Abstract

Enlarged group index has been reported previously when surface plasmons propagate through the graphene sheet, yet a clear slow wave performance in graphene has not been explored. We proposed and numerically analyzed here for the first time to the best of our knowledge an extremely wideband slow surface wave in a graphene-based grating waveguide. The strongly delayed wave (120<ng<167) with extremely large bandwidth (2.7THz>Δf>0.7THz) can be dynamically controlled via the gate-voltage dependent optical properties of graphene. Our results suggest that graphene may be a very promising slow light medium, promoting future slow light devices based on graphene.

© 2014 Optical Society of America

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2013 (2)

Y. Xu, J. Zhang, and G. Song, IEEE Photon. Technol. Lett. 25, 410 (2013).
[CrossRef]

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, Appl. Phys. Lett. 103, 061116 (2013).
[CrossRef]

2012 (2)

2011 (3)

A. Zadok, A. Eyal, and M. Tur, Appl. Opt. 50, E38 (2011).
[CrossRef]

A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 84, 161407 (2011).
[CrossRef]

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

2010 (6)

W. Song, R. Integlia, and W. Jiang, Phys. Rev. B 82, 235306 (2010).
[CrossRef]

R. Hao, E. Cassan, X. Le Roux, D. Gao, V. Khanh, L. Vivien, D. Marris-Morini, and X. Zhang, Opt. Express 18, 16309 (2010).
[CrossRef]

R. Integlia, W. Song, J. Tan, and W. Jiang, J. Nanosci. Nanotechnol. 10, 1596 (2010).
[CrossRef]

D. Gao, J. Hou, R. Hao, H. Wu, J. Guo, E. Cassan, and X. Zhang, IEEE Photon. Technol. Lett. 22, 1135 (2010).
[CrossRef]

R. Hao, E. Cassan, H. Kurt, X. Le Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, Opt. Express 18, 5942 (2010).
[CrossRef]

R. Hao, E. Cassan, K. Hamza, J. Hou, X. Le Roux, D. Marris-Morini, L. Vivien, D. Gao, Z. Zhou, and X. Zhang, IEEE Photon. Technol. Lett. 22, 844 (2010).
[CrossRef]

2008 (2)

2004 (1)

Almeida, V.

Casas-Bedoya, A.

Cassan, E.

R. Hao, E. Cassan, X. Le Roux, D. Gao, V. Khanh, L. Vivien, D. Marris-Morini, and X. Zhang, Opt. Express 18, 16309 (2010).
[CrossRef]

D. Gao, J. Hou, R. Hao, H. Wu, J. Guo, E. Cassan, and X. Zhang, IEEE Photon. Technol. Lett. 22, 1135 (2010).
[CrossRef]

R. Hao, E. Cassan, H. Kurt, X. Le Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, Opt. Express 18, 5942 (2010).
[CrossRef]

R. Hao, E. Cassan, K. Hamza, J. Hou, X. Le Roux, D. Marris-Morini, L. Vivien, D. Gao, Z. Zhou, and X. Zhang, IEEE Photon. Technol. Lett. 22, 844 (2010).
[CrossRef]

Chen, H.

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, Appl. Phys. Lett. 103, 061116 (2013).
[CrossRef]

Domachuk, P.

Du, W.

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, Appl. Phys. Lett. 103, 061116 (2013).
[CrossRef]

Eggleton, B. J.

Engheta, N.

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Eyal, A.

Faolain, L.

Gao, D.

R. Hao, E. Cassan, K. Hamza, J. Hou, X. Le Roux, D. Marris-Morini, L. Vivien, D. Gao, Z. Zhou, and X. Zhang, IEEE Photon. Technol. Lett. 22, 844 (2010).
[CrossRef]

R. Hao, E. Cassan, X. Le Roux, D. Gao, V. Khanh, L. Vivien, D. Marris-Morini, and X. Zhang, Opt. Express 18, 16309 (2010).
[CrossRef]

D. Gao, J. Hou, R. Hao, H. Wu, J. Guo, E. Cassan, and X. Zhang, IEEE Photon. Technol. Lett. 22, 1135 (2010).
[CrossRef]

Garcia-Vidal, F.

A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 84, 161407 (2011).
[CrossRef]

Gomez-Iglesias, A.

Grillet, C.

Guinea, F.

A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 84, 161407 (2011).
[CrossRef]

Guo, J.

D. Gao, J. Hou, R. Hao, H. Wu, J. Guo, E. Cassan, and X. Zhang, IEEE Photon. Technol. Lett. 22, 1135 (2010).
[CrossRef]

Gutman, N.

Hamza, K.

R. Hao, E. Cassan, K. Hamza, J. Hou, X. Le Roux, D. Marris-Morini, L. Vivien, D. Gao, Z. Zhou, and X. Zhang, IEEE Photon. Technol. Lett. 22, 844 (2010).
[CrossRef]

Hao, R.

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, Appl. Phys. Lett. 103, 061116 (2013).
[CrossRef]

R. Hao, E. Cassan, H. Kurt, X. Le Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, Opt. Express 18, 5942 (2010).
[CrossRef]

R. Hao, E. Cassan, K. Hamza, J. Hou, X. Le Roux, D. Marris-Morini, L. Vivien, D. Gao, Z. Zhou, and X. Zhang, IEEE Photon. Technol. Lett. 22, 844 (2010).
[CrossRef]

D. Gao, J. Hou, R. Hao, H. Wu, J. Guo, E. Cassan, and X. Zhang, IEEE Photon. Technol. Lett. 22, 1135 (2010).
[CrossRef]

R. Hao, E. Cassan, X. Le Roux, D. Gao, V. Khanh, L. Vivien, D. Marris-Morini, and X. Zhang, Opt. Express 18, 16309 (2010).
[CrossRef]

Hou, J.

D. Gao, J. Hou, R. Hao, H. Wu, J. Guo, E. Cassan, and X. Zhang, IEEE Photon. Technol. Lett. 22, 1135 (2010).
[CrossRef]

R. Hao, E. Cassan, K. Hamza, J. Hou, X. Le Roux, D. Marris-Morini, L. Vivien, D. Gao, Z. Zhou, and X. Zhang, IEEE Photon. Technol. Lett. 22, 844 (2010).
[CrossRef]

Husko, C.

Integlia, R.

R. Integlia, W. Song, J. Tan, and W. Jiang, J. Nanosci. Nanotechnol. 10, 1596 (2010).
[CrossRef]

W. Song, R. Integlia, and W. Jiang, Phys. Rev. B 82, 235306 (2010).
[CrossRef]

Jiang, W.

W. Song, R. Integlia, and W. Jiang, Phys. Rev. B 82, 235306 (2010).
[CrossRef]

R. Integlia, W. Song, J. Tan, and W. Jiang, J. Nanosci. Nanotechnol. 10, 1596 (2010).
[CrossRef]

Jin, X.

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, Appl. Phys. Lett. 103, 061116 (2013).
[CrossRef]

Khanh, V.

Krauss, T.

Krauss, T. F.

T. F. Krauss, Nat. Photonics 2, 448 (2008).
[CrossRef]

Kurt, H.

Le Roux, X.

Li, E.

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, Appl. Phys. Lett. 103, 061116 (2013).
[CrossRef]

Li, J.

Lipson, M.

Marris-Morini, D.

Martin-Moreno, L.

A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 84, 161407 (2011).
[CrossRef]

Monat, C.

Nikitin, A.

A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 84, 161407 (2011).
[CrossRef]

Panepucci, R.

Song, G.

Y. Xu, J. Zhang, and G. Song, IEEE Photon. Technol. Lett. 25, 410 (2013).
[CrossRef]

Song, W.

R. Integlia, W. Song, J. Tan, and W. Jiang, J. Nanosci. Nanotechnol. 10, 1596 (2010).
[CrossRef]

W. Song, R. Integlia, and W. Jiang, Phys. Rev. B 82, 235306 (2010).
[CrossRef]

Tan, J.

R. Integlia, W. Song, J. Tan, and W. Jiang, J. Nanosci. Nanotechnol. 10, 1596 (2010).
[CrossRef]

Tur, M.

Vakil, A.

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Vivien, L.

Wang, Q.

Y. Zhang, Y. Zhao, D. Wu, and Q. Wang, Sens. Actuators B 173, 505 (2012).
[CrossRef]

White, T.

Wu, D.

Y. Zhang, Y. Zhao, D. Wu, and Q. Wang, Sens. Actuators B 173, 505 (2012).
[CrossRef]

Wu, H.

R. Hao, E. Cassan, H. Kurt, X. Le Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, Opt. Express 18, 5942 (2010).
[CrossRef]

D. Gao, J. Hou, R. Hao, H. Wu, J. Guo, E. Cassan, and X. Zhang, IEEE Photon. Technol. Lett. 22, 1135 (2010).
[CrossRef]

Xu, Q.

Xu, Y.

Y. Xu, J. Zhang, and G. Song, IEEE Photon. Technol. Lett. 25, 410 (2013).
[CrossRef]

Yang, L.

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, Appl. Phys. Lett. 103, 061116 (2013).
[CrossRef]

Zadok, A.

Zhang, J.

Y. Xu, J. Zhang, and G. Song, IEEE Photon. Technol. Lett. 25, 410 (2013).
[CrossRef]

Zhang, X.

R. Hao, E. Cassan, X. Le Roux, D. Gao, V. Khanh, L. Vivien, D. Marris-Morini, and X. Zhang, Opt. Express 18, 16309 (2010).
[CrossRef]

D. Gao, J. Hou, R. Hao, H. Wu, J. Guo, E. Cassan, and X. Zhang, IEEE Photon. Technol. Lett. 22, 1135 (2010).
[CrossRef]

R. Hao, E. Cassan, H. Kurt, X. Le Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, Opt. Express 18, 5942 (2010).
[CrossRef]

R. Hao, E. Cassan, K. Hamza, J. Hou, X. Le Roux, D. Marris-Morini, L. Vivien, D. Gao, Z. Zhou, and X. Zhang, IEEE Photon. Technol. Lett. 22, 844 (2010).
[CrossRef]

Zhang, Y.

Y. Zhang, Y. Zhao, D. Wu, and Q. Wang, Sens. Actuators B 173, 505 (2012).
[CrossRef]

Zhao, Y.

Y. Zhang, Y. Zhao, D. Wu, and Q. Wang, Sens. Actuators B 173, 505 (2012).
[CrossRef]

Zhou, Z.

R. Hao, E. Cassan, K. Hamza, J. Hou, X. Le Roux, D. Marris-Morini, L. Vivien, D. Gao, Z. Zhou, and X. Zhang, IEEE Photon. Technol. Lett. 22, 844 (2010).
[CrossRef]

R. Hao, E. Cassan, H. Kurt, X. Le Roux, D. Marris-Morini, L. Vivien, H. Wu, Z. Zhou, and X. Zhang, Opt. Express 18, 5942 (2010).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, Appl. Phys. Lett. 103, 061116 (2013).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

Y. Xu, J. Zhang, and G. Song, IEEE Photon. Technol. Lett. 25, 410 (2013).
[CrossRef]

D. Gao, J. Hou, R. Hao, H. Wu, J. Guo, E. Cassan, and X. Zhang, IEEE Photon. Technol. Lett. 22, 1135 (2010).
[CrossRef]

R. Hao, E. Cassan, K. Hamza, J. Hou, X. Le Roux, D. Marris-Morini, L. Vivien, D. Gao, Z. Zhou, and X. Zhang, IEEE Photon. Technol. Lett. 22, 844 (2010).
[CrossRef]

J. Nanosci. Nanotechnol. (1)

R. Integlia, W. Song, J. Tan, and W. Jiang, J. Nanosci. Nanotechnol. 10, 1596 (2010).
[CrossRef]

Nat. Photonics (1)

T. F. Krauss, Nat. Photonics 2, 448 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B (2)

A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. B 84, 161407 (2011).
[CrossRef]

W. Song, R. Integlia, and W. Jiang, Phys. Rev. B 82, 235306 (2010).
[CrossRef]

Science (1)

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Sens. Actuators B (1)

Y. Zhang, Y. Zhao, D. Wu, and Q. Wang, Sens. Actuators B 173, 505 (2012).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Proposed graphene-based slow light waveguide. A uniformed graphene sheet is deposited on top of a waveguide made up of three parts: an 1D grating with a right-side sawtooth (waveguide A), a stripe waveguide (waveguide B), and a grating with a left-side sawtooth (waveguide C). The parameter values are d = 50 nm , w = 40 nm , p = 90 nm and h = 0 nm .

Fig. 2.
Fig. 2.

(a) Electric field energy versus frequency and wave number. The electric field energy is obtained by the sum of the Fourier transformation of the electric fields in these time monitors over all the time steps. (b) The corresponding group index versus frequency. (c)–(e) The intrinsic electric field distribution in one unit cell at (c) k = 0 , (d)  k = 0.5 ( 2 π / p ) , and (e)  k = 0.2535 ( 2 π / p ) .

Fig. 3.
Fig. 3.

(a) FDTD simulation configuration. The electric field intensity versus time recorded at (b) monitor 1, (c) monitor 2, (d) monitor 3, and (e) monitor 4.

Fig. 4.
Fig. 4.

Group index curves versus frequency under different chemical potentials. The graphene A and C are fixed at a chemical potential of 0.35 eV, while the chemical potential of the central graphene B is gradually increased from 0.4 to 0.6 eV.

Equations (1)

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β 2 = k 0 2 [ 1 ( 2 / η 0 σ g ) 2 ] ,

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