Abstract

A second-order theory is developed for the reflection and transmission of light by a slightly rough surface. The general results are discussed, especially for a rough interface between vacuum and a free-electron-like metal, where surface-plasma excitation can occur. The influence of the damping of the electron gas and of the shape of the roughness is discussed. Some different previous theories for reflection by a rough surface are shown to be limiting cases of the present theory.

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  1. H. E. Bennett, J. Opt. Soc. Am. 53, 1389 (1963).
  2. J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).
  3. A. Daude, A. Savary, and S. Robin, J. Opt. Soc. Am. 62, 1 (1972).
  4. J. G. Endriz and W. E. Spicer, Phys. Rev. B 4, 4144 (1971).
  5. E. Kretschmann, thesis (Universität Hamburg, 1972).
  6. J. M. Elson, and R. H. Ritchie, Phys. Rev. B 4, 4129 (1971); J. Crowell and R. H. Ritchie, J. Opt. Soc. Am. 60, 794 (1970); E. Kretschmann, Z. Phys. 237, 1 (1970).
  7. J. M. Elson and R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974).
  8. D. Beaglehole and O. Hunderi, Phys. Rev. B 2, 309 (1970).
  9. H. E. Bennett, J. Opt. Soc. Am. 51, 123 (1961); H. Davies, Proc. IEEE 101, 209 (1954); P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1973).
  10. E. Kröger and E. Kretschmann, Z. Phys. 237, 1 (1970).
  11. S. O. Rice, Comm. Pure Appl. Math. 4, 351 (1951).
  12. H. J. Juranek, Z. Phys. 233, 324 (1970).
  13. Reference 11, Eq. (7.29).
  14. Equation (22) is valid for complex ε also.

Bennett, H. E.

H. E. Bennett, J. Opt. Soc. Am. 51, 123 (1961); H. Davies, Proc. IEEE 101, 209 (1954); P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1973).

Arakawa, E. T.

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

Ashley, E. J.

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

Beaglehole, D.

D. Beaglehole and O. Hunderi, Phys. Rev. B 2, 309 (1970).

Bennett, H. E.

H. E. Bennett, J. Opt. Soc. Am. 53, 1389 (1963).

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

Bennett, J. M.

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

Daude, A.

A. Daude, A. Savary, and S. Robin, J. Opt. Soc. Am. 62, 1 (1972).

Elson, J. M.

J. M. Elson and R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974).

J. M. Elson, and R. H. Ritchie, Phys. Rev. B 4, 4129 (1971); J. Crowell and R. H. Ritchie, J. Opt. Soc. Am. 60, 794 (1970); E. Kretschmann, Z. Phys. 237, 1 (1970).

Endriz, J. G.

J. G. Endriz and W. E. Spicer, Phys. Rev. B 4, 4144 (1971).

Hunderi, O.

D. Beaglehole and O. Hunderi, Phys. Rev. B 2, 309 (1970).

Juranek, H. J.

H. J. Juranek, Z. Phys. 233, 324 (1970).

Kretschmann, E.

E. Kretschmann, thesis (Universität Hamburg, 1972).

E. Kröger and E. Kretschmann, Z. Phys. 237, 1 (1970).

Kröger, E.

E. Kröger and E. Kretschmann, Z. Phys. 237, 1 (1970).

Rice, S. O.

S. O. Rice, Comm. Pure Appl. Math. 4, 351 (1951).

Ritchie, R. H.

J. M. Elson, and R. H. Ritchie, Phys. Rev. B 4, 4129 (1971); J. Crowell and R. H. Ritchie, J. Opt. Soc. Am. 60, 794 (1970); E. Kretschmann, Z. Phys. 237, 1 (1970).

J. M. Elson and R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974).

Robin, S.

A. Daude, A. Savary, and S. Robin, J. Opt. Soc. Am. 62, 1 (1972).

Savary, A.

A. Daude, A. Savary, and S. Robin, J. Opt. Soc. Am. 62, 1 (1972).

Spicer, W. E.

J. G. Endriz and W. E. Spicer, Phys. Rev. B 4, 4144 (1971).

Stanford, J. L.

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

Other (14)

H. E. Bennett, J. Opt. Soc. Am. 53, 1389 (1963).

J. L. Stanford, H. E. Bennett, J. M. Bennett, E. J. Ashley, and E. T. Arakawa, Bull. Am. Phys. Soc. 13, 989 (1968).

A. Daude, A. Savary, and S. Robin, J. Opt. Soc. Am. 62, 1 (1972).

J. G. Endriz and W. E. Spicer, Phys. Rev. B 4, 4144 (1971).

E. Kretschmann, thesis (Universität Hamburg, 1972).

J. M. Elson, and R. H. Ritchie, Phys. Rev. B 4, 4129 (1971); J. Crowell and R. H. Ritchie, J. Opt. Soc. Am. 60, 794 (1970); E. Kretschmann, Z. Phys. 237, 1 (1970).

J. M. Elson and R. H. Ritchie, Phys. Status Solidi B 62, 461 (1974).

D. Beaglehole and O. Hunderi, Phys. Rev. B 2, 309 (1970).

H. E. Bennett, J. Opt. Soc. Am. 51, 123 (1961); H. Davies, Proc. IEEE 101, 209 (1954); P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1973).

E. Kröger and E. Kretschmann, Z. Phys. 237, 1 (1970).

S. O. Rice, Comm. Pure Appl. Math. 4, 351 (1951).

H. J. Juranek, Z. Phys. 233, 324 (1970).

Reference 11, Eq. (7.29).

Equation (22) is valid for complex ε also.

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