Abstract

We demonstrate an all-optical thermo-plasmonic effect to switch/modulate the surface plasmon resonance signal intensity excited at the metal-air interface. This optically addressed thermo-plasmonic measurement scheme is suitable to amplify very small changes in the complex dielectric constant (εm(T)) of thin gold (Au) film, induced by the Ar+ laser. The predominant contributions due to small but highly repeatable transient photo-thermal effects in the complex metal dielectric constant is confirmed to be the reason behind the highly reproducible all-optical thermo-plasmonic device performance presented here.

© 2011 Optical Society of America

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  1. S. K. Ozdemir and G. Turhan-Sayan, “Temperature effects on surface plasmon resonance: design considerations for an optical temperature sensor,” J. Lightwave Technol. 21, 805–814 (2003).
    [CrossRef]
  2. H. P. Chiang, C.-W. Chen, J. J. Wu, H. L. Li, T. Y. Lin, E. J. Sanchez, and P. T. Leung, “Effects of temperature on the surface plasmon resonance at a metal-semiconductor interface,” Thin Solid Films 515, 6953–6961 (2007).
    [CrossRef]
  3. I. T. Kim and K. D. Kihm, “Full-field and real-time surface plasmon resonance imaging thermometry,” Opt. Lett. 32, 3456–3458 (2007).
    [CrossRef]
  4. K.-Q. Lin, L.-M. Wei, D.-G. Zhang, R.-S. Zheng, P. Wang, Y.-H. Lu, and H. Ming, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24, 3081–3084 (2007).
    [CrossRef]
  5. C. S. Moreira, A. M. N. Lima, H. Neff, and C. Thirstrup, “Temperature-dependent sensitivity of surface plasmon resonance sensors at the gold-water interface,” Sens. Actuators B 134, 854–862 (2008).
  6. S. Saha, N. Mehan, K. Sreenivas, and V. Gupta, “Temperature dependent optical properties of (002) oriented ZnO thin film using surface plasmon resonance,” Appl. Phys. Lett. 95, 071106 (2009).
    [CrossRef]
  7. A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol. A 26, 836–841(2008).
  8. R. H. M. Groeneveld, R. Prrik, and Ad Lagendijk, “Ultrafast relaxation of electrons by surface plasmons at a thin silver film,” Phys. Rev. Lett. 64, 784–787 (1990).
    [CrossRef]
  9. S. Herminghuas and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys. A 51, 350–353(1990).
    [CrossRef]
  10. X. Xiao, J. Xiang, and F. Zhou, “Laser-induced thermal effect in surface plasmon resonance,” Anal. Chim. Acta 676, 75–80(2010).
    [CrossRef]
  11. A. Passian, A. L. Lereu, E. T. Arakawa, A. Wig, T. Thundat, and T. L. Ferrell, “Modulation of multiple photon energies by use of surface plasmons,” Opt. Lett. 30, 41–43 (2005).
    [CrossRef]
  12. A. L. Lereu, A. Passian, J-P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects on surface plasmons,” Appl. Phys. Lett. 86, 154101 (2005).
    [CrossRef]
  13. A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006).
    [CrossRef]
  14. E. Kretschmann and H. Raether, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. A 23, 2135–2316 (1968).
  15. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer Verlag, 1986).

2010 (1)

X. Xiao, J. Xiang, and F. Zhou, “Laser-induced thermal effect in surface plasmon resonance,” Anal. Chim. Acta 676, 75–80(2010).
[CrossRef]

2009 (1)

S. Saha, N. Mehan, K. Sreenivas, and V. Gupta, “Temperature dependent optical properties of (002) oriented ZnO thin film using surface plasmon resonance,” Appl. Phys. Lett. 95, 071106 (2009).
[CrossRef]

2008 (2)

A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol. A 26, 836–841(2008).

C. S. Moreira, A. M. N. Lima, H. Neff, and C. Thirstrup, “Temperature-dependent sensitivity of surface plasmon resonance sensors at the gold-water interface,” Sens. Actuators B 134, 854–862 (2008).

2007 (3)

K.-Q. Lin, L.-M. Wei, D.-G. Zhang, R.-S. Zheng, P. Wang, Y.-H. Lu, and H. Ming, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24, 3081–3084 (2007).
[CrossRef]

H. P. Chiang, C.-W. Chen, J. J. Wu, H. L. Li, T. Y. Lin, E. J. Sanchez, and P. T. Leung, “Effects of temperature on the surface plasmon resonance at a metal-semiconductor interface,” Thin Solid Films 515, 6953–6961 (2007).
[CrossRef]

I. T. Kim and K. D. Kihm, “Full-field and real-time surface plasmon resonance imaging thermometry,” Opt. Lett. 32, 3456–3458 (2007).
[CrossRef]

2006 (1)

A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006).
[CrossRef]

2005 (2)

A. Passian, A. L. Lereu, E. T. Arakawa, A. Wig, T. Thundat, and T. L. Ferrell, “Modulation of multiple photon energies by use of surface plasmons,” Opt. Lett. 30, 41–43 (2005).
[CrossRef]

A. L. Lereu, A. Passian, J-P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects on surface plasmons,” Appl. Phys. Lett. 86, 154101 (2005).
[CrossRef]

2003 (1)

1990 (2)

R. H. M. Groeneveld, R. Prrik, and Ad Lagendijk, “Ultrafast relaxation of electrons by surface plasmons at a thin silver film,” Phys. Rev. Lett. 64, 784–787 (1990).
[CrossRef]

S. Herminghuas and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys. A 51, 350–353(1990).
[CrossRef]

1968 (1)

E. Kretschmann and H. Raether, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. A 23, 2135–2316 (1968).

Arakawa, E. T.

Chen, C.-W.

H. P. Chiang, C.-W. Chen, J. J. Wu, H. L. Li, T. Y. Lin, E. J. Sanchez, and P. T. Leung, “Effects of temperature on the surface plasmon resonance at a metal-semiconductor interface,” Thin Solid Films 515, 6953–6961 (2007).
[CrossRef]

Chiang, H. P.

H. P. Chiang, C.-W. Chen, J. J. Wu, H. L. Li, T. Y. Lin, E. J. Sanchez, and P. T. Leung, “Effects of temperature on the surface plasmon resonance at a metal-semiconductor interface,” Thin Solid Films 515, 6953–6961 (2007).
[CrossRef]

Farahi, R. H.

A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol. A 26, 836–841(2008).

Ferrell, T. L.

A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol. A 26, 836–841(2008).

A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006).
[CrossRef]

A. Passian, A. L. Lereu, E. T. Arakawa, A. Wig, T. Thundat, and T. L. Ferrell, “Modulation of multiple photon energies by use of surface plasmons,” Opt. Lett. 30, 41–43 (2005).
[CrossRef]

A. L. Lereu, A. Passian, J-P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects on surface plasmons,” Appl. Phys. Lett. 86, 154101 (2005).
[CrossRef]

Goudonnet, J-P.

A. L. Lereu, A. Passian, J-P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects on surface plasmons,” Appl. Phys. Lett. 86, 154101 (2005).
[CrossRef]

Groeneveld, R. H. M.

R. H. M. Groeneveld, R. Prrik, and Ad Lagendijk, “Ultrafast relaxation of electrons by surface plasmons at a thin silver film,” Phys. Rev. Lett. 64, 784–787 (1990).
[CrossRef]

Gupta, V.

S. Saha, N. Mehan, K. Sreenivas, and V. Gupta, “Temperature dependent optical properties of (002) oriented ZnO thin film using surface plasmon resonance,” Appl. Phys. Lett. 95, 071106 (2009).
[CrossRef]

Herminghuas, S.

S. Herminghuas and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys. A 51, 350–353(1990).
[CrossRef]

Kihm, K. D.

Kim, I. T.

Kretschmann, E.

E. Kretschmann and H. Raether, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. A 23, 2135–2316 (1968).

Lagendijk, Ad

R. H. M. Groeneveld, R. Prrik, and Ad Lagendijk, “Ultrafast relaxation of electrons by surface plasmons at a thin silver film,” Phys. Rev. Lett. 64, 784–787 (1990).
[CrossRef]

Leiderer, P.

S. Herminghuas and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys. A 51, 350–353(1990).
[CrossRef]

Lereu, A. L.

A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol. A 26, 836–841(2008).

A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006).
[CrossRef]

A. Passian, A. L. Lereu, E. T. Arakawa, A. Wig, T. Thundat, and T. L. Ferrell, “Modulation of multiple photon energies by use of surface plasmons,” Opt. Lett. 30, 41–43 (2005).
[CrossRef]

A. L. Lereu, A. Passian, J-P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects on surface plasmons,” Appl. Phys. Lett. 86, 154101 (2005).
[CrossRef]

Leung, P. T.

H. P. Chiang, C.-W. Chen, J. J. Wu, H. L. Li, T. Y. Lin, E. J. Sanchez, and P. T. Leung, “Effects of temperature on the surface plasmon resonance at a metal-semiconductor interface,” Thin Solid Films 515, 6953–6961 (2007).
[CrossRef]

Li, H. L.

H. P. Chiang, C.-W. Chen, J. J. Wu, H. L. Li, T. Y. Lin, E. J. Sanchez, and P. T. Leung, “Effects of temperature on the surface plasmon resonance at a metal-semiconductor interface,” Thin Solid Films 515, 6953–6961 (2007).
[CrossRef]

Lima, A. M. N.

C. S. Moreira, A. M. N. Lima, H. Neff, and C. Thirstrup, “Temperature-dependent sensitivity of surface plasmon resonance sensors at the gold-water interface,” Sens. Actuators B 134, 854–862 (2008).

Lin, K.-Q.

K.-Q. Lin, L.-M. Wei, D.-G. Zhang, R.-S. Zheng, P. Wang, Y.-H. Lu, and H. Ming, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24, 3081–3084 (2007).
[CrossRef]

Lin, T. Y.

H. P. Chiang, C.-W. Chen, J. J. Wu, H. L. Li, T. Y. Lin, E. J. Sanchez, and P. T. Leung, “Effects of temperature on the surface plasmon resonance at a metal-semiconductor interface,” Thin Solid Films 515, 6953–6961 (2007).
[CrossRef]

Lu, Y.-H.

K.-Q. Lin, L.-M. Wei, D.-G. Zhang, R.-S. Zheng, P. Wang, Y.-H. Lu, and H. Ming, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24, 3081–3084 (2007).
[CrossRef]

Mehan, N.

S. Saha, N. Mehan, K. Sreenivas, and V. Gupta, “Temperature dependent optical properties of (002) oriented ZnO thin film using surface plasmon resonance,” Appl. Phys. Lett. 95, 071106 (2009).
[CrossRef]

Meriaudeau, F.

A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006).
[CrossRef]

Ming, H.

K.-Q. Lin, L.-M. Wei, D.-G. Zhang, R.-S. Zheng, P. Wang, Y.-H. Lu, and H. Ming, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24, 3081–3084 (2007).
[CrossRef]

Moreira, C. S.

C. S. Moreira, A. M. N. Lima, H. Neff, and C. Thirstrup, “Temperature-dependent sensitivity of surface plasmon resonance sensors at the gold-water interface,” Sens. Actuators B 134, 854–862 (2008).

Neff, H.

C. S. Moreira, A. M. N. Lima, H. Neff, and C. Thirstrup, “Temperature-dependent sensitivity of surface plasmon resonance sensors at the gold-water interface,” Sens. Actuators B 134, 854–862 (2008).

Ozdemir, S. K.

Passian, A.

A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol. A 26, 836–841(2008).

A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006).
[CrossRef]

A. Passian, A. L. Lereu, E. T. Arakawa, A. Wig, T. Thundat, and T. L. Ferrell, “Modulation of multiple photon energies by use of surface plasmons,” Opt. Lett. 30, 41–43 (2005).
[CrossRef]

A. L. Lereu, A. Passian, J-P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects on surface plasmons,” Appl. Phys. Lett. 86, 154101 (2005).
[CrossRef]

Prrik, R.

R. H. M. Groeneveld, R. Prrik, and Ad Lagendijk, “Ultrafast relaxation of electrons by surface plasmons at a thin silver film,” Phys. Rev. Lett. 64, 784–787 (1990).
[CrossRef]

Raether, H.

E. Kretschmann and H. Raether, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. A 23, 2135–2316 (1968).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer Verlag, 1986).

Ritchie, R. H.

A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006).
[CrossRef]

Saha, S.

S. Saha, N. Mehan, K. Sreenivas, and V. Gupta, “Temperature dependent optical properties of (002) oriented ZnO thin film using surface plasmon resonance,” Appl. Phys. Lett. 95, 071106 (2009).
[CrossRef]

Sanchez, E. J.

H. P. Chiang, C.-W. Chen, J. J. Wu, H. L. Li, T. Y. Lin, E. J. Sanchez, and P. T. Leung, “Effects of temperature on the surface plasmon resonance at a metal-semiconductor interface,” Thin Solid Films 515, 6953–6961 (2007).
[CrossRef]

Sreenivas, K.

S. Saha, N. Mehan, K. Sreenivas, and V. Gupta, “Temperature dependent optical properties of (002) oriented ZnO thin film using surface plasmon resonance,” Appl. Phys. Lett. 95, 071106 (2009).
[CrossRef]

Thirstrup, C.

C. S. Moreira, A. M. N. Lima, H. Neff, and C. Thirstrup, “Temperature-dependent sensitivity of surface plasmon resonance sensors at the gold-water interface,” Sens. Actuators B 134, 854–862 (2008).

Thundat, T.

A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol. A 26, 836–841(2008).

A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006).
[CrossRef]

A. Passian, A. L. Lereu, E. T. Arakawa, A. Wig, T. Thundat, and T. L. Ferrell, “Modulation of multiple photon energies by use of surface plasmons,” Opt. Lett. 30, 41–43 (2005).
[CrossRef]

A. L. Lereu, A. Passian, J-P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects on surface plasmons,” Appl. Phys. Lett. 86, 154101 (2005).
[CrossRef]

Turhan-Sayan, G.

van Hulst, N. F.

A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol. A 26, 836–841(2008).

Wang, P.

K.-Q. Lin, L.-M. Wei, D.-G. Zhang, R.-S. Zheng, P. Wang, Y.-H. Lu, and H. Ming, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24, 3081–3084 (2007).
[CrossRef]

Wei, L.-M.

K.-Q. Lin, L.-M. Wei, D.-G. Zhang, R.-S. Zheng, P. Wang, Y.-H. Lu, and H. Ming, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24, 3081–3084 (2007).
[CrossRef]

Wig, A.

Wu, J. J.

H. P. Chiang, C.-W. Chen, J. J. Wu, H. L. Li, T. Y. Lin, E. J. Sanchez, and P. T. Leung, “Effects of temperature on the surface plasmon resonance at a metal-semiconductor interface,” Thin Solid Films 515, 6953–6961 (2007).
[CrossRef]

Xiang, J.

X. Xiao, J. Xiang, and F. Zhou, “Laser-induced thermal effect in surface plasmon resonance,” Anal. Chim. Acta 676, 75–80(2010).
[CrossRef]

Xiao, X.

X. Xiao, J. Xiang, and F. Zhou, “Laser-induced thermal effect in surface plasmon resonance,” Anal. Chim. Acta 676, 75–80(2010).
[CrossRef]

Zhang, D.-G.

K.-Q. Lin, L.-M. Wei, D.-G. Zhang, R.-S. Zheng, P. Wang, Y.-H. Lu, and H. Ming, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24, 3081–3084 (2007).
[CrossRef]

Zheng, R.-S.

K.-Q. Lin, L.-M. Wei, D.-G. Zhang, R.-S. Zheng, P. Wang, Y.-H. Lu, and H. Ming, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24, 3081–3084 (2007).
[CrossRef]

Zhou, F.

X. Xiao, J. Xiang, and F. Zhou, “Laser-induced thermal effect in surface plasmon resonance,” Anal. Chim. Acta 676, 75–80(2010).
[CrossRef]

Anal. Chim. Acta (1)

X. Xiao, J. Xiang, and F. Zhou, “Laser-induced thermal effect in surface plasmon resonance,” Anal. Chim. Acta 676, 75–80(2010).
[CrossRef]

Appl. Phys. A (1)

S. Herminghuas and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys. A 51, 350–353(1990).
[CrossRef]

Appl. Phys. Lett. (2)

A. L. Lereu, A. Passian, J-P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects on surface plasmons,” Appl. Phys. Lett. 86, 154101 (2005).
[CrossRef]

S. Saha, N. Mehan, K. Sreenivas, and V. Gupta, “Temperature dependent optical properties of (002) oriented ZnO thin film using surface plasmon resonance,” Appl. Phys. Lett. 95, 071106 (2009).
[CrossRef]

Chin. Phys. Lett. (1)

K.-Q. Lin, L.-M. Wei, D.-G. Zhang, R.-S. Zheng, P. Wang, Y.-H. Lu, and H. Ming, “Temperature effects on prism-based surface plasmon resonance sensor,” Chin. Phys. Lett. 24, 3081–3084 (2007).
[CrossRef]

J. Lightwave Technol. (1)

J. Vac. Sci. Technol. A (1)

A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol. A 26, 836–841(2008).

Opt. Lett. (2)

Phys. Rev. Lett. (1)

R. H. M. Groeneveld, R. Prrik, and Ad Lagendijk, “Ultrafast relaxation of electrons by surface plasmons at a thin silver film,” Phys. Rev. Lett. 64, 784–787 (1990).
[CrossRef]

Sens. Actuators B (1)

C. S. Moreira, A. M. N. Lima, H. Neff, and C. Thirstrup, “Temperature-dependent sensitivity of surface plasmon resonance sensors at the gold-water interface,” Sens. Actuators B 134, 854–862 (2008).

Thin Solid Films (2)

A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006).
[CrossRef]

H. P. Chiang, C.-W. Chen, J. J. Wu, H. L. Li, T. Y. Lin, E. J. Sanchez, and P. T. Leung, “Effects of temperature on the surface plasmon resonance at a metal-semiconductor interface,” Thin Solid Films 515, 6953–6961 (2007).
[CrossRef]

Z. Naturforsch. A (1)

E. Kretschmann and H. Raether, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. A 23, 2135–2316 (1968).

Other (1)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer Verlag, 1986).

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