Abstract

The Pockels electro-optic effect at a surface of a centrosymmetric metal is described and is experimentally demonstrated on Ag surfaces in connection with surface plasmon excitation in attenuated total reflection measurements. It is shown that it is sufficient to know only the linear-optical properties of the metal in order to predict its electro-optic properties. The experimental data seem to be in good agreement with the theoretical model even without the introduction of phenomenological fitting parameters into the theory. We predict extremely large electro-optic effects near the plasma edge of the metal.

© 1993 Optical Society of America

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References

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  1. O. Keller, “On the nonlocal response theory of optical rectification and second-harmonic generation in centrosymmetric superconductors,” in Nonlinear Optics in Solids, Vol. 9 of Springer Series on Wave Phenomena, O. Keller, ed. (Springer-Verlag, New York, 1989), pp. 78–107.
    [CrossRef]
  2. J.-L. Coutaz, “Surface enhanced second harmonic generation from metals,” in Nonlinear Optics in Solids, Vol. 9 of Springer Series on Wave Phenomena, O. Keller, ed. (Springer-Verlag, New York, 1989), pp. 44–72.
    [CrossRef]
  3. J. D. E. McIntyre and D. E. Aspnes, “Electroreflectance spectra of noble metals,” Bull. Am. Phys. Soc. 15, 366 (1970).
  4. J. D. E. McIntyre, “Electrochemical modulation spectroscopy,” Surf. Sci. 37, 658–682 (1973).
    [CrossRef]
  5. F. Abelés, T. Lopez-Rios, and A. Tadjeddine, “Investigation of the metal electrolyte interface using surface plasma waves with ellipsometric detection,” Solid State Commun. 16, 843–847 (1975).
    [CrossRef]
  6. R. Kötz, D. M. Kolb, and J. K. Sass, “Electron density effects in surface plasmon excitation on silver and gold electrodes,” Surf. Sci. 69, 359–364 (1977).
    [CrossRef]
  7. A. Tadjeddine, D. M. Kolb, and R. Kötz, “The study of single crystal electrode surfaces by surface plasmon excitation,” Surf. Sci. 101, 277–285 (1980).
    [CrossRef]
  8. F. Chao and M. Costa, “The electrochemical interface, a stratified medium studied by ellipsometry,” Surf. Sci. 135, 497–520 (1983).
    [CrossRef]
  9. E. Kretschmann and H. Raether, “Radiative decay of non radiative surface plasmons excited by light,” Z. Naturforch. 23a, 2135–2136 (1968).
  10. E. Kretschmann, “Die Bestimmung optisher Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 214, 313–324 (1971).
  11. F. Abelés, “Surface electromagnetic waves,” in Electromagnetic Surface Excitations, Vol. 3 of Springer Series on Wave Phenomena, R. F. Wallis and G. I. Stegeman, eds. (Springer-Verlag, New York, 1986), pp. 8–29.
  12. K. Welford, “Tutorial review: surface plasmon-polaritons and their uses,” Opt. Quantum Electron. 23, 1–27 (1991).
    [CrossRef]
  13. M. Born and E. Wolf, 6th ed., Principles of Optics (Pergamon, New York, 1980).
  14. M. Dumont and Y. Lévy, “Measurement of electrooptic properties of organic thin films by attenuated total reflection,” in Nonlinear Optics of Organics and Semiconductors, Vol. 36 of Springer Proceedings of Physics, T. Kobaysky, ed. (Springer-Verlag, New York, 1989), pp. 256–266.
    [CrossRef]
  15. W M. K. P. Wijekoon, B. Asgharian, M. Casstevens, M. Samoc, G. B. Talapatra, P. N. Prasad, T. Geisler, and S. Rosenkilde, “Electrooptic effect in Langmuir–Blodgett films of 2-docosylamino-5-nitropyridine probed by surface plasmon waves,” Langmuir 8, 135–139 (1992).
    [CrossRef]

1992 (1)

W M. K. P. Wijekoon, B. Asgharian, M. Casstevens, M. Samoc, G. B. Talapatra, P. N. Prasad, T. Geisler, and S. Rosenkilde, “Electrooptic effect in Langmuir–Blodgett films of 2-docosylamino-5-nitropyridine probed by surface plasmon waves,” Langmuir 8, 135–139 (1992).
[CrossRef]

1991 (1)

K. Welford, “Tutorial review: surface plasmon-polaritons and their uses,” Opt. Quantum Electron. 23, 1–27 (1991).
[CrossRef]

1983 (1)

F. Chao and M. Costa, “The electrochemical interface, a stratified medium studied by ellipsometry,” Surf. Sci. 135, 497–520 (1983).
[CrossRef]

1980 (1)

A. Tadjeddine, D. M. Kolb, and R. Kötz, “The study of single crystal electrode surfaces by surface plasmon excitation,” Surf. Sci. 101, 277–285 (1980).
[CrossRef]

1977 (1)

R. Kötz, D. M. Kolb, and J. K. Sass, “Electron density effects in surface plasmon excitation on silver and gold electrodes,” Surf. Sci. 69, 359–364 (1977).
[CrossRef]

1975 (1)

F. Abelés, T. Lopez-Rios, and A. Tadjeddine, “Investigation of the metal electrolyte interface using surface plasma waves with ellipsometric detection,” Solid State Commun. 16, 843–847 (1975).
[CrossRef]

1973 (1)

J. D. E. McIntyre, “Electrochemical modulation spectroscopy,” Surf. Sci. 37, 658–682 (1973).
[CrossRef]

1971 (1)

E. Kretschmann, “Die Bestimmung optisher Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 214, 313–324 (1971).

1970 (1)

J. D. E. McIntyre and D. E. Aspnes, “Electroreflectance spectra of noble metals,” Bull. Am. Phys. Soc. 15, 366 (1970).

1968 (1)

E. Kretschmann and H. Raether, “Radiative decay of non radiative surface plasmons excited by light,” Z. Naturforch. 23a, 2135–2136 (1968).

Abelés, F.

F. Abelés, T. Lopez-Rios, and A. Tadjeddine, “Investigation of the metal electrolyte interface using surface plasma waves with ellipsometric detection,” Solid State Commun. 16, 843–847 (1975).
[CrossRef]

F. Abelés, “Surface electromagnetic waves,” in Electromagnetic Surface Excitations, Vol. 3 of Springer Series on Wave Phenomena, R. F. Wallis and G. I. Stegeman, eds. (Springer-Verlag, New York, 1986), pp. 8–29.

Asgharian, B.

W M. K. P. Wijekoon, B. Asgharian, M. Casstevens, M. Samoc, G. B. Talapatra, P. N. Prasad, T. Geisler, and S. Rosenkilde, “Electrooptic effect in Langmuir–Blodgett films of 2-docosylamino-5-nitropyridine probed by surface plasmon waves,” Langmuir 8, 135–139 (1992).
[CrossRef]

Aspnes, D. E.

J. D. E. McIntyre and D. E. Aspnes, “Electroreflectance spectra of noble metals,” Bull. Am. Phys. Soc. 15, 366 (1970).

Born, M.

M. Born and E. Wolf, 6th ed., Principles of Optics (Pergamon, New York, 1980).

Casstevens, M.

W M. K. P. Wijekoon, B. Asgharian, M. Casstevens, M. Samoc, G. B. Talapatra, P. N. Prasad, T. Geisler, and S. Rosenkilde, “Electrooptic effect in Langmuir–Blodgett films of 2-docosylamino-5-nitropyridine probed by surface plasmon waves,” Langmuir 8, 135–139 (1992).
[CrossRef]

Chao, F.

F. Chao and M. Costa, “The electrochemical interface, a stratified medium studied by ellipsometry,” Surf. Sci. 135, 497–520 (1983).
[CrossRef]

Costa, M.

F. Chao and M. Costa, “The electrochemical interface, a stratified medium studied by ellipsometry,” Surf. Sci. 135, 497–520 (1983).
[CrossRef]

Coutaz, J.-L.

J.-L. Coutaz, “Surface enhanced second harmonic generation from metals,” in Nonlinear Optics in Solids, Vol. 9 of Springer Series on Wave Phenomena, O. Keller, ed. (Springer-Verlag, New York, 1989), pp. 44–72.
[CrossRef]

Dumont, M.

M. Dumont and Y. Lévy, “Measurement of electrooptic properties of organic thin films by attenuated total reflection,” in Nonlinear Optics of Organics and Semiconductors, Vol. 36 of Springer Proceedings of Physics, T. Kobaysky, ed. (Springer-Verlag, New York, 1989), pp. 256–266.
[CrossRef]

Geisler, T.

W M. K. P. Wijekoon, B. Asgharian, M. Casstevens, M. Samoc, G. B. Talapatra, P. N. Prasad, T. Geisler, and S. Rosenkilde, “Electrooptic effect in Langmuir–Blodgett films of 2-docosylamino-5-nitropyridine probed by surface plasmon waves,” Langmuir 8, 135–139 (1992).
[CrossRef]

Keller, O.

O. Keller, “On the nonlocal response theory of optical rectification and second-harmonic generation in centrosymmetric superconductors,” in Nonlinear Optics in Solids, Vol. 9 of Springer Series on Wave Phenomena, O. Keller, ed. (Springer-Verlag, New York, 1989), pp. 78–107.
[CrossRef]

Kolb, D. M.

A. Tadjeddine, D. M. Kolb, and R. Kötz, “The study of single crystal electrode surfaces by surface plasmon excitation,” Surf. Sci. 101, 277–285 (1980).
[CrossRef]

R. Kötz, D. M. Kolb, and J. K. Sass, “Electron density effects in surface plasmon excitation on silver and gold electrodes,” Surf. Sci. 69, 359–364 (1977).
[CrossRef]

Kötz, R.

A. Tadjeddine, D. M. Kolb, and R. Kötz, “The study of single crystal electrode surfaces by surface plasmon excitation,” Surf. Sci. 101, 277–285 (1980).
[CrossRef]

R. Kötz, D. M. Kolb, and J. K. Sass, “Electron density effects in surface plasmon excitation on silver and gold electrodes,” Surf. Sci. 69, 359–364 (1977).
[CrossRef]

Kretschmann, E.

E. Kretschmann, “Die Bestimmung optisher Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 214, 313–324 (1971).

E. Kretschmann and H. Raether, “Radiative decay of non radiative surface plasmons excited by light,” Z. Naturforch. 23a, 2135–2136 (1968).

Lévy, Y.

M. Dumont and Y. Lévy, “Measurement of electrooptic properties of organic thin films by attenuated total reflection,” in Nonlinear Optics of Organics and Semiconductors, Vol. 36 of Springer Proceedings of Physics, T. Kobaysky, ed. (Springer-Verlag, New York, 1989), pp. 256–266.
[CrossRef]

Lopez-Rios, T.

F. Abelés, T. Lopez-Rios, and A. Tadjeddine, “Investigation of the metal electrolyte interface using surface plasma waves with ellipsometric detection,” Solid State Commun. 16, 843–847 (1975).
[CrossRef]

McIntyre, J. D. E.

J. D. E. McIntyre, “Electrochemical modulation spectroscopy,” Surf. Sci. 37, 658–682 (1973).
[CrossRef]

J. D. E. McIntyre and D. E. Aspnes, “Electroreflectance spectra of noble metals,” Bull. Am. Phys. Soc. 15, 366 (1970).

Prasad, P. N.

W M. K. P. Wijekoon, B. Asgharian, M. Casstevens, M. Samoc, G. B. Talapatra, P. N. Prasad, T. Geisler, and S. Rosenkilde, “Electrooptic effect in Langmuir–Blodgett films of 2-docosylamino-5-nitropyridine probed by surface plasmon waves,” Langmuir 8, 135–139 (1992).
[CrossRef]

Raether, H.

E. Kretschmann and H. Raether, “Radiative decay of non radiative surface plasmons excited by light,” Z. Naturforch. 23a, 2135–2136 (1968).

Rosenkilde, S.

W M. K. P. Wijekoon, B. Asgharian, M. Casstevens, M. Samoc, G. B. Talapatra, P. N. Prasad, T. Geisler, and S. Rosenkilde, “Electrooptic effect in Langmuir–Blodgett films of 2-docosylamino-5-nitropyridine probed by surface plasmon waves,” Langmuir 8, 135–139 (1992).
[CrossRef]

Samoc, M.

W M. K. P. Wijekoon, B. Asgharian, M. Casstevens, M. Samoc, G. B. Talapatra, P. N. Prasad, T. Geisler, and S. Rosenkilde, “Electrooptic effect in Langmuir–Blodgett films of 2-docosylamino-5-nitropyridine probed by surface plasmon waves,” Langmuir 8, 135–139 (1992).
[CrossRef]

Sass, J. K.

R. Kötz, D. M. Kolb, and J. K. Sass, “Electron density effects in surface plasmon excitation on silver and gold electrodes,” Surf. Sci. 69, 359–364 (1977).
[CrossRef]

Tadjeddine, A.

A. Tadjeddine, D. M. Kolb, and R. Kötz, “The study of single crystal electrode surfaces by surface plasmon excitation,” Surf. Sci. 101, 277–285 (1980).
[CrossRef]

F. Abelés, T. Lopez-Rios, and A. Tadjeddine, “Investigation of the metal electrolyte interface using surface plasma waves with ellipsometric detection,” Solid State Commun. 16, 843–847 (1975).
[CrossRef]

Talapatra, G. B.

W M. K. P. Wijekoon, B. Asgharian, M. Casstevens, M. Samoc, G. B. Talapatra, P. N. Prasad, T. Geisler, and S. Rosenkilde, “Electrooptic effect in Langmuir–Blodgett films of 2-docosylamino-5-nitropyridine probed by surface plasmon waves,” Langmuir 8, 135–139 (1992).
[CrossRef]

Welford, K.

K. Welford, “Tutorial review: surface plasmon-polaritons and their uses,” Opt. Quantum Electron. 23, 1–27 (1991).
[CrossRef]

Wijekoon, W M. K. P.

W M. K. P. Wijekoon, B. Asgharian, M. Casstevens, M. Samoc, G. B. Talapatra, P. N. Prasad, T. Geisler, and S. Rosenkilde, “Electrooptic effect in Langmuir–Blodgett films of 2-docosylamino-5-nitropyridine probed by surface plasmon waves,” Langmuir 8, 135–139 (1992).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, 6th ed., Principles of Optics (Pergamon, New York, 1980).

Bull. Am. Phys. Soc. (1)

J. D. E. McIntyre and D. E. Aspnes, “Electroreflectance spectra of noble metals,” Bull. Am. Phys. Soc. 15, 366 (1970).

Langmuir (1)

W M. K. P. Wijekoon, B. Asgharian, M. Casstevens, M. Samoc, G. B. Talapatra, P. N. Prasad, T. Geisler, and S. Rosenkilde, “Electrooptic effect in Langmuir–Blodgett films of 2-docosylamino-5-nitropyridine probed by surface plasmon waves,” Langmuir 8, 135–139 (1992).
[CrossRef]

Opt. Quantum Electron. (1)

K. Welford, “Tutorial review: surface plasmon-polaritons and their uses,” Opt. Quantum Electron. 23, 1–27 (1991).
[CrossRef]

Solid State Commun. (1)

F. Abelés, T. Lopez-Rios, and A. Tadjeddine, “Investigation of the metal electrolyte interface using surface plasma waves with ellipsometric detection,” Solid State Commun. 16, 843–847 (1975).
[CrossRef]

Surf. Sci. (4)

R. Kötz, D. M. Kolb, and J. K. Sass, “Electron density effects in surface plasmon excitation on silver and gold electrodes,” Surf. Sci. 69, 359–364 (1977).
[CrossRef]

A. Tadjeddine, D. M. Kolb, and R. Kötz, “The study of single crystal electrode surfaces by surface plasmon excitation,” Surf. Sci. 101, 277–285 (1980).
[CrossRef]

F. Chao and M. Costa, “The electrochemical interface, a stratified medium studied by ellipsometry,” Surf. Sci. 135, 497–520 (1983).
[CrossRef]

J. D. E. McIntyre, “Electrochemical modulation spectroscopy,” Surf. Sci. 37, 658–682 (1973).
[CrossRef]

Z. Naturforch. (1)

E. Kretschmann and H. Raether, “Radiative decay of non radiative surface plasmons excited by light,” Z. Naturforch. 23a, 2135–2136 (1968).

Z. Phys. (1)

E. Kretschmann, “Die Bestimmung optisher Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 214, 313–324 (1971).

Other (5)

F. Abelés, “Surface electromagnetic waves,” in Electromagnetic Surface Excitations, Vol. 3 of Springer Series on Wave Phenomena, R. F. Wallis and G. I. Stegeman, eds. (Springer-Verlag, New York, 1986), pp. 8–29.

O. Keller, “On the nonlocal response theory of optical rectification and second-harmonic generation in centrosymmetric superconductors,” in Nonlinear Optics in Solids, Vol. 9 of Springer Series on Wave Phenomena, O. Keller, ed. (Springer-Verlag, New York, 1989), pp. 78–107.
[CrossRef]

J.-L. Coutaz, “Surface enhanced second harmonic generation from metals,” in Nonlinear Optics in Solids, Vol. 9 of Springer Series on Wave Phenomena, O. Keller, ed. (Springer-Verlag, New York, 1989), pp. 44–72.
[CrossRef]

M. Born and E. Wolf, 6th ed., Principles of Optics (Pergamon, New York, 1980).

M. Dumont and Y. Lévy, “Measurement of electrooptic properties of organic thin films by attenuated total reflection,” in Nonlinear Optics of Organics and Semiconductors, Vol. 36 of Springer Proceedings of Physics, T. Kobaysky, ed. (Springer-Verlag, New York, 1989), pp. 256–266.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Geometry of the metal layer with an applied electric field Ez in the z direction.

Fig. 2
Fig. 2

Effective electro-optic coefficient of an Ag surface layer versus vacuum wavelength calculated from Eq. (9): solid curve, real part of r333; dashed curve, imaginary part of r333. The data taken for Ag are n = 5.86 × 1028 m−3, m* = 1.0257me, τ = 1.8 × 10−14 s, EF = 5.49 eV, and λL = 330.2 nm.

Fig. 3
Fig. 3

Modulation of the electric field in the Kretschmann configuration. The z axis of the coordinate system is shown, and the positive directions of the electric field and the applied voltage are indicated. In the experimental setup used here the probe beam is totally reflected at one side of the prism in order to retroreflect the beam.

Fig. 4
Fig. 4

Experimental reflectance R versus angle of incidence θi of a 48.4-nm Ag layer in the Kretschmann configuration. The solid curve shows a least-squares fit of the multilayer model [Eqs. (12) and (13)] to the experimental data.

Fig. 5
Fig. 5

(a) Measured ΔR versus angle of incidence θi of a 48.4-nm Ag layer in the Kretschmann configuration. The solid curve is the least-squares fit of the ΔR model [Eqs. (15) and (16)] to the experimental data. (b) The fitted curves are shown as a ΔR/R curve.

Fig. 6
Fig. 6

Measured ΔR versus applied voltage V with the angle of incidence θi held fixed at the value that gives largest ΔR.

Fig. 7
Fig. 7

Measured ΔR versus air pressure. The angle of incidence θi is held fixed at the value that gives largest ΔR.

Tables (1)

Tables Icon

Table 1 Experimental and Theoretical Values of the Electro-optic Effect of Ag Layers

Equations (32)

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m = ω p 2 ω [ ω + ( i / τ ) ] , ω p 2 n e 2 0 m * ,
Δ n s = σ e = 0 e E z ,
Δ = e 2 0 m * 1 ω [ ω + ( i / τ ) ] Δ n s δ ,
δ Δ = ( m ) Δ n s n = ( m ) 0 n e E z
δ = ( 2 3 0 dc E F e 2 n ) 1 / 2 ,
r i j k = 4 i i j j χ i j k ( 2 ) ( ω ; ω , 0 ) ,
χ i j z ( 2 ) ( ω ; ω , 0 ) = Δ i j E z ,
r 113 = r 223 = r 333 = 4 m 2 ( m ) 0 e n δ .
r 333 = 1 ω L 2 ω [ ω + ( i / τ ) ] [ ω 2 ω L 2 + i ( ω / τ ) ] 2 ( 24 0 dc n E F ) 1 / 2 ,
ω L 2 ω p 2 / .
Δ η = 1 2 η 3 r 333 E z .
r p m a = ρ p m + ρ m a exp ( 2 i k m z d ) 1 + ρ p m ρ m a exp ( 2 i k m z d ) ,
R = | r p m a | 2 .
r m m a = ρ m m + ρ m a exp ( 2 i k m z δ ) 1 + ρ m m ρ m a exp ( 2 i k m z δ ) exp ( 2 i k m z δ ) ,
r m m a a k m z m k a z a k m z + m k a z + 2 i k m z ( m k a z + a k m z ) 2 ( a 2 m k x 2 m k a z 2 ) δ Δ .
Δ R = R ( δ Δ ) ( R ) ( δ Δ ) ( R ) + R ( δ Δ ) ( I ) ( δ Δ ) ( I ) ,
r m m a = ρ m m + ρ m a exp ( 2 i k m z δ ) 1 + ρ m m ρ m a exp ( 2 i k m z δ ) exp ( 2 i k m z δ ) .
ρ m m = m k m z m k m z m k m z + m k m z , ρ m a = a k m z m k a z a k m z + m k a z
| k m z δ | 1 ,
| k m z δ | 1
r m m a a k m z m k a z a k m z + m k a z + 2 i k m z ( m k a z + a k m z ) 2 ( m 2 m m m 2 ) k a z 2 + a 2 m k m z 2 m δ .
r m m a a k m z m k a z a k m z + m k a z + 2 i k m z ( m k a z + a k m z ) 2 a 2 k x 2 m 2 k a z 2 m Δ k a z 2 m + Δ δ Δ ,
k 2 m = k m z 2 + k x 2 ,
k 2 ( m + Δ ) = k m z 2 + k x 2 ,
Δ m ,
r m m a a k m z m k a z a k m z + m k a z + 2 i k m z ( m k a z + a k m z ) 2 ( a 2 m k x 2 m k a z 2 ) δ Δ .
r p m m a ( δ Δ ) = ( 1 ρ p m 2 ) r m m a [ 1 + ρ p m r m m a exp ( 2 i k m z d ) ] 2 r m m a ( δ Δ ) ,
r m m a = ρ m a = a k m z m k a z a k m z + m k a z ,
r m m a ( δ Δ ) = 2 i k m z ( m k a z + a k m z ) 2 ( a 2 m k x 2 m k a z 2 ) .
r m m a ( δ Δ ) = r m m a ( δ Δ ) ( R ) = 1 i r m m a ( δ Δ ) ( I ) .
R ( δ Δ ) ( R ) = r p m m a ( r p m m a [ δ Δ ] ( R ) ) * + c . c . = 2 Re [ r p m m a * r p m m a ( δ Δ ) ] ,
R ( δ Δ ) ( I ) = r p m m a ( r p m m a [ δ Δ ] ( I ) ) * + c . c . = 2 Im [ r p m m a * r p m m a ( δ Δ ) ] ,

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