Abstract

In this paper we propose a graphene plasmons isolator based on non-reciprocal coupling within double graphene layer waveguide structure on a magneto-optical substrate. The difference in modal indices of graphene plasmons in opposite directions enables non-reciprocal coupling, which is theoretically investigated via coupled mode theory (CMT) and shows good agreement with numerical finite elements methods (FEM). The non-reciprocal coupling endows such system functionalities as magnetically controlled “plasmons circulator” or “plasmons isolator”. For the latter case, systematical investigations of the insertion losses and isolation ratios with respect to the structural parameters, material properties, environmental parameters, fabrication errors as well as dielectric damping are presented. Theoretical investigation has shown an isolation ratio as 42 dB. The proposed plasmons circulator and isolator may serve as potential building blocks in graphene plasmons circuits.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2015 (1)

2014 (3)

2013 (3)

H. Iizuka and S. H. Fan, “Deep subwavelength plasmonic waveguide switch in double graphene layer structure,” Appl. Phys. Lett. 103(23), 233107 (2013).
[Crossref]

Y. Francescato, V. Giannini, and S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013).
[Crossref]

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

2012 (9)

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical Isolator Utilizing Surface Plasmons,” Materials (Basel) 5(12), 857–871 (2012).
[Crossref]

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

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

L. Demkó, G. A. H. Schober, V. Kocsis, M. S. Bahramy, H. Murakawa, J. S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, and Y. Tokura, “Enhanced Infrared Magneto-Optical Response of the Nonmagnetic Semiconductor BiTeI Driven by Bulk Rashba Splitting,” Phys. Rev. Lett. 109(16), 167401 (2012).
[Crossref] [PubMed]

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

C. M. Jaworski, R. C. Myers, E. Johnston-Halperin, and J. P. Heremans, “Giant spin Seebeck effect in a non-magnetic material,” Nature 487(7406), 210–213 (2012).
[Crossref] [PubMed]

L. P. Rokhinson, X. Liu, and J. K. Furdyna, “The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles,” Nat. Phys. 8(11), 795–799 (2012).
[Crossref]

2010 (2)

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: Toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[Crossref]

D. R. Andersen, “Graphene-based long-wave infrared TM surface plasmon modulator,” J. Opt. Soc. Am. B 27(4), 818–823 (2010).
[Crossref]

2009 (2)

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

B. Biel, F. Triozon, X. Blase, and S. Roche, “Chemically induced mobility gaps in graphene nanoribbons: a route for upscaling device performances,” Nano Lett. 9(7), 2725–2729 (2009).
[Crossref] [PubMed]

2008 (3)

L. A. Falkovsky, “Optical properties of graphene and IV–VI semiconductors,” Phys.-Usp. 51(9), 887–897 (2008).
[Crossref]

T. Stauber, N. Peres, and A. Castro Neto, “Conductivity of suspended and non-suspended graphene at finite gate voltage,” Phys. Rev. B 78(8), 085418 (2008).
[Crossref]

T. R. Zaman, X. Guo, and R. J. Ram, “Semiconductor Waveguide Isolators,” J. Lightwave Technol. 26(2), 291–301 (2008).
[Crossref]

2005 (2)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

J. G. Rivas, C. Janke, P. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express 13(3), 847–859 (2005).
[Crossref] [PubMed]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

1989 (1)

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

1972 (1)

J. Brion, R. Wallis, A. Hartstein, and E. Burstein, “Theory of Surface Magnetoplasmons in Semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

1970 (1)

E. D. Palik and J. K. Furdyna, “Infrared and Microwave Magnetoplasma Effects in Semiconductors,” Rep. Prog. Phys. 33(3), 1193–1322 (1970).
[Crossref]

1962 (1)

M. Hass and B. W. Henvis, “Infrared lattice reflection spectra of III–V compound semiconductors,” J. Phys. Chem. Solids 23(8), 1099–1104 (1962).
[Crossref]

1955 (1)

G. Dresselhaus, A. F. Kip, C. Kittel, and G. Wagoner, “Cyclotron and Spin Resonance in Indium Antimonide,” Phys. Rev. 98(2), 556–557 (1955).
[Crossref]

Andersen, D. R.

Ando, K.

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical Isolator Utilizing Surface Plasmons,” Materials (Basel) 5(12), 857–871 (2012).
[Crossref]

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Ang, L. K.

Arita, R.

L. Demkó, G. A. H. Schober, V. Kocsis, M. S. Bahramy, H. Murakawa, J. S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, and Y. Tokura, “Enhanced Infrared Magneto-Optical Response of the Nonmagnetic Semiconductor BiTeI Driven by Bulk Rashba Splitting,” Phys. Rev. Lett. 109(16), 167401 (2012).
[Crossref] [PubMed]

Bahramy, M. S.

L. Demkó, G. A. H. Schober, V. Kocsis, M. S. Bahramy, H. Murakawa, J. S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, and Y. Tokura, “Enhanced Infrared Magneto-Optical Response of the Nonmagnetic Semiconductor BiTeI Driven by Bulk Rashba Splitting,” Phys. Rev. Lett. 109(16), 167401 (2012).
[Crossref] [PubMed]

Bai, P.

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Barnham, K. W. J.

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Biel, B.

B. Biel, F. Triozon, X. Blase, and S. Roche, “Chemically induced mobility gaps in graphene nanoribbons: a route for upscaling device performances,” Nano Lett. 9(7), 2725–2729 (2009).
[Crossref] [PubMed]

Blase, X.

B. Biel, F. Triozon, X. Blase, and S. Roche, “Chemically induced mobility gaps in graphene nanoribbons: a route for upscaling device performances,” Nano Lett. 9(7), 2725–2729 (2009).
[Crossref] [PubMed]

Bolivar, P.

Brener, I.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: Toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[Crossref]

Brion, J.

J. Brion, R. Wallis, A. Hartstein, and E. Burstein, “Theory of Surface Magnetoplasmons in Semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Burstein, E.

J. Brion, R. Wallis, A. Hartstein, and E. Burstein, “Theory of Surface Magnetoplasmons in Semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Castro Neto, A.

T. Stauber, N. Peres, and A. Castro Neto, “Conductivity of suspended and non-suspended graphene at finite gate voltage,” Phys. Rev. B 78(8), 085418 (2008).
[Crossref]

Castro Neto, A. H.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Chen, J.

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

Chong, Y. D.

Chu, H. S.

Crassee, I.

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

Demkó, L.

L. Demkó, G. A. H. Schober, V. Kocsis, M. S. Bahramy, H. Murakawa, J. S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, and Y. Tokura, “Enhanced Infrared Magneto-Optical Response of the Nonmagnetic Semiconductor BiTeI Driven by Bulk Rashba Splitting,” Phys. Rev. Lett. 109(16), 167401 (2012).
[Crossref] [PubMed]

Dominguez, G.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Dresselhaus, G.

G. Dresselhaus, A. F. Kip, C. Kittel, and G. Wagoner, “Cyclotron and Spin Resonance in Indium Antimonide,” Phys. Rev. 98(2), 556–557 (1955).
[Crossref]

Droopad, R.

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Dubrovkin, A.

Falkovsky, L. A.

L. A. Falkovsky, “Optical properties of graphene and IV–VI semiconductors,” Phys.-Usp. 51(9), 887–897 (2008).
[Crossref]

Fan, S. H.

H. Iizuka and S. H. Fan, “Deep subwavelength plasmonic waveguide switch in double graphene layer structure,” Appl. Phys. Lett. 103(23), 233107 (2013).
[Crossref]

Fei, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Fogler, M. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Francescato, Y.

Y. Francescato, V. Giannini, and S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013).
[Crossref]

Furdyna, J. K.

L. P. Rokhinson, X. Liu, and J. K. Furdyna, “The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles,” Nat. Phys. 8(11), 795–799 (2012).
[Crossref]

E. D. Palik and J. K. Furdyna, “Infrared and Microwave Magnetoplasma Effects in Semiconductors,” Rep. Prog. Phys. 33(3), 1193–1322 (1970).
[Crossref]

Gao, W.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Gaponenko, I.

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

Geim, A. K.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Giannini, V.

Y. Francescato, V. Giannini, and S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013).
[Crossref]

Gin, A.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: Toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[Crossref]

Gómez-Díaz, J. S.

Goodhue, W.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: Toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[Crossref]

Grigorenko, A. N.

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

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Guo, X.

Hartstein, A.

J. Brion, R. Wallis, A. Hartstein, and E. Burstein, “Theory of Surface Magnetoplasmons in Semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Hass, M.

M. Hass and B. W. Henvis, “Infrared lattice reflection spectra of III–V compound semiconductors,” J. Phys. Chem. Solids 23(8), 1099–1104 (1962).
[Crossref]

Henvis, B. W.

M. Hass and B. W. Henvis, “Infrared lattice reflection spectra of III–V compound semiconductors,” J. Phys. Chem. Solids 23(8), 1099–1104 (1962).
[Crossref]

Heremans, J. P.

C. M. Jaworski, R. C. Myers, E. Johnston-Halperin, and J. P. Heremans, “Giant spin Seebeck effect in a non-magnetic material,” Nature 487(7406), 210–213 (2012).
[Crossref] [PubMed]

Holmes, S. N.

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

Hu, B.

Iizuka, H.

H. Iizuka and S. H. Fan, “Deep subwavelength plasmonic waveguide switch in double graphene layer structure,” Appl. Phys. Lett. 103(23), 233107 (2013).
[Crossref]

Jablan, M.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Janke, C.

Jaworski, C. M.

C. M. Jaworski, R. C. Myers, E. Johnston-Halperin, and J. P. Heremans, “Giant spin Seebeck effect in a non-magnetic material,” Nature 487(7406), 210–213 (2012).
[Crossref] [PubMed]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Johnston-Halperin, E.

C. M. Jaworski, R. C. Myers, E. Johnston-Halperin, and J. P. Heremans, “Giant spin Seebeck effect in a non-magnetic material,” Nature 487(7406), 210–213 (2012).
[Crossref] [PubMed]

Katsnelson, M. I.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Keilmann, F.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Kézsmárki, I.

L. Demkó, G. A. H. Schober, V. Kocsis, M. S. Bahramy, H. Murakawa, J. S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, and Y. Tokura, “Enhanced Infrared Magneto-Optical Response of the Nonmagnetic Semiconductor BiTeI Driven by Bulk Rashba Splitting,” Phys. Rev. Lett. 109(16), 167401 (2012).
[Crossref] [PubMed]

Kip, A. F.

G. Dresselhaus, A. F. Kip, C. Kittel, and G. Wagoner, “Cyclotron and Spin Resonance in Indium Antimonide,” Phys. Rev. 98(2), 556–557 (1955).
[Crossref]

Kittel, C.

G. Dresselhaus, A. F. Kip, C. Kittel, and G. Wagoner, “Cyclotron and Spin Resonance in Indium Antimonide,” Phys. Rev. 98(2), 556–557 (1955).
[Crossref]

Kocsis, V.

L. Demkó, G. A. H. Schober, V. Kocsis, M. S. Bahramy, H. Murakawa, J. S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, and Y. Tokura, “Enhanced Infrared Magneto-Optical Response of the Nonmagnetic Semiconductor BiTeI Driven by Bulk Rashba Splitting,” Phys. Rev. Lett. 109(16), 167401 (2012).
[Crossref] [PubMed]

Kurz, H.

Kuzmenko, A. B.

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

Langston, W.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: Toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[Crossref]

Lau, C. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Laverty, J.

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

Lee, J. S.

L. Demkó, G. A. H. Schober, V. Kocsis, M. S. Bahramy, H. Murakawa, J. S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, and Y. Tokura, “Enhanced Infrared Magneto-Optical Response of the Nonmagnetic Semiconductor BiTeI Driven by Bulk Rashba Splitting,” Phys. Rev. Lett. 109(16), 167401 (2012).
[Crossref] [PubMed]

Liu, F.

Liu, X.

L. P. Rokhinson, X. Liu, and J. K. Furdyna, “The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles,” Nat. Phys. 8(11), 795–799 (2012).
[Crossref]

Maier, S. A.

Y. Francescato, V. Giannini, and S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013).
[Crossref]

McLeod, A. S.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Miao, X.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: Toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[Crossref]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Murakawa, H.

L. Demkó, G. A. H. Schober, V. Kocsis, M. S. Bahramy, H. Murakawa, J. S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, and Y. Tokura, “Enhanced Infrared Magneto-Optical Response of the Nonmagnetic Semiconductor BiTeI Driven by Bulk Rashba Splitting,” Phys. Rev. Lett. 109(16), 167401 (2012).
[Crossref] [PubMed]

Myers, R. C.

C. M. Jaworski, R. C. Myers, E. Johnston-Halperin, and J. P. Heremans, “Giant spin Seebeck effect in a non-magnetic material,” Nature 487(7406), 210–213 (2012).
[Crossref] [PubMed]

Nagaosa, N.

L. Demkó, G. A. H. Schober, V. Kocsis, M. S. Bahramy, H. Murakawa, J. S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, and Y. Tokura, “Enhanced Infrared Magneto-Optical Response of the Nonmagnetic Semiconductor BiTeI Driven by Bulk Rashba Splitting,” Phys. Rev. Lett. 109(16), 167401 (2012).
[Crossref] [PubMed]

Novoselov, K. S.

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

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Ooi, K. J.

Orlita, M.

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

Ostler, M.

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

Palik, E. D.

E. D. Palik and J. K. Furdyna, “Infrared and Microwave Magnetoplasma Effects in Semiconductors,” Rep. Prog. Phys. 33(3), 1193–1322 (1970).
[Crossref]

Parker, S. D.

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

Pashley, D. W.

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

Passmore, B.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: Toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[Crossref]

Peres, N.

T. Stauber, N. Peres, and A. Castro Neto, “Conductivity of suspended and non-suspended graphene at finite gate voltage,” Phys. Rev. B 78(8), 085418 (2008).
[Crossref]

Perruisseau-Carrier, J.

Phillips, C. C.

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

Pike, N. A.

N. A. Pike and D. Stroud, “Model for the spin-dependent Seebeck coefficient of InSb in a magnetic field,” Phys. Rev. B 90(17), 174435 (2014).
[Crossref]

Polini, M.

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

Potemski, M.

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

Qian, C.

Qiu, C.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Ram, R. J.

Rivas, J. G.

Roche, S.

B. Biel, F. Triozon, X. Blase, and S. Roche, “Chemically induced mobility gaps in graphene nanoribbons: a route for upscaling device performances,” Nano Lett. 9(7), 2725–2729 (2009).
[Crossref] [PubMed]

Rodin, A. S.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Rokhinson, L. P.

L. P. Rokhinson, X. Liu, and J. K. Furdyna, “The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles,” Nat. Phys. 8(11), 795–799 (2012).
[Crossref]

Saito, H.

V. Zayets, H. Saito, K. Ando, and S. Yuasa, “Optical Isolator Utilizing Surface Plasmons,” Materials (Basel) 5(12), 857–871 (2012).
[Crossref]

Schober, G. A. H.

L. Demkó, G. A. H. Schober, V. Kocsis, M. S. Bahramy, H. Murakawa, J. S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, and Y. Tokura, “Enhanced Infrared Magneto-Optical Response of the Nonmagnetic Semiconductor BiTeI Driven by Bulk Rashba Splitting,” Phys. Rev. Lett. 109(16), 167401 (2012).
[Crossref] [PubMed]

Seyller, T.

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

Shaner, E.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: Toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[Crossref]

Shu, J.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Skuras, E.

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Staton-Bevan, A.

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

Stauber, T.

T. Stauber, N. Peres, and A. Castro Neto, “Conductivity of suspended and non-suspended graphene at finite gate voltage,” Phys. Rev. B 78(8), 085418 (2008).
[Crossref]

Stradling, R. A.

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

Stroud, D.

N. A. Pike and D. Stroud, “Model for the spin-dependent Seebeck coefficient of InSb in a magnetic field,” Phys. Rev. B 90(17), 174435 (2014).
[Crossref]

Tao, J.

Teng, J.

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

Thiemens, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Thomas, R.

S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

Tokura, Y.

L. Demkó, G. A. H. Schober, V. Kocsis, M. S. Bahramy, H. Murakawa, J. S. Lee, I. Kézsmárki, R. Arita, N. Nagaosa, and Y. Tokura, “Enhanced Infrared Magneto-Optical Response of the Nonmagnetic Semiconductor BiTeI Driven by Bulk Rashba Splitting,” Phys. Rev. Lett. 109(16), 167401 (2012).
[Crossref] [PubMed]

Triozon, F.

B. Biel, F. Triozon, X. Blase, and S. Roche, “Chemically induced mobility gaps in graphene nanoribbons: a route for upscaling device performances,” Nano Lett. 9(7), 2725–2729 (2009).
[Crossref] [PubMed]

Vangala, S.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: Toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[Crossref]

Wagner, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

Wagoner, G.

G. Dresselhaus, A. F. Kip, C. Kittel, and G. Wagoner, “Cyclotron and Spin Resonance in Indium Antimonide,” Phys. Rev. 98(2), 556–557 (1955).
[Crossref]

Wallis, R.

J. Brion, R. Wallis, A. Hartstein, and E. Burstein, “Theory of Surface Magnetoplasmons in Semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Walter, A. L.

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

Wang, B.

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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
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[Crossref] [PubMed]

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S. D. Parker, R. L. Williams, R. Droopad, R. A. Stradling, K. W. J. Barnham, S. N. Holmes, J. Laverty, C. C. Phillips, E. Skuras, R. Thomas, X. Zhang, A. Staton-Bevan, and D. W. Pashley, “Observation and control of the amphoteric behaviour of Si-doped InSb grown on GaAs by MBE,” Semicond. Sci. Technol. 4(8), 663–676 (1989).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Schematic view (a) and the cross section on plane xy (b) of the double graphene layers system, the applied magnetic field (red arrow) is parallel to z axis.
Fig. 2
Fig. 2 Dependencies of the real modal indice of graphene plasmons along x + direction on the wavelengths (a) and upper space medium permittivity ε1 (b) with distinct magnetic fields.
Fig. 3
Fig. 3 Dependencies of the transmittance on overlap length L2 for opposite magnetic fields. (a) for B = 3T and (b) for B = −3T. Insets show the |E| field profiles with power flow (red arrows) under overlap length L2 = 280 nm. The medium permittivity ε1 = 3, operation wavelength λ = 9μm and interspace length D = 20 nm.
Fig. 4
Fig. 4 The normalized electric field |E| profiles, plasmons input directions (white arrows), and power flow directions (red arrows) for the coupled graphene sheet waveguide structure as the plasmons input from Port #1 (a,e), Port #3 (b,f) and Port #2 (c,g) and corresponding schematics of plasmons circulators (d,h). The ε1 = 3, λ = 9μm , L2 = 200 nm and D = 40 nm.
Fig. 5
Fig. 5 The insertion loss (a) and isolation ratio (b) with respect to the overlap length L2 and interspace length D. The medium permittivity ε1 = 3, the magnetic field B = 3 T and wavelength λ = 9 μm.
Fig. 6
Fig. 6 The dependencies of the insertion loss (a) and isolation ratio (b) of the isolator on the chemical potential μc and overlap length L2 . The wavelength λ = 9μm, interspace length D = 40 nm, magnetic field B = 3T, carrier mobility μ = 10000 cm2/(V.s) and permittivity ε1 = 3.
Fig. 7
Fig. 7 The dependencies of the insertion loss (a) and isolation ratio (b) in units of dB of the isolator on the graphene carrier mobility μ and overlap length L2 . The wavelength λ = 9μm, interspace length D = 40 nm, magnetic field B = 3T, chemical potential μc = 0.45eV and permittivity ε1 = 3.
Fig. 8
Fig. 8 The dependencies of the insertion loss (a) and isolation ratio (b) in units of dB of the isolator on the magnetic field B and overlap length L2 . The wavelength λ = 9μm, carrier mobility μ = 10000 cm2/(V.s), chemical potential μc = 0.45eV, interspace length D = 40 nm and permittivity ε1 = 3.
Fig. 9
Fig. 9 The dependencies of the insertion loss (a) and isolation ratio (b) in units of dB of the isolator on the surround medium permittivity ε1 and overlap length L2 . The wavelength λ = 9μm, carrier mobility is μ = 10000 cm2/(V.s), chemical potential μc = 0.45eV and magnetic field B = 3T.
Fig. 10
Fig. 10 The dependencies of the insertion loss (a) and isolation ratio (b) in units of dB of the isolator on the surround medium permittivity ε1 and overlap length L2 . The wavelength λ = 9μm, carrier mobility μ = 10000 cm2/(V.s), chemical potential is μc = 0.45eV, permittivity ε1 = 3 and magnetic field B = 3T. The initial interspace length is D = 40 nm and the distance is H = 100 nm.
Fig. 11
Fig. 11 The dependencies of insertion loss (a) and isolation ratio (b) in units of dB as functions of overlap length L2 with and without damping in InSb substrate. The wavelength λ = 9μm, the magnetic field B = 3T, permittivity ε1 = 3, carrier mobility μ = 10000 cm2/(V.s) and chemical potential μc = 0.45eV. The structural parameters are D = 40 nm, H = 100 nm, L1 = L4 = 50 nm, L2 = 210 nm, L3 = 30 nm and R1 = R2 = R3 = R4 = 30 nm.

Equations (6)

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β 2 2 π 2 ε 0 ε 1 e 2 μ c ( 1 + i ω τ ) ω 2 ,
ε s ε [ ε x x i ε x y 0 i ε x y ε y y 0 0 0 ε z z ] ,
ε 1 k 2 + ε x x 2 ε x y 2 k 1 ε x x + β 1 ε x y + i σ ω ε 0 = 0 ,
[ a 1 ( L 1 + L 2 ) a 2 ( L 1 + L 2 ) ] = [ A 1 , 1 A 1 , 2 A 2 , 1 A 2 , 2 ] [ a 1 ( L 1 ) a 2 ( L 1 ) ] ,
| a 1 ( L 1 + L 2 ) / a 1 ( L 1 ) | 2 = | A 1 , 1 | 2 , | a 2 ( L 1 + L 2 ) / a 1 ( L 1 ) | 2 = | A 2 , 1 | 2 ,
A 1 , 1 = cos ( β 0 L 2 ) + i [ ( β 2 β 1 ) / ( 2 β 0 ) ] sin ( β 0 L 2 ) , A 2 , 1 = ( κ 21 / β 0 ) sin ( β 0 L 2 ) , β 0 = [ ( β 1 β 2 ) / 2 ] 2 + | κ 12 | 2 , | κ 12 | = ( 1 / 2 ) ( β d β c ) 2 ( β 1 β 2 ) 2 .

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