Abstract

We measured the decay rates of two degenerate surface plasmon modes in Au nanohole arrays with different hole sizes by angle-resolved reflectivity spectroscopy. For each hole size, at the spectral region where resonant coupling occurs, we observed a large modification in decay rates, leading to the formation of dark and bright modes. The change in decay rates is well explained by temporal coupled mode theory. The deduced coupling constant is found to increase with increasing hole diameter. This study provides us a simple and effective means to control the decay rates of dark and bright modes, which are useful in plasmonic applications.

© 2012 Optical Society of America

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  1. C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, Phys. Rev. Lett. 94, 113901 (2005).
    [CrossRef]
  2. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
    [CrossRef]
  3. F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, ACS Nano 3, 643 (2009).
    [CrossRef]
  4. Y. Chu and K. B. Crozier, Opt. Lett. 34, 244 (2009).
    [CrossRef]
  5. F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
    [CrossRef]
  6. Y. Chu, M. G. Banaee, and K. B. Crozier, ACS Nano 4, 2804 (2010).
    [CrossRef]
  7. M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, Phys. Rev. Lett. 102, 107401 (2009).
    [CrossRef]
  8. D. Y. Lei, J. Li, A. I. Fernandez-Dominguez, H. C. Ong, and S. A. Maier, ACS Nano 4, 432 (2010).
    [CrossRef]
  9. H. A. Haus, Waves and Fields in Optoelectronics(Prentice-Hall, 1984).
  10. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033104 (2010).
    [CrossRef]
  11. J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 94, 183112 (2009).
    [CrossRef]
  12. P. B. Johnson and R. W. Chirty, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  13. U. Fano and J. Cooper, Phys. Rev. 137, A1364 (1965).
    [CrossRef]
  14. S. H. Chang, S. Gray, and G. Schatz, Opt. Express 13, 3150 (2005).
    [CrossRef]
  15. M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, Phys. Rev. B 67, 085415 (2003).
    [CrossRef]
  16. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, Phys. Rev. B 77, 115437 (2008).
    [CrossRef]

2010 (3)

D. Y. Lei, J. Li, A. I. Fernandez-Dominguez, H. C. Ong, and S. A. Maier, ACS Nano 4, 432 (2010).
[CrossRef]

Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033104 (2010).
[CrossRef]

Y. Chu, M. G. Banaee, and K. B. Crozier, ACS Nano 4, 2804 (2010).
[CrossRef]

2009 (4)

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef]

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 94, 183112 (2009).
[CrossRef]

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, ACS Nano 3, 643 (2009).
[CrossRef]

Y. Chu and K. B. Crozier, Opt. Lett. 34, 244 (2009).
[CrossRef]

2008 (2)

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, Phys. Rev. B 77, 115437 (2008).
[CrossRef]

2005 (2)

S. H. Chang, S. Gray, and G. Schatz, Opt. Express 13, 3150 (2005).
[CrossRef]

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, Phys. Rev. Lett. 94, 113901 (2005).
[CrossRef]

2004 (1)

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

2003 (1)

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, Phys. Rev. B 67, 085415 (2003).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Chirty, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1965 (1)

U. Fano and J. Cooper, Phys. Rev. 137, A1364 (1965).
[CrossRef]

Banaee, M. G.

Y. Chu, M. G. Banaee, and K. B. Crozier, ACS Nano 4, 2804 (2010).
[CrossRef]

Chan, Y.

Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033104 (2010).
[CrossRef]

Chang, S. H.

Chirty, R. W.

P. B. Johnson and R. W. Chirty, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Chu, Y.

Y. Chu, M. G. Banaee, and K. B. Crozier, ACS Nano 4, 2804 (2010).
[CrossRef]

Y. Chu and K. B. Crozier, Opt. Lett. 34, 244 (2009).
[CrossRef]

Cooper, J.

U. Fano and J. Cooper, Phys. Rev. 137, A1364 (1965).
[CrossRef]

Crozier, K. B.

Y. Chu, M. G. Banaee, and K. B. Crozier, ACS Nano 4, 2804 (2010).
[CrossRef]

Y. Chu and K. B. Crozier, Opt. Lett. 34, 244 (2009).
[CrossRef]

de Dood, J. A.

J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, Phys. Rev. B 77, 115437 (2008).
[CrossRef]

Dorpe, P. V.

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, ACS Nano 3, 643 (2009).
[CrossRef]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

Driessen, E. F. C.

J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, Phys. Rev. B 77, 115437 (2008).
[CrossRef]

Fano, U.

U. Fano and J. Cooper, Phys. Rev. 137, A1364 (1965).
[CrossRef]

Fernandez-Dominguez, A. I.

D. Y. Lei, J. Li, A. I. Fernandez-Dominguez, H. C. Ong, and S. A. Maier, ACS Nano 4, 432 (2010).
[CrossRef]

Gray, S.

Gray, S. K.

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef]

Guyot-Sionnest, P.

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef]

Halas, N. J.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

Hao, F.

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, ACS Nano 3, 643 (2009).
[CrossRef]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics(Prentice-Hall, 1984).

Ho, H. P.

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 94, 183112 (2009).
[CrossRef]

Iu, H.

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 94, 183112 (2009).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Chirty, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kim, D. S.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, Phys. Rev. Lett. 94, 113901 (2005).
[CrossRef]

Kim, J.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, Phys. Rev. Lett. 94, 113901 (2005).
[CrossRef]

Lee, T.-W.

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef]

Lei, D. Y.

D. Y. Lei, J. Li, A. I. Fernandez-Dominguez, H. C. Ong, and S. A. Maier, ACS Nano 4, 432 (2010).
[CrossRef]

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 94, 183112 (2009).
[CrossRef]

Li, J.

D. Y. Lei, J. Li, A. I. Fernandez-Dominguez, H. C. Ong, and S. A. Maier, ACS Nano 4, 432 (2010).
[CrossRef]

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 94, 183112 (2009).
[CrossRef]

Li, K.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Lienau, C.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, Phys. Rev. Lett. 94, 113901 (2005).
[CrossRef]

Liu, M.

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef]

Maier, S. A.

D. Y. Lei, J. Li, A. I. Fernandez-Dominguez, H. C. Ong, and S. A. Maier, ACS Nano 4, 432 (2010).
[CrossRef]

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, ACS Nano 3, 643 (2009).
[CrossRef]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

Nordlander, P.

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, ACS Nano 3, 643 (2009).
[CrossRef]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Ong, H. C.

D. Y. Lei, J. Li, A. I. Fernandez-Dominguez, H. C. Ong, and S. A. Maier, ACS Nano 4, 432 (2010).
[CrossRef]

Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033104 (2010).
[CrossRef]

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 94, 183112 (2009).
[CrossRef]

Oubre, C.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Park, D. J.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, Phys. Rev. Lett. 94, 113901 (2005).
[CrossRef]

Pelton, M.

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef]

Prodan, E.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Ropers, C.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, Phys. Rev. Lett. 94, 113901 (2005).
[CrossRef]

Sarrazin, M.

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, Phys. Rev. B 67, 085415 (2003).
[CrossRef]

Schatz, G.

Sonnefraud, Y.

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, ACS Nano 3, 643 (2009).
[CrossRef]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

Steinmeyer, G.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, Phys. Rev. Lett. 94, 113901 (2005).
[CrossRef]

Stibenz, G.

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, Phys. Rev. Lett. 94, 113901 (2005).
[CrossRef]

Stockman, M. I.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Stolwijk, D.

J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, Phys. Rev. B 77, 115437 (2008).
[CrossRef]

van Exter, M. P.

J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, Phys. Rev. B 77, 115437 (2008).
[CrossRef]

Vigneron, J.-P.

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, Phys. Rev. B 67, 085415 (2003).
[CrossRef]

Vigoureux, J.-M.

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, Phys. Rev. B 67, 085415 (2003).
[CrossRef]

Wan, J. T. K.

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 94, 183112 (2009).
[CrossRef]

Waye, M. Y.

Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033104 (2010).
[CrossRef]

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 94, 183112 (2009).
[CrossRef]

Xu, J. B.

Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033104 (2010).
[CrossRef]

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 94, 183112 (2009).
[CrossRef]

ACS Nano (3)

Y. Chu, M. G. Banaee, and K. B. Crozier, ACS Nano 4, 2804 (2010).
[CrossRef]

D. Y. Lei, J. Li, A. I. Fernandez-Dominguez, H. C. Ong, and S. A. Maier, ACS Nano 4, 432 (2010).
[CrossRef]

F. Hao, P. Nordlander, Y. Sonnefraud, P. V. Dorpe, and S. A. Maier, ACS Nano 3, 643 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033104 (2010).
[CrossRef]

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 94, 183112 (2009).
[CrossRef]

Nano Lett. (2)

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. (1)

U. Fano and J. Cooper, Phys. Rev. 137, A1364 (1965).
[CrossRef]

Phys. Rev. B (3)

P. B. Johnson and R. W. Chirty, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, Phys. Rev. B 67, 085415 (2003).
[CrossRef]

J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, Phys. Rev. B 77, 115437 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, Phys. Rev. Lett. 94, 113901 (2005).
[CrossRef]

M. Liu, T.-W. Lee, S. K. Gray, P. Guyot-Sionnest, and M. Pelton, Phys. Rev. Lett. 102, 107401 (2009).
[CrossRef]

Other (1)

H. A. Haus, Waves and Fields in Optoelectronics(Prentice-Hall, 1984).

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Figures (4)

Fig. 1.
Fig. 1.

Sample and setup geometry.

Fig. 2.
Fig. 2.

(a) and (b) S-polarized reflectivity mappings of hole arrays with D=151 and 428 nm taken at θ=12°. SEM image of the arrays are shown in the insets. The lines are the SP dispersion curves deduced from the phase-matching equation; (c) S-polarized reflectivity spectra of the corresponding arrays extracted from φ=4°. The dashed lines are the best fits by using the Fano model.

Fig. 3.
Fig. 3.

(a)–(c) Resonant frequency and (d)–(f) decay rate against azimuth angle of (0,1) and (0,+1) modes for different hole diameters. Dots, measured data points; solid lines, fitted curve by CMT; dashed lines, when the coupling is turned off.

Fig. 4.
Fig. 4.

Real (W) and imaginary (Γc) parts of coupling constant against hole diameter.

Equations (2)

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

ksp2=(ωcsinθcosφ+2mπa)2+(ωcsinθsinφ+2nπa)2,
ω±=ωa+ωb+2V2iΓa+Γb2±(ωaωb2iΓaΓb2)2+(W+iΓc)2,

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