Abstract

We have devised a simple method to determine the absorption and radiative decay rates of surface plasmon polaritons in an Au nanohole array by combining polarization-resolved reflectivity spectroscopy and temporal coupled-mode theory. The dependence of two rates on wavelength has been measured and they are found to agree with finite-difference time-domain simulations. As both absorption and radiative decay rates play a key role in several plasmonic applications, our approach offers a simple and effective means in determining them.

© 2012 Optical Society of America

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
    [CrossRef]
  2. C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033014 (2010).
    [CrossRef]
  3. J. Li, J. B. Xu, and H. C. Ong, Appl. Phys. Lett. 94, 241114 (2009).
    [CrossRef]
  4. C. Min, J. Li, G. Veronis, J. Y. Lee, S. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
    [CrossRef]
  5. S. Linic, P. Christopher, and D. B. Ingram, D. B. Nat. Mater. 10, 911 (2011).
    [CrossRef]
  6. L. Zhang, C. Y. Chan, J. Li, and H. C. Ong, Opt. Express 20, 12601 (2012).
    [CrossRef]
  7. M. L. Juan, M. Righini, and R. Quidant, Nat. Photonics 5, 349 (2011).
    [CrossRef]
  8. 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]
  9. D. Y. Lei, J. Li, A. I. Fernandez–Dominguez, H. C. Ong, and S. A. Maier, ACS Nano 4, 432 (2010).
    [CrossRef]
  10. C. Ropers, D. J. Park, G. Stibenz, G. Steinmeyer, J. Kim, D. S. Kim, and C. Lienau, Phys. Rev. Lett. 94, 113901 (2005).
    [CrossRef]
  11. T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, Phys. Rev. B 28, 1740 (1983).
    [CrossRef]
  12. H. A. Haus, Waves and Fields in Optoelectronics(Prentice-Hall, 1984).
  13. M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, Phys. Rev. B 77, 115437 (2008).
    [CrossRef]
  14. K. Tetz, V. Lomakin, M. P. Nezhad, L. Pang, and Y. Fainman, J. Opt. Soc. Am. A 27, 911 (2010).
    [CrossRef]
  15. C. A. Ross, S. Haratani, F. J. Castano, Y. Hao, B. Vogeli, M. Farhoud, M. Walsh, and H. I. Smith, J. Appl. Phys. 91, 6848 (2002).
    [CrossRef]
  16. S. Buil, J. Laverdant, B. Berini, P. Maso, J. Hermier, and X. Quélin, Opt. Mater. Express 20, 11968 (2012).
    [CrossRef]

2012 (2)

L. Zhang, C. Y. Chan, J. Li, and H. C. Ong, Opt. Express 20, 12601 (2012).
[CrossRef]

S. Buil, J. Laverdant, B. Berini, P. Maso, J. Hermier, and X. Quélin, Opt. Mater. Express 20, 11968 (2012).
[CrossRef]

2011 (2)

S. Linic, P. Christopher, and D. B. Ingram, D. B. Nat. Mater. 10, 911 (2011).
[CrossRef]

M. L. Juan, M. Righini, and R. Quidant, Nat. Photonics 5, 349 (2011).
[CrossRef]

2010 (4)

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

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033014 (2010).
[CrossRef]

C. Min, J. Li, G. Veronis, J. Y. Lee, S. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

K. Tetz, V. Lomakin, M. P. Nezhad, L. Pang, and Y. Fainman, J. Opt. Soc. Am. A 27, 911 (2010).
[CrossRef]

2009 (2)

J. Li, J. B. Xu, and H. C. Ong, Appl. Phys. Lett. 94, 241114 (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]

2008 (1)

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

2005 (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]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

2002 (1)

C. A. Ross, S. Haratani, F. J. Castano, Y. Hao, B. Vogeli, M. Farhoud, M. Walsh, and H. I. Smith, J. Appl. Phys. 91, 6848 (2002).
[CrossRef]

1983 (1)

T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, Phys. Rev. B 28, 1740 (1983).
[CrossRef]

Arakawa, E. T.

T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, Phys. Rev. B 28, 1740 (1983).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Berini, B.

S. Buil, J. Laverdant, B. Berini, P. Maso, J. Hermier, and X. Quélin, Opt. Mater. Express 20, 11968 (2012).
[CrossRef]

Buil, S.

S. Buil, J. Laverdant, B. Berini, P. Maso, J. Hermier, and X. Quélin, Opt. Mater. Express 20, 11968 (2012).
[CrossRef]

Castano, F. J.

C. A. Ross, S. Haratani, F. J. Castano, Y. Hao, B. Vogeli, M. Farhoud, M. Walsh, and H. I. Smith, J. Appl. Phys. 91, 6848 (2002).
[CrossRef]

Chan, C. Y.

L. Zhang, C. Y. Chan, J. Li, and H. C. Ong, Opt. Express 20, 12601 (2012).
[CrossRef]

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033014 (2010).
[CrossRef]

Christopher, P.

S. Linic, P. Christopher, and D. B. Ingram, D. B. Nat. Mater. 10, 911 (2011).
[CrossRef]

de Dood, M. J. A.

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

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Driessen, E. F. C.

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

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Fainman, Y.

Fan, S.

C. Min, J. Li, G. Veronis, J. Y. Lee, S. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

Farhoud, M.

C. A. Ross, S. Haratani, F. J. Castano, Y. Hao, B. Vogeli, M. Farhoud, M. Walsh, and H. I. Smith, J. Appl. Phys. 91, 6848 (2002).
[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]

Hao, Y.

C. A. Ross, S. Haratani, F. J. Castano, Y. Hao, B. Vogeli, M. Farhoud, M. Walsh, and H. I. Smith, J. Appl. Phys. 91, 6848 (2002).
[CrossRef]

Haratani, S.

C. A. Ross, S. Haratani, F. J. Castano, Y. Hao, B. Vogeli, M. Farhoud, M. Walsh, and H. I. Smith, J. Appl. Phys. 91, 6848 (2002).
[CrossRef]

Haus, H. A.

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

Hermier, J.

S. Buil, J. Laverdant, B. Berini, P. Maso, J. Hermier, and X. Quélin, Opt. Mater. Express 20, 11968 (2012).
[CrossRef]

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]

Inagaki, T.

T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, Phys. Rev. B 28, 1740 (1983).
[CrossRef]

Ingram, D. B.

S. Linic, P. Christopher, and D. B. Ingram, D. B. Nat. Mater. 10, 911 (2011).
[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]

Juan, M. L.

M. L. Juan, M. Righini, and R. Quidant, Nat. Photonics 5, 349 (2011).
[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]

Laverdant, J.

S. Buil, J. Laverdant, B. Berini, P. Maso, J. Hermier, and X. Quélin, Opt. Mater. Express 20, 11968 (2012).
[CrossRef]

Lee, J. Y.

C. Min, J. Li, G. Veronis, J. Y. Lee, S. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[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.

L. Zhang, C. Y. Chan, J. Li, and H. C. Ong, Opt. Express 20, 12601 (2012).
[CrossRef]

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

C. Min, J. Li, G. Veronis, J. Y. Lee, S. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (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]

J. Li, J. B. Xu, and H. C. Ong, Appl. Phys. Lett. 94, 241114 (2009).
[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]

Linic, S.

S. Linic, P. Christopher, and D. B. Ingram, D. B. Nat. Mater. 10, 911 (2011).
[CrossRef]

Lomakin, V.

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]

Maso, P.

S. Buil, J. Laverdant, B. Berini, P. Maso, J. Hermier, and X. Quélin, Opt. Mater. Express 20, 11968 (2012).
[CrossRef]

Min, C.

C. Min, J. Li, G. Veronis, J. Y. Lee, S. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

Motosuga, M.

T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, Phys. Rev. B 28, 1740 (1983).
[CrossRef]

Nezhad, M. P.

Ong, H. C.

L. Zhang, C. Y. Chan, J. Li, and H. C. Ong, Opt. Express 20, 12601 (2012).
[CrossRef]

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

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033014 (2010).
[CrossRef]

J. Li, J. B. Xu, and H. C. Ong, Appl. Phys. Lett. 94, 241114 (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]

Pang, L.

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]

Peumans, P.

C. Min, J. Li, G. Veronis, J. Y. Lee, S. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

Quélin, X.

S. Buil, J. Laverdant, B. Berini, P. Maso, J. Hermier, and X. Quélin, Opt. Mater. Express 20, 11968 (2012).
[CrossRef]

Quidant, R.

M. L. Juan, M. Righini, and R. Quidant, Nat. Photonics 5, 349 (2011).
[CrossRef]

Righini, M.

M. L. Juan, M. Righini, and R. Quidant, Nat. Photonics 5, 349 (2011).
[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]

Ross, C. A.

C. A. Ross, S. Haratani, F. J. Castano, Y. Hao, B. Vogeli, M. Farhoud, M. Walsh, and H. I. Smith, J. Appl. Phys. 91, 6848 (2002).
[CrossRef]

Smith, H. I.

C. A. Ross, S. Haratani, F. J. Castano, Y. Hao, B. Vogeli, M. Farhoud, M. Walsh, and H. I. Smith, J. Appl. Phys. 91, 6848 (2002).
[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]

Stolwijk, D.

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

Tetz, K.

van Exter, M. P.

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

Veronis, G.

C. Min, J. Li, G. Veronis, J. Y. Lee, S. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (2010).
[CrossRef]

Vogeli, B.

C. A. Ross, S. Haratani, F. J. Castano, Y. Hao, B. Vogeli, M. Farhoud, M. Walsh, and H. I. Smith, J. Appl. Phys. 91, 6848 (2002).
[CrossRef]

Walsh, M.

C. A. Ross, S. Haratani, F. J. Castano, Y. Hao, B. Vogeli, M. Farhoud, M. Walsh, and H. I. Smith, J. Appl. Phys. 91, 6848 (2002).
[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.

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033014 (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.

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033014 (2010).
[CrossRef]

J. Li, J. B. Xu, and H. C. Ong, Appl. Phys. Lett. 94, 241114 (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]

Yamamori, K.

T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, Phys. Rev. B 28, 1740 (1983).
[CrossRef]

Zhang, L.

L. Zhang, C. Y. Chan, J. Li, and H. C. Ong, Opt. Express 20, 12601 (2012).
[CrossRef]

ACS Nano (1)

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

Appl. Phys. Lett. (4)

C. Y. Chan, J. B. Xu, M. Y. Waye, and H. C. Ong, Appl. Phys. Lett. 96, 033014 (2010).
[CrossRef]

J. Li, J. B. Xu, and H. C. Ong, Appl. Phys. Lett. 94, 241114 (2009).
[CrossRef]

C. Min, J. Li, G. Veronis, J. Y. Lee, S. Fan, and P. Peumans, Appl. Phys. Lett. 96, 133302 (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]

D. B. Nat. Mater. (1)

S. Linic, P. Christopher, and D. B. Ingram, D. B. Nat. Mater. 10, 911 (2011).
[CrossRef]

J. Appl. Phys. (1)

C. A. Ross, S. Haratani, F. J. Castano, Y. Hao, B. Vogeli, M. Farhoud, M. Walsh, and H. I. Smith, J. Appl. Phys. 91, 6848 (2002).
[CrossRef]

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

Nat. Photonics (1)

M. L. Juan, M. Righini, and R. Quidant, Nat. Photonics 5, 349 (2011).
[CrossRef]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Opt. Express (1)

L. Zhang, C. Y. Chan, J. Li, and H. C. Ong, Opt. Express 20, 12601 (2012).
[CrossRef]

Opt. Mater. Express (1)

S. Buil, J. Laverdant, B. Berini, P. Maso, J. Hermier, and X. Quélin, Opt. Mater. Express 20, 11968 (2012).
[CrossRef]

Phys. Rev. B (2)

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

T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, Phys. Rev. B 28, 1740 (1983).
[CrossRef]

Phys. Rev. Lett. (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]

Other (1)

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

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Figures (3)

Fig. 1.
Fig. 1.

(a) p-polarized and (b) orthogonal specular reflectivity mappings. The SEM image is shown in the inset. The red dashed line deduced from the phase-matching equation indicates the (1,0) SPP mode is excited.

Fig. 2.
Fig. 2.

Several (a) p-polarized and (b) orthogonal reflectivity spectra taken at different incident angles. Red dashed curves are the best fits by using Fano-like and Lorentzian reflectivity models. (c) Plots of experimentally deduced Γtot, Γabs, and Γrad against resonant wavelength in log-log scale. Analytical Γabs obtained from flat Au is also plotted as a solid curve for comparison. The linear fit of Γrad is shown as a dashed curve, showing Γradλres3.6.

Fig. 3.
Fig. 3.

(a) Plane and cross-section views of the unit cell for FDTD simulation. (b) Simulated p-polarized and orthogonal specular reflectivity spectra for different incident angles. Their best fits by using Fano-like and Lorentzian models are shown as dashed curves. Plots of FDTD deduced (c) Γrad and (d) Γabs by using frequency (black square) and time (centered circle) methods. Experimental data is also shown for comparison (blue triangle). (e) Total time decay lines of field intensity for different resonant wavelengths together with their linear fits. (f) Decay time lines of field intensity with 1/10 imaginary part of Au dielectric function for different resonant wavelengths together with their linear fits.

Equations (3)

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

Rp=|rp+κ2Γradei(ϕ+φ)/2i(ωωres)+Γtot/2|2,
Rorth=(κ2Γrad/2)24[(ωωres)2+(Γtot/2)2],
Γabs=(|rp|2Rp)Γtot2/2(κ2Γrad).

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