Abstract

With spectroscopic ellipsometry one can measure the real and imaginary parts of the refractive index of a medium simultaneously. To determine this index in the infrared for a number of technical liquids, use was made of attenuated total internal reflection at the glass–liquid interface of a specially designed prism. This attenuated total reflection approach warrants minimal signal loss and is, for strongly absorbing liquids, the only way to measure the complex refractive index. A surprising phenomenon, observed when BK-7 prism glass was used, is scattering in the vicinity of the absorption wavelengths of the glass. A simple model that can be used to describe the relations among absorption, scattering, and depolarization was successfully used to correct the measurements. Refractive indices for demineralized water, Freon 113, heptane, benzene, gas oil, and crude oil in the wave number range from 5000 to 10,000 cm−1 (1–2 μm) are presented.

© 1995 Optical Society of America

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References

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  1. E. E. Jelley, in Physical Methods of Organic Chemistry, A. Weissberger, ed. (Interscience, New York, 1960), Part 2, Chap. 21, p. 1458.
  2. W. L. Wolfe, “Properties of optical materials,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 7, p. 7-2.
  3. W. Nebe, “Routine- und Präzisionsmessungen an Flüs-sigkeiten und Gläsern,” Mess. Steuern Regeln 9, 177–179 (1971); Mess. Steuern Regeln 11, 216–220 (1971).
  4. Ph. Marteau, G. Montixi, J. Obriot, T. K. Bose, J. M. St Arnaud, “Simple method for the accurate determination of the refractive index of liquids in the infrared,” in Infrared Technology XVI, I. J. Spiro, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1341, 275–278 (1990).
  5. T. Li, X. Tan, “Stepwise interferometric method of measuring the refractive index of liquid samples,” Appl. Opt. 32, 2274–2277 (1993).
    [Crossref] [PubMed]
  6. E. Moreels, C. de Greef, R. Finsy, “Laser light refractometer,” Appl. Opt. 23, 3010–3013 (1984).
    [Crossref] [PubMed]
  7. M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).
  8. M. A. Havstad, W. McLean, S. A. Self, “Measurement of the thermal radiative properties of liquid uranium,” in Developments in Radiative Heat Transfer, S. T. Thynell, ed., HTD Vol. 203 (American Society of Mechanical Engineers, New York, 1992), pp. 9–17.
  9. M. Brückner, J. H. Schäfer, C. Schiffer, J. Uhlenbusch, “Measurement of the optical constants of solid and molten gold and tin at λ = 10.6 μm,” J. Appl. Phys. 70, 1642–1647 (1991).
    [Crossref]
  10. N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967), p. 13.
  11. J. H. W. G. den Boer, G. M. W. Kroesen, M. Haverlag, F. J. de Hoog, “Spectroscopic IR ellipsometry with imperfect components,” Thin Solid Films 234, 323–326 (1993).
    [Crossref]
  12. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979), p. 274.
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 48.
  14. A. T. M. Wilbers, G. M. W. Kroesen, C. J. Timmermans, D. C. Schram, “Characteristic quantities of a cascade arc used as a light source for spectroscopic techniques,” Meas. Sci. Technol. 1, 1326–1332 (1990).
    [Crossref]
  15. Ref. 13, p. 97.
  16. A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990), p. 58.
  17. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 278.

1993 (2)

T. Li, X. Tan, “Stepwise interferometric method of measuring the refractive index of liquid samples,” Appl. Opt. 32, 2274–2277 (1993).
[Crossref] [PubMed]

J. H. W. G. den Boer, G. M. W. Kroesen, M. Haverlag, F. J. de Hoog, “Spectroscopic IR ellipsometry with imperfect components,” Thin Solid Films 234, 323–326 (1993).
[Crossref]

1991 (1)

M. Brückner, J. H. Schäfer, C. Schiffer, J. Uhlenbusch, “Measurement of the optical constants of solid and molten gold and tin at λ = 10.6 μm,” J. Appl. Phys. 70, 1642–1647 (1991).
[Crossref]

1990 (1)

A. T. M. Wilbers, G. M. W. Kroesen, C. J. Timmermans, D. C. Schram, “Characteristic quantities of a cascade arc used as a light source for spectroscopic techniques,” Meas. Sci. Technol. 1, 1326–1332 (1990).
[Crossref]

1984 (1)

1983 (1)

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).

1971 (1)

W. Nebe, “Routine- und Präzisionsmessungen an Flüs-sigkeiten und Gläsern,” Mess. Steuern Regeln 9, 177–179 (1971); Mess. Steuern Regeln 11, 216–220 (1971).

Arnaud, J. M. St

Ph. Marteau, G. Montixi, J. Obriot, T. K. Bose, J. M. St Arnaud, “Simple method for the accurate determination of the refractive index of liquids in the infrared,” in Infrared Technology XVI, I. J. Spiro, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1341, 275–278 (1990).

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979), p. 274.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979), p. 274.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 48.

Bose, T. K.

Ph. Marteau, G. Montixi, J. Obriot, T. K. Bose, J. M. St Arnaud, “Simple method for the accurate determination of the refractive index of liquids in the infrared,” in Infrared Technology XVI, I. J. Spiro, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1341, 275–278 (1990).

Brückner, M.

M. Brückner, J. H. Schäfer, C. Schiffer, J. Uhlenbusch, “Measurement of the optical constants of solid and molten gold and tin at λ = 10.6 μm,” J. Appl. Phys. 70, 1642–1647 (1991).
[Crossref]

de Greef, C.

de Hoog, F. J.

J. H. W. G. den Boer, G. M. W. Kroesen, M. Haverlag, F. J. de Hoog, “Spectroscopic IR ellipsometry with imperfect components,” Thin Solid Films 234, 323–326 (1993).
[Crossref]

den Boer, J. H. W. G.

J. H. W. G. den Boer, G. M. W. Kroesen, M. Haverlag, F. J. de Hoog, “Spectroscopic IR ellipsometry with imperfect components,” Thin Solid Films 234, 323–326 (1993).
[Crossref]

Finsy, R.

Harrick, N. J.

N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967), p. 13.

Haverlag, M.

J. H. W. G. den Boer, G. M. W. Kroesen, M. Haverlag, F. J. de Hoog, “Spectroscopic IR ellipsometry with imperfect components,” Thin Solid Films 234, 323–326 (1993).
[Crossref]

Havstad, M. A.

M. A. Havstad, W. McLean, S. A. Self, “Measurement of the thermal radiative properties of liquid uranium,” in Developments in Radiative Heat Transfer, S. T. Thynell, ed., HTD Vol. 203 (American Society of Mechanical Engineers, New York, 1992), pp. 9–17.

Jelley, E. E.

E. E. Jelley, in Physical Methods of Organic Chemistry, A. Weissberger, ed. (Interscience, New York, 1960), Part 2, Chap. 21, p. 1458.

Kroesen, G. M. W.

J. H. W. G. den Boer, G. M. W. Kroesen, M. Haverlag, F. J. de Hoog, “Spectroscopic IR ellipsometry with imperfect components,” Thin Solid Films 234, 323–326 (1993).
[Crossref]

A. T. M. Wilbers, G. M. W. Kroesen, C. J. Timmermans, D. C. Schram, “Characteristic quantities of a cascade arc used as a light source for spectroscopic techniques,” Meas. Sci. Technol. 1, 1326–1332 (1990).
[Crossref]

Li, T.

Marteau, Ph.

Ph. Marteau, G. Montixi, J. Obriot, T. K. Bose, J. M. St Arnaud, “Simple method for the accurate determination of the refractive index of liquids in the infrared,” in Infrared Technology XVI, I. J. Spiro, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1341, 275–278 (1990).

McLean, W.

M. A. Havstad, W. McLean, S. A. Self, “Measurement of the thermal radiative properties of liquid uranium,” in Developments in Radiative Heat Transfer, S. T. Thynell, ed., HTD Vol. 203 (American Society of Mechanical Engineers, New York, 1992), pp. 9–17.

Montixi, G.

Ph. Marteau, G. Montixi, J. Obriot, T. K. Bose, J. M. St Arnaud, “Simple method for the accurate determination of the refractive index of liquids in the infrared,” in Infrared Technology XVI, I. J. Spiro, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1341, 275–278 (1990).

Moreels, E.

Murty, M. V. R. K.

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).

Nebe, W.

W. Nebe, “Routine- und Präzisionsmessungen an Flüs-sigkeiten und Gläsern,” Mess. Steuern Regeln 9, 177–179 (1971); Mess. Steuern Regeln 11, 216–220 (1971).

Obriot, J.

Ph. Marteau, G. Montixi, J. Obriot, T. K. Bose, J. M. St Arnaud, “Simple method for the accurate determination of the refractive index of liquids in the infrared,” in Infrared Technology XVI, I. J. Spiro, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1341, 275–278 (1990).

Röseler, A.

A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990), p. 58.

Schäfer, J. H.

M. Brückner, J. H. Schäfer, C. Schiffer, J. Uhlenbusch, “Measurement of the optical constants of solid and molten gold and tin at λ = 10.6 μm,” J. Appl. Phys. 70, 1642–1647 (1991).
[Crossref]

Schiffer, C.

M. Brückner, J. H. Schäfer, C. Schiffer, J. Uhlenbusch, “Measurement of the optical constants of solid and molten gold and tin at λ = 10.6 μm,” J. Appl. Phys. 70, 1642–1647 (1991).
[Crossref]

Schram, D. C.

A. T. M. Wilbers, G. M. W. Kroesen, C. J. Timmermans, D. C. Schram, “Characteristic quantities of a cascade arc used as a light source for spectroscopic techniques,” Meas. Sci. Technol. 1, 1326–1332 (1990).
[Crossref]

Self, S. A.

M. A. Havstad, W. McLean, S. A. Self, “Measurement of the thermal radiative properties of liquid uranium,” in Developments in Radiative Heat Transfer, S. T. Thynell, ed., HTD Vol. 203 (American Society of Mechanical Engineers, New York, 1992), pp. 9–17.

Shukla, R. P.

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).

Tan, X.

Timmermans, C. J.

A. T. M. Wilbers, G. M. W. Kroesen, C. J. Timmermans, D. C. Schram, “Characteristic quantities of a cascade arc used as a light source for spectroscopic techniques,” Meas. Sci. Technol. 1, 1326–1332 (1990).
[Crossref]

Uhlenbusch, J.

M. Brückner, J. H. Schäfer, C. Schiffer, J. Uhlenbusch, “Measurement of the optical constants of solid and molten gold and tin at λ = 10.6 μm,” J. Appl. Phys. 70, 1642–1647 (1991).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 278.

Wilbers, A. T. M.

A. T. M. Wilbers, G. M. W. Kroesen, C. J. Timmermans, D. C. Schram, “Characteristic quantities of a cascade arc used as a light source for spectroscopic techniques,” Meas. Sci. Technol. 1, 1326–1332 (1990).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 48.

Wolfe, W. L.

W. L. Wolfe, “Properties of optical materials,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 7, p. 7-2.

Appl. Opt. (2)

J. Appl. Phys. (1)

M. Brückner, J. H. Schäfer, C. Schiffer, J. Uhlenbusch, “Measurement of the optical constants of solid and molten gold and tin at λ = 10.6 μm,” J. Appl. Phys. 70, 1642–1647 (1991).
[Crossref]

Meas. Sci. Technol. (1)

A. T. M. Wilbers, G. M. W. Kroesen, C. J. Timmermans, D. C. Schram, “Characteristic quantities of a cascade arc used as a light source for spectroscopic techniques,” Meas. Sci. Technol. 1, 1326–1332 (1990).
[Crossref]

Mess. Steuern Regeln (1)

W. Nebe, “Routine- und Präzisionsmessungen an Flüs-sigkeiten und Gläsern,” Mess. Steuern Regeln 9, 177–179 (1971); Mess. Steuern Regeln 11, 216–220 (1971).

Opt. Eng. (1)

M. V. R. K. Murty, R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).

Thin Solid Films (1)

J. H. W. G. den Boer, G. M. W. Kroesen, M. Haverlag, F. J. de Hoog, “Spectroscopic IR ellipsometry with imperfect components,” Thin Solid Films 234, 323–326 (1993).
[Crossref]

Other (10)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979), p. 274.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 48.

N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967), p. 13.

Ref. 13, p. 97.

A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990), p. 58.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 278.

M. A. Havstad, W. McLean, S. A. Self, “Measurement of the thermal radiative properties of liquid uranium,” in Developments in Radiative Heat Transfer, S. T. Thynell, ed., HTD Vol. 203 (American Society of Mechanical Engineers, New York, 1992), pp. 9–17.

Ph. Marteau, G. Montixi, J. Obriot, T. K. Bose, J. M. St Arnaud, “Simple method for the accurate determination of the refractive index of liquids in the infrared,” in Infrared Technology XVI, I. J. Spiro, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1341, 275–278 (1990).

E. E. Jelley, in Physical Methods of Organic Chemistry, A. Weissberger, ed. (Interscience, New York, 1960), Part 2, Chap. 21, p. 1458.

W. L. Wolfe, “Properties of optical materials,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), Chap. 7, p. 7-2.

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Figures (11)

Fig. 1
Fig. 1

BK-7 prism, the light is incident through the left side, reflects at the fluid–glass interface at the bottom, and leaves the prism through the right side. A small difference in angle between the left and the right sides prevents multiple reflections in the prism.

Fig. 2
Fig. 2

Spectroscopic ellipsometer setup with 1, cascaded arc light source; 2, Bruker IFS66 spectrometer; 3, Rochon prism polarizer; 4, diaphragm; 5, sample holder and prism; 6, Rochon prism polarizer; 7, diaphragm; 8, imaging lens; 9, HgCdTe detector.

Fig. 3
Fig. 3

Fourier coefficient b versus wave number calculated from a measurement with air behind the prism. Note the sudden drop in value in the vicinity of σ = 5000 cm−1.

Fig. 4
Fig. 4

Logarithm of Fourier coefficient b and matching fit of Lorentz profiles plotted versus wave number. Note the structure that relates to Lorentz profiles centered at 4024, 4158, 4296, 4454, 4719, and 4897 cm−1. The Fourier coefficient was obtained by a measurement with air behind the prism. The value of 0.8662 is the average value of the Fourier coefficient in an undisturbed range of the spectrum from 5000 to 6000 cm−1.

Fig. 5
Fig. 5

Fourier coefficient b versus wave number before (b*) and after (b) correction for depolarization. Since the ellipsometer was not well calibrated during this experiment, the absolute values are too low. Translating these results to the refractive index of air would give n values slightly below 1. This does not, however, affect the polarization degree.

Fig. 6
Fig. 6

Real and imaginary parts of the refractive index of demineralized water plotted versus wave number. The structure in the imaginary part is in agreement with absorption measurements of water.

Fig. 7
Fig. 7

Real and imaginary parts of the refractive index of heptane [CH3(CH2)5CH3] plotted versus wave number.

Fig. 8
Fig. 8

Real and imaginary parts of the refractive index of Freon 113 plotted versus wave number.

Fig. 9
Fig. 9

Real part of the refractive index of gas oil plotted versus wave number.

Fig. 10
Fig. 10

Real part of the refractive index of benzene (C6H6) plotted versus wave number.

Fig. 11
Fig. 11

Real part of the refractive index of crude oil (Eider ’89) plotted versus wave number.

Equations (17)

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I = g ( 1 + a cos 2 A + b sin 2 A ) ,
cos 2 Ψ = - a ,             cos Δ = b / 1 - a 2 .
r p = n 1 cos θ 0 - n 0 cos θ 1 n 1 cos θ 0 + n 0 cos θ 1 , r s = n 0 cos θ 0 - n 1 cos θ 1 n 0 cos θ 0 + n 1 cos θ 1 ,
ρ tan Ψ exp i Δ r p / r s .
n 0 sin θ 0 = n 1 sin θ 1
n 1 = n 0 sin θ 0 [ 1 + ( 1 - ρ 1 + ρ ) 2 tan 2 θ 0 ] 1 / 2 .
tan Δ 2 = - cos θ 0 [ sin 2 θ 0 - ( n 1 n 0 ) 2 ] 1 / 2 sin 2 θ 0 .
tan Ψ = ± sin 2 θ 0 - cos θ 0 [ ( n 1 n 0 ) 2 - sin 2 θ 0 ] 1 / 2 sin 2 θ 0 + cos θ 0 [ ( n 1 n 0 ) 2 - sin 2 θ 0 ] 1 / 2 ,
{ + : Δ = 0 ° arctan ( n 1 / n 0 ) θ 0 < arcsin ( n 1 / n 0 ) , - : Δ = 180 ° θ 0 < arctan ( n 1 / n 0 ) .
t p = 2 n 0 n 1 cos θ 0 + n 0 cos θ 1 , t s = 2 n 0 n 0 cos θ 0 + n 1 cos θ 1 .
tan Ψ t t p t s = n 0 n 1 cos θ 0 + n 1 ( n 1 2 - n 0 2 sin 2 θ 0 ) 1 / 2 n 1 2 cos θ 0 + n 0 ( n 1 2 - n 0 2 sin 2 θ 0 ) 1 / 2 .
tan Ψ eff = tan Ψ tan Ψ t .
a * = P a = - P cos 2 Ψ , b * = P 2 b = P 2 cos Δ sin 2 Ψ .
Q = 2 π r ξ σ k .
P = exp ( - Q ) .
k ( σ ) = i = 1 6 k i a i 2 + ( σ - σ i ) 2 .
P = exp [ - 2 π r ξ i = 1 6 k i σ a i 2 + ( σ - σ i ) 2 ] .

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