Abstract

The three-layer system consisting of coupling prism, gap, and sample has been studied in an external magnetic field to calculate the attenuated-total-reflection spectrum due to surface plasmons. The sample is taken to be a nonpolar or polar semiconductor with free carriers, which becomes an anisotropic dielectric medium when the magnetic field is applied. Dispersion curves for the surface-polariton modes are discussed. Computed reflection spectra are shown for two of the three magnetic-field geometries considered. Computed results are compared with experimental results.

© 1974 Optical Society of America

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  1. J. Fahrenfort, Spectrochim. Acta 17, 698 (1961).
    [Crossref]
  2. J. Fahrenfort and W. M. Visser, Spectrochim. Acta 21, 1433 (1965).
    [Crossref]
  3. N. J. Harrick, Internal Reflection Spectroscopy (Wiley–Interscience, New York, 1967), Ch. 2.
  4. M. V. Klein, Optics (Wiley, New York, 1970), Ch. 11.3.
  5. A. Otto, Z. Phys. 216, 398 (1968).
    [Crossref]
  6. A. S. Barker, Phys. Rev. Lett. 28, 892 (1972).
    [Crossref]
  7. J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, Phys. Rev. Lett. 28, 1455 (1972).
    [Crossref]
  8. K. W. Chiu and J. J. Quinn, Phys. Rev. Lett. 29, 600 (1972).
    [Crossref]
  9. E. D. Palik, R. Kaplan, R. W. Gammon, H. Kaplan, J. J. Quinn, and R. F. Wallis, Phys. Lett. A 45, 143 (1973).
    [Crossref]
  10. A. Hartstein and E. Burstein, Solid State Commun. 14, 1223 (1974).
    [Crossref]
  11. H. Wolter, Handbuch der Physik, Vol. 24, edited by S. Flügge (Springer, Berlin, 1956), p. 461.
    [Crossref]
  12. I. L. Tyler, B. Fischer, and R. J. Bell, Opt. Commun. 8, 145 (1973).
    [Crossref]
  13. F. Abelès, Ann. Phys. (Paris) 5, 596 (1950); Ann. Phys. (Paris) 5, 706 (1950).
  14. R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Phys. Rev. B 9, 3424 (1974).
    [Crossref]
  15. J. J. Quinn and K. W. Chiu, Taormina Research Conference on the Structure of Matter—Polaritons, 1972.
  16. N. J. M. Horing and M. Yildiz (private communication).
  17. See L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960) for further references.
  18. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).
  19. See K. W. Chiu and J. J. Quinn, Am. J. Phys. 40, 1847 (1972), and the references therein.
    [Crossref]
  20. See J. Picht, Abhandlungen der Deutschen Akademie der Wissenschaften zu Berlin, Klasse für Mathematik, Physik und Technik, Jahrgang, 1955.
  21. K. W. Chiu and J. J. Quinn, Nuovo Cimento 10, 1 (1972).
  22. R. E. DeWames and W. F. Hall, Phys. Rev. Lett. 29, 172 (1972).
    [Crossref]
  23. R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Proceedings of the Eleventh International Conference on the Physics of Semiconductors (PWN-Polish Scientific Publishers, Warsaw, 1972), p. 1448.
  24. A. Otto (private communication).
  25. B. Fischer, N. Marschall, and H. J. Queisser, Surf. Sci. 34, 50 (1973).
    [Crossref]
  26. A. S. Barker, Surf. Sci. 34, 62 (1973).
    [Crossref]
  27. M. Hass, in Semiconductors and Semimetals, Vol. 3, edited by R. K. Willardson and A. C. Beer (Academic, New York, 1967), p. 3.
    [Crossref]
  28. R. W. Gammon and E. D. Palik, J. Opt. Soc. Am. 64, 350 (1974).
    [Crossref]
  29. E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie, Phys. Rev. Lett. 31, 1127 (1973).
    [Crossref]
  30. R. W. Alexander, G. S. Kovener, and R. J. Bell, Phys. Rev. Lett. 32, 154 (1974).
    [Crossref]
  31. V. V. Bryksin, Y. M. Gerbshtein, and D. N. Mirlin, Fiz. Tverd. Tela 13, 2125 (1971) [Sov. Phys.-Solid State 13, 1779 (1972)].
  32. E. D. Palik, B. W. Henvis, J. R. Stevenson, and S. Iwasa, Solid State Commun. 6, 721 (1968).
    [Crossref]
  33. V. V. Bryksin, D. N. Mirlin, and I. I. Reshina, Solid State Commun. 11, 695 (1972).
  34. E. D. Palik, S. Teitler, B. W. Henvis, and R. F. Wallis, in Reports of the International Conference on the Physics of Semiconductors, Exeter, 1962 (The Institute of Physics and the Physical Society of London, 1962), p. 288.

1974 (4)

A. Hartstein and E. Burstein, Solid State Commun. 14, 1223 (1974).
[Crossref]

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Phys. Rev. B 9, 3424 (1974).
[Crossref]

R. W. Gammon and E. D. Palik, J. Opt. Soc. Am. 64, 350 (1974).
[Crossref]

R. W. Alexander, G. S. Kovener, and R. J. Bell, Phys. Rev. Lett. 32, 154 (1974).
[Crossref]

1973 (5)

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie, Phys. Rev. Lett. 31, 1127 (1973).
[Crossref]

B. Fischer, N. Marschall, and H. J. Queisser, Surf. Sci. 34, 50 (1973).
[Crossref]

A. S. Barker, Surf. Sci. 34, 62 (1973).
[Crossref]

I. L. Tyler, B. Fischer, and R. J. Bell, Opt. Commun. 8, 145 (1973).
[Crossref]

E. D. Palik, R. Kaplan, R. W. Gammon, H. Kaplan, J. J. Quinn, and R. F. Wallis, Phys. Lett. A 45, 143 (1973).
[Crossref]

1972 (7)

A. S. Barker, Phys. Rev. Lett. 28, 892 (1972).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, Phys. Rev. Lett. 28, 1455 (1972).
[Crossref]

K. W. Chiu and J. J. Quinn, Phys. Rev. Lett. 29, 600 (1972).
[Crossref]

See K. W. Chiu and J. J. Quinn, Am. J. Phys. 40, 1847 (1972), and the references therein.
[Crossref]

K. W. Chiu and J. J. Quinn, Nuovo Cimento 10, 1 (1972).

R. E. DeWames and W. F. Hall, Phys. Rev. Lett. 29, 172 (1972).
[Crossref]

V. V. Bryksin, D. N. Mirlin, and I. I. Reshina, Solid State Commun. 11, 695 (1972).

1971 (1)

V. V. Bryksin, Y. M. Gerbshtein, and D. N. Mirlin, Fiz. Tverd. Tela 13, 2125 (1971) [Sov. Phys.-Solid State 13, 1779 (1972)].

1968 (2)

E. D. Palik, B. W. Henvis, J. R. Stevenson, and S. Iwasa, Solid State Commun. 6, 721 (1968).
[Crossref]

A. Otto, Z. Phys. 216, 398 (1968).
[Crossref]

1965 (1)

J. Fahrenfort and W. M. Visser, Spectrochim. Acta 21, 1433 (1965).
[Crossref]

1961 (1)

J. Fahrenfort, Spectrochim. Acta 17, 698 (1961).
[Crossref]

1950 (1)

F. Abelès, Ann. Phys. (Paris) 5, 596 (1950); Ann. Phys. (Paris) 5, 706 (1950).

Abelès, F.

F. Abelès, Ann. Phys. (Paris) 5, 596 (1950); Ann. Phys. (Paris) 5, 706 (1950).

Alexander, R. W.

R. W. Alexander, G. S. Kovener, and R. J. Bell, Phys. Rev. Lett. 32, 154 (1974).
[Crossref]

Arakawa, E. T.

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie, Phys. Rev. Lett. 31, 1127 (1973).
[Crossref]

Barker, A. S.

A. S. Barker, Surf. Sci. 34, 62 (1973).
[Crossref]

A. S. Barker, Phys. Rev. Lett. 28, 892 (1972).
[Crossref]

Bell, R. J.

R. W. Alexander, G. S. Kovener, and R. J. Bell, Phys. Rev. Lett. 32, 154 (1974).
[Crossref]

I. L. Tyler, B. Fischer, and R. J. Bell, Opt. Commun. 8, 145 (1973).
[Crossref]

Brekhovskikh, L. M.

See L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960) for further references.

Brion, J. J.

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Phys. Rev. B 9, 3424 (1974).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, Phys. Rev. Lett. 28, 1455 (1972).
[Crossref]

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Proceedings of the Eleventh International Conference on the Physics of Semiconductors (PWN-Polish Scientific Publishers, Warsaw, 1972), p. 1448.

Bryksin, V. V.

V. V. Bryksin, D. N. Mirlin, and I. I. Reshina, Solid State Commun. 11, 695 (1972).

V. V. Bryksin, Y. M. Gerbshtein, and D. N. Mirlin, Fiz. Tverd. Tela 13, 2125 (1971) [Sov. Phys.-Solid State 13, 1779 (1972)].

Burstein, E.

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Phys. Rev. B 9, 3424 (1974).
[Crossref]

A. Hartstein and E. Burstein, Solid State Commun. 14, 1223 (1974).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, Phys. Rev. Lett. 28, 1455 (1972).
[Crossref]

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Proceedings of the Eleventh International Conference on the Physics of Semiconductors (PWN-Polish Scientific Publishers, Warsaw, 1972), p. 1448.

Chiu, K. W.

See K. W. Chiu and J. J. Quinn, Am. J. Phys. 40, 1847 (1972), and the references therein.
[Crossref]

K. W. Chiu and J. J. Quinn, Nuovo Cimento 10, 1 (1972).

K. W. Chiu and J. J. Quinn, Phys. Rev. Lett. 29, 600 (1972).
[Crossref]

J. J. Quinn and K. W. Chiu, Taormina Research Conference on the Structure of Matter—Polaritons, 1972.

DeWames, R. E.

R. E. DeWames and W. F. Hall, Phys. Rev. Lett. 29, 172 (1972).
[Crossref]

Fahrenfort, J.

J. Fahrenfort and W. M. Visser, Spectrochim. Acta 21, 1433 (1965).
[Crossref]

J. Fahrenfort, Spectrochim. Acta 17, 698 (1961).
[Crossref]

Fischer, B.

I. L. Tyler, B. Fischer, and R. J. Bell, Opt. Commun. 8, 145 (1973).
[Crossref]

B. Fischer, N. Marschall, and H. J. Queisser, Surf. Sci. 34, 50 (1973).
[Crossref]

Gammon, R. W.

R. W. Gammon and E. D. Palik, J. Opt. Soc. Am. 64, 350 (1974).
[Crossref]

E. D. Palik, R. Kaplan, R. W. Gammon, H. Kaplan, J. J. Quinn, and R. F. Wallis, Phys. Lett. A 45, 143 (1973).
[Crossref]

Gerbshtein, Y. M.

V. V. Bryksin, Y. M. Gerbshtein, and D. N. Mirlin, Fiz. Tverd. Tela 13, 2125 (1971) [Sov. Phys.-Solid State 13, 1779 (1972)].

Hall, W. F.

R. E. DeWames and W. F. Hall, Phys. Rev. Lett. 29, 172 (1972).
[Crossref]

Hamm, R. N.

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie, Phys. Rev. Lett. 31, 1127 (1973).
[Crossref]

Harrick, N. J.

N. J. Harrick, Internal Reflection Spectroscopy (Wiley–Interscience, New York, 1967), Ch. 2.

Hartstein, A.

A. Hartstein and E. Burstein, Solid State Commun. 14, 1223 (1974).
[Crossref]

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Phys. Rev. B 9, 3424 (1974).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, Phys. Rev. Lett. 28, 1455 (1972).
[Crossref]

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Proceedings of the Eleventh International Conference on the Physics of Semiconductors (PWN-Polish Scientific Publishers, Warsaw, 1972), p. 1448.

Hass, M.

M. Hass, in Semiconductors and Semimetals, Vol. 3, edited by R. K. Willardson and A. C. Beer (Academic, New York, 1967), p. 3.
[Crossref]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

Henvis, B. W.

E. D. Palik, B. W. Henvis, J. R. Stevenson, and S. Iwasa, Solid State Commun. 6, 721 (1968).
[Crossref]

E. D. Palik, S. Teitler, B. W. Henvis, and R. F. Wallis, in Reports of the International Conference on the Physics of Semiconductors, Exeter, 1962 (The Institute of Physics and the Physical Society of London, 1962), p. 288.

Horing, N. J. M.

N. J. M. Horing and M. Yildiz (private communication).

Iwasa, S.

E. D. Palik, B. W. Henvis, J. R. Stevenson, and S. Iwasa, Solid State Commun. 6, 721 (1968).
[Crossref]

Kaplan, H.

E. D. Palik, R. Kaplan, R. W. Gammon, H. Kaplan, J. J. Quinn, and R. F. Wallis, Phys. Lett. A 45, 143 (1973).
[Crossref]

Kaplan, R.

E. D. Palik, R. Kaplan, R. W. Gammon, H. Kaplan, J. J. Quinn, and R. F. Wallis, Phys. Lett. A 45, 143 (1973).
[Crossref]

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970), Ch. 11.3.

Kovener, G. S.

R. W. Alexander, G. S. Kovener, and R. J. Bell, Phys. Rev. Lett. 32, 154 (1974).
[Crossref]

Marschall, N.

B. Fischer, N. Marschall, and H. J. Queisser, Surf. Sci. 34, 50 (1973).
[Crossref]

Mirlin, D. N.

V. V. Bryksin, D. N. Mirlin, and I. I. Reshina, Solid State Commun. 11, 695 (1972).

V. V. Bryksin, Y. M. Gerbshtein, and D. N. Mirlin, Fiz. Tverd. Tela 13, 2125 (1971) [Sov. Phys.-Solid State 13, 1779 (1972)].

Otto, A.

A. Otto, Z. Phys. 216, 398 (1968).
[Crossref]

A. Otto (private communication).

Palik, E. D.

R. W. Gammon and E. D. Palik, J. Opt. Soc. Am. 64, 350 (1974).
[Crossref]

E. D. Palik, R. Kaplan, R. W. Gammon, H. Kaplan, J. J. Quinn, and R. F. Wallis, Phys. Lett. A 45, 143 (1973).
[Crossref]

E. D. Palik, B. W. Henvis, J. R. Stevenson, and S. Iwasa, Solid State Commun. 6, 721 (1968).
[Crossref]

E. D. Palik, S. Teitler, B. W. Henvis, and R. F. Wallis, in Reports of the International Conference on the Physics of Semiconductors, Exeter, 1962 (The Institute of Physics and the Physical Society of London, 1962), p. 288.

Picht, J.

See J. Picht, Abhandlungen der Deutschen Akademie der Wissenschaften zu Berlin, Klasse für Mathematik, Physik und Technik, Jahrgang, 1955.

Queisser, H. J.

B. Fischer, N. Marschall, and H. J. Queisser, Surf. Sci. 34, 50 (1973).
[Crossref]

Quinn, J. J.

E. D. Palik, R. Kaplan, R. W. Gammon, H. Kaplan, J. J. Quinn, and R. F. Wallis, Phys. Lett. A 45, 143 (1973).
[Crossref]

K. W. Chiu and J. J. Quinn, Phys. Rev. Lett. 29, 600 (1972).
[Crossref]

K. W. Chiu and J. J. Quinn, Nuovo Cimento 10, 1 (1972).

See K. W. Chiu and J. J. Quinn, Am. J. Phys. 40, 1847 (1972), and the references therein.
[Crossref]

J. J. Quinn and K. W. Chiu, Taormina Research Conference on the Structure of Matter—Polaritons, 1972.

Reshina, I. I.

V. V. Bryksin, D. N. Mirlin, and I. I. Reshina, Solid State Commun. 11, 695 (1972).

Ritchie, R. H.

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie, Phys. Rev. Lett. 31, 1127 (1973).
[Crossref]

Stevenson, J. R.

E. D. Palik, B. W. Henvis, J. R. Stevenson, and S. Iwasa, Solid State Commun. 6, 721 (1968).
[Crossref]

Teitler, S.

E. D. Palik, S. Teitler, B. W. Henvis, and R. F. Wallis, in Reports of the International Conference on the Physics of Semiconductors, Exeter, 1962 (The Institute of Physics and the Physical Society of London, 1962), p. 288.

Tyler, I. L.

I. L. Tyler, B. Fischer, and R. J. Bell, Opt. Commun. 8, 145 (1973).
[Crossref]

Visser, W. M.

J. Fahrenfort and W. M. Visser, Spectrochim. Acta 21, 1433 (1965).
[Crossref]

Wallis, R. F.

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Phys. Rev. B 9, 3424 (1974).
[Crossref]

E. D. Palik, R. Kaplan, R. W. Gammon, H. Kaplan, J. J. Quinn, and R. F. Wallis, Phys. Lett. A 45, 143 (1973).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, Phys. Rev. Lett. 28, 1455 (1972).
[Crossref]

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Proceedings of the Eleventh International Conference on the Physics of Semiconductors (PWN-Polish Scientific Publishers, Warsaw, 1972), p. 1448.

E. D. Palik, S. Teitler, B. W. Henvis, and R. F. Wallis, in Reports of the International Conference on the Physics of Semiconductors, Exeter, 1962 (The Institute of Physics and the Physical Society of London, 1962), p. 288.

Williams, M. W.

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie, Phys. Rev. Lett. 31, 1127 (1973).
[Crossref]

Wolter, H.

H. Wolter, Handbuch der Physik, Vol. 24, edited by S. Flügge (Springer, Berlin, 1956), p. 461.
[Crossref]

Yildiz, M.

N. J. M. Horing and M. Yildiz (private communication).

Am. J. Phys. (1)

See K. W. Chiu and J. J. Quinn, Am. J. Phys. 40, 1847 (1972), and the references therein.
[Crossref]

Ann. Phys. (Paris) (1)

F. Abelès, Ann. Phys. (Paris) 5, 596 (1950); Ann. Phys. (Paris) 5, 706 (1950).

Fiz. Tverd. Tela (1)

V. V. Bryksin, Y. M. Gerbshtein, and D. N. Mirlin, Fiz. Tverd. Tela 13, 2125 (1971) [Sov. Phys.-Solid State 13, 1779 (1972)].

J. Opt. Soc. Am. (1)

Nuovo Cimento (1)

K. W. Chiu and J. J. Quinn, Nuovo Cimento 10, 1 (1972).

Opt. Commun. (1)

I. L. Tyler, B. Fischer, and R. J. Bell, Opt. Commun. 8, 145 (1973).
[Crossref]

Phys. Lett. A (1)

E. D. Palik, R. Kaplan, R. W. Gammon, H. Kaplan, J. J. Quinn, and R. F. Wallis, Phys. Lett. A 45, 143 (1973).
[Crossref]

Phys. Rev. B (1)

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Phys. Rev. B 9, 3424 (1974).
[Crossref]

Phys. Rev. Lett. (6)

A. S. Barker, Phys. Rev. Lett. 28, 892 (1972).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, Phys. Rev. Lett. 28, 1455 (1972).
[Crossref]

K. W. Chiu and J. J. Quinn, Phys. Rev. Lett. 29, 600 (1972).
[Crossref]

R. E. DeWames and W. F. Hall, Phys. Rev. Lett. 29, 172 (1972).
[Crossref]

E. T. Arakawa, M. W. Williams, R. N. Hamm, and R. H. Ritchie, Phys. Rev. Lett. 31, 1127 (1973).
[Crossref]

R. W. Alexander, G. S. Kovener, and R. J. Bell, Phys. Rev. Lett. 32, 154 (1974).
[Crossref]

Solid State Commun. (3)

E. D. Palik, B. W. Henvis, J. R. Stevenson, and S. Iwasa, Solid State Commun. 6, 721 (1968).
[Crossref]

V. V. Bryksin, D. N. Mirlin, and I. I. Reshina, Solid State Commun. 11, 695 (1972).

A. Hartstein and E. Burstein, Solid State Commun. 14, 1223 (1974).
[Crossref]

Spectrochim. Acta (2)

J. Fahrenfort, Spectrochim. Acta 17, 698 (1961).
[Crossref]

J. Fahrenfort and W. M. Visser, Spectrochim. Acta 21, 1433 (1965).
[Crossref]

Surf. Sci. (2)

B. Fischer, N. Marschall, and H. J. Queisser, Surf. Sci. 34, 50 (1973).
[Crossref]

A. S. Barker, Surf. Sci. 34, 62 (1973).
[Crossref]

Z. Phys. (1)

A. Otto, Z. Phys. 216, 398 (1968).
[Crossref]

Other (12)

See J. Picht, Abhandlungen der Deutschen Akademie der Wissenschaften zu Berlin, Klasse für Mathematik, Physik und Technik, Jahrgang, 1955.

J. J. Quinn and K. W. Chiu, Taormina Research Conference on the Structure of Matter—Polaritons, 1972.

N. J. M. Horing and M. Yildiz (private communication).

See L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960) for further references.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

N. J. Harrick, Internal Reflection Spectroscopy (Wiley–Interscience, New York, 1967), Ch. 2.

M. V. Klein, Optics (Wiley, New York, 1970), Ch. 11.3.

H. Wolter, Handbuch der Physik, Vol. 24, edited by S. Flügge (Springer, Berlin, 1956), p. 461.
[Crossref]

M. Hass, in Semiconductors and Semimetals, Vol. 3, edited by R. K. Willardson and A. C. Beer (Academic, New York, 1967), p. 3.
[Crossref]

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, Proceedings of the Eleventh International Conference on the Physics of Semiconductors (PWN-Polish Scientific Publishers, Warsaw, 1972), p. 1448.

A. Otto (private communication).

E. D. Palik, S. Teitler, B. W. Henvis, and R. F. Wallis, in Reports of the International Conference on the Physics of Semiconductors, Exeter, 1962 (The Institute of Physics and the Physical Society of London, 1962), p. 288.

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Figures (9)

Fig. 1
Fig. 1

Coordinate system for the multilayer system. The field vectors are indicated on each side of each interface.

Fig. 2
Fig. 2

Experimental three-layer system to observe surface plasmons. For Hdc = 0, surface plasmons are only observable with Eip-polarized light. The first and third media are assumed semi-infinite in the calculation.

Fig. 3
Fig. 3

(a) Calculated dispersion curves for surface optic phonons on a polar crystal with carrier density N = 0, dotted curve; surface plasmons for a nonpolar crystal with ωT = ωL and N ≠ 0, dot-dash curve; and coupled plasmon-optic phonons in InSb, solid curve. The dashed lines are evanescent light lines. (b) Dielectric constants for the three cases indicated in (a).

Fig. 4
Fig. 4

(a) Dispersion curves for InSb for the geometry ky, +Hx-showing the shift of the surface modes. The short branches terminate at k2 = (ω2/c2)V, the long branches asymptotically approach 1 + 11 + i∊12 = 0. The solid curves are Hdc = 0, short-dash curves 10 kG, long-dash curves 20 kG, and dotted curves 30 kG. (b) Dispersion curves for InSb for the geometry ky, −Hx showing the shift of the surface modes. The short branches terminate at k2 = (ω2/c2)V, the long branches asymptotically approach 1 + 11i∊12 = 0.

Fig. 5
Fig. 5

(a) Calculated ATR spectra (Erp) for θ = 35°, d = 4.5 μm, +Hx, and Eip. The two main peaks for H = 0 are due to photon-energy loss to the surface modes. These shift up in frequency as H is increased. Weaker, broader lines are due to bulk losses in the sample. The arrows indicate the intersections of the 35° light line with the long branches of the dispersion curves in Fig. 4. Overcoupling produces the slight shift between the arrow position and the ATR line position. The solid curves are Hdc = 0, short-dash curves 10 kG, long-dash curves 20 kG, and dotted curves 30 kG. (b) Calculated ATR spectra (Erp) for θ = 35°, d = 4.5 μm, −Hx, and Eip. The two main peaks that indicate positions of surface modes shift down in frequency as H is increased.

Fig. 6
Fig. 6

Calculated ATR spectra (Erp) for θ = 20°, d = 22 μm, +Hx, and Eip. For each H ≠ 0, four peaks indicate the positions of surface modes. The arrows indicate the intersections of the 20° light line with the long branches of the dispersion curves in Fig. 4; the vertical bars indicate intersections with the short branches. Overcoupling produces the small differences between these intersections and the actual ATR absorption line. The solid curves are Hdc = 0, short-dash curves 10 kG, long-dash curves 20 kG, and dotted curves 30 kG. (b) Calculated ATR spectra for θ = 20°, d = 22 μm, −Hx, and Eip. For each H ≠ 0, four peaks indicate the position of surface modes.

Fig. 7
Fig. 7

Calculated ATR spectrum (Ers) for θ = 35°, d = 4.5 μm, +Hx, and Eis is given by the solid curve; for θ = 20°, d = 22 μm by the dotted curve. In this case, no surface-mode peaks are observable and absorption peaks are due to bulk losses. The spectra are independent of Hx and the sign of Hx.

Fig. 8
Fig. 8

(a) Experimental ATR spectra for θ = 35°, d = 3 μm, +Hx, and Eip. (b) Experimental results for θ = 35°, d = 3 μm, −Hx, and Eip. Figure 8 is to be compared with Fig. 5.

Fig. 9
Fig. 9

(a) Calculated pp polarized ATR spectra for θ = 35°, d = 4.5 μm, and Hy. In this case we have Eip and Erp. The solid curves are Hdc = 0 kG, short-dash curves 10 kG, long-dash curves 20 kG, and dotted curves 30 kG. The two strong absorption lines are due to surface modes. (b) Calculated ps and sp polarized ATR spectra for θ = 35°, d = 4.5 μm, and Hy with Eip,s and Ers,p. In this case the Hdc = 0 kG spectrum is given by the solid base line since it has no intensity. Reflectance peaks are due to surface modes shifting with increasing Hdc. Note that ps is identical to sp. (c) Calculated ss polarized ATR spectra for θ = 35°, d = 4.5 μm, and Hy with Eis and Ers. The broader Hdc = 0 lines are due to bulk modes. The stronger Hdc ≠ 0 absorption lines are due to surface modes with some bulk-mode lines also apparent.

Equations (35)

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k l × E l = ( ω c ) H l , k l × H l = - ( ω c ) ɛ l · E l .
V l = P l V l ,
V l - 1 = B l - 1 , l V l ,
V 1 = B 1 , 2 P 2 B 2 , 3 P 3 P N - 1 B N - 1 , N V N .
3 = ( 33 0 0 0 11 12 0 - 12 11 ) .
3 = ( 11 0 - 12 0 33 0 12 0 11 ) .
3 = ( 11 12 0 - 12 11 0 0 0 33 ) .
= 11 ( 1 0 0 0 1 0 0 0 1 ) .
k 31 k 32 } = ± k 1 3 ,             k 33 k 34 } = ± k 2 3 .
k 11 k 12 } = ± k 1 1 ,             k 13 k 14 } = ± k 2 1 ,
A 2 1 = E i s , C 2 1 = E r s , A 1 1 1 = E i p , C 1 1 1 = E r p , A 1 1 = H i s , C 1 1 = H r s , A 2 1 1 = H i p , C 2 1 1 = H r p .
V 1 = B 1 , 2 P 2 B 2 , 3 V 3 B V 3 ,
R = 1 C 2 1 2 + C 1 1 2 1 A 2 1 2 + A 1 1 2 .
R = R TM 1 + R TM 2 , R TM 1 = | C 1 1 A 1 1 | 2 = | B 21 B 33 - B 23 B 31 B 11 B 33 - B 13 B 31 | 2 , R TM 2 = 1 | C 2 1 A 1 1 | 2 = 1 | B 41 B 33 - B 43 B 31 B 11 B 33 - B 13 B 31 | 2 .
R = R TE 1 + R TE 2 R TE 1 = 1 1 | C 1 1 A 2 1 | 2 = 1 1 | B 11 B 23 - B 21 B 13 B 33 B 11 - B 31 B 13 | 2 R TE 2 = | C 2 1 A 2 1 | 2 = | B 11 B 43 - B 41 B 13 B 33 B 11 - B 31 B 13 | 2 .
B 1 , 2 = 1 2 [ ( 1 + Z 1 12 ) ( 1 - Z 1 12 ) 0 0 ( 1 - Z 1 12 ) ( 1 + Z 1 12 ) 0 0 0 0 ( 1 + Z 2 12 ) ( 1 - Z 2 12 ) 0 0 ( 1 - Z 2 12 ) ( 1 + Z 2 12 ) ] ,
K 1 = - ( 1 - K 2 ) 1 2 , K 2 = - i ( K 2 - 2 ) 1 2 ,
P 2 = [ η 0 0 0 0 η - 1 0 0 0 0 η 0 0 0 0 η - 1 ] ,
B 2 , 3 = 1 2 [ ( 1 + Z 1 23 ) ( 1 - Z 1 23 ) 0 0 ( 1 - Z 1 23 ) ( 1 + Z 1 23 ) 0 0 0 0 ( 1 + Z 2 23 ) ( 1 - Z 2 23 ) 0 0 ( 1 - Z 2 23 ) ( 1 + Z 2 23 ) ] ,
Z 1 23 = 2 ( K 1 3 + K 12 / 11 ) V K 2
Z 2 23 = K 2 3 K 2 ,             V = 11 2 + 12 2 11 .
[ V - K 2 - K 3 2 0 0 33 - K 2 - K 3 2 ] ( H x E x ) = 0.
B 2 , 3 = 1 2 [ ( 1 + Z 11 23 ) ( 1 - Z 11 23 ) α ( 1 + Z 12 23 ) α ( 1 - Z 12 23 ) ( 1 - Z 11 23 ) ( 1 + Z 11 23 ) α ( 1 - Z 12 23 ) α ( 1 + Z 12 23 ) β ( 1 + Z 21 23 ) β ( 1 - Z 21 23 ) ( 1 + Z 22 23 ) ( 1 - Z 22 23 ) β ( 1 - Z 21 23 ) β ( 1 + Z 21 23 ) ( 1 - Z 22 23 ) ( 1 + Z 22 23 ) ] .
Z 11 23 = K 1 3 K 2 2 33 ,             Z 12 23 = K 2 3 K 2 2 33 , Z 21 23 = K 1 3 K 2 ,             K 22 23 = K 2 3 K 2 , α = - K 12 11 [ 1 - K 2 / 11 - ( K 2 3 ) 2 / 33 ] , β = K 12 11 [ V - K 2 - ( K 1 3 ) 2 ] .
[ 1 - K 2 11 - ( K 3 ) 2 33 12 K 11 - 12 K 11 V - K 2 - ( K 3 ) 2 ] ( H x E x ) = 0.
B 2 , 3 = 1 2 [ ( 1 + Z 11 23 ) ( 1 - Z 11 23 ) ( - α ) ( 1 + Z 12 23 ) α ( 1 - Z 12 32 ) ( 1 - Z 11 23 ) ( 1 + Z 11 23 ) ( - α ) ( 1 - Z 12 23 ) α ( 1 + Z 12 23 ) ( - β ) ( 1 + Z 21 23 ) β ( 1 - Z 21 23 ) ( 1 + Z 22 23 ) ( 1 - Z 22 23 ) ( - β ) ( 1 - Z 21 23 ) β ( 1 + Z 21 23 ) ( 1 - Z 22 23 ) ( 1 + Z 22 23 ) ] .
Z 11 23 = - 2 K 2 K 1 3 ( K 2 33 - 1 ) ,             Z 12 23 = - 2 K 2 K 2 3 ( K 2 33 - 1 ) , Z 21 23 = K 1 3 K 2 ,             Z 22 23 = K 2 3 K 2 , α = - 12 11 ( K 2 3 1 - K 2 / 33 - ( K 2 3 ) 2 / 11 ) , β = 12 11 ( K 1 3 V - K 2 - ( K 1 3 ) 2 ) .
[ 1 - K 2 33 - ( K 3 ) 2 11 K 3 12 11 - K 3 12 11 V - K 2 - ( K 3 ) 2 ] ( H x E x ) = 0.
B 11 B 33 - B 13 B 31 = 0.
k 2 = ω 2 c 2 2 3 2 + 3 ,
V K 2 + 2 K 1 3 + 2 12 11 K = 0.
FC = [ - ω p 2 ω ( ω + i γ ) 0 0 0 - ω p 2 ( ω + i γ ) ω [ ( ω + i γ ) 2 - ω c 2 ] - i ω p 2 ω c ω [ ( ω + i γ ) 2 - ω c 2 ] 0 i ω p 2 ω c ω [ ( ω + i γ ) 2 - ω c 2 ] - ω p 2 ( ω + i γ ) ω [ ( ω + i γ ) 2 - ω c 2 ] ] .
= [ 1 + ω L 2 - ω T 2 ω T 2 - ω 2 - i Γ ω ]
= [ 1 - ω p 2 ω ( ω + i γ ) ]
= [ 1 + ω L 2 - ω T 2 ω T 2 - ω 2 - i Γ ω - ω p 2 ω ( ω + i γ ) ]