

A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett. 101(23), 231605 (2012).
[Crossref]

Pimenov, A.

A. Shuvaev, G. Astakhov, A. Pimenov, C. Brüne, H. Buhmann, and L. Molenkamp, “Giant magneto-optical faraday effect in hgte thin films in the terahertz spectral range,” Phys. Rev. Lett. 106(10), 107404 (2011).
[Crossref] [PubMed]

Pitanti, A.

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

Polini, M.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

Potemski, M.

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
[Crossref]

Poumirol, J.-M.

M. Tamagnone, C. Moldovan, J.-M. Poumirol, A. B. Kuzmenko, A. M. Ionescu, J. R. Mosig, and J. Perruisseau-Carrier, “Near optimal graphene terahertz non-reciprocal isolator,” Nat. Commun. 7, 11216 (2016).
[Crossref] [PubMed]

Principi, A.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Qi, M.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

Qiu, C.-W.

H. Da, Q. Bao, R. Sanaei, J. Teng, K. P. Loh, F. J. Garcia-Vidal, and C.-W. Qiu, “Monolayer graphene photonic metastructures: Giant faraday rotation and nearly perfect transmission,” Phys. Rev. B 88(20), 205405 (2013).
[Crossref]

Quan, B.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

Quema, A.

O. Morikawa, A. Quema, S. Nashima, H. Sumikura, T. Nagashima, and M. Hangyo, “Faraday ellipticity and faraday rotation of a doped-silicon wafer studied by terahertz time-domain spectroscopy,” J. Appl. Phys. 100(3), 033105 (2006).
[Crossref]

Razzari, L.

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

Ren, Z.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

Rotenberg, E.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
[Crossref]

Sanaei, R.

H. Da, Q. Bao, R. Sanaei, J. Teng, K. P. Loh, F. J. Garcia-Vidal, and C.-W. Qiu, “Monolayer graphene photonic metastructures: Giant faraday rotation and nearly perfect transmission,” Phys. Rev. B 88(20), 205405 (2013).
[Crossref]

Seyller, T.

N. Ubrig, I. Crassee, J. Levallois, I. O. Nedoliuk, F. Fromm, M. Kaiser, T. Seyller, and A. B. Kuzmenko, “Fabry-Pérot enhanced faraday rotation in graphene,” Opt. Express 21(21), 24736–24741 (2013).
[Crossref] [PubMed]

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
[Crossref]

Shalaby, M.

M. Shalaby, M. Peccianti, Y. Ozturk, and R. Morandotti, “A magnetic non-reciprocal isolator for broadband terahertz operation,” Nat. Commun. 4, 1558 (2013).
[Crossref] [PubMed]

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

Shuvaev, A.

A. Shuvaev, G. Astakhov, A. Pimenov, C. Brüne, H. Buhmann, and L. Molenkamp, “Giant magneto-optical faraday effect in hgte thin films in the terahertz spectral range,” Phys. Rev. Lett. 106(10), 107404 (2011).
[Crossref] [PubMed]

Skorobogatiy, M.

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

Smirnova, E.

J. F. O’Hara, E. Smirnova, A. K. Azad, H.-T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

Steinberg, B. Z.

Y. Hadad, A. R. Davoyan, N. Engheta, and B. Z. Steinberg, “Extreme and quantized magneto-optics with graphene meta-atoms and metasurfaces,” ACS Photonics 1(10), 1068–1073 (2014).
[Crossref]

Stepniewski, R.

A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
[Crossref]

Strupinski, W.

A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
[Crossref]

Sumikura, H.

O. Morikawa, A. Quema, S. Nashima, H. Sumikura, T. Nagashima, and M. Hangyo, “Faraday ellipticity and faraday rotation of a doped-silicon wafer studied by terahertz time-domain spectroscopy,” J. Appl. Phys. 100(3), 033105 (2006).
[Crossref]

Tamagnone, M.

M. Tamagnone, C. Moldovan, J.-M. Poumirol, A. B. Kuzmenko, A. M. Ionescu, J. R. Mosig, and J. Perruisseau-Carrier, “Near optimal graphene terahertz non-reciprocal isolator,” Nat. Commun. 7, 11216 (2016).
[Crossref] [PubMed]

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photon. 8(7), 556–563 (2014).
[Crossref]

Taniguchi, T.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Taylor, A. J.

J. F. O’Hara, E. Smirnova, A. K. Azad, H.-T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

Teng, J.

H. Da, Q. Bao, R. Sanaei, J. Teng, K. P. Loh, F. J. Garcia-Vidal, and C.-W. Qiu, “Monolayer graphene photonic metastructures: Giant faraday rotation and nearly perfect transmission,” Phys. Rev. B 88(20), 205405 (2013).
[Crossref]

Tredicucci, A.

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

A. Tredicucci and M. S. Vitiello, “Device concepts for graphene-based terahertz photonics,” IEEE J. Sel. Topics Quantum Electron. 20(1), 130–138 (2014).
[Crossref]

Ubrig, N.

Van Der Marel, D.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
[Crossref]

Vignale, G.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Vitiello, M. S.

A. Tredicucci and M. S. Vitiello, “Device concepts for graphene-based terahertz photonics,” IEEE J. Sel. Topics Quantum Electron. 20(1), 130–138 (2014).
[Crossref]

Walter, A. L.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
[Crossref]

Wang, L.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

Watanabe, K.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Withayachumnankul, W.

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009).
[Crossref]

Witowski, A.

A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
[Crossref]

Woessner, A.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Wysmolek, A.

A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
[Crossref]

Xu, X.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

Zanotto, S.

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

Zhou, Y.

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

ACS Photonics (1)

Y. Hadad, A. R. Davoyan, N. Engheta, and B. Z. Steinberg, “Extreme and quantized magneto-optics with graphene meta-atoms and metasurfaces,” ACS Photonics 1(10), 1068–1073 (2014).
[Crossref]

Act. Passive Electron. Compon. (1)

J. F. O’Hara, E. Smirnova, A. K. Azad, H.-T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

Appl. Phys. Lett. (4)

A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett. 101(23), 231605 (2012).
[Crossref]

S. Zanotto, C. Lange, T. Maag, A. Pitanti, V. Miseikis, C. Coletti, R. Degl’Innocenti, L. Baldacci, R. Huber, and A. Tredicucci, “Magneto-optic transmittance modulation observed in a hybrid graphene–split ring resonator terahertz metasurface,” Appl. Phys. Lett. 107(12), 121104 (2015).
[Crossref]

H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett. 98(26), 261915 (2011).
[Crossref]

M. Shalaby, M. Peccianti, Y. Ozturk, M. Clerici, I. Al-Naib, L. Razzari, T. Ozaki, A. Mazhorova, M. Skorobogatiy, and R. Morandotti, “Terahertz faraday rotation in a magnetic liquid: High magneto-optical figure of merit and broadband operation in a ferrofluid,” Appl. Phys. Lett. 100(24), 241107 (2012).
[Crossref]

Carbon (1)

J. Li, Y. Zhou, B. Quan, X. Pan, X. Xu, Z. Ren, F. Hu, H. Fan, M. Qi, J. Bai, L. Wang, J. Li, and C. Gu, “Graphene–metamaterial hybridization for enhanced terahertz response,” Carbon 8, 102–112 (2014).
[Crossref]

IEEE J. Sel. Topics Quantum Electron. (1)

A. Tredicucci and M. S. Vitiello, “Device concepts for graphene-based terahertz photonics,” IEEE J. Sel. Topics Quantum Electron. 20(1), 130–138 (2014).
[Crossref]

IEEE Photon. J. (1)

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009).
[Crossref]

J. Appl. Phys. (1)

O. Morikawa, A. Quema, S. Nashima, H. Sumikura, T. Nagashima, and M. Hangyo, “Faraday ellipticity and faraday rotation of a doped-silicon wafer studied by terahertz time-domain spectroscopy,” J. Appl. Phys. 100(3), 033105 (2006).
[Crossref]

Nano Lett. (1)

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12(5), 2470–2474 (2012).
[Crossref] [PubMed]

Nat. Commun. (2)

M. Shalaby, M. Peccianti, Y. Ozturk, and R. Morandotti, “A magnetic non-reciprocal isolator for broadband terahertz operation,” Nat. Commun. 4, 1558 (2013).
[Crossref] [PubMed]

M. Tamagnone, C. Moldovan, J.-M. Poumirol, A. B. Kuzmenko, A. M. Ionescu, J. R. Mosig, and J. Perruisseau-Carrier, “Near optimal graphene terahertz non-reciprocal isolator,” Nat. Commun. 7, 11216 (2016).
[Crossref] [PubMed]

Nat. Mater. (1)

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene–boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref]

Nat. Photon. (1)

M. Tamagnone, A. Fallahi, J. R. Mosig, and J. Perruisseau-Carrier, “Fundamental limits and near-optimal design of graphene modulators and non-reciprocal devices,” Nat. Photon. 8(7), 556–563 (2014).
[Crossref]

Nat. Phys. (1)

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. Van Der Marel, and A. B. Kuzmenko, “Giant faraday rotation in single-and multilayer graphene,” Nat. Phys. 7(1), 48–51 (2011).
[Crossref]

New J. Phys. (1)

M. Orlita, I. Crassee, C. Faugeras, A. Kuzmenko, F. Fromm, M. Ostler, T. Seyller, G. Martinez, M. Polini, and M. Potemski, “Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption,” New J. Phys. 14(9), 095008 (2012).
[Crossref]

Opt. Express (1)

Phys. Rev. B (2)

H. Da, Q. Bao, R. Sanaei, J. Teng, K. P. Loh, F. J. Garcia-Vidal, and C.-W. Qiu, “Monolayer graphene photonic metastructures: Giant faraday rotation and nearly perfect transmission,” Phys. Rev. B 88(20), 205405 (2013).
[Crossref]

A. Witowski, M. Orlita, R. Stepniewski, A. Wysmołek, J. Baranowski, W. Strupiński, C. Faugeras, G. Martinez, and M. Potemski, “Quasiclassical cyclotron resonance of dirac fermions in highly doped graphene,” Phys. Rev. B 82(16), 165305 (2010).
[Crossref]

Phys. Rev. Lett. (2)

A. Shuvaev, G. Astakhov, A. Pimenov, C. Brüne, H. Buhmann, and L. Molenkamp, “Giant magneto-optical faraday effect in hgte thin films in the terahertz spectral range,” Phys. Rev. Lett. 106(10), 107404 (2011).
[Crossref] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

Proc. IEEE (1)

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95(8), 1658–1665 (2007).
[Crossref]

Rev. Mod. Phys. (1)

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

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Figures (7)
Fig. 1
Fig. 1 (a) Device sketch showing the geometry of the simulated structure: a monolayer graphene is separated by a 200 nm thick layer of SiO2 from the 100 nm thick gold metasurface. This stack is placed above an ideally infinite and transparent substrate. Linearly polarized light with electric field Ei is incident on the structure. It is transmitted with electric field Et rotated of an angle θF, i.e. the Faraday angle. The same effect is possible in reflection giving rise to the Kerr rotation with a polarization rotation of an angle θK, i.e the Kerr angle. The direction of the magnetic field is parallel to the direction of propagation and its verse points towards the positive z-axis. The magnetically induced circular dichroism of graphene gives rise to a small degree of ellipticity in the polarization of both reflected and transmitted waves. (b) Internal view of the mesh grid of the simulated unit cell. The inset highlights the mesh in the metasurface plane with the resonator in yellow.

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Fig. 2
Fig. 2 Panels a–c: Three geometric shapes of the resonators belonging to the D2, D4 and D8 symmetry groups, respectively. Each of them constitutes the unit element of a metasurface arranged in a square array. The unit cell length a and the four parameters that characterize the resonator (b, g, p and w) are indicated in panel (a). Depending on the specific shape, the values of these parameters change in order to optimize the non-reciprocal behaviour of the system. The values of these parameters for each geometry are reported in Table 1. Panels d–f: Transmittance (T, blue curve) and Faraday angle (θF, red curve) calculated by FEM simulations in the frequency range between 5 and 9 THz for the structure in Fig. 1 with the shapes of the resonator shown in panels (a), (b) and (c), respectively. The graphene Fermi energy is fixed at 0.3 eV for all the three geometries. The refractive index of the substrate, considered of infinite extension for simplicity, is set to 1.5 in all the simulations, while the external magnetic field is fixed to 7 T, the maximum used in [7]. (g) Spatial distribution in the metasurface plane of the square modulus of the electric (E) and magnetic (H) field of the propagating light at 6.5 THz using a logarithmic color scale. The direction of polarization is always parallel to the x-axis, i.e. E ‖ x̂.

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Fig. 3
Fig. 3 Calculated values of the figure of merit γF for the Faraday effect given in Eq. (1) for the three studied geometries. Panels (a), (b) and (c), i.e. the left column, show the results obtained for a refractive index, n, of the substrate equal to 1.5, while panels (d), (e) and (f), right column, present that for n = 2.5. In each column, the graphs are sorted accordingly to the structure symmetry, passing from D2 (panels (a) and (d)) to D4 ((b) and (e)) and then to D8 ((c) and (f)). In each panel the values of γF were obtained for four different Fermi energies (0.1, 0.2, 0.3 and 0.4 eV). The external magnetic field is always fixed at 7T.

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Fig. 4
Fig. 4 (a) Evolution of the maximum value assumed by the figure of merit γF of the system defined in Eq. (1) as a function of the symmetry group of the resonator shape. The red and blue curves show the results for the refractive index n equal to 1.5 and 2.5, respectively. The three dashed vertical lines indicate the studied symmetry groups, D2, D4 and D8, shown by the three insets. (b) The simulated γF for the bare monolayer graphene is shown for comparison in the frequency range of interest.

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Fig. 5
Fig. 5 Transmittance T, Faraday angle θF and figure of merit γF for three geometries: the D4-geometry presented in Fig. 2 and two geometries belonging to the C4 symmetry group, named C4 - a and C4 - b. These last structures are obtained from D4 by modifying the central part of the resonator but maintaining the same values for the geometric parameters defined in Fig. 2.

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Fig. 6
Fig. 6 (a, b) Simulated Kerr angle θK and reflectance R for the metasurface with resonator geometry belonging to D8 symmetry group in the case of refractive index of the substrate equal to 1.5. The curves were obtained for four values of the Fermi energy of graphene EF = 0.1, 0.2, 0.3 and 0.4 eV. (c) Results for the figure of merit γK for the Kerr effect obtained from the values of θK and R presented in panel a and b. As a comparison, the dashed curve represents γF for the same geometry at EF = 0.3 eV. (d) Axial ratio (AR) obtained for both the Faraday rotation (red curve) and Kerr rotation (blue curve) in the case of EF = 0.3 eV for the hybrid metasurface (HM). The brown curve represents the simulated AR for the Faraday effect of monolayer graphene. The external magnetic field is fixed at 7T.

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Fig. 7
Fig. 7 Results for the system with the D8 metasurface geometry allowed to work only in reflection by the presence of a 50 nm thick gold layer at the bottom of the structure shown in Fig. 1. Simulations are performed for two different values of thickness d of the substrate with refractive index n = 1.5 in the frequency range from 5 to 7 THz. In the left column, panels (a) and (b), the reflectance (R), Kerr angle (θK), the corresponding figure of merit (γK) and the axial ratio (AR) are shown for d = 10 μm. In the right column, panels (c) and (d), the same quantities are reported for d = 20 μm. The graphene Fermi energy is set to 0.3 eV.

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Tables (1)

Tables Icon

Table 1 Values of the geometric parameters for the three described shapes belonging to the D2, D4 and D8 symmetry group in the cases of refractive index n equal to 1.5 and 2.5. These values were chosen in order to have approximately the maximum of the figure of merit for EF = 0.2 eV at 6.9 THz.

View Table

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

γ F ( T , θ F ) = | 2 T sin θ F | 2 ( 1 − T 2 ) 2
γ NR = ( B e τ v F 2 E F ) 2 = ( μ B ) 2

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