Abstract

A modified hybrid waveguide with a wide-range coupling and long propagation has been proposed and the coupled mode theory has been applied to study the hybrid waveguide systematically. Two structures are comparatively discussed, namely, a dielectric wire and a circular capillary tube, which are buried in a polymer matrix and separated from the silver substrate by a gap. The simulated results indicate that the circular capillary tube demonstrates a stronger coupling between the surface plasmon polariton and the waveguide mode compared to the solid dielectric wire. Furthermore, the electric field is highly confined in the gap area and can propagate several hundred micrometers.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics 1(6), 303–305 (2007).
    [CrossRef]
  2. C. Z. Ning, “Semiconductor nanolasers,” Phys. Status Solidi B 247, 774–788 (2010).
  3. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
    [CrossRef]
  4. S. A. Maier, “Waveguiding—the best of both worlds,” Nat. Photonics 2(8), 460–461 (2008).
    [CrossRef]
  5. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
    [CrossRef] [PubMed]
  6. M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Propagation characteristics of hybrid modes supported by metal-low-high index waveguides and bends,” Opt. Express 18(12), 12971–12979 (2010).
    [CrossRef] [PubMed]
  7. I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18(1), 348–363 (2010).
    [CrossRef] [PubMed]
  8. Y. F. Xiao, B. B. Li, X. Jiang, X. Y. Hu, Y. Li, and Q. H. Gong, “High quality factor, small mode volume, ring-type plasmonic microresonator on a silver chip,” J. Phys. At. Mol. Opt. Phys. 43(3), 035402 (2010).
    [CrossRef]
  9. D. R. Chen, “Cylindrical hybrid plasmonic waveguide for subwavelength confinement of light,” Appl. Opt. 49(36), 6868–6871 (2010).
    [CrossRef] [PubMed]
  10. Y. S. Bian, Z. Zheng, Y. Liu, J. S. Zhu, and T. Zhou, “Dielectric-loaded surface plasmon polariton waveguide with a holey ridge for propagation-loss reduction and subwavelength mode confinement,” Opt. Express 18(23), 23756–23762 (2010).
    [CrossRef] [PubMed]
  11. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
    [CrossRef]
  12. H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84(22), 4547–4549 (2004).
    [CrossRef]
  13. G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun. 163(1-3), 95–102 (1999).
    [CrossRef]
  14. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  15. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [CrossRef] [PubMed]

2010

2009

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

2008

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

S. A. Maier, “Waveguiding—the best of both worlds,” Nat. Photonics 2(8), 460–461 (2008).
[CrossRef]

2007

R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics 1(6), 303–305 (2007).
[CrossRef]

2004

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84(22), 4547–4549 (2004).
[CrossRef]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

1999

G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun. 163(1-3), 95–102 (1999).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Aitchison, J. S.

Alam, M. Z.

An, K.

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84(22), 4547–4549 (2004).
[CrossRef]

Avrutsky, I.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Bian, Y. S.

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

Buchwald, W.

Chen, D. R.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Ghosh, G.

G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun. 163(1-3), 95–102 (1999).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Gong, Q. H.

Y. F. Xiao, B. B. Li, X. Jiang, X. Y. Hu, Y. Li, and Q. H. Gong, “High quality factor, small mode volume, ring-type plasmonic microresonator on a silver chip,” J. Phys. At. Mol. Opt. Phys. 43(3), 035402 (2010).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

Hu, X. Y.

Y. F. Xiao, B. B. Li, X. Jiang, X. Y. Hu, Y. Li, and Q. H. Gong, “High quality factor, small mode volume, ring-type plasmonic microresonator on a silver chip,” J. Phys. At. Mol. Opt. Phys. 43(3), 035402 (2010).
[CrossRef]

Jiang, X.

Y. F. Xiao, B. B. Li, X. Jiang, X. Y. Hu, Y. Li, and Q. H. Gong, “High quality factor, small mode volume, ring-type plasmonic microresonator on a silver chip,” J. Phys. At. Mol. Opt. Phys. 43(3), 035402 (2010).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kimerling, L.

R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics 1(6), 303–305 (2007).
[CrossRef]

Kirchain, R.

R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics 1(6), 303–305 (2007).
[CrossRef]

Lee, J. H.

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84(22), 4547–4549 (2004).
[CrossRef]

Lee, S. B.

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84(22), 4547–4549 (2004).
[CrossRef]

Li, B. B.

Y. F. Xiao, B. B. Li, X. Jiang, X. Y. Hu, Y. Li, and Q. H. Gong, “High quality factor, small mode volume, ring-type plasmonic microresonator on a silver chip,” J. Phys. At. Mol. Opt. Phys. 43(3), 035402 (2010).
[CrossRef]

Li, Y.

Y. F. Xiao, B. B. Li, X. Jiang, X. Y. Hu, Y. Li, and Q. H. Gong, “High quality factor, small mode volume, ring-type plasmonic microresonator on a silver chip,” J. Phys. At. Mol. Opt. Phys. 43(3), 035402 (2010).
[CrossRef]

Liu, Y.

Ma, R.-M.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Maier, S. A.

S. A. Maier, “Waveguiding—the best of both worlds,” Nat. Photonics 2(8), 460–461 (2008).
[CrossRef]

Meier, J.

Mojahedi, M.

Moon, H. J.

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84(22), 4547–4549 (2004).
[CrossRef]

Ning, C. Z.

C. Z. Ning, “Semiconductor nanolasers,” Phys. Status Solidi B 247, 774–788 (2010).

Oulton, R. F.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Park, G. W.

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84(22), 4547–4549 (2004).
[CrossRef]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Soref, R.

Sorger, V. J.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Xiao, Y. F.

Y. F. Xiao, B. B. Li, X. Jiang, X. Y. Hu, Y. Li, and Q. H. Gong, “High quality factor, small mode volume, ring-type plasmonic microresonator on a silver chip,” J. Phys. At. Mol. Opt. Phys. 43(3), 035402 (2010).
[CrossRef]

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Zhang, X.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Zheng, Z.

Zhou, T.

Zhu, J. S.

Appl. Opt.

Appl. Phys. Lett.

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84(22), 4547–4549 (2004).
[CrossRef]

J. Phys. At. Mol. Opt. Phys.

Y. F. Xiao, B. B. Li, X. Jiang, X. Y. Hu, Y. Li, and Q. H. Gong, “High quality factor, small mode volume, ring-type plasmonic microresonator on a silver chip,” J. Phys. At. Mol. Opt. Phys. 43(3), 035402 (2010).
[CrossRef]

Nat. Photonics

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics 1(6), 303–305 (2007).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

S. A. Maier, “Waveguiding—the best of both worlds,” Nat. Photonics 2(8), 460–461 (2008).
[CrossRef]

Nature

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Opt. Commun.

G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun. 163(1-3), 95–102 (1999).
[CrossRef]

Opt. Express

Phys. Rev. B

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Phys. Status Solidi B

C. Z. Ning, “Semiconductor nanolasers,” Phys. Status Solidi B 247, 774–788 (2010).

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 (5)

Fig. 1
Fig. 1

Schematic diagram of the hybrid waveguides. (a) The conventional and (b) the proposed structure.

Fig. 2
Fig. 2

Calculated electric energy density of hybrid modes. (a), (b), (c) The traditional model for different gap widths h = 30, 200, 400 nm, respectively. (d), (e), (f) The proposed model with the same parameters and the inner diameter D = 1.8 µm.

Fig. 3
Fig. 3

Electric energy density of the hybrid mode along y direction (x = 0) of the proposed mode in the case of D = 1.8 µm as a function of h

Fig. 4
Fig. 4

(a) The effective index and (b) the mode character of hybrid mode for different h compared with pure cylinder mode and SPP mode of metal – polymer (dotted line). The vertical red dashed line denotes the strong coupling regime.

Fig. 5
Fig. 5

Propagation distance of the hybrid mode compared with two pure SPP modes: metal–oxide (SPP1) and metal–polymer (SPP2).

Equations (3)

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

ψ h y b ( D . h ) = a ( D , h ) ψ c c t ( D ) + b ( D , h ) ψ s p p
a ( D , h ) 2 = n h y b ( D , h ) n s p p n h y b ( D , h ) n c c t ( D ) + n h y b ( D , h ) n s p p
L p = 1 / ( 2 Im [ k h y b ( D , h ) ]

Metrics