Abstract

We propose a semiconductor–graphene cylinder that can serve as a terahertz (THz) photonic crystal. In such a structure, graphene plays a role in achieving a strong mismatch of the dielectric constant at the semiconductor–graphene interface due to its two-dimensional nature and relatively low value of the dielectric constant. We find that when the radius of the outer semiconductor layer is about ρ1100μm, the frequencies of the photonic modes are within the THz bandwidth and they can be efficiently tuned via varying ρ1. Furthermore, the dispersion relation of the photonic modes shows that a semiconductor–graphene cylinder is of excellent light transport properties, which can be utilized for the THz waveguide. This study is pertinent to the application of graphene as THz photonic devices.

© 2012 Optical Society of America

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    [CrossRef]
  2. S. John, Phys. Rev. Lett. 58, 2486 (1987).
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    [CrossRef]
  4. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
    [CrossRef]
  5. P. L. Gourley, J. R. Wendt, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 64, 687 (1994).
    [CrossRef]
  6. Z. Y. Li, L. L. Lin, and Z. Q. Zhang, Phys. Rev. Lett. 84, 4341 (2000).
    [CrossRef]
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    [CrossRef]
  9. X. Wang, L. Zhi, and K. Müllen, Nano Lett. 8, 323 (2008).
    [CrossRef]
  10. W. Xu, Y. P. Gong, L. W. Liu, H. Qin, and Y. L. Shi, Nanoscale Res. Lett. 6, 250 (2011).
    [CrossRef]
  11. P. Diament, Wave Transmission and Fiber Optics(Macmillan, 1990).
  12. G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).
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    [CrossRef]
  14. For a review, see, e.g., P. H. Siegel, IEEE Trans. Microw. Theory Technol. 50, 910 (2002).
    [CrossRef]

2011

W. Xu, Y. P. Gong, L. W. Liu, H. Qin, and Y. L. Shi, Nanoscale Res. Lett. 6, 250 (2011).
[CrossRef]

2009

For a review, see, e.g., A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

2008

X. Wang, L. Zhi, and K. Müllen, Nano Lett. 8, 323 (2008).
[CrossRef]

2004

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

2002

B. Ferguson and X. C. Zhang, Nat. Mater. 1, 26 (2002).
[CrossRef]

For a review, see, e.g., P. H. Siegel, IEEE Trans. Microw. Theory Technol. 50, 910 (2002).
[CrossRef]

2000

Z. Y. Li, L. L. Lin, and Z. Q. Zhang, Phys. Rev. Lett. 84, 4341 (2000).
[CrossRef]

1999

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

1998

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

1994

P. L. Gourley, J. R. Wendt, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 64, 687 (1994).
[CrossRef]

1987

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).

Brennan, T. M.

P. L. Gourley, J. R. Wendt, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 64, 687 (1994).
[CrossRef]

Castro Neto, A. H.

For a review, see, e.g., A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

Diament, P.

P. Diament, Wave Transmission and Fiber Optics(Macmillan, 1990).

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Ferguson, B.

B. Ferguson and X. C. Zhang, Nat. Mater. 1, 26 (2002).
[CrossRef]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Geim, A. K.

For a review, see, e.g., A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Gong, Y. P.

W. Xu, Y. P. Gong, L. W. Liu, H. Qin, and Y. L. Shi, Nanoscale Res. Lett. 6, 250 (2011).
[CrossRef]

Gourley, P. L.

P. L. Gourley, J. R. Wendt, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 64, 687 (1994).
[CrossRef]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Guinea, F.

For a review, see, e.g., A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

Hammons, B. E.

P. L. Gourley, J. R. Wendt, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 64, 687 (1994).
[CrossRef]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Li, Z. Y.

Z. Y. Li, L. L. Lin, and Z. Q. Zhang, Phys. Rev. Lett. 84, 4341 (2000).
[CrossRef]

Lin, L. L.

Z. Y. Li, L. L. Lin, and Z. Q. Zhang, Phys. Rev. Lett. 84, 4341 (2000).
[CrossRef]

Liu, L. W.

W. Xu, Y. P. Gong, L. W. Liu, H. Qin, and Y. L. Shi, Nanoscale Res. Lett. 6, 250 (2011).
[CrossRef]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Müllen, K.

X. Wang, L. Zhi, and K. Müllen, Nano Lett. 8, 323 (2008).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Novoselov, K. S.

For a review, see, e.g., A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Peres, N. M. R.

For a review, see, e.g., A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

Qin, H.

W. Xu, Y. P. Gong, L. W. Liu, H. Qin, and Y. L. Shi, Nanoscale Res. Lett. 6, 250 (2011).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Shi, Y. L.

W. Xu, Y. P. Gong, L. W. Liu, H. Qin, and Y. L. Shi, Nanoscale Res. Lett. 6, 250 (2011).
[CrossRef]

Siegel, P. H.

For a review, see, e.g., P. H. Siegel, IEEE Trans. Microw. Theory Technol. 50, 910 (2002).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Vawter, G. A.

P. L. Gourley, J. R. Wendt, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 64, 687 (1994).
[CrossRef]

Wang, X.

X. Wang, L. Zhi, and K. Müllen, Nano Lett. 8, 323 (2008).
[CrossRef]

Wendt, J. R.

P. L. Gourley, J. R. Wendt, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 64, 687 (1994).
[CrossRef]

Xu, W.

W. Xu, Y. P. Gong, L. W. Liu, H. Qin, and Y. L. Shi, Nanoscale Res. Lett. 6, 250 (2011).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

Zhang, X. C.

B. Ferguson and X. C. Zhang, Nat. Mater. 1, 26 (2002).
[CrossRef]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Zhang, Z. Q.

Z. Y. Li, L. L. Lin, and Z. Q. Zhang, Phys. Rev. Lett. 84, 4341 (2000).
[CrossRef]

Zhi, L.

X. Wang, L. Zhi, and K. Müllen, Nano Lett. 8, 323 (2008).
[CrossRef]

Appl. Phys. Lett.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1370 (1999).
[CrossRef]

P. L. Gourley, J. R. Wendt, G. A. Vawter, T. M. Brennan, and B. E. Hammons, Appl. Phys. Lett. 64, 687 (1994).
[CrossRef]

IEEE Trans. Microw. Theory Technol.

For a review, see, e.g., P. H. Siegel, IEEE Trans. Microw. Theory Technol. 50, 910 (2002).
[CrossRef]

Nano Lett.

X. Wang, L. Zhi, and K. Müllen, Nano Lett. 8, 323 (2008).
[CrossRef]

Nanoscale Res. Lett.

W. Xu, Y. P. Gong, L. W. Liu, H. Qin, and Y. L. Shi, Nanoscale Res. Lett. 6, 250 (2011).
[CrossRef]

Nat. Mater.

B. Ferguson and X. C. Zhang, Nat. Mater. 1, 26 (2002).
[CrossRef]

Phys. Rev. B

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef]

Z. Y. Li, L. L. Lin, and Z. Q. Zhang, Phys. Rev. Lett. 84, 4341 (2000).
[CrossRef]

Rev. Mod. Phys.

For a review, see, e.g., A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

Science

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef]

Other

P. Diament, Wave Transmission and Fiber Optics(Macmillan, 1990).

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).

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Figures (4)

Fig. 1.
Fig. 1.

Cross section of the PC based on graphene. The shaded areas stand for two semiconductor layers (areas I and III), between which is the graphene layer (area II). Here ρ0 and ρ1 correspond, respectively, to the radial position of the inner and outer semiconductor layers. The thickness of the graphene layer is d, which can be considered to be thin. The outermost (area IV) is air.

Fig. 2.
Fig. 2.

Frequency of the photonic modes versus the position of the graphene cylinder ρ0 at a fixed radius of the outer semiconductor layer ρ1=100μm. Here the propagation constant kz=0 and n stands for the nth solution of R(ρ).

Fig. 3.
Fig. 3.

Frequency of the photonic states as a function of the radius of the outer semiconductor layer at a fixed ρ0=10μm and kz=0.

Fig. 4.
Fig. 4.

Dispersion relation of the photonic states at the fixed ρ0 and ρ1, as indicated.

Equations (5)

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

ε(ρ)={ε1,forρ<ρ0(areaI);εG,forρ0ρρd(areaII);ε2,forρd<ρ<ρ1(areaIII);1.0,forρρ1(areaIV).
2F+μ0ε0ε(ρ)ω2F=0,
R(ρ)+R(ρ)/ρ+[kc2m2/ρ2]R(ρ)=0,
{Jm(k1ρ0)=A2Im(kGρ0)+B2Km(kGρ0),A2Im(kGρd)+B2Km(kGρd)=A3Jm(k2ρd)+B3Ym(k2ρd),A3Jm(k2ρ1)+B3Ym(k2ρ1)=0.
{k1Jm(k1ρ0)=A2kGIm(kGρ0)+B2kGKm(kGρ0),A2kGIm(kGρd)+B2kGKm(kGρd)=A3k2Jm(k2ρd)+B3k2Ym(k2ρd).

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