Abstract

We present an ultracompact electro-optic modulator with a length of 15 nm by utilizing a permittivity-tunable metamaterial channel, which is composed of alternative layers of graphene and silica. Optical waves can propagate through the metamaterial channel only if its permittivity is tuned to be near zero. The finite-difference time-domain (FDTD) simulations show the insertion loss is roughly 0.27dB while the 3 dB extinction ratio is obtained with a 0.8 V gate voltage. The device’s footprint is as small as 0.01μm2. This modulator consumes low power and can potentially be ultrafast.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
    [CrossRef]
  2. M. Silveirinha and N. Engheta, Phys. Rev. B 76, 245109 (2007).
    [CrossRef]
  3. A. Alù and N. Engheta, Phys. Rev. B 78, 035440 (2008).
    [CrossRef]
  4. A. Alù, M. G. Silveirinha, and N. Engheta, Phys. Rev. E 78, 016604 (2008).
    [CrossRef]
  5. A. Alù and N. Engheta, Phys. Rev. B 78, 045102 (2008).
    [CrossRef]
  6. B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
    [CrossRef]
  7. R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, Phys. Rev. Lett. 100, 023903 (2008).
    [CrossRef]
  8. B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, J. Appl. Phys. 105, 044905 (2009).
    [CrossRef]
  9. J. Hao, W. Yan, and M. Qiu, Appl. Phys. Lett. 96, 101109 (2010).
    [CrossRef]
  10. Y. Xu and H. Chen, Appl. Phys. Lett. 98, 113501 (2011).
    [CrossRef]
  11. J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, Appl. Phys. Lett. 100, 221903 (2012).
    [CrossRef]
  12. A. Ourir, A. Maurel, and V. Pagneux, Opt. Lett. 38, 2092 (2013).
    [CrossRef]
  13. G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).
    [CrossRef]
  14. F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
    [CrossRef]
  15. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
    [CrossRef]
  16. Z. Lu and W. Zhao, J. Opt. Soc. Am. B 29, 1490 (2012).
    [CrossRef]
  17. B. Zhu, G. Ren, S. Zheng, Z. Lin, and S. Jian, Opt. Express 21, 17089 (2013).
    [CrossRef]
  18. L. Yang, T. Hu, R. Hao, C. Qiu, C. Xu, H. Yu, Y. Xu, X. Jiang, Y. Li, and J. Yang, Opt. Lett. 38, 2512 (2013).
    [CrossRef]
  19. A. Vakil and N. Engheta, Science 332, 1291 (2011).
    [CrossRef]

2013 (3)

2012 (2)

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, Appl. Phys. Lett. 100, 221903 (2012).
[CrossRef]

Z. Lu and W. Zhao, J. Opt. Soc. Am. B 29, 1490 (2012).
[CrossRef]

2011 (3)

Y. Xu and H. Chen, Appl. Phys. Lett. 98, 113501 (2011).
[CrossRef]

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

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

2010 (1)

J. Hao, W. Yan, and M. Qiu, Appl. Phys. Lett. 96, 101109 (2010).
[CrossRef]

2009 (2)

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, J. Appl. Phys. 105, 044905 (2009).
[CrossRef]

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

2008 (6)

G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. B 78, 035440 (2008).
[CrossRef]

A. Alù, M. G. Silveirinha, and N. Engheta, Phys. Rev. E 78, 016604 (2008).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. B 78, 045102 (2008).
[CrossRef]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, Phys. Rev. Lett. 100, 023903 (2008).
[CrossRef]

2007 (1)

M. Silveirinha and N. Engheta, Phys. Rev. B 76, 245109 (2007).
[CrossRef]

2006 (1)

M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Alù, A.

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, J. Appl. Phys. 105, 044905 (2009).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. B 78, 035440 (2008).
[CrossRef]

A. Alù, M. G. Silveirinha, and N. Engheta, Phys. Rev. E 78, 016604 (2008).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. B 78, 045102 (2008).
[CrossRef]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

Avouris, P.

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

Chen, H.

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, Appl. Phys. Lett. 100, 221903 (2012).
[CrossRef]

Y. Xu and H. Chen, Appl. Phys. Lett. 98, 113501 (2011).
[CrossRef]

Cheng, Q.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, Phys. Rev. Lett. 100, 023903 (2008).
[CrossRef]

Cui, T. J.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, Phys. Rev. Lett. 100, 023903 (2008).
[CrossRef]

Cummer, S. A.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, Phys. Rev. Lett. 100, 023903 (2008).
[CrossRef]

Edwards, B.

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, J. Appl. Phys. 105, 044905 (2009).
[CrossRef]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

Engheta, N.

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

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, J. Appl. Phys. 105, 044905 (2009).
[CrossRef]

A. Alù, M. G. Silveirinha, and N. Engheta, Phys. Rev. E 78, 016604 (2008).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. B 78, 045102 (2008).
[CrossRef]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. B 78, 035440 (2008).
[CrossRef]

M. Silveirinha and N. Engheta, Phys. Rev. B 76, 245109 (2007).
[CrossRef]

M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Gao, L.

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, Appl. Phys. Lett. 100, 221903 (2012).
[CrossRef]

Geng, B.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Hand, T.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, Phys. Rev. Lett. 100, 023903 (2008).
[CrossRef]

Hanson, G. W.

G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).
[CrossRef]

Hao, J.

J. Hao, W. Yan, and M. Qiu, Appl. Phys. Lett. 96, 101109 (2010).
[CrossRef]

Hao, R.

Hou, B.

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, Appl. Phys. Lett. 100, 221903 (2012).
[CrossRef]

Hu, T.

Jian, S.

Jiang, X.

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Lai, Y.

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, Appl. Phys. Lett. 100, 221903 (2012).
[CrossRef]

Li, Y.

Lin, Y.-M.

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

Lin, Z.

Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Liu, R.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, Phys. Rev. Lett. 100, 023903 (2008).
[CrossRef]

Lu, Z.

Luo, J.

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, Appl. Phys. Lett. 100, 221903 (2012).
[CrossRef]

Maurel, A.

Mock, J. J.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, Phys. Rev. Lett. 100, 023903 (2008).
[CrossRef]

Mueller, T.

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

Ourir, A.

Pagneux, V.

Qiu, C.

Qiu, M.

J. Hao, W. Yan, and M. Qiu, Appl. Phys. Lett. 96, 101109 (2010).
[CrossRef]

Ren, G.

Silveirinha, M.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

M. Silveirinha and N. Engheta, Phys. Rev. B 76, 245109 (2007).
[CrossRef]

M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Silveirinha, M. G.

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, J. Appl. Phys. 105, 044905 (2009).
[CrossRef]

A. Alù, M. G. Silveirinha, and N. Engheta, Phys. Rev. E 78, 016604 (2008).
[CrossRef]

Smith, D. R.

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, Phys. Rev. Lett. 100, 023903 (2008).
[CrossRef]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Vakil, A.

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

Valdes-Garcia, A.

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Xia, F.

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

Xu, C.

Xu, P.

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, Appl. Phys. Lett. 100, 221903 (2012).
[CrossRef]

Xu, Y.

Yan, W.

J. Hao, W. Yan, and M. Qiu, Appl. Phys. Lett. 96, 101109 (2010).
[CrossRef]

Yang, J.

Yang, L.

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Young, M. E.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

Yu, H.

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Zhao, W.

Zheng, S.

Zhu, B.

Appl. Phys. Lett. (3)

J. Hao, W. Yan, and M. Qiu, Appl. Phys. Lett. 96, 101109 (2010).
[CrossRef]

Y. Xu and H. Chen, Appl. Phys. Lett. 98, 113501 (2011).
[CrossRef]

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, Appl. Phys. Lett. 100, 221903 (2012).
[CrossRef]

J. Appl. Phys. (2)

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, J. Appl. Phys. 105, 044905 (2009).
[CrossRef]

G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nat. Nanotechnol. (1)

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, Nat. Nanotechnol. 4, 839 (2009).
[CrossRef]

Nature (1)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, Nature 474, 64 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (3)

M. Silveirinha and N. Engheta, Phys. Rev. B 76, 245109 (2007).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. B 78, 035440 (2008).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. B 78, 045102 (2008).
[CrossRef]

Phys. Rev. E (1)

A. Alù, M. G. Silveirinha, and N. Engheta, Phys. Rev. E 78, 016604 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, Phys. Rev. Lett. 100, 023903 (2008).
[CrossRef]

M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Science (1)

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

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 (4)

Fig. 1.
Fig. 1.

Illustration of the modulator’s structure together with the construction of the metamaterial. (a) Optical energy is input from the left port. It is squeezed and tunneled through the metamaterial channel and output from the right port. (b) The metamaterial consists of graphene sheets and silica layers. The permittivity of silicon and silica are 11.9 and 2.1 in the simulation for the wavelength λ=1550nm, respectively.

Fig. 2.
Fig. 2.

Horizontal direction permittivity of the metamaterial. (a) Permittivity against different graphene’s chemical potentials for a fixed wavelength λ=1550nm. The ENZ point appears at μc=0.689eV. (b) Permittivity against different wavelengths for a fixed chemical potential μc=0.689eV. The red solid lines represent the real part of the permittivity and the blue dashed lines stand for the imaginary part.

Fig. 3.
Fig. 3.

Optimization of the modulator’s geometric structure for the wavelength λ=1550nm. The black dashed line represents the theoretical results of the transmission coefficients according to Eq. (6). The red and blue lines stand for the simulation results for different graphene’s chemical potentials. The green line shows the ER of the modulator between μc=0.689eV and μc=0.4eV.

Fig. 4.
Fig. 4.

Modulation effects of the device. (a) The transmission coefficient against the gate voltage. The initial bias point is at μc=0.689eV to set the modulator as the ON status. (b) and (c) The magnetic field distribution inside the modulator in z direction for the ON and OFF status, respectively.

Equations (7)

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

σintra=ie2π2(ω+i2Γ)[0ε(fd(ε)εfd(ε)ε)dε],
σinter=ie2(ω+i2Γ)π2[0fd(ε)fd(ε)(ω+i2Γ)24(ε/)2dε],
εg,xx=εg,zz=1+iσωε0Δ=1Im(σ)ωε0Δ+iRe(σ)ωε0Δ,
εxx=εzz=fgεg,xx+(1fg)εd,
εyy=fgεg,yy+1fgεd.
T=2a1(a1+a2)cos(kxd)i(εyya1a2ach+μr,pach)k0dsinc(kxd),
μc=vFπ|η(Vg+V0)|,

Metrics