Abstract

An experimental arrangement is described for determining refractive indices of absorbing liquids and solids over a wide spectral range. Reflection and transmission measurements are carried out. Refractive indices of rhodamine 6G–methanol solutions around the S1 absorption band are presented.

© 1984 Optical Society of America

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References

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  1. H. Kessler, in Handbuch der Physik XVIII. Geometrische Optik, optische Konstante, optische Instrumente, H. Geiger, K. Scheel, Eds. (Springer, Berlin, 1927), p. 623.
  2. G. E. Fishter, in Applied Optics and Optical Engineering, Vol. 5, Part 1, R. Kingslake, Ed. (Academic, New York, 1967), p. 363.
  3. K. Schmid, A. Penzkofer, Appl. Opt. 22, 1824 (1983).
    [CrossRef] [PubMed]
  4. W. König, in Handbuch der Physik XX. Licht als Wellenbewegung, H. Geiger, K. Scheel, Eds. (Springer, Berlin, 1928), p. 242.
  5. R. W. Ditchburn, Light (Academic, London, 1976), p. 534.
  6. H. Gobrecht, in Bergmann-Schaefer Lehrbuch der Experimentalphysik, Band III Optik, H. Gobrecht, Ed. (Walter de Gruyter, Berlin, 1974), p. 265.
  7. R. H. Muller, Surf. Sci. 16, 14 (1969).
    [CrossRef]
  8. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  9. A. V. Sokolov, Optical Properties of Metals (American Elsevier, New York, 1967).
  10. F. Abelés, Phys. Thin Films 6, 151 (1971).
  11. F. Oswald, R. Schade, Z. Naturforsch. Teil A 9, 611 (1954).
  12. T. E. Denton, R. D. Campbell, S. G. Tomlin, J. Phys. D 5, 852 (1972).
    [CrossRef]
  13. J. R. Beattie, G. K. T. Conn, Philos. Mag. 46, 135 (1955).
  14. O. Hunderi, Appl. Opt. 11, 1572 (1972).
    [CrossRef] [PubMed]
  15. V. M. Bermudez, Surf. Sci. 94, 29 (1980).
    [CrossRef]
  16. R. M. A. Azzam, J. Opt. Soc. Am. 72, 1439 (1982).
    [CrossRef]
  17. R. Tousey, J. Opt. Soc. Am. 29, 235 (1939).
    [CrossRef]
  18. I. Simon, J. Opt. Soc. Am. 41, 336 (1951).
    [CrossRef]
  19. D. G. Avery, Proc. Phys. Soc. London Sect. B 65, 425 (1952).
    [CrossRef]
  20. N. Neuroth, Z. Phys. 144, 85 (1956).
    [CrossRef]
  21. S. P. F. Humpreys-Owen, Proc. Phys. Soc. London 77, 949 (1961).
    [CrossRef]
  22. T. Hirschfeld, Appl. Spectrosc. 24, 277 (1970).
    [CrossRef]
  23. D. M. Kolb, J. Opt. Soc. Am. 62, 599 (1972).
    [CrossRef]
  24. A. B. Buckman, N. M. Bashara, Phys. Rev. 174, 719 (1968).
    [CrossRef]
  25. C. L. Nagendra, G. K. M. Thutupalli, J. Phys. D 15, 1153 (1982).
    [CrossRef]
  26. J. C. Phillips, Solid State Phys. 18, 56 (1966).
  27. W. Leupacher, A. Penzkofer, to be submitted.
  28. M. Thalhammer, A. Penzkofer, Appl. Phys. B 32, 137 (1983).
    [CrossRef]
  29. M. R. Query, J. Opt. Soc. Am. 59, 876 (1969).
    [CrossRef]
  30. W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
    [CrossRef]
  31. H. B. Holl, J. Opt. Soc. Am. 57, 683 (1967).
    [CrossRef]
  32. H. E. Bennett, J. M. Bennett, Phys. Thin Films 4, 1 (1967).
  33. Landolt-Börnstein Tables, Optische Konstanten, K. H. Hellwege, A. M. Hellwege, Eds. (Springer, Berlin, 1962), Part 8, pp. 5–565.
  34. W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer, Berlin, 1981).

1983 (2)

K. Schmid, A. Penzkofer, Appl. Opt. 22, 1824 (1983).
[CrossRef] [PubMed]

M. Thalhammer, A. Penzkofer, Appl. Phys. B 32, 137 (1983).
[CrossRef]

1982 (2)

C. L. Nagendra, G. K. M. Thutupalli, J. Phys. D 15, 1153 (1982).
[CrossRef]

R. M. A. Azzam, J. Opt. Soc. Am. 72, 1439 (1982).
[CrossRef]

1980 (1)

V. M. Bermudez, Surf. Sci. 94, 29 (1980).
[CrossRef]

1972 (3)

1971 (1)

F. Abelés, Phys. Thin Films 6, 151 (1971).

1970 (1)

1969 (2)

1968 (1)

A. B. Buckman, N. M. Bashara, Phys. Rev. 174, 719 (1968).
[CrossRef]

1967 (2)

H. B. Holl, J. Opt. Soc. Am. 57, 683 (1967).
[CrossRef]

H. E. Bennett, J. M. Bennett, Phys. Thin Films 4, 1 (1967).

1966 (1)

J. C. Phillips, Solid State Phys. 18, 56 (1966).

1965 (1)

1961 (1)

S. P. F. Humpreys-Owen, Proc. Phys. Soc. London 77, 949 (1961).
[CrossRef]

1956 (1)

N. Neuroth, Z. Phys. 144, 85 (1956).
[CrossRef]

1955 (1)

J. R. Beattie, G. K. T. Conn, Philos. Mag. 46, 135 (1955).

1954 (1)

F. Oswald, R. Schade, Z. Naturforsch. Teil A 9, 611 (1954).

1952 (1)

D. G. Avery, Proc. Phys. Soc. London Sect. B 65, 425 (1952).
[CrossRef]

1951 (1)

1939 (1)

Abelés, F.

F. Abelés, Phys. Thin Films 6, 151 (1971).

Avery, D. G.

D. G. Avery, Proc. Phys. Soc. London Sect. B 65, 425 (1952).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, J. Opt. Soc. Am. 72, 1439 (1982).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bashara, N. M.

A. B. Buckman, N. M. Bashara, Phys. Rev. 174, 719 (1968).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Beattie, J. R.

J. R. Beattie, G. K. T. Conn, Philos. Mag. 46, 135 (1955).

Bennett, H. E.

H. E. Bennett, J. M. Bennett, Phys. Thin Films 4, 1 (1967).

Bennett, J. M.

H. E. Bennett, J. M. Bennett, Phys. Thin Films 4, 1 (1967).

Bermudez, V. M.

V. M. Bermudez, Surf. Sci. 94, 29 (1980).
[CrossRef]

Buckman, A. B.

A. B. Buckman, N. M. Bashara, Phys. Rev. 174, 719 (1968).
[CrossRef]

Campbell, R. D.

T. E. Denton, R. D. Campbell, S. G. Tomlin, J. Phys. D 5, 852 (1972).
[CrossRef]

Conn, G. K. T.

J. R. Beattie, G. K. T. Conn, Philos. Mag. 46, 135 (1955).

Demtröder, W.

W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer, Berlin, 1981).

Denton, T. E.

T. E. Denton, R. D. Campbell, S. G. Tomlin, J. Phys. D 5, 852 (1972).
[CrossRef]

Ditchburn, R. W.

R. W. Ditchburn, Light (Academic, London, 1976), p. 534.

Fishter, G. E.

G. E. Fishter, in Applied Optics and Optical Engineering, Vol. 5, Part 1, R. Kingslake, Ed. (Academic, New York, 1967), p. 363.

Gobrecht, H.

H. Gobrecht, in Bergmann-Schaefer Lehrbuch der Experimentalphysik, Band III Optik, H. Gobrecht, Ed. (Walter de Gruyter, Berlin, 1974), p. 265.

Hirschfeld, T.

Holl, H. B.

Humpreys-Owen, S. P. F.

S. P. F. Humpreys-Owen, Proc. Phys. Soc. London 77, 949 (1961).
[CrossRef]

Hunderi, O.

Hunter, W. R.

Kessler, H.

H. Kessler, in Handbuch der Physik XVIII. Geometrische Optik, optische Konstante, optische Instrumente, H. Geiger, K. Scheel, Eds. (Springer, Berlin, 1927), p. 623.

Kolb, D. M.

König, W.

W. König, in Handbuch der Physik XX. Licht als Wellenbewegung, H. Geiger, K. Scheel, Eds. (Springer, Berlin, 1928), p. 242.

Leupacher, W.

W. Leupacher, A. Penzkofer, to be submitted.

Muller, R. H.

R. H. Muller, Surf. Sci. 16, 14 (1969).
[CrossRef]

Nagendra, C. L.

C. L. Nagendra, G. K. M. Thutupalli, J. Phys. D 15, 1153 (1982).
[CrossRef]

Neuroth, N.

N. Neuroth, Z. Phys. 144, 85 (1956).
[CrossRef]

Oswald, F.

F. Oswald, R. Schade, Z. Naturforsch. Teil A 9, 611 (1954).

Penzkofer, A.

K. Schmid, A. Penzkofer, Appl. Opt. 22, 1824 (1983).
[CrossRef] [PubMed]

M. Thalhammer, A. Penzkofer, Appl. Phys. B 32, 137 (1983).
[CrossRef]

W. Leupacher, A. Penzkofer, to be submitted.

Phillips, J. C.

J. C. Phillips, Solid State Phys. 18, 56 (1966).

Query, M. R.

Schade, R.

F. Oswald, R. Schade, Z. Naturforsch. Teil A 9, 611 (1954).

Schmid, K.

Simon, I.

Sokolov, A. V.

A. V. Sokolov, Optical Properties of Metals (American Elsevier, New York, 1967).

Thalhammer, M.

M. Thalhammer, A. Penzkofer, Appl. Phys. B 32, 137 (1983).
[CrossRef]

Thutupalli, G. K. M.

C. L. Nagendra, G. K. M. Thutupalli, J. Phys. D 15, 1153 (1982).
[CrossRef]

Tomlin, S. G.

T. E. Denton, R. D. Campbell, S. G. Tomlin, J. Phys. D 5, 852 (1972).
[CrossRef]

Tousey, R.

Appl. Opt. (2)

Appl. Phys. B (1)

M. Thalhammer, A. Penzkofer, Appl. Phys. B 32, 137 (1983).
[CrossRef]

Appl. Spectrosc. (1)

J. Opt. Soc. Am. (7)

J. Phys. D (2)

T. E. Denton, R. D. Campbell, S. G. Tomlin, J. Phys. D 5, 852 (1972).
[CrossRef]

C. L. Nagendra, G. K. M. Thutupalli, J. Phys. D 15, 1153 (1982).
[CrossRef]

Philos. Mag. (1)

J. R. Beattie, G. K. T. Conn, Philos. Mag. 46, 135 (1955).

Phys. Rev. (1)

A. B. Buckman, N. M. Bashara, Phys. Rev. 174, 719 (1968).
[CrossRef]

Phys. Thin Films (2)

H. E. Bennett, J. M. Bennett, Phys. Thin Films 4, 1 (1967).

F. Abelés, Phys. Thin Films 6, 151 (1971).

Proc. Phys. Soc. London (1)

S. P. F. Humpreys-Owen, Proc. Phys. Soc. London 77, 949 (1961).
[CrossRef]

Proc. Phys. Soc. London Sect. B (1)

D. G. Avery, Proc. Phys. Soc. London Sect. B 65, 425 (1952).
[CrossRef]

Solid State Phys. (1)

J. C. Phillips, Solid State Phys. 18, 56 (1966).

Surf. Sci. (2)

V. M. Bermudez, Surf. Sci. 94, 29 (1980).
[CrossRef]

R. H. Muller, Surf. Sci. 16, 14 (1969).
[CrossRef]

Z. Naturforsch. Teil A (1)

F. Oswald, R. Schade, Z. Naturforsch. Teil A 9, 611 (1954).

Z. Phys. (1)

N. Neuroth, Z. Phys. 144, 85 (1956).
[CrossRef]

Other (10)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

A. V. Sokolov, Optical Properties of Metals (American Elsevier, New York, 1967).

H. Kessler, in Handbuch der Physik XVIII. Geometrische Optik, optische Konstante, optische Instrumente, H. Geiger, K. Scheel, Eds. (Springer, Berlin, 1927), p. 623.

G. E. Fishter, in Applied Optics and Optical Engineering, Vol. 5, Part 1, R. Kingslake, Ed. (Academic, New York, 1967), p. 363.

W. König, in Handbuch der Physik XX. Licht als Wellenbewegung, H. Geiger, K. Scheel, Eds. (Springer, Berlin, 1928), p. 242.

R. W. Ditchburn, Light (Academic, London, 1976), p. 534.

H. Gobrecht, in Bergmann-Schaefer Lehrbuch der Experimentalphysik, Band III Optik, H. Gobrecht, Ed. (Walter de Gruyter, Berlin, 1974), p. 265.

Landolt-Börnstein Tables, Optische Konstanten, K. H. Hellwege, A. M. Hellwege, Eds. (Springer, Berlin, 1962), Part 8, pp. 5–565.

W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer, Berlin, 1981).

W. Leupacher, A. Penzkofer, to be submitted.

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Figures (6)

Fig. 1
Fig. 1

Reflection and refraction at a plane interface.

Fig. 2
Fig. 2

Reflectance curves for perpendicular (R), parallel (R||), and unpolarized (Ru) incident light. The selected optical constants are (i) n = 1.5 and k = 0 (solid curves), (ii) n = 1.5 and k = 1 (dashed curves), and (iii) n = 2.42 and k = 0 (dash–dot curves).

Fig. 3
Fig. 3

Dependence of refractive index n on reflectance R for various extinction coefficients k. Angle of incidence is φ = 0°.

Fig. 4
Fig. 4

Analysis of the sensitivity of refractive-index determination of reflectance measurement: solid curves, (dn/n)/(dR/R) vs R; dashed curves, difference of refractive indices |n(0) − n(k)| vs R. Curves are valid for angle of incidence φ = 0 and for both branches of the n(R) curves of Fig. 3.

Fig. 5
Fig. 5

Experimental setup: L, lamp; M, light collecting mirror; S1 and S2, slits (widths S1: 0.1 mm, S2: 0.5 mm); A, aperture (opening ~1 cm); L1–L4, lenses (focal lengths L1: 1.33 m, L2: 15 cm, L3: 1 m, L4: 5 cm); BS, beam splitter; F, filters; LG, fiber-optic light-guide; P1–P4, 90° deflection prisms; S, sample; SP, 30-cm spectrometer (grating with 1200 lines/mm); DA, silicon diode array (Tracor DARRS).

Fig. 6
Fig. 6

Refractive indices and extinction coefficients vs wavelength. Temperature 20.2°C. Solid curves, dispersion of refractive indices, (1) 0.1-M rhodamine 6G in methanol, (2) 0.01-M rhodamine 6G in methanol, (3) methanol. Dash–dot curve, dispersion of water (reference). Dashed curve, extinction coefficient of 0.01-M rhodamine 6G in methanol.

Equations (9)

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E r E i = cos φ - n μ cos χ cos φ + n μ cos χ = cos φ - μ ( n 2 - sin 2 φ ) 1 / 2 cos φ + μ ( n 2 - sin 2 φ ) 1 / 2 ,
E r | | E i | | = n μ cos φ - cos χ n μ cos φ - cos χ = n 2 μ cos φ - ( n 2 - sin 2 φ ) 1 / 2 n 2 μ cos φ + ( n 2 - sin 2 φ ) 1 / 2 .
sin φ = n sin χ ,
R = cos 2 φ + μ 2 A - 2 μ A 1 / 2 cos φ cos B cos 2 φ + μ 2 A + 2 μ A 1 / 2 cos φ cos B ,
R | | = μ 2 ( C 2 + D 2 ) cos 2 φ + A - 2 μ A 1 / 2 cos φ ( C cos B + D sin B ) μ 2 ( C 2 + D 2 ) cos 2 φ + A + 2 μ A 1 / 2 cos φ ( C cos B + D sin B ) ,
R u = 1 2 ( R + R | | ) .
R = R | | = R = R u = | 1 - μ n 1 + μ n | 2 = ( 1 - μ n ) 2 + μ 2 k 2 ( 1 + μ n ) 2 + μ 2 k 2 ,
n = 1 μ { 1 + R 1 - R ± [ ( 1 + R 1 - R ) 2 - 1 - μ 2 k 2 ] 1 / 2 } .
R u ( λ ) = R u , ref ( λ ) S ( λ ) S ref ( λ ) .

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