Abstract

Calculations for optical reflection, transmission, and attenuated-total-reflection of a two-dimensional distribution system of metal particles are carried out in two different ways; one is the usual way utilizing a fictitious plane-parallel film model and the other is the integration method of scattered waves. Both results are compared and discussed.

© 1978 Optical Society of America

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  1. J. C. Maxwell-Garnett, Phil. Trans. R. Soc. A 203, 385 (1904).
  2. E. David, Z. Phys. 114, 389 (1939).
  3. T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 18, 63 (1973).
  4. T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 21, 173 (1974).
  5. T. Yamaguchi and A. Kinbara, Proc. 6th International Vacuum Congress, Jpn. J. Appl. Phys. Suppl. 2, Pt. 1, 677 (1974).
  6. The factors π2/24 and π2/12 are different from the previous paper (Refs. 7 and 8). In the calculation of the dipole-dipole interactions, the following type of summation appears:[equation],where rj is the distance to the jth interacting particle from the reference one placed at the origin. Here we calculated the summation by the crude assumption that 2πm particles are on a circle of radius ma, where a is the mean distance between particles and m the integer:[equation]In Ref. 7 the factor π2/12 is replaced by 0.716, which was computed numerically assuming that the island particles are distributed onto lattice points of a square array of lattice constant a, whereas in Ref. 8 it is replaced by unity, which was obtained by another crude assumption. These calculations are based on the static field dipole-dipole interactions. Although for a thicker film, retarded dipole-dipole interactions (Ref. 9) are needed, the static one is sufficient in a thinner film considered in the present paper.
  7. T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 13, 261 (1972).
  8. S. Yamaguchi, J. Phys. Soc. Jpn. 15, 1577 (1960).
  9. T. Yamaguchi, S. Yoshida, and A. Kinbara, J. Opt. Soc. Am. 64, 1563 (1974).
  10. The optical anisotropy was directly observed by ellipsometric study of silver island films; T. Yamaguchi, S. Yoshida, and A. Kinbara, J. Opt. Soc. Am. 62, 634 (1972).
  11. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), p. 61.
  12. Reference 11, p. 670.
  13. Reference 11, p. 81.
  14. Reference 11, p. 753.
  15. T. Yamaguchi and H. Takahashi, Surface Sci. (in press).

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), p. 61.

David, E.

E. David, Z. Phys. 114, 389 (1939).

Kinbara, A.

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 21, 173 (1974).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 13, 261 (1972).

T. Yamaguchi and A. Kinbara, Proc. 6th International Vacuum Congress, Jpn. J. Appl. Phys. Suppl. 2, Pt. 1, 677 (1974).

T. Yamaguchi, S. Yoshida, and A. Kinbara, J. Opt. Soc. Am. 64, 1563 (1974).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 18, 63 (1973).

Maxwell-Garnett, J. C.

J. C. Maxwell-Garnett, Phil. Trans. R. Soc. A 203, 385 (1904).

Takahashi, H.

T. Yamaguchi and H. Takahashi, Surface Sci. (in press).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), p. 61.

Yamaguchi, S.

S. Yamaguchi, J. Phys. Soc. Jpn. 15, 1577 (1960).

Yamaguchi, T.

T. Yamaguchi and H. Takahashi, Surface Sci. (in press).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 21, 173 (1974).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 13, 261 (1972).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 18, 63 (1973).

T. Yamaguchi, S. Yoshida, and A. Kinbara, J. Opt. Soc. Am. 64, 1563 (1974).

T. Yamaguchi and A. Kinbara, Proc. 6th International Vacuum Congress, Jpn. J. Appl. Phys. Suppl. 2, Pt. 1, 677 (1974).

Yoshida, S.

T. Yamaguchi, S. Yoshida, and A. Kinbara, J. Opt. Soc. Am. 64, 1563 (1974).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 18, 63 (1973).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 13, 261 (1972).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 21, 173 (1974).

Other (15)

J. C. Maxwell-Garnett, Phil. Trans. R. Soc. A 203, 385 (1904).

E. David, Z. Phys. 114, 389 (1939).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 18, 63 (1973).

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 21, 173 (1974).

T. Yamaguchi and A. Kinbara, Proc. 6th International Vacuum Congress, Jpn. J. Appl. Phys. Suppl. 2, Pt. 1, 677 (1974).

The factors π2/24 and π2/12 are different from the previous paper (Refs. 7 and 8). In the calculation of the dipole-dipole interactions, the following type of summation appears:[equation],where rj is the distance to the jth interacting particle from the reference one placed at the origin. Here we calculated the summation by the crude assumption that 2πm particles are on a circle of radius ma, where a is the mean distance between particles and m the integer:[equation]In Ref. 7 the factor π2/12 is replaced by 0.716, which was computed numerically assuming that the island particles are distributed onto lattice points of a square array of lattice constant a, whereas in Ref. 8 it is replaced by unity, which was obtained by another crude assumption. These calculations are based on the static field dipole-dipole interactions. Although for a thicker film, retarded dipole-dipole interactions (Ref. 9) are needed, the static one is sufficient in a thinner film considered in the present paper.

T. Yamaguchi, S. Yoshida, and A. Kinbara, Thin Solid Films 13, 261 (1972).

S. Yamaguchi, J. Phys. Soc. Jpn. 15, 1577 (1960).

T. Yamaguchi, S. Yoshida, and A. Kinbara, J. Opt. Soc. Am. 64, 1563 (1974).

The optical anisotropy was directly observed by ellipsometric study of silver island films; T. Yamaguchi, S. Yoshida, and A. Kinbara, J. Opt. Soc. Am. 62, 634 (1972).

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), p. 61.

Reference 11, p. 670.

Reference 11, p. 81.

Reference 11, p. 753.

T. Yamaguchi and H. Takahashi, Surface Sci. (in press).

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