Abstract

Terahertz plasmons and magnetoplasmons propagating along electrically and chemically doped graphene p-n junctions are investigated. It is shown that such junctions support non-reciprocal magnetoplasmonic modes which get concentrated at the middle of the junction in one direction and split away from the middle of the junction in the other direction under the application of an external static magnetic field. This phenomenon follows from the combined effects of circular birefringence and carrier density non-uniformity. It can be exploited for the realization of plasmonic isolators.

© 2013 OSA

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  1. K. S.  Novoselov, A. K.  Geim, S. V.  Morozov, D.  Jiang, Y.  Zhang, S. V.  Dubonos, I. V.  Grigorieva, A. A.  Firsov, “Electric field effect in atomically thin carbon films,” Science22 306, 666–669 (2004).
    [CrossRef]
  2. A. K.  Geim, K. S.  Novoselov, “The rise of graphene,” Nature Materials 6, 183–191 (2007).
    [CrossRef] [PubMed]
  3. A. N.  Grigorenko, M.  Polini, K. S.  Novoselov, “Graphene plasmonics,” Nat. Photon. 6, 7490 758 (2012).
    [CrossRef]
  4. S. A.  Mikhailov, K.  Ziegler, “New Electromagnetic Mode in Graphene,” Phys. Rev. Lett. 99, 016 803 (2007).
    [CrossRef]
  5. G. W.  Hanson, “Dyadic Greens functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064 302 (2008).
    [CrossRef]
  6. I.  Crassee, M.  Orlita, M.  Potemski, A. L.  Walter, M.  Ostler, T.  Seyller, I.  Gaponenko, J.  Chen, A. B.  Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Letters 12, 2470–2474 (2012).
    [CrossRef] [PubMed]
  7. A.  Vakil, N.  Engheta, “Transformation Optics Using Graphene,” Science 332, 1291–1294 (2011).
    [CrossRef] [PubMed]
  8. P. G.  Silvestrov, K. B.  Efetov, “Charge accumulation at the boundaries of a graphene strip induced by a gate voltage: Electrostatic approach,” Phys. Rev. B 77, 155 436 (2008).
    [CrossRef]
  9. E. G.  Mishchenko, A. V.  Shytov, P. G.  Silvestrov, “Guided Plasmons in Graphene p-n Junctions,” Phys. Rev. Lett. 104, 156 806 (2010).
    [CrossRef]
  10. S.  Thongrattanasiri, I.  Silveiro, F. J. G.  de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett. 100, 201 105 (2012).
    [CrossRef]
  11. I.  Petković, F. I. B.  Williams, K.  Bennaceur, F.  Portier, P.  Roche, D. C.  Glattli, “Carrier Drift Velocity and Edge Magnetoplasmons in Graphene,” Phys. Rev. Lett. 110, 016 801 (2013).
    [CrossRef]
  12. T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
    [CrossRef] [PubMed]
  13. T.  Mueller, F.  Xia, P.  Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photon. 4, 297–301 (2010).
    [CrossRef]
  14. N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
    [CrossRef] [PubMed]
  15. N.  Chamanara, D.  Sounas, C.  Caloz, “Non-reciprocal magnetoplasmon graphene coupler,” Opt. Express 21, 11248–11256 (2013).
    [CrossRef] [PubMed]
  16. D. L.  Sounas, C.  Caloz, “Edge surface modes in magnetically biased chemically doped graphene strips,” Appl. Phys. Lett. 99, 231 902:13 (2011).
    [CrossRef]
  17. Y.  Zhao, K.  Wu, K. M.  Cheng, “A Compact 2-D Full-Wave Finite-Difference Frequency-Domain Method for General Guided Wave Structures,” IEEE Trans. Microwave Theory Tech. 50, 1844–1848 (2002).
    [CrossRef]
  18. V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “Magneto-optical conductivity in graphene,” Journal of Physics: Condensed Matter 19, 026 222 (2007).
    [CrossRef]
  19. V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics 11, 095 013 (2009).
    [CrossRef]
  20. D. M.  Pozar, Microwave engineering(Danvers, MA: Wiley, 2005), 3rd edn.
  21. D.  Jalas, A.  Petrov, M.  Eich, W.  Freude, S.  Fan, Z.  Yu, H.  Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
    [CrossRef]

2013 (3)

I.  Petković, F. I. B.  Williams, K.  Bennaceur, F.  Portier, P.  Roche, D. C.  Glattli, “Carrier Drift Velocity and Edge Magnetoplasmons in Graphene,” Phys. Rev. Lett. 110, 016 801 (2013).
[CrossRef]

N.  Chamanara, D.  Sounas, C.  Caloz, “Non-reciprocal magnetoplasmon graphene coupler,” Opt. Express 21, 11248–11256 (2013).
[CrossRef] [PubMed]

D.  Jalas, A.  Petrov, M.  Eich, W.  Freude, S.  Fan, Z.  Yu, H.  Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[CrossRef]

2012 (3)

S.  Thongrattanasiri, I.  Silveiro, F. J. G.  de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett. 100, 201 105 (2012).
[CrossRef]

A. N.  Grigorenko, M.  Polini, K. S.  Novoselov, “Graphene plasmonics,” Nat. Photon. 6, 7490 758 (2012).
[CrossRef]

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

2011 (4)

A.  Vakil, N.  Engheta, “Transformation Optics Using Graphene,” Science 332, 1291–1294 (2011).
[CrossRef] [PubMed]

N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
[CrossRef] [PubMed]

T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef] [PubMed]

D. L.  Sounas, C.  Caloz, “Edge surface modes in magnetically biased chemically doped graphene strips,” Appl. Phys. Lett. 99, 231 902:13 (2011).
[CrossRef]

2010 (2)

T.  Mueller, F.  Xia, P.  Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photon. 4, 297–301 (2010).
[CrossRef]

E. G.  Mishchenko, A. V.  Shytov, P. G.  Silvestrov, “Guided Plasmons in Graphene p-n Junctions,” Phys. Rev. Lett. 104, 156 806 (2010).
[CrossRef]

2009 (1)

V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics 11, 095 013 (2009).
[CrossRef]

2008 (2)

G. W.  Hanson, “Dyadic Greens functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064 302 (2008).
[CrossRef]

P. G.  Silvestrov, K. B.  Efetov, “Charge accumulation at the boundaries of a graphene strip induced by a gate voltage: Electrostatic approach,” Phys. Rev. B 77, 155 436 (2008).
[CrossRef]

2007 (3)

S. A.  Mikhailov, K.  Ziegler, “New Electromagnetic Mode in Graphene,” Phys. Rev. Lett. 99, 016 803 (2007).
[CrossRef]

A. K.  Geim, K. S.  Novoselov, “The rise of graphene,” Nature Materials 6, 183–191 (2007).
[CrossRef] [PubMed]

V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “Magneto-optical conductivity in graphene,” Journal of Physics: Condensed Matter 19, 026 222 (2007).
[CrossRef]

2004 (1)

K. S.  Novoselov, A. K.  Geim, S. V.  Morozov, D.  Jiang, Y.  Zhang, S. V.  Dubonos, I. V.  Grigorieva, A. A.  Firsov, “Electric field effect in atomically thin carbon films,” Science22 306, 666–669 (2004).
[CrossRef]

2002 (1)

Y.  Zhao, K.  Wu, K. M.  Cheng, “A Compact 2-D Full-Wave Finite-Difference Frequency-Domain Method for General Guided Wave Structures,” IEEE Trans. Microwave Theory Tech. 50, 1844–1848 (2002).
[CrossRef]

Avouris, P.

T.  Mueller, F.  Xia, P.  Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photon. 4, 297–301 (2010).
[CrossRef]

Bennaceur, K.

I.  Petković, F. I. B.  Williams, K.  Bennaceur, F.  Portier, P.  Roche, D. C.  Glattli, “Carrier Drift Velocity and Edge Magnetoplasmons in Graphene,” Phys. Rev. Lett. 110, 016 801 (2013).
[CrossRef]

Britnell, L.

T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef] [PubMed]

Caloz, C.

N.  Chamanara, D.  Sounas, C.  Caloz, “Non-reciprocal magnetoplasmon graphene coupler,” Opt. Express 21, 11248–11256 (2013).
[CrossRef] [PubMed]

D. L.  Sounas, C.  Caloz, “Edge surface modes in magnetically biased chemically doped graphene strips,” Appl. Phys. Lett. 99, 231 902:13 (2011).
[CrossRef]

Carbotte, J. P.

V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics 11, 095 013 (2009).
[CrossRef]

V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “Magneto-optical conductivity in graphene,” Journal of Physics: Condensed Matter 19, 026 222 (2007).
[CrossRef]

Chamanara, N.

Chen, J.

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

Cheng, K. M.

Y.  Zhao, K.  Wu, K. M.  Cheng, “A Compact 2-D Full-Wave Finite-Difference Frequency-Domain Method for General Guided Wave Structures,” IEEE Trans. Microwave Theory Tech. 50, 1844–1848 (2002).
[CrossRef]

Crassee, I.

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

de Abajo, F. J. G.

S.  Thongrattanasiri, I.  Silveiro, F. J. G.  de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett. 100, 201 105 (2012).
[CrossRef]

Dubonos, S. V.

K. S.  Novoselov, A. K.  Geim, S. V.  Morozov, D.  Jiang, Y.  Zhang, S. V.  Dubonos, I. V.  Grigorieva, A. A.  Firsov, “Electric field effect in atomically thin carbon films,” Science22 306, 666–669 (2004).
[CrossRef]

Echtermeyer, T.

T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef] [PubMed]

Efetov, K. B.

P. G.  Silvestrov, K. B.  Efetov, “Charge accumulation at the boundaries of a graphene strip induced by a gate voltage: Electrostatic approach,” Phys. Rev. B 77, 155 436 (2008).
[CrossRef]

Eich, M.

D.  Jalas, A.  Petrov, M.  Eich, W.  Freude, S.  Fan, Z.  Yu, H.  Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[CrossRef]

Engheta, N.

A.  Vakil, N.  Engheta, “Transformation Optics Using Graphene,” Science 332, 1291–1294 (2011).
[CrossRef] [PubMed]

Fan, S.

D.  Jalas, A.  Petrov, M.  Eich, W.  Freude, S.  Fan, Z.  Yu, H.  Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[CrossRef]

Ferrari, A.

T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef] [PubMed]

Firsov, A. A.

K. S.  Novoselov, A. K.  Geim, S. V.  Morozov, D.  Jiang, Y.  Zhang, S. V.  Dubonos, I. V.  Grigorieva, A. A.  Firsov, “Electric field effect in atomically thin carbon films,” Science22 306, 666–669 (2004).
[CrossRef]

Freude, W.

D.  Jalas, A.  Petrov, M.  Eich, W.  Freude, S.  Fan, Z.  Yu, H.  Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[CrossRef]

Gabor, N. M.

N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
[CrossRef] [PubMed]

Gaponenko, I.

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

Geim, A.

T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef] [PubMed]

Geim, A. K.

A. K.  Geim, K. S.  Novoselov, “The rise of graphene,” Nature Materials 6, 183–191 (2007).
[CrossRef] [PubMed]

K. S.  Novoselov, A. K.  Geim, S. V.  Morozov, D.  Jiang, Y.  Zhang, S. V.  Dubonos, I. V.  Grigorieva, A. A.  Firsov, “Electric field effect in atomically thin carbon films,” Science22 306, 666–669 (2004).
[CrossRef]

Glattli, D. C.

I.  Petković, F. I. B.  Williams, K.  Bennaceur, F.  Portier, P.  Roche, D. C.  Glattli, “Carrier Drift Velocity and Edge Magnetoplasmons in Graphene,” Phys. Rev. Lett. 110, 016 801 (2013).
[CrossRef]

Gorbachev, R.

T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef] [PubMed]

Grigorenko, A.

T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef] [PubMed]

Grigorenko, A. N.

A. N.  Grigorenko, M.  Polini, K. S.  Novoselov, “Graphene plasmonics,” Nat. Photon. 6, 7490 758 (2012).
[CrossRef]

Grigorieva, I. V.

K. S.  Novoselov, A. K.  Geim, S. V.  Morozov, D.  Jiang, Y.  Zhang, S. V.  Dubonos, I. V.  Grigorieva, A. A.  Firsov, “Electric field effect in atomically thin carbon films,” Science22 306, 666–669 (2004).
[CrossRef]

Gusynin, V. P.

V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics 11, 095 013 (2009).
[CrossRef]

V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “Magneto-optical conductivity in graphene,” Journal of Physics: Condensed Matter 19, 026 222 (2007).
[CrossRef]

Hanson, G. W.

G. W.  Hanson, “Dyadic Greens functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064 302 (2008).
[CrossRef]

Jalas, D.

D.  Jalas, A.  Petrov, M.  Eich, W.  Freude, S.  Fan, Z.  Yu, H.  Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[CrossRef]

Jarillo-Herrero, P.

N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
[CrossRef] [PubMed]

Jasnos, P.

T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef] [PubMed]

Jiang, D.

K. S.  Novoselov, A. K.  Geim, S. V.  Morozov, D.  Jiang, Y.  Zhang, S. V.  Dubonos, I. V.  Grigorieva, A. A.  Firsov, “Electric field effect in atomically thin carbon films,” Science22 306, 666–669 (2004).
[CrossRef]

Kuzmenko, A. B.

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

Levitov, L. S.

N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
[CrossRef] [PubMed]

Lombardo, A.

T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef] [PubMed]

Ma, Q.

N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
[CrossRef] [PubMed]

Mikhailov, S. A.

S. A.  Mikhailov, K.  Ziegler, “New Electromagnetic Mode in Graphene,” Phys. Rev. Lett. 99, 016 803 (2007).
[CrossRef]

Mishchenko, E. G.

E. G.  Mishchenko, A. V.  Shytov, P. G.  Silvestrov, “Guided Plasmons in Graphene p-n Junctions,” Phys. Rev. Lett. 104, 156 806 (2010).
[CrossRef]

Morozov, S. V.

K. S.  Novoselov, A. K.  Geim, S. V.  Morozov, D.  Jiang, Y.  Zhang, S. V.  Dubonos, I. V.  Grigorieva, A. A.  Firsov, “Electric field effect in atomically thin carbon films,” Science22 306, 666–669 (2004).
[CrossRef]

Mueller, T.

T.  Mueller, F.  Xia, P.  Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photon. 4, 297–301 (2010).
[CrossRef]

Nair, N. L.

N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
[CrossRef] [PubMed]

Novoselov, K.

T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef] [PubMed]

Novoselov, K. S.

A. N.  Grigorenko, M.  Polini, K. S.  Novoselov, “Graphene plasmonics,” Nat. Photon. 6, 7490 758 (2012).
[CrossRef]

A. K.  Geim, K. S.  Novoselov, “The rise of graphene,” Nature Materials 6, 183–191 (2007).
[CrossRef] [PubMed]

K. S.  Novoselov, A. K.  Geim, S. V.  Morozov, D.  Jiang, Y.  Zhang, S. V.  Dubonos, I. V.  Grigorieva, A. A.  Firsov, “Electric field effect in atomically thin carbon films,” Science22 306, 666–669 (2004).
[CrossRef]

Orlita, M.

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

Ostler, M.

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

Petkovic, I.

I.  Petković, F. I. B.  Williams, K.  Bennaceur, F.  Portier, P.  Roche, D. C.  Glattli, “Carrier Drift Velocity and Edge Magnetoplasmons in Graphene,” Phys. Rev. Lett. 110, 016 801 (2013).
[CrossRef]

Petrov, A.

D.  Jalas, A.  Petrov, M.  Eich, W.  Freude, S.  Fan, Z.  Yu, H.  Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[CrossRef]

Polini, M.

A. N.  Grigorenko, M.  Polini, K. S.  Novoselov, “Graphene plasmonics,” Nat. Photon. 6, 7490 758 (2012).
[CrossRef]

Portier, F.

I.  Petković, F. I. B.  Williams, K.  Bennaceur, F.  Portier, P.  Roche, D. C.  Glattli, “Carrier Drift Velocity and Edge Magnetoplasmons in Graphene,” Phys. Rev. Lett. 110, 016 801 (2013).
[CrossRef]

Potemski, M.

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

Pozar, D. M.

D. M.  Pozar, Microwave engineering(Danvers, MA: Wiley, 2005), 3rd edn.

Renner, H.

D.  Jalas, A.  Petrov, M.  Eich, W.  Freude, S.  Fan, Z.  Yu, H.  Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[CrossRef]

Roche, P.

I.  Petković, F. I. B.  Williams, K.  Bennaceur, F.  Portier, P.  Roche, D. C.  Glattli, “Carrier Drift Velocity and Edge Magnetoplasmons in Graphene,” Phys. Rev. Lett. 110, 016 801 (2013).
[CrossRef]

Seyller, T.

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

Sharapov, S. G.

V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics 11, 095 013 (2009).
[CrossRef]

V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “Magneto-optical conductivity in graphene,” Journal of Physics: Condensed Matter 19, 026 222 (2007).
[CrossRef]

Shytov, A. V.

E. G.  Mishchenko, A. V.  Shytov, P. G.  Silvestrov, “Guided Plasmons in Graphene p-n Junctions,” Phys. Rev. Lett. 104, 156 806 (2010).
[CrossRef]

Silveiro, I.

S.  Thongrattanasiri, I.  Silveiro, F. J. G.  de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett. 100, 201 105 (2012).
[CrossRef]

Silvestrov, P. G.

E. G.  Mishchenko, A. V.  Shytov, P. G.  Silvestrov, “Guided Plasmons in Graphene p-n Junctions,” Phys. Rev. Lett. 104, 156 806 (2010).
[CrossRef]

P. G.  Silvestrov, K. B.  Efetov, “Charge accumulation at the boundaries of a graphene strip induced by a gate voltage: Electrostatic approach,” Phys. Rev. B 77, 155 436 (2008).
[CrossRef]

Song, J. C. W.

N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
[CrossRef] [PubMed]

Sounas, D.

Sounas, D. L.

D. L.  Sounas, C.  Caloz, “Edge surface modes in magnetically biased chemically doped graphene strips,” Appl. Phys. Lett. 99, 231 902:13 (2011).
[CrossRef]

Taniguchi, T.

N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
[CrossRef] [PubMed]

Taychatanapat, T.

N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
[CrossRef] [PubMed]

Thongrattanasiri, S.

S.  Thongrattanasiri, I.  Silveiro, F. J. G.  de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett. 100, 201 105 (2012).
[CrossRef]

Vakil, A.

A.  Vakil, N.  Engheta, “Transformation Optics Using Graphene,” Science 332, 1291–1294 (2011).
[CrossRef] [PubMed]

Walter, A. L.

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

Watanabe, K.

N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
[CrossRef] [PubMed]

Williams, F. I. B.

I.  Petković, F. I. B.  Williams, K.  Bennaceur, F.  Portier, P.  Roche, D. C.  Glattli, “Carrier Drift Velocity and Edge Magnetoplasmons in Graphene,” Phys. Rev. Lett. 110, 016 801 (2013).
[CrossRef]

Wu, K.

Y.  Zhao, K.  Wu, K. M.  Cheng, “A Compact 2-D Full-Wave Finite-Difference Frequency-Domain Method for General Guided Wave Structures,” IEEE Trans. Microwave Theory Tech. 50, 1844–1848 (2002).
[CrossRef]

Xia, F.

T.  Mueller, F.  Xia, P.  Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photon. 4, 297–301 (2010).
[CrossRef]

Yu, Z.

D.  Jalas, A.  Petrov, M.  Eich, W.  Freude, S.  Fan, Z.  Yu, H.  Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[CrossRef]

Zhang, Y.

K. S.  Novoselov, A. K.  Geim, S. V.  Morozov, D.  Jiang, Y.  Zhang, S. V.  Dubonos, I. V.  Grigorieva, A. A.  Firsov, “Electric field effect in atomically thin carbon films,” Science22 306, 666–669 (2004).
[CrossRef]

Zhao, Y.

Y.  Zhao, K.  Wu, K. M.  Cheng, “A Compact 2-D Full-Wave Finite-Difference Frequency-Domain Method for General Guided Wave Structures,” IEEE Trans. Microwave Theory Tech. 50, 1844–1848 (2002).
[CrossRef]

Ziegler, K.

S. A.  Mikhailov, K.  Ziegler, “New Electromagnetic Mode in Graphene,” Phys. Rev. Lett. 99, 016 803 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

S.  Thongrattanasiri, I.  Silveiro, F. J. G.  de Abajo, “Plasmons in electrostatically doped graphene,” Appl. Phys. Lett. 100, 201 105 (2012).
[CrossRef]

D. L.  Sounas, C.  Caloz, “Edge surface modes in magnetically biased chemically doped graphene strips,” Appl. Phys. Lett. 99, 231 902:13 (2011).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

Y.  Zhao, K.  Wu, K. M.  Cheng, “A Compact 2-D Full-Wave Finite-Difference Frequency-Domain Method for General Guided Wave Structures,” IEEE Trans. Microwave Theory Tech. 50, 1844–1848 (2002).
[CrossRef]

J. Appl. Phys. (1)

G. W.  Hanson, “Dyadic Greens functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064 302 (2008).
[CrossRef]

Journal of Physics: Condensed Matter (1)

V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “Magneto-optical conductivity in graphene,” Journal of Physics: Condensed Matter 19, 026 222 (2007).
[CrossRef]

Nano Letters (1)

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

Nat. Photon. (1)

A. N.  Grigorenko, M.  Polini, K. S.  Novoselov, “Graphene plasmonics,” Nat. Photon. 6, 7490 758 (2012).
[CrossRef]

Nat. Commun. (1)

T.  Echtermeyer, L.  Britnell, P.  Jasnos, A.  Lombardo, R.  Gorbachev, A.  Grigorenko, A.  Geim, A.  Ferrari, K.  Novoselov, “Strong plasmonic enhancement of photovoltage in graphene,” Nat. Commun. 2, 458 (2011).
[CrossRef] [PubMed]

Nat. Photon. (1)

T.  Mueller, F.  Xia, P.  Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photon. 4, 297–301 (2010).
[CrossRef]

Nature Materials (1)

A. K.  Geim, K. S.  Novoselov, “The rise of graphene,” Nature Materials 6, 183–191 (2007).
[CrossRef] [PubMed]

Nature Photonics (1)

D.  Jalas, A.  Petrov, M.  Eich, W.  Freude, S.  Fan, Z.  Yu, H.  Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[CrossRef]

New Journal of Physics (1)

V. P.  Gusynin, S. G.  Sharapov, J. P.  Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics 11, 095 013 (2009).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

P. G.  Silvestrov, K. B.  Efetov, “Charge accumulation at the boundaries of a graphene strip induced by a gate voltage: Electrostatic approach,” Phys. Rev. B 77, 155 436 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

E. G.  Mishchenko, A. V.  Shytov, P. G.  Silvestrov, “Guided Plasmons in Graphene p-n Junctions,” Phys. Rev. Lett. 104, 156 806 (2010).
[CrossRef]

S. A.  Mikhailov, K.  Ziegler, “New Electromagnetic Mode in Graphene,” Phys. Rev. Lett. 99, 016 803 (2007).
[CrossRef]

I.  Petković, F. I. B.  Williams, K.  Bennaceur, F.  Portier, P.  Roche, D. C.  Glattli, “Carrier Drift Velocity and Edge Magnetoplasmons in Graphene,” Phys. Rev. Lett. 110, 016 801 (2013).
[CrossRef]

Science (3)

N. M.  Gabor, J. C. W.  Song, Q.  Ma, N. L.  Nair, T.  Taychatanapat, K.  Watanabe, T.  Taniguchi, L. S.  Levitov, P.  Jarillo-Herrero, “Hot carrierassisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011).
[CrossRef] [PubMed]

K. S.  Novoselov, A. K.  Geim, S. V.  Morozov, D.  Jiang, Y.  Zhang, S. V.  Dubonos, I. V.  Grigorieva, A. A.  Firsov, “Electric field effect in atomically thin carbon films,” Science22 306, 666–669 (2004).
[CrossRef]

A.  Vakil, N.  Engheta, “Transformation Optics Using Graphene,” Science 332, 1291–1294 (2011).
[CrossRef] [PubMed]

Other (1)

D. M.  Pozar, Microwave engineering(Danvers, MA: Wiley, 2005), 3rd edn.

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Figures (10)

Fig. 1
Fig. 1

(a) Electrically and (b) chemically doped graphene p-n junctions.

Fig. 2
Fig. 2

Net carrier density and electric potential for a graphene strip doped with an electric field; w = 50 μm and E0 = 108 V/m.

Fig. 3
Fig. 3

Thermally excited electron and hole densities at room temperature for a graphene strip doped with an electric field; w = 50 μm, E0 = 108 V/m, T = 300 K.

Fig. 4
Fig. 4

Chemical potential and Kubo conductivity for a graphene strip doped with an electric field; w = 50 μm and E0 = 108 V/m, B0 = 0 T, τ = 0.1 ps, T = 300 K, f = 1 THz.

Fig. 5
Fig. 5

Slow-wave factor and loss for a graphene strip biased by an electric field; w = 50 μm, E0 = 108 V/m, B0 = 0 T, τ = 0.1 ps, T = 300 K. The p-n junction mode is represented in red. The insets show the electric field patterns.

Fig. 6
Fig. 6

Dispersion curves for a magnetically biased graphene strip biased by an electric field; w = 50 μm, E0 = 108 V/m, B0 = 0.1 T, τ = 0.1 ps, T = 300 K. The p-n junction mode is represented in red. The grey area represents the light cone.

Fig. 7
Fig. 7

Slow-wave factor and loss for the structure in Fig. 1(b) with no magnetic bias; w = 100 μm, s = 10 nm, n = p = 1013 cm−2, B0 = 0 T, τ = 0.1 ps, T = 300 K. The p-n junction mode is represented in red.

Fig. 8
Fig. 8

Slow-wave factor and loss for the magnetoplasmonic isolator in Fig. 1(b); w = 100 μm, s = 10 nm, n = p = 1013 cm−2, B0 = 1 T, τ = 0.1 ps, T = 300 K. The p-n junction mode is represented in red. The grey area represents the light cone.

Fig. 9
Fig. 9

Electric field pattern in the plane of graphene for the structure of Fig. 1(b) with B0 = 0 T. Points R on the right strip sees a clock-wise rotating electric field in the forward direction and a counter clock-wise rotating electric field in the backward direction as the wave propagates. Point L on the left strip sees an oppositely rotating electric field to point R in each direction.

Fig. 10
Fig. 10

Evolution of the electric field pattern of the mode propagating at the p-n junction (mode 1) for the forward and backward propagations as the magnetic field is increased.

Equations (3)

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

w / 2 w / 2 ρ ( x , y ) G ( x , y ; x , y ) d x E 0 x = 0 ,
w / 2 x w / 2 , y = 0 , y = 0 ,
n net = 0 f d ( E , μ c ) N ( E ) d E 0 [ 1 f d ( E , μ c ) ] N ( E ) d E ,

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