Abstract

By quantitatively examining dispersion curves of surface plasmons along Ag, Al, Ni, and Fe films, we find that the incidence angle θo that produces a reflection minimum in a variety of ATR geometries is actually different from the angle θp that corresponds to the phase-matching condition. The difference between θp and θo is most significant in the Otto and Kretschmann geometries using metal films with large damping loss, such as Ni or Fe. In addition, we determine the angle θm at which maximum power density is coupled into the metal surface and show that in general the value of θm is also different from both θo and θp, the difference being again largest in the Otto or Kretschmann geometries. The differences between θo, θp, and θm are much smaller, but still detectable, in long-range surface plasmon and extended-range surface plasmon geometries. In all cases, the preferred incidence angle depends on whether one needs to optimize either the plasmon field composition or the power density in the metal.

© 1988 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Otto, “Excitation of Non-Radiative Surface Plasma Waves in Silver by the Method of Frustrated Total Reflection,” Z. Phys. 216, 398 (1968).
    [Crossref]
  2. E. Kretschmann, H. Raether, “Radiative Decay of Non-Radiative Surface Plasmons Excited by Light,” Z. Phys. 239, 2135 (1968).
  3. S. R. Bruns, H. Raether, “Plasmon Resonance Radiation from Non-radiative Plasmons,” Z. Phys. 237, 98 (1970).
    [Crossref]
  4. E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
    [Crossref]
  5. H. Raether, “Surface Plasma Oscillations and their Applications,” in Physics of Thin Films, Vol. 9, G. Hass, Ed. (Academic, New York, 1977), p. 230.
  6. A. S. Barker, “Direct Optical Coupling to Surface Excitations,” Phys. Rev. Lett. 28, 892 (1972).
    [Crossref]
  7. P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
    [Crossref]
  8. B. Fischer, N. Marschall, H. J. Queisser, “Experimental Studies of Optical Surface Excitations,” Surf. Sci. 34, 50 (1973).
    [Crossref]
  9. T. Hollstein, U. Kreibig, F. Leis, “Optical Properties of Cu and Ag in the Intermediate Region Between Pure Drude and Interband Absorption,” Phys. Status Solidi B 82, 545 (1977).
    [Crossref]
  10. A. S. Barker, “Response Functions for Surface Polaritons at Interfaces in Solids,” Surf. Sci. 34, 62 (1973).
    [Crossref]
  11. W. H. Weber, “Modulated Surface-Plasmon Resonance for in Situ Metal-Film Surface Studies,” Phys. Rev. Lett. 39, 153 (1977).
    [Crossref]
  12. J. Bosenberg, “Photoelectrons from the Optically Excited Non-Radiative Surface Plasma Oscillations,” Phys. Lett. A 37, 439 (1975).
    [Crossref]
  13. F. Abeles, “Surface Plasmon (SEW) Phenomena,” in Electromagnetic Surface Excitations, R. F. Wallis, G. I. Stegeman, Eds. (Springer-Verlag, New York, 1986), p. 8.
    [Crossref]
  14. D. Sarid, “Long-Range Surface Plasma Waves on Very Thin Metal Films,” Phys. Rev. Lett. 47, 1927 (1981).
    [Crossref]
  15. G. I. Stegeman, J. J. Burke, D. G. Hall, “Non-Linear Optics of Long-Range Surface Plasmons,” Appl. Phys. Lett. 41, 906 (1982).
    [Crossref]
  16. F.-Y. Kou, T. Tamir, “Range Extension of Surface Plasmons by Dielectric Layers,” Opt. Lett. 12, 367 (1987).
    [Crossref] [PubMed]
  17. L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, NJ1973), Sec. 2.4.
  18. A. A. Maradudin, D. L. Mills, “Effect of Spatial Dispersion on the Properties of a Semi-Infinite Dielectric,” Phys. Rev. B 7, 2787 (1973).
    [Crossref]
  19. D. Sarid, R. T. Deck, A. E. Craig, R. K. Hickernell, R. S. Jameson, J. J. Fasano, “Optical Field Enhancement by Long-Range Surface Plasma Waves,” Appl. Opt. 21, 3993 (1982).
    [Crossref] [PubMed]
  20. E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182, 539 (1969).
    [Crossref]

1987 (1)

1982 (2)

1981 (1)

D. Sarid, “Long-Range Surface Plasma Waves on Very Thin Metal Films,” Phys. Rev. Lett. 47, 1927 (1981).
[Crossref]

1977 (2)

W. H. Weber, “Modulated Surface-Plasmon Resonance for in Situ Metal-Film Surface Studies,” Phys. Rev. Lett. 39, 153 (1977).
[Crossref]

T. Hollstein, U. Kreibig, F. Leis, “Optical Properties of Cu and Ag in the Intermediate Region Between Pure Drude and Interband Absorption,” Phys. Status Solidi B 82, 545 (1977).
[Crossref]

1975 (1)

J. Bosenberg, “Photoelectrons from the Optically Excited Non-Radiative Surface Plasma Oscillations,” Phys. Lett. A 37, 439 (1975).
[Crossref]

1973 (3)

B. Fischer, N. Marschall, H. J. Queisser, “Experimental Studies of Optical Surface Excitations,” Surf. Sci. 34, 50 (1973).
[Crossref]

A. A. Maradudin, D. L. Mills, “Effect of Spatial Dispersion on the Properties of a Semi-Infinite Dielectric,” Phys. Rev. B 7, 2787 (1973).
[Crossref]

A. S. Barker, “Response Functions for Surface Polaritons at Interfaces in Solids,” Surf. Sci. 34, 62 (1973).
[Crossref]

1972 (2)

A. S. Barker, “Direct Optical Coupling to Surface Excitations,” Phys. Rev. Lett. 28, 892 (1972).
[Crossref]

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
[Crossref]

1971 (1)

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
[Crossref]

1970 (1)

S. R. Bruns, H. Raether, “Plasmon Resonance Radiation from Non-radiative Plasmons,” Z. Phys. 237, 98 (1970).
[Crossref]

1969 (1)

E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182, 539 (1969).
[Crossref]

1968 (2)

A. Otto, “Excitation of Non-Radiative Surface Plasma Waves in Silver by the Method of Frustrated Total Reflection,” Z. Phys. 216, 398 (1968).
[Crossref]

E. Kretschmann, H. Raether, “Radiative Decay of Non-Radiative Surface Plasmons Excited by Light,” Z. Phys. 239, 2135 (1968).

Abeles, F.

F. Abeles, “Surface Plasmon (SEW) Phenomena,” in Electromagnetic Surface Excitations, R. F. Wallis, G. I. Stegeman, Eds. (Springer-Verlag, New York, 1986), p. 8.
[Crossref]

Barker, A. S.

A. S. Barker, “Response Functions for Surface Polaritons at Interfaces in Solids,” Surf. Sci. 34, 62 (1973).
[Crossref]

A. S. Barker, “Direct Optical Coupling to Surface Excitations,” Phys. Rev. Lett. 28, 892 (1972).
[Crossref]

Bosenberg, J.

J. Bosenberg, “Photoelectrons from the Optically Excited Non-Radiative Surface Plasma Oscillations,” Phys. Lett. A 37, 439 (1975).
[Crossref]

Bruns, S. R.

S. R. Bruns, H. Raether, “Plasmon Resonance Radiation from Non-radiative Plasmons,” Z. Phys. 237, 98 (1970).
[Crossref]

Burke, J. J.

G. I. Stegeman, J. J. Burke, D. G. Hall, “Non-Linear Optics of Long-Range Surface Plasmons,” Appl. Phys. Lett. 41, 906 (1982).
[Crossref]

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
[Crossref]

Craig, A. E.

Deck, R. T.

Economou, E. N.

E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182, 539 (1969).
[Crossref]

Fasano, J. J.

Felsen, L. B.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, NJ1973), Sec. 2.4.

Fischer, B.

B. Fischer, N. Marschall, H. J. Queisser, “Experimental Studies of Optical Surface Excitations,” Surf. Sci. 34, 50 (1973).
[Crossref]

Hall, D. G.

G. I. Stegeman, J. J. Burke, D. G. Hall, “Non-Linear Optics of Long-Range Surface Plasmons,” Appl. Phys. Lett. 41, 906 (1982).
[Crossref]

Hickernell, R. K.

Hollstein, T.

T. Hollstein, U. Kreibig, F. Leis, “Optical Properties of Cu and Ag in the Intermediate Region Between Pure Drude and Interband Absorption,” Phys. Status Solidi B 82, 545 (1977).
[Crossref]

Jameson, R. S.

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
[Crossref]

Kou, F.-Y.

Kreibig, U.

T. Hollstein, U. Kreibig, F. Leis, “Optical Properties of Cu and Ag in the Intermediate Region Between Pure Drude and Interband Absorption,” Phys. Status Solidi B 82, 545 (1977).
[Crossref]

Kretschmann, E.

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
[Crossref]

E. Kretschmann, H. Raether, “Radiative Decay of Non-Radiative Surface Plasmons Excited by Light,” Z. Phys. 239, 2135 (1968).

Leis, F.

T. Hollstein, U. Kreibig, F. Leis, “Optical Properties of Cu and Ag in the Intermediate Region Between Pure Drude and Interband Absorption,” Phys. Status Solidi B 82, 545 (1977).
[Crossref]

Maradudin, A. A.

A. A. Maradudin, D. L. Mills, “Effect of Spatial Dispersion on the Properties of a Semi-Infinite Dielectric,” Phys. Rev. B 7, 2787 (1973).
[Crossref]

Marcuvitz, N.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, NJ1973), Sec. 2.4.

Marschall, N.

B. Fischer, N. Marschall, H. J. Queisser, “Experimental Studies of Optical Surface Excitations,” Surf. Sci. 34, 50 (1973).
[Crossref]

Mills, D. L.

A. A. Maradudin, D. L. Mills, “Effect of Spatial Dispersion on the Properties of a Semi-Infinite Dielectric,” Phys. Rev. B 7, 2787 (1973).
[Crossref]

Otto, A.

A. Otto, “Excitation of Non-Radiative Surface Plasma Waves in Silver by the Method of Frustrated Total Reflection,” Z. Phys. 216, 398 (1968).
[Crossref]

Queisser, H. J.

B. Fischer, N. Marschall, H. J. Queisser, “Experimental Studies of Optical Surface Excitations,” Surf. Sci. 34, 50 (1973).
[Crossref]

Raether, H.

S. R. Bruns, H. Raether, “Plasmon Resonance Radiation from Non-radiative Plasmons,” Z. Phys. 237, 98 (1970).
[Crossref]

E. Kretschmann, H. Raether, “Radiative Decay of Non-Radiative Surface Plasmons Excited by Light,” Z. Phys. 239, 2135 (1968).

H. Raether, “Surface Plasma Oscillations and their Applications,” in Physics of Thin Films, Vol. 9, G. Hass, Ed. (Academic, New York, 1977), p. 230.

Sarid, D.

Stegeman, G. I.

G. I. Stegeman, J. J. Burke, D. G. Hall, “Non-Linear Optics of Long-Range Surface Plasmons,” Appl. Phys. Lett. 41, 906 (1982).
[Crossref]

Tamir, T.

Weber, W. H.

W. H. Weber, “Modulated Surface-Plasmon Resonance for in Situ Metal-Film Surface Studies,” Phys. Rev. Lett. 39, 153 (1977).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. I. Stegeman, J. J. Burke, D. G. Hall, “Non-Linear Optics of Long-Range Surface Plasmons,” Appl. Phys. Lett. 41, 906 (1982).
[Crossref]

Opt. Lett. (1)

Phys. Lett. A (1)

J. Bosenberg, “Photoelectrons from the Optically Excited Non-Radiative Surface Plasma Oscillations,” Phys. Lett. A 37, 439 (1975).
[Crossref]

Phys. Rev. (1)

E. N. Economou, “Surface Plasmons in Thin Films,” Phys. Rev. 182, 539 (1969).
[Crossref]

Phys. Rev. B (2)

A. A. Maradudin, D. L. Mills, “Effect of Spatial Dispersion on the Properties of a Semi-Infinite Dielectric,” Phys. Rev. B 7, 2787 (1973).
[Crossref]

P. B. Johnson, R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370 (1972).
[Crossref]

Phys. Rev. Lett. (3)

D. Sarid, “Long-Range Surface Plasma Waves on Very Thin Metal Films,” Phys. Rev. Lett. 47, 1927 (1981).
[Crossref]

A. S. Barker, “Direct Optical Coupling to Surface Excitations,” Phys. Rev. Lett. 28, 892 (1972).
[Crossref]

W. H. Weber, “Modulated Surface-Plasmon Resonance for in Situ Metal-Film Surface Studies,” Phys. Rev. Lett. 39, 153 (1977).
[Crossref]

Phys. Status Solidi B (1)

T. Hollstein, U. Kreibig, F. Leis, “Optical Properties of Cu and Ag in the Intermediate Region Between Pure Drude and Interband Absorption,” Phys. Status Solidi B 82, 545 (1977).
[Crossref]

Surf. Sci. (2)

A. S. Barker, “Response Functions for Surface Polaritons at Interfaces in Solids,” Surf. Sci. 34, 62 (1973).
[Crossref]

B. Fischer, N. Marschall, H. J. Queisser, “Experimental Studies of Optical Surface Excitations,” Surf. Sci. 34, 50 (1973).
[Crossref]

Z. Phys. (4)

A. Otto, “Excitation of Non-Radiative Surface Plasma Waves in Silver by the Method of Frustrated Total Reflection,” Z. Phys. 216, 398 (1968).
[Crossref]

E. Kretschmann, H. Raether, “Radiative Decay of Non-Radiative Surface Plasmons Excited by Light,” Z. Phys. 239, 2135 (1968).

S. R. Bruns, H. Raether, “Plasmon Resonance Radiation from Non-radiative Plasmons,” Z. Phys. 237, 98 (1970).
[Crossref]

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
[Crossref]

Other (3)

H. Raether, “Surface Plasma Oscillations and their Applications,” in Physics of Thin Films, Vol. 9, G. Hass, Ed. (Academic, New York, 1977), p. 230.

F. Abeles, “Surface Plasmon (SEW) Phenomena,” in Electromagnetic Surface Excitations, R. F. Wallis, G. I. Stegeman, Eds. (Springer-Verlag, New York, 1986), p. 8.
[Crossref]

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, NJ1973), Sec. 2.4.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Typical ATR configurations for exciting surface plasmons: (a) Otto; (b) Kretschmann; (c) long-range surface plasmon; and (d) extended-range surface plasmon geometries. In all cases, m denotes the dielectric constant of the metal film.

Fig. 2
Fig. 2

Variation of the magnitude of the reflection coefficient |r(κi)| and the normalized power density Pm at the metal surface in the Otto geometry shown in the inset. Po is a normalization constant. In this case, κ o κ n κ p κ m.

Fig. 3
Fig. 3

Same as in Fig. 2, except that the curves are calculated for the Kretschmann geometry shown in the inset.

Fig. 4
Fig. 4

Curves of κ p , κ n , κm, and δ as functions of the free-space wavelength λ for the Otto geometry shown in the inset. The loss factor δ is given by δ = - m / m .

Fig. 5
Fig. 5

Same as in Fig. 4, except that the curves are obtained for the Kretschmann geometry shown in the inset.

Fig. 6
Fig. 6

Same as in Fig. 4, except that the curves are obtained for the LRSP geometry shown in the inset.

Tables (2)

Tables Icon

Table I Typical Values of Δθi = θpθn; In All Cases u = 4 and the Dielectric Materials In Evanescence (Nonguiding) Layers have a Constant = 2.25

Tables Icon

Table II Values of Δθi = θiθp, in the ATR Geometries Used for Table I

Equations (25)

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

H i = exp [ i k ( κ x + τ u z ) ] ,
H r = r ( κ ) , exp [ i k ( κ x + τ u z ) ] ,
r ( κ ) = m 12 - ( Z s m 22 - Z u m 11 ) - Z u Z s m 21 Z 12 - ( Z s m 22 + Z u m 11 ) + Z u Z s m 21 = N ( κ ) D ( κ ) ,
[ m 11 m 12 m 21 m 22 ] = M l M l - 1 M 2 M 1 ,
M j = [ cos ( k τ j z j ) i Z j sin ( k τ j z j ) i Y j sin ( k τ j z j ) cos ( k τ j z j ) ] ,
Z j = 1 Y j = τ j / j ,
τ j = ± ( j - κ 2 ) 1 / 2 ,             j = u , 1 , 2 , , l - 1 , l , s ,
D ( κ p ) = m 12 - ( Z s m 22 + Z u m 11 ) + Z u Z s m 21 = 0.
κ i = u sin θ i = u sin θ p = κ p ,
H j = [ H j + exp ( i k τ j p z j ) - H j - exp ( - i k τ j p z j ) ] exp ( i k κ p x ) ,
z j = z - n = 1 j - 1 t n
[ ( H j + + H j - ) Z j H j + - H j - ] = M j - 1 { [ H ( j - 1 ) + + H ( j - 1 ) - ] Z ( j - 1 ) H ( j - 1 ) + - H ( j - 1 ) + } .
[ ( H j + + H j - ) Z j H j + - H j - ] = M j - 1 M j - 2 M 2 M 1 [ ( 1 + r ( κ ) ) Z j 1 - r ( κ ) ] .
P = ½ Re ( E × H * ) ,
D ( κ o ) N ( κ o ) .
N ( κ n ) = 0.
κ o κ n = u sin θ n κ p .
m = m + i m ,
m = 1 - ω p 2 t s 2 ω 2 t s 2 + 1 ,
m = t s ω p 2 ω ( ω 2 t s 2 + 1 ) .
m ( λ ) = 1 - [ 1 - m ( λ o ) ] ( γ o 2 + 1 ) ( λ o λ ) 2 γ o 2 + 1 ,
m = λ [ 1 - m ( λ ) ] λ o γ o ,
γ o = 1 - m ( λ o ) m ( λ o ) .
m = 1 - 23.89 1 + 0.72 ( 0.6328 λ ) 2 ,
m = λ ( 1 - m ) 0.5379 .

Metrics