Abstract

We investigate the excitation of surface plasmon polaritons on silver tubes with finite-difference time-domain simulations. These surface plasmon polaritons exhibit azimuthal whispering gallery modes with quality factors in the hundreds. We show that the high quality factors arise from the coupling of the surface plasmon modes to photonic modes inside the tube. We examine the influence of a gain material on the quality factors and find that for material data of rhodamine 6G, the quality factors are enhanced significantly up to values of 3000.

© 2011 Optical Society of America

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References

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  1. A. Polman, Science 322, 868 (2008).
    [CrossRef] [PubMed]
  2. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
    [CrossRef] [PubMed]
  3. M. Kuttge, E. J. R. Vesseur, and A. Polman, Appl. Phys. Lett. 94, 183104 (2009).
    [CrossRef]
  4. Y. Xiao, B. Li, X. Jiang, X. Hu, Y. Li, and Q. Gong, J. Phys. B 43, 035402 (2010).
    [CrossRef]
  5. B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, Nature 457, 455 (2009).
    [CrossRef] [PubMed]
  6. O. Schumacher, S. Mendach, H. Welsch, A. Schramm, C. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109(2005).
    [CrossRef]
  7. S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
    [CrossRef] [PubMed]
  8. T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, Phys. Rev. Lett. 96, 077403 (2006).
    [CrossRef] [PubMed]
  9. Lumerical Solutions, Inc., http://www.lumerical.com/fdtd.php, Lumerical FDTD Solutions homepage.
  10. E. Palik, Handbook of Optical Constants of Solids(Academic, 1985).
  11. Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, Phys. Rev. Lett. 105, 153902 (2010).
    [CrossRef]
  12. J. Wiersig and M. Hentschel, Phys. Rev. Lett. 100, 033901(2008).
    [CrossRef] [PubMed]
  13. F. J. García de Abajo, J. Phys. Chem. C 112, 17983 (2008).
    [CrossRef]
  14. A. A. Govyadinov and V. A. Podolskiy, Phys. Rev. Lett. 97, 223902 (2006).
    [CrossRef] [PubMed]

2010 (2)

Y. Xiao, B. Li, X. Jiang, X. Hu, Y. Li, and Q. Gong, J. Phys. B 43, 035402 (2010).
[CrossRef]

Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, Phys. Rev. Lett. 105, 153902 (2010).
[CrossRef]

2009 (3)

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, Nature 457, 455 (2009).
[CrossRef] [PubMed]

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef] [PubMed]

M. Kuttge, E. J. R. Vesseur, and A. Polman, Appl. Phys. Lett. 94, 183104 (2009).
[CrossRef]

2008 (3)

A. Polman, Science 322, 868 (2008).
[CrossRef] [PubMed]

J. Wiersig and M. Hentschel, Phys. Rev. Lett. 100, 033901(2008).
[CrossRef] [PubMed]

F. J. García de Abajo, J. Phys. Chem. C 112, 17983 (2008).
[CrossRef]

2006 (2)

A. A. Govyadinov and V. A. Podolskiy, Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, Phys. Rev. Lett. 96, 077403 (2006).
[CrossRef] [PubMed]

2005 (2)

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, C. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109(2005).
[CrossRef]

Aussenegg, F. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Bröll, M.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef] [PubMed]

Ditlbacher, H.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Dong, C.-H.

Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, Phys. Rev. Lett. 105, 153902 (2010).
[CrossRef]

García de Abajo, F. J.

F. J. García de Abajo, J. Phys. Chem. C 112, 17983 (2008).
[CrossRef]

Gong, Q.

Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, Phys. Rev. Lett. 105, 153902 (2010).
[CrossRef]

Y. Xiao, B. Li, X. Jiang, X. Hu, Y. Li, and Q. Gong, J. Phys. B 43, 035402 (2010).
[CrossRef]

Govyadinov, A. A.

A. A. Govyadinov and V. A. Podolskiy, Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

Han, Z.-F.

Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, Phys. Rev. Lett. 105, 153902 (2010).
[CrossRef]

Hansen, W.

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, C. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109(2005).
[CrossRef]

Heitmann, D.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef] [PubMed]

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, Phys. Rev. Lett. 96, 077403 (2006).
[CrossRef] [PubMed]

Hentschel, M.

J. Wiersig and M. Hentschel, Phys. Rev. Lett. 100, 033901(2008).
[CrossRef] [PubMed]

Heyn, C.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef] [PubMed]

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, C. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109(2005).
[CrossRef]

Heyn, Ch.

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, Phys. Rev. Lett. 96, 077403 (2006).
[CrossRef] [PubMed]

Hofer, F.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Hohenau, A.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Hu, X.

Y. Xiao, B. Li, X. Jiang, X. Hu, Y. Li, and Q. Gong, J. Phys. B 43, 035402 (2010).
[CrossRef]

Jiang, X.

Y. Xiao, B. Li, X. Jiang, X. Hu, Y. Li, and Q. Gong, J. Phys. B 43, 035402 (2010).
[CrossRef]

Kipp, T.

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, Phys. Rev. Lett. 96, 077403 (2006).
[CrossRef] [PubMed]

Kreibig, U.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Krenn, J. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Krohn, A.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef] [PubMed]

Kuttge, M.

M. Kuttge, E. J. R. Vesseur, and A. Polman, Appl. Phys. Lett. 94, 183104 (2009).
[CrossRef]

Li, B.

Y. Xiao, B. Li, X. Jiang, X. Hu, Y. Li, and Q. Gong, J. Phys. B 43, 035402 (2010).
[CrossRef]

Li, B.-B.

Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, Phys. Rev. Lett. 105, 153902 (2010).
[CrossRef]

Li, Y.

Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, Phys. Rev. Lett. 105, 153902 (2010).
[CrossRef]

Y. Xiao, B. Li, X. Jiang, X. Hu, Y. Li, and Q. Gong, J. Phys. B 43, 035402 (2010).
[CrossRef]

Mendach, S.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef] [PubMed]

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, C. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109(2005).
[CrossRef]

Min, B.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, Nature 457, 455 (2009).
[CrossRef] [PubMed]

Ostby, E.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, Nature 457, 455 (2009).
[CrossRef] [PubMed]

Palik, E.

E. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

Podolskiy, V. A.

A. A. Govyadinov and V. A. Podolskiy, Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

Polman, A.

M. Kuttge, E. J. R. Vesseur, and A. Polman, Appl. Phys. Lett. 94, 183104 (2009).
[CrossRef]

A. Polman, Science 322, 868 (2008).
[CrossRef] [PubMed]

Rogers, M.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Schramm, A.

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, C. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109(2005).
[CrossRef]

Schumacher, O.

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, C. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109(2005).
[CrossRef]

Schwaiger, S.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef] [PubMed]

Sorger, V.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, Nature 457, 455 (2009).
[CrossRef] [PubMed]

Stark, Y.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef] [PubMed]

Stemmann, A.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef] [PubMed]

Stickler, D.

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef] [PubMed]

Strelow, Ch.

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, Phys. Rev. Lett. 96, 077403 (2006).
[CrossRef] [PubMed]

Ulin-Avila, E.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, Nature 457, 455 (2009).
[CrossRef] [PubMed]

Vahala, K.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, Nature 457, 455 (2009).
[CrossRef] [PubMed]

Vesseur, E. J. R.

M. Kuttge, E. J. R. Vesseur, and A. Polman, Appl. Phys. Lett. 94, 183104 (2009).
[CrossRef]

Wagner, D.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Welsch, H.

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, Phys. Rev. Lett. 96, 077403 (2006).
[CrossRef] [PubMed]

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, C. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109(2005).
[CrossRef]

Wiersig, J.

J. Wiersig and M. Hentschel, Phys. Rev. Lett. 100, 033901(2008).
[CrossRef] [PubMed]

Xiao, Y.

Y. Xiao, B. Li, X. Jiang, X. Hu, Y. Li, and Q. Gong, J. Phys. B 43, 035402 (2010).
[CrossRef]

Xiao, Y.-F.

Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, Phys. Rev. Lett. 105, 153902 (2010).
[CrossRef]

Yang, L.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, Nature 457, 455 (2009).
[CrossRef] [PubMed]

Zhang, X.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, Nature 457, 455 (2009).
[CrossRef] [PubMed]

Zou, C.-L.

Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, Phys. Rev. Lett. 105, 153902 (2010).
[CrossRef]

Appl. Phys. Lett. (2)

M. Kuttge, E. J. R. Vesseur, and A. Polman, Appl. Phys. Lett. 94, 183104 (2009).
[CrossRef]

O. Schumacher, S. Mendach, H. Welsch, A. Schramm, C. Heyn, and W. Hansen, Appl. Phys. Lett. 86, 143109(2005).
[CrossRef]

J. Phys. B (1)

Y. Xiao, B. Li, X. Jiang, X. Hu, Y. Li, and Q. Gong, J. Phys. B 43, 035402 (2010).
[CrossRef]

J. Phys. Chem. C (1)

F. J. García de Abajo, J. Phys. Chem. C 112, 17983 (2008).
[CrossRef]

Nature (1)

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, Nature 457, 455 (2009).
[CrossRef] [PubMed]

Phys. Rev. Lett. (6)

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

S. Schwaiger, M. Bröll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, Phys. Rev. Lett. 102, 163903 (2009).
[CrossRef] [PubMed]

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, Phys. Rev. Lett. 96, 077403 (2006).
[CrossRef] [PubMed]

A. A. Govyadinov and V. A. Podolskiy, Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

Y.-F. Xiao, C.-L. Zou, B.-B. Li, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, Phys. Rev. Lett. 105, 153902 (2010).
[CrossRef]

J. Wiersig and M. Hentschel, Phys. Rev. Lett. 100, 033901(2008).
[CrossRef] [PubMed]

Science (1)

A. Polman, Science 322, 868 (2008).
[CrossRef] [PubMed]

Other (2)

Lumerical Solutions, Inc., http://www.lumerical.com/fdtd.php, Lumerical FDTD Solutions homepage.

E. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

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Figures (3)

Fig. 1
Fig. 1

Fourier transformed intensity spectrum plotted versus wavelength, obtained for the simulated structure in the inset—a silver tube of inner radius 1.5 μm and silver thickness of 100 nm is irradiated by a dipole source in the vicinity of the object (in this case, 50 nm ).

Fig. 2
Fig. 2

(a) Distribution of the magnetic field on a tube with inner radius 1.5 μm and a film thickness of 100 nm excited at a wavelength of 407 nm . This corresponds to the mode number m = 29 in Fig. 1. (b) The same data as in (a) with magnified intensity scale. The photonic modes inside the tube can clearly be seen. (c) and (d) The magnetic field distribution in the vicinity of 407 nm [ 405 nm in (c) and 408 nm in (d)]. It is found that the field strengths of the photonic modes inside the tube are an order of magnitude smaller than in (b). (e) The field intensity distribution in radial distance from the tube center at 407 nm . (f) Quality factors of the SPP mode at 549 nm plotted versus increasing material gain. The investigated structure is the above tube together with a gain cladding layer of 10 nm thickness, which was set around the silver tube.

Fig. 3
Fig. 3

Calculated Q factors plotted versus mode number for a full cylinder with radius 1.6 μm (triangles), for tubes with inner radius 1.5 μm and silver thickness t = 30 nm (stars) and t = 100 nm (squares), and for a tube with an absorber (circles). In the case of t = 100 nm , the mode with mode number m = 21 is strongly suppressed. Dashed and full lines connect the data points for clarity.

Equations (1)

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ϵ gain ( ω ) = ϵ ω 0 2 ξ ω 0 2 i ω γ ω 2 ,

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