Abstract

One-dimensional topological photonic crystals (TPCs) with graphene sheet have been proposed to enhance the Faraday rotation (FR). Because of the strong localized field of the topological interface state, the enhanced FR angle with high transmittance has been confirmed. The effects of external magnetic field, unit cell number and multiple interface states of multilayers on FR angle and transmittance are studied. As a result, the FR is raised, which shows a field enhancement constraint at the interface between the TPCs with graphene. The FR angle can reach 16.2° with the high transmission (70%). By constructing multiple interface states, multiple transmission peaks and FR angles are further achieved. Our result would give a fresh idea, which could be applied in nonreciprocal photonic device or optical communication systems.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Mansuripur, The Physical Principles of Magneto-Optical Recording (Cambridge University Press, 1998).
  2. Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
    [Crossref]
  3. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
    [Crossref]
  4. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
    [Crossref]
  5. M. C. Lemme, T. J. Echtermeyer, M. Baus, and H. Kurz, “A graphene field-effect device,” IEEE Electron Device Lett. 28(4), 282–284 (2007).
    [Crossref]
  6. N. Stander, B. Huard, and D. Goldhaber-Gordon, “Evidence for Klein tunneling in graphene p− n junctions,” Phys. Rev. Lett. 102(2), 026807 (2009).
    [Crossref]
  7. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
    [Crossref]
  8. A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84(23), 235410 (2011).
    [Crossref]
  9. H. Da and G. Liang, “Enhanced Faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett. 98(26), 261915 (2011).
    [Crossref]
  10. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314(5806), 1757–1761 (2006).
    [Crossref]
  11. W. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
    [Crossref]
  12. W.-P. Su, J. R. Schrieffer, and A. J. Heeger, “Soliton excitations in polyacetylene,” Phys. Rev. B 22(4), 2099–2111 (1980).
    [Crossref]
  13. A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W.-P. Su, “Solitons in conducting polymers,” Rev. Mod. Phys. 60(3), 781–850 (1988).
    [Crossref]
  14. O. A. Pankratov, S. V. Pakhomov, and B. A. Volkov, “Supersymmetry in heterojunctions: Band-inverting contact on the basis of Pb1-xSnxTe and Hg1-xCdxTe,” Solid State Commun. 61(2), 93–96 (1987).
    [Crossref]
  15. M. Z. Hasan, S.-Y. Xu, and M. Neupane, “Topological insulators, topological crystalline insulators, and topological Kondo insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010).
    [Crossref]
  16. L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
    [Crossref]
  17. W. Gao, X. Hu, C. Li, J. Yang, Z. Chai, J. Xie, and Q. Gong, “Fano-resonance in one-dimensional topological photonic crystal heterostructure,” Opt. Express 26(7), 8634–8644 (2018).
    [Crossref]
  18. K. H. Choi, C. W. Ling, K. F. Lee, Y. H. Tsang, and K. H. Fung, “Simultaneous multi-frequency topological edge modes between one-dimensional photonic crystals,” Opt. Lett. 41(7), 1644–1647 (2016).
    [Crossref]
  19. J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989).
    [Crossref]
  20. M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
    [Crossref]
  21. Š. Višňovský, K. Postava, and T. Yamaguchi, “Magneto-optic polar Kerr and Faraday effects in magnetic superlattices,” Czech. J. Phys. 51(9), 917–949 (2001).
    [Crossref]
  22. T. Tang, C. Li, L. Luo, Y. Zhang, and Q. Yuan, “Thermo-optic Imbert-Fedorov effect in a prism-waveguide coupling system with silicon-on-insulator,” Opt. Commun. 370, 49–54 (2016).
    [Crossref]
  23. W. Wang, S. P. Apell, and J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86(12), 125450 (2012).
    [Crossref]
  24. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley New York, 1984), 5.
  25. 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]
  26. 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]

2018 (1)

2016 (2)

K. H. Choi, C. W. Ling, K. F. Lee, Y. H. Tsang, and K. H. Fung, “Simultaneous multi-frequency topological edge modes between one-dimensional photonic crystals,” Opt. Lett. 41(7), 1644–1647 (2016).
[Crossref]

T. Tang, C. Li, L. Luo, Y. Zhang, and Q. Yuan, “Thermo-optic Imbert-Fedorov effect in a prism-waveguide coupling system with silicon-on-insulator,” Opt. Commun. 370, 49–54 (2016).
[Crossref]

2014 (2)

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

2012 (3)

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]

W. Wang, S. P. Apell, and J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86(12), 125450 (2012).
[Crossref]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

2011 (4)

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84(23), 235410 (2011).
[Crossref]

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

2010 (2)

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

M. Z. Hasan, S.-Y. Xu, and M. Neupane, “Topological insulators, topological crystalline insulators, and topological Kondo insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010).
[Crossref]

2009 (1)

N. Stander, B. Huard, and D. Goldhaber-Gordon, “Evidence for Klein tunneling in graphene p− n junctions,” Phys. Rev. Lett. 102(2), 026807 (2009).
[Crossref]

2007 (1)

M. C. Lemme, T. J. Echtermeyer, M. Baus, and H. Kurz, “A graphene field-effect device,” IEEE Electron Device Lett. 28(4), 282–284 (2007).
[Crossref]

2006 (1)

B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314(5806), 1757–1761 (2006).
[Crossref]

2005 (1)

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref]

2001 (1)

Š. Višňovský, K. Postava, and T. Yamaguchi, “Magneto-optic polar Kerr and Faraday effects in magnetic superlattices,” Czech. J. Phys. 51(9), 917–949 (2001).
[Crossref]

1989 (1)

J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989).
[Crossref]

1988 (1)

A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W.-P. Su, “Solitons in conducting polymers,” Rev. Mod. Phys. 60(3), 781–850 (1988).
[Crossref]

1987 (1)

O. A. Pankratov, S. V. Pakhomov, and B. A. Volkov, “Supersymmetry in heterojunctions: Band-inverting contact on the basis of Pb1-xSnxTe and Hg1-xCdxTe,” Solid State Commun. 61(2), 93–96 (1987).
[Crossref]

1980 (1)

W.-P. Su, J. R. Schrieffer, and A. J. Heeger, “Soliton excitations in polyacetylene,” Phys. Rev. B 22(4), 2099–2111 (1980).
[Crossref]

1979 (1)

W. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
[Crossref]

Alonso-González, P.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Apell, S. P.

W. Wang, S. P. Apell, and J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86(12), 125450 (2012).
[Crossref]

Badioli, M.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Bao, Q.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Baus, M.

M. C. Lemme, T. J. Echtermeyer, M. Baus, and H. Kurz, “A graphene field-effect device,” IEEE Electron Device Lett. 28(4), 282–284 (2007).
[Crossref]

Bernevig, B. A.

B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314(5806), 1757–1761 (2006).
[Crossref]

Bludov, Y. V.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84(23), 235410 (2011).
[Crossref]

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (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]

Centeno, A.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Chai, Z.

Chan, C. T.

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

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]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Choi, K. H.

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]

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

Echtermeyer, T. J.

M. C. Lemme, T. J. Echtermeyer, M. Baus, and H. Kurz, “A graphene field-effect device,” IEEE Electron Device Lett. 28(4), 282–284 (2007).
[Crossref]

Ferrari, A. C.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Ferreira, A.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84(23), 235410 (2011).
[Crossref]

Fung, K. H.

Gao, W.

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]

Godignon, P.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Goldhaber-Gordon, D.

N. Stander, B. Huard, and D. Goldhaber-Gordon, “Evidence for Klein tunneling in graphene p− n junctions,” Phys. Rev. Lett. 102(2), 026807 (2009).
[Crossref]

Gong, Q.

Hasan, M. Z.

M. Z. Hasan, S.-Y. Xu, and M. Neupane, “Topological insulators, topological crystalline insulators, and topological Kondo insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010).
[Crossref]

Hasan, T.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Heeger, A. J.

A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W.-P. Su, “Solitons in conducting polymers,” Rev. Mod. Phys. 60(3), 781–850 (1988).
[Crossref]

W.-P. Su, J. R. Schrieffer, and A. J. Heeger, “Soliton excitations in polyacetylene,” Phys. Rev. B 22(4), 2099–2111 (1980).
[Crossref]

W. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
[Crossref]

Hu, X.

Huard, B.

N. Stander, B. Huard, and D. Goldhaber-Gordon, “Evidence for Klein tunneling in graphene p− n junctions,” Phys. Rev. Lett. 102(2), 026807 (2009).
[Crossref]

Hughes, T. L.

B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314(5806), 1757–1761 (2006).
[Crossref]

Huth, F.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Joannopoulos, J. D.

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

Kim, P.

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref]

Kinaret, J. M.

W. Wang, S. P. Apell, and J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86(12), 125450 (2012).
[Crossref]

Kivelson, S.

A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W.-P. Su, “Solitons in conducting polymers,” Rev. Mod. Phys. 60(3), 781–850 (1988).
[Crossref]

Kurz, H.

M. C. Lemme, T. J. Echtermeyer, M. Baus, and H. Kurz, “A graphene field-effect device,” IEEE Electron Device Lett. 28(4), 282–284 (2007).
[Crossref]

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]

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]

Lee, K. F.

Lemme, M. C.

M. C. Lemme, T. J. Echtermeyer, M. Baus, and H. Kurz, “A graphene field-effect device,” IEEE Electron Device Lett. 28(4), 282–284 (2007).
[Crossref]

Levallois, J.

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, C.

W. Gao, X. Hu, C. Li, J. Yang, Z. Chai, J. Xie, and Q. Gong, “Fano-resonance in one-dimensional topological photonic crystal heterostructure,” Opt. Express 26(7), 8634–8644 (2018).
[Crossref]

T. Tang, C. Li, L. Luo, Y. Zhang, and Q. Yuan, “Thermo-optic Imbert-Fedorov effect in a prism-waveguide coupling system with silicon-on-insulator,” Opt. Commun. 370, 49–54 (2016).
[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]

Lim, C. H. Y. X.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Ling, C. W.

Loh, K. P.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Lu, L.

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

Luo, L.

T. Tang, C. Li, L. Luo, Y. Zhang, and Q. Yuan, “Thermo-optic Imbert-Fedorov effect in a prism-waveguide coupling system with silicon-on-insulator,” Opt. Commun. 370, 49–54 (2016).
[Crossref]

Mansuripur, M.

M. Mansuripur, The Physical Principles of Magneto-Optical Recording (Cambridge University Press, 1998).

Neto, A. C.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84(23), 235410 (2011).
[Crossref]

Neupane, M.

M. Z. Hasan, S.-Y. Xu, and M. Neupane, “Topological insulators, topological crystalline insulators, and topological Kondo insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010).
[Crossref]

Ni, Z.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

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]

Osmond, J.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

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]

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]

Pakhomov, S. V.

O. A. Pankratov, S. V. Pakhomov, and B. A. Volkov, “Supersymmetry in heterojunctions: Band-inverting contact on the basis of Pb1-xSnxTe and Hg1-xCdxTe,” Solid State Commun. 61(2), 93–96 (1987).
[Crossref]

Pankratov, O. A.

O. A. Pankratov, S. V. Pakhomov, and B. A. Volkov, “Supersymmetry in heterojunctions: Band-inverting contact on the basis of Pb1-xSnxTe and Hg1-xCdxTe,” Solid State Commun. 61(2), 93–96 (1987).
[Crossref]

Pereira, V.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84(23), 235410 (2011).
[Crossref]

Peres, N. M. R.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84(23), 235410 (2011).
[Crossref]

Pesquera, A.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Postava, K.

Š. Višňovský, K. Postava, and T. Yamaguchi, “Magneto-optic polar Kerr and Faraday effects in magnetic superlattices,” Czech. J. Phys. 51(9), 917–949 (2001).
[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]

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]

Schrieffer, J. R.

A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W.-P. Su, “Solitons in conducting polymers,” Rev. Mod. Phys. 60(3), 781–850 (1988).
[Crossref]

W.-P. Su, J. R. Schrieffer, and A. J. Heeger, “Soliton excitations in polyacetylene,” Phys. Rev. B 22(4), 2099–2111 (1980).
[Crossref]

W. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
[Crossref]

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]

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]

Soljacic, M.

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

Spasenovic, M.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Stander, N.

N. Stander, B. Huard, and D. Goldhaber-Gordon, “Evidence for Klein tunneling in graphene p− n junctions,” Phys. Rev. Lett. 102(2), 026807 (2009).
[Crossref]

Stormer, H. L.

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref]

Su, W.

W. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
[Crossref]

Su, W.-P.

A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W.-P. Su, “Solitons in conducting polymers,” Rev. Mod. Phys. 60(3), 781–850 (1988).
[Crossref]

W.-P. Su, J. R. Schrieffer, and A. J. Heeger, “Soliton excitations in polyacetylene,” Phys. Rev. B 22(4), 2099–2111 (1980).
[Crossref]

Sun, Z.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Tan, Y.-W.

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref]

Tang, D. Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Tang, T.

T. Tang, C. Li, L. Luo, Y. Zhang, and Q. Yuan, “Thermo-optic Imbert-Fedorov effect in a prism-waveguide coupling system with silicon-on-insulator,” Opt. Commun. 370, 49–54 (2016).
[Crossref]

Thongrattanasiri, S.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Tsang, Y. H.

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]

Viana-Gomes, J.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84(23), 235410 (2011).
[Crossref]

Višnovský, Š.

Š. Višňovský, K. Postava, and T. Yamaguchi, “Magneto-optic polar Kerr and Faraday effects in magnetic superlattices,” Czech. J. Phys. 51(9), 917–949 (2001).
[Crossref]

Volkov, B. A.

O. A. Pankratov, S. V. Pakhomov, and B. A. Volkov, “Supersymmetry in heterojunctions: Band-inverting contact on the basis of Pb1-xSnxTe and Hg1-xCdxTe,” Solid State Commun. 61(2), 93–96 (1987).
[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]

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, B.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Wang, W.

W. Wang, S. P. Apell, and J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86(12), 125450 (2012).
[Crossref]

Wang, Y.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Xiao, M.

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

Xie, J.

Xu, S.-Y.

M. Z. Hasan, S.-Y. Xu, and M. Neupane, “Topological insulators, topological crystalline insulators, and topological Kondo insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010).
[Crossref]

Yamaguchi, T.

Š. Višňovský, K. Postava, and T. Yamaguchi, “Magneto-optic polar Kerr and Faraday effects in magnetic superlattices,” Czech. J. Phys. 51(9), 917–949 (2001).
[Crossref]

Yang, J.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley New York, 1984), 5.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley New York, 1984), 5.

Yuan, Q.

T. Tang, C. Li, L. Luo, Y. Zhang, and Q. Yuan, “Thermo-optic Imbert-Fedorov effect in a prism-waveguide coupling system with silicon-on-insulator,” Opt. Commun. 370, 49–54 (2016).
[Crossref]

Zak, J.

J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989).
[Crossref]

Zhang, H.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Zhang, S.-C.

B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314(5806), 1757–1761 (2006).
[Crossref]

Zhang, Y.

T. Tang, C. Li, L. Luo, Y. Zhang, and Q. Yuan, “Thermo-optic Imbert-Fedorov effect in a prism-waveguide coupling system with silicon-on-insulator,” Opt. Commun. 370, 49–54 (2016).
[Crossref]

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref]

Zhang, Z. Q.

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

Appl. Phys. Lett. (1)

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

Czech. J. Phys. (1)

Š. Višňovský, K. Postava, and T. Yamaguchi, “Magneto-optic polar Kerr and Faraday effects in magnetic superlattices,” Czech. J. Phys. 51(9), 917–949 (2001).
[Crossref]

IEEE Electron Device Lett. (1)

M. C. Lemme, T. J. Echtermeyer, M. Baus, and H. Kurz, “A graphene field-effect device,” IEEE Electron Device Lett. 28(4), 282–284 (2007).
[Crossref]

Nano Lett. (1)

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]

Nat. Photonics (3)

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (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]

Nature (2)

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref]

Opt. Commun. (1)

T. Tang, C. Li, L. Luo, Y. Zhang, and Q. Yuan, “Thermo-optic Imbert-Fedorov effect in a prism-waveguide coupling system with silicon-on-insulator,” Opt. Commun. 370, 49–54 (2016).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (3)

W.-P. Su, J. R. Schrieffer, and A. J. Heeger, “Soliton excitations in polyacetylene,” Phys. Rev. B 22(4), 2099–2111 (1980).
[Crossref]

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. C. Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84(23), 235410 (2011).
[Crossref]

W. Wang, S. P. Apell, and J. M. Kinaret, “Edge magnetoplasmons and the optical excitations in graphene disks,” Phys. Rev. B 86(12), 125450 (2012).
[Crossref]

Phys. Rev. Lett. (3)

N. Stander, B. Huard, and D. Goldhaber-Gordon, “Evidence for Klein tunneling in graphene p− n junctions,” Phys. Rev. Lett. 102(2), 026807 (2009).
[Crossref]

W. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Phys. Rev. Lett. 42(25), 1698–1701 (1979).
[Crossref]

J. Zak, “Berry’s phase for energy bands in solids,” Phys. Rev. Lett. 62(23), 2747–2750 (1989).
[Crossref]

Phys. Rev. X (1)

M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014).
[Crossref]

Rev. Mod. Phys. (2)

A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W.-P. Su, “Solitons in conducting polymers,” Rev. Mod. Phys. 60(3), 781–850 (1988).
[Crossref]

M. Z. Hasan, S.-Y. Xu, and M. Neupane, “Topological insulators, topological crystalline insulators, and topological Kondo insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010).
[Crossref]

Science (1)

B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314(5806), 1757–1761 (2006).
[Crossref]

Solid State Commun. (1)

O. A. Pankratov, S. V. Pakhomov, and B. A. Volkov, “Supersymmetry in heterojunctions: Band-inverting contact on the basis of Pb1-xSnxTe and Hg1-xCdxTe,” Solid State Commun. 61(2), 93–96 (1987).
[Crossref]

Other (2)

M. Mansuripur, The Physical Principles of Magneto-Optical Recording (Cambridge University Press, 1998).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley New York, 1984), 5.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1. (a)Structure diagram, where graphene is caught between PhC X and PhC Y. An external magnetic field is parallel to the incident light;(b) Schematic diagram of the 1D TPC model. Both X and Y contain n unit cells. The slab A in x is sandwiched by half layer B, and slab B in Y is sandwiched by half layer A. Where the slab A is TiO2, slab B is SiO2.
Fig. 2.
Fig. 2. (a), (b) The band structures of PhC X and PhC Y, respectively. The Zak phase is marked by the green font in the center of the passband. The band gap is represented by blue and purple, and the value in the bracket on the right indicates the superposition of Zak below the band gap; (c) Transmission of PhC X + PhC Y, and the repetitions m is 6. Topological interface states exist on the red arrow surface.
Fig. 3.
Fig. 3. (a) Transmittance and the FR angle versus wavelength of single graphene and G-TPC, where m=3; (b) Electric field of the structure.
Fig. 4.
Fig. 4. (a) Transmittance of 1D G-TPC with repetitions m=2, 4, and 6; (b) Relationship between FR angle and wavelength;
Fig. 5.
Fig. 5. The real part of permittivity components (a) $ {\varepsilon _{xx}}$ and (b) ${\varepsilon _{xy}}$ of graphene in magnetic field B=3,4,5 T. (c) Transmittance and (d) FR angle fo 1D G-TPCs with m=5 under B=3, 4 and 5 T.
Fig. 6.
Fig. 6. (a) Transmission and (b) FR angle of structure PhC Y-PhC X-G-PhC Y; (c) Transmittance and (d) FR angle of structure PhC Y-PhC X-G-PhC Y-PhC X.

Equations (6)

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

ε = 1 + i ω d g ε 0 ( σ x x σ x y 0 σ x y σ y y 0 0 0 σ z ) .
σ x x = σ y y = D π i ( ω + i / τ ) ( ω + i / τ ) 2 ω c 2 ,
σ x y = σ y x = D π ω c ( ω + i / τ ) 2 ω c 2 .
cos ( Q Λ ) = cos ( k A d A ) cos ( k B d B ) + ( Z A Z B + Z B Z A ) sin ( k A d A ) sin ( k B d B ) .
θ m Z a k = π Λ π Λ [ i u n i t   c e l l ε ( z ) u m , K ( z ) K u m , K ( z ) d z ] d K ,
sgn [ ς ( n ) ] = ( 1 ) n ( 1 ) l exp ( i m = 0 n 1 θ m Z a k ) ,

Metrics