Abstract

An experimental arrangement is described for determination of refractive indices n and extinction coefficients k of strongly absorbing liquids and solids over a wide spectral region. The reflectivity of parallel polarized light vs angle of incidence is measured, and the optical constants are calculated from the minimum parallel reflectivity and the corresponding Brewster angle. The accuracy of n and k determination is analyzed. The refractive indices and extinction coefficients of 0.4-M rhodamine 6G in methanol are presented around the S1 absorption band.

© 1986 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Kessler, “Optische Konstanten,” in Handbuch der Physik, Vol. 18: Geometrische Optik, optische Konstante, optische Instrumente, H. Geiger, K. Scheel, Eds. (Springer-Verlag, Berlin, 1927), p. 623.
  2. G. E. Fishter, “Refractometry,” in Applied Optics and Optical Engineering, Vol. 5, Part 1, R. Kingslake, Ed. (Academic, New York, 1967), p. 363.
  3. K. Schmid, A. Penzkofer, “Refractive-Index Measurements with a Pellin-Broca Prism Apparatus,” Appl. Opt. 22, 1824 (1983).
    [CrossRef] [PubMed]
  4. L. G. Schulz, F. R. Tangherlini, “Optical Constants of Silver, Gold, Copper, and Aluminum. II. The Index of Refraction n,” J. Opt. Soc. Am 44, 362 (1954).
    [CrossRef]
  5. F. Oswald, R. Schade, “Über die Bestimmung der Optixhen Konslanten von Hulbleitern des Typus AIII-BV im Infraroten,” Z. Naturforsch. Teil A 9, 611 (1954).
  6. L. I. Alperovich, “Use of Layers of Uneven Thickness for Measuring Optical Constants of Liquids in the Region of Strong Absorption,” Opt. Spectrosc. 15, 181 (1963).
  7. E. Denton, R. D. Campbell, S. G. Tomlin, “The Determination of the Optical Constants of Thin Films from Measurements of Reflectance and Transmittance at Normal Incidence,” J. Phys. D 5, 852 (1972).
    [CrossRef]
  8. W. Leupacher, A. Penzkofer, “Refractive-Index Measurement of Absorbing Condensed Media,” Appl. Opt. 23, 1554 (1984).
    [CrossRef] [PubMed]
  9. S. P. F. Humphreys-Owen, “Comparison of Reflection Methods for Measuring Optical Constants without Polarimetric Analysis, and Proposal for New Methods Based on the Brewster Angle,” Proc. Phys. Soc. London 77, 949 (1961).
    [CrossRef]
  10. I. Simon, “Spectroscopy in Infrared by Reflection and Its Use for Highly Absorbing Substances,” J. Opt. Soc. Am. 41, 336 (1951).
    [CrossRef]
  11. M. R. Philpott, “Optial Reflection Spectroscopy of Organic Solids,” Ann. Rev. Phys. Chem. 31, 97 (1980).
    [CrossRef]
  12. L. K. Chopra, Thin Film Phenomena (McGraw-Hill, New York, 1969), Chap. 11.
  13. J. R. Beattie, G. K. T. Conn, “Optical Constants of Metals in the Infra-Red—Principles of Measurement,” Philos. Mag. 46, 222 (1955).
  14. R. M. A. Azzam, “Explicit Determination of the Complex Refractive Index of an Absorbing Medium from Reflectance Measurements at and near Normal Incidence,” J. Opt. Soc. Am. 72, 1439 (1982).
    [CrossRef]
  15. R. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).
  16. J. F. McChelland, “Photoacoustic Spectroscopy,” Anal. Chem. 55, 89A (1983).
  17. J. B. Kinney, R. H. Staley, “Applications of Photoacoustic Spectroscopy,” Ann. Rev. Mater. Sci. 12, 295 (1982).
    [CrossRef]
  18. W. König, “Electromagnetische Lichttheone,” in Handbuch der Physik, Vol. 20: Licht als Wellenbewegung, H. Geiger, K. Scheel, Eds. (Springer-Verlag, Berlin, 1928), p. 242.
  19. H. Gobrecht, “Dispersion und Absorption des Lichtes,”in Bergmann-Schaefer, Lehrbuch der Experimentalphysik, Band III: Optik, H. Gobrecht, Ed. (Walter de Gruyter, Berlin, 1974), p. 265.
  20. R. W. Ditchburn, Light (Academic, London, 1976).
  21. W. W. Wendlandt, H. C. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).
  22. J. Fahrenfort, “Attenuated Total Reflection. A New Principle for the Production of Useful Infra-Red Reflection Spectra of Organic Compounds,” Spectrochim. Acta 17, 698 (1961).
    [CrossRef]
  23. N. J. Harrick, “Study of Physics and Chemistry of Surfaces from Frustrated Total Internal Reflections, ” Phys. Rev. Lett. 4, 224 (1960).
    [CrossRef]
  24. J. Fahrenfort, W. M. Visser, “On the Determination of Optical Constants in the Infrared by Attenuated Total Reflection,” Spectrochim. Acta 18, 1103 (1962).
  25. N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967).
  26. E. G. Baranova, “Study of the Association of Rhodamine 3G in Ethanol and Glycerol Solutions,” Opt. Spectrosc. 13, 452 (1962).
  27. J. E. Selwyn, J. L. Steinfeld, “Aggregation Equilibria of Xanthene Dyes,” J. Phys. Chem. 76, 762 (1972).
    [CrossRef]

1984 (1)

1983 (2)

1982 (2)

1980 (1)

M. R. Philpott, “Optial Reflection Spectroscopy of Organic Solids,” Ann. Rev. Phys. Chem. 31, 97 (1980).
[CrossRef]

1972 (2)

J. E. Selwyn, J. L. Steinfeld, “Aggregation Equilibria of Xanthene Dyes,” J. Phys. Chem. 76, 762 (1972).
[CrossRef]

E. Denton, R. D. Campbell, S. G. Tomlin, “The Determination of the Optical Constants of Thin Films from Measurements of Reflectance and Transmittance at Normal Incidence,” J. Phys. D 5, 852 (1972).
[CrossRef]

1963 (1)

L. I. Alperovich, “Use of Layers of Uneven Thickness for Measuring Optical Constants of Liquids in the Region of Strong Absorption,” Opt. Spectrosc. 15, 181 (1963).

1962 (2)

J. Fahrenfort, W. M. Visser, “On the Determination of Optical Constants in the Infrared by Attenuated Total Reflection,” Spectrochim. Acta 18, 1103 (1962).

E. G. Baranova, “Study of the Association of Rhodamine 3G in Ethanol and Glycerol Solutions,” Opt. Spectrosc. 13, 452 (1962).

1961 (2)

S. P. F. Humphreys-Owen, “Comparison of Reflection Methods for Measuring Optical Constants without Polarimetric Analysis, and Proposal for New Methods Based on the Brewster Angle,” Proc. Phys. Soc. London 77, 949 (1961).
[CrossRef]

J. Fahrenfort, “Attenuated Total Reflection. A New Principle for the Production of Useful Infra-Red Reflection Spectra of Organic Compounds,” Spectrochim. Acta 17, 698 (1961).
[CrossRef]

1960 (1)

N. J. Harrick, “Study of Physics and Chemistry of Surfaces from Frustrated Total Internal Reflections, ” Phys. Rev. Lett. 4, 224 (1960).
[CrossRef]

1955 (1)

J. R. Beattie, G. K. T. Conn, “Optical Constants of Metals in the Infra-Red—Principles of Measurement,” Philos. Mag. 46, 222 (1955).

1954 (2)

L. G. Schulz, F. R. Tangherlini, “Optical Constants of Silver, Gold, Copper, and Aluminum. II. The Index of Refraction n,” J. Opt. Soc. Am 44, 362 (1954).
[CrossRef]

F. Oswald, R. Schade, “Über die Bestimmung der Optixhen Konslanten von Hulbleitern des Typus AIII-BV im Infraroten,” Z. Naturforsch. Teil A 9, 611 (1954).

1951 (1)

Alperovich, L. I.

L. I. Alperovich, “Use of Layers of Uneven Thickness for Measuring Optical Constants of Liquids in the Region of Strong Absorption,” Opt. Spectrosc. 15, 181 (1963).

Azzam, R. M. A.

Baranova, E. G.

E. G. Baranova, “Study of the Association of Rhodamine 3G in Ethanol and Glycerol Solutions,” Opt. Spectrosc. 13, 452 (1962).

Beattie, J. R.

J. R. Beattie, G. K. T. Conn, “Optical Constants of Metals in the Infra-Red—Principles of Measurement,” Philos. Mag. 46, 222 (1955).

Campbell, R. D.

E. Denton, R. D. Campbell, S. G. Tomlin, “The Determination of the Optical Constants of Thin Films from Measurements of Reflectance and Transmittance at Normal Incidence,” J. Phys. D 5, 852 (1972).
[CrossRef]

Chopra, L. K.

L. K. Chopra, Thin Film Phenomena (McGraw-Hill, New York, 1969), Chap. 11.

Conn, G. K. T.

J. R. Beattie, G. K. T. Conn, “Optical Constants of Metals in the Infra-Red—Principles of Measurement,” Philos. Mag. 46, 222 (1955).

Denton, E.

E. Denton, R. D. Campbell, S. G. Tomlin, “The Determination of the Optical Constants of Thin Films from Measurements of Reflectance and Transmittance at Normal Incidence,” J. Phys. D 5, 852 (1972).
[CrossRef]

Ditchburn, R. W.

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

Fahrenfort, J.

J. Fahrenfort, W. M. Visser, “On the Determination of Optical Constants in the Infrared by Attenuated Total Reflection,” Spectrochim. Acta 18, 1103 (1962).

J. Fahrenfort, “Attenuated Total Reflection. A New Principle for the Production of Useful Infra-Red Reflection Spectra of Organic Compounds,” Spectrochim. Acta 17, 698 (1961).
[CrossRef]

Fishter, G. E.

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

Gobrecht, H.

H. Gobrecht, “Dispersion und Absorption des Lichtes,”in Bergmann-Schaefer, Lehrbuch der Experimentalphysik, Band III: Optik, H. Gobrecht, Ed. (Walter de Gruyter, Berlin, 1974), p. 265.

Harrick, N. J.

N. J. Harrick, “Study of Physics and Chemistry of Surfaces from Frustrated Total Internal Reflections, ” Phys. Rev. Lett. 4, 224 (1960).
[CrossRef]

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

Hecht, H. C.

W. W. Wendlandt, H. C. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).

Humphreys-Owen, S. P. F.

S. P. F. Humphreys-Owen, “Comparison of Reflection Methods for Measuring Optical Constants without Polarimetric Analysis, and Proposal for New Methods Based on the Brewster Angle,” Proc. Phys. Soc. London 77, 949 (1961).
[CrossRef]

Kessler, H.

H. Kessler, “Optische Konstanten,” in Handbuch der Physik, Vol. 18: Geometrische Optik, optische Konstante, optische Instrumente, H. Geiger, K. Scheel, Eds. (Springer-Verlag, Berlin, 1927), p. 623.

Kinney, J. B.

J. B. Kinney, R. H. Staley, “Applications of Photoacoustic Spectroscopy,” Ann. Rev. Mater. Sci. 12, 295 (1982).
[CrossRef]

König, W.

W. König, “Electromagnetische Lichttheone,” in Handbuch der Physik, Vol. 20: Licht als Wellenbewegung, H. Geiger, K. Scheel, Eds. (Springer-Verlag, Berlin, 1928), p. 242.

Leupacher, W.

McChelland, J. F.

J. F. McChelland, “Photoacoustic Spectroscopy,” Anal. Chem. 55, 89A (1983).

Oswald, F.

F. Oswald, R. Schade, “Über die Bestimmung der Optixhen Konslanten von Hulbleitern des Typus AIII-BV im Infraroten,” Z. Naturforsch. Teil A 9, 611 (1954).

Penzkofer, A.

Philpott, M. R.

M. R. Philpott, “Optial Reflection Spectroscopy of Organic Solids,” Ann. Rev. Phys. Chem. 31, 97 (1980).
[CrossRef]

Rosencwaig, R.

R. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).

Schade, R.

F. Oswald, R. Schade, “Über die Bestimmung der Optixhen Konslanten von Hulbleitern des Typus AIII-BV im Infraroten,” Z. Naturforsch. Teil A 9, 611 (1954).

Schmid, K.

Schulz, L. G.

L. G. Schulz, F. R. Tangherlini, “Optical Constants of Silver, Gold, Copper, and Aluminum. II. The Index of Refraction n,” J. Opt. Soc. Am 44, 362 (1954).
[CrossRef]

Selwyn, J. E.

J. E. Selwyn, J. L. Steinfeld, “Aggregation Equilibria of Xanthene Dyes,” J. Phys. Chem. 76, 762 (1972).
[CrossRef]

Simon, I.

Staley, R. H.

J. B. Kinney, R. H. Staley, “Applications of Photoacoustic Spectroscopy,” Ann. Rev. Mater. Sci. 12, 295 (1982).
[CrossRef]

Steinfeld, J. L.

J. E. Selwyn, J. L. Steinfeld, “Aggregation Equilibria of Xanthene Dyes,” J. Phys. Chem. 76, 762 (1972).
[CrossRef]

Tangherlini, F. R.

L. G. Schulz, F. R. Tangherlini, “Optical Constants of Silver, Gold, Copper, and Aluminum. II. The Index of Refraction n,” J. Opt. Soc. Am 44, 362 (1954).
[CrossRef]

Tomlin, S. G.

E. Denton, R. D. Campbell, S. G. Tomlin, “The Determination of the Optical Constants of Thin Films from Measurements of Reflectance and Transmittance at Normal Incidence,” J. Phys. D 5, 852 (1972).
[CrossRef]

Visser, W. M.

J. Fahrenfort, W. M. Visser, “On the Determination of Optical Constants in the Infrared by Attenuated Total Reflection,” Spectrochim. Acta 18, 1103 (1962).

Wendlandt, W. W.

W. W. Wendlandt, H. C. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).

Anal. Chem. (1)

J. F. McChelland, “Photoacoustic Spectroscopy,” Anal. Chem. 55, 89A (1983).

Ann. Rev. Mater. Sci. (1)

J. B. Kinney, R. H. Staley, “Applications of Photoacoustic Spectroscopy,” Ann. Rev. Mater. Sci. 12, 295 (1982).
[CrossRef]

Ann. Rev. Phys. Chem. (1)

M. R. Philpott, “Optial Reflection Spectroscopy of Organic Solids,” Ann. Rev. Phys. Chem. 31, 97 (1980).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am (1)

L. G. Schulz, F. R. Tangherlini, “Optical Constants of Silver, Gold, Copper, and Aluminum. II. The Index of Refraction n,” J. Opt. Soc. Am 44, 362 (1954).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. Chem. (1)

J. E. Selwyn, J. L. Steinfeld, “Aggregation Equilibria of Xanthene Dyes,” J. Phys. Chem. 76, 762 (1972).
[CrossRef]

J. Phys. D (1)

E. Denton, R. D. Campbell, S. G. Tomlin, “The Determination of the Optical Constants of Thin Films from Measurements of Reflectance and Transmittance at Normal Incidence,” J. Phys. D 5, 852 (1972).
[CrossRef]

Opt. Spectrosc. (2)

E. G. Baranova, “Study of the Association of Rhodamine 3G in Ethanol and Glycerol Solutions,” Opt. Spectrosc. 13, 452 (1962).

L. I. Alperovich, “Use of Layers of Uneven Thickness for Measuring Optical Constants of Liquids in the Region of Strong Absorption,” Opt. Spectrosc. 15, 181 (1963).

Philos. Mag. (1)

J. R. Beattie, G. K. T. Conn, “Optical Constants of Metals in the Infra-Red—Principles of Measurement,” Philos. Mag. 46, 222 (1955).

Phys. Rev. Lett. (1)

N. J. Harrick, “Study of Physics and Chemistry of Surfaces from Frustrated Total Internal Reflections, ” Phys. Rev. Lett. 4, 224 (1960).
[CrossRef]

Proc. Phys. Soc. London (1)

S. P. F. Humphreys-Owen, “Comparison of Reflection Methods for Measuring Optical Constants without Polarimetric Analysis, and Proposal for New Methods Based on the Brewster Angle,” Proc. Phys. Soc. London 77, 949 (1961).
[CrossRef]

Spectrochim. Acta (2)

J. Fahrenfort, “Attenuated Total Reflection. A New Principle for the Production of Useful Infra-Red Reflection Spectra of Organic Compounds,” Spectrochim. Acta 17, 698 (1961).
[CrossRef]

J. Fahrenfort, W. M. Visser, “On the Determination of Optical Constants in the Infrared by Attenuated Total Reflection,” Spectrochim. Acta 18, 1103 (1962).

Z. Naturforsch. Teil A (1)

F. Oswald, R. Schade, “Über die Bestimmung der Optixhen Konslanten von Hulbleitern des Typus AIII-BV im Infraroten,” Z. Naturforsch. Teil A 9, 611 (1954).

Other (9)

H. Kessler, “Optische Konstanten,” in Handbuch der Physik, Vol. 18: Geometrische Optik, optische Konstante, optische Instrumente, H. Geiger, K. Scheel, Eds. (Springer-Verlag, Berlin, 1927), p. 623.

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

W. König, “Electromagnetische Lichttheone,” in Handbuch der Physik, Vol. 20: Licht als Wellenbewegung, H. Geiger, K. Scheel, Eds. (Springer-Verlag, Berlin, 1928), p. 242.

H. Gobrecht, “Dispersion und Absorption des Lichtes,”in Bergmann-Schaefer, Lehrbuch der Experimentalphysik, Band III: Optik, H. Gobrecht, Ed. (Walter de Gruyter, Berlin, 1974), p. 265.

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

W. W. Wendlandt, H. C. Hecht, Reflectance Spectroscopy (Interscience, New York, 1966).

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

R. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).

L. K. Chopra, Thin Film Phenomena (McGraw-Hill, New York, 1969), Chap. 11.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Reflectivity curves for light polarized parallel to plane of incidence. Dashed curves, n = 0.7; solid curves, n = 0.7−1 = 1.428.

Fig. 2
Fig. 2

Location of optical constants (n,k) in (R∥min,ϕB) plane. Dashed curves, k = constant; solid curves, n = constant.

Fig. 3
Fig. 3

Accuracy estimation of optical constants: (a) ratio of dk/k to dR∥min/R∥min vs extinction coefficient k for various refractive-index values; (b) change of refractive index with Brewster angle (dn/dϕB)/n vs refractive index n. The function is independent of extinction coefficient k.

Fig. 4
Fig. 4

Experimental setup: L, lamp; M, light collecting mirror; S1, S2, slits (widths S1: 0.2 mm, S2: 0.5 mm); A1, A2, variable apertures. L1–L4, lenses (focal lengths L1: 1.33m, L2: 15cm, L3: 1m, L4: 5 cm); BS1, BS2, beam splitters; F, filters; LG, fiber-optic lightguide; P1, P2, 90° deflection prisms; PO1, PO2, Glan polarizers; M1, M2, plane aluminum mirrors; S, sample; ST, beam stop with cross hair; SP, 30-cm spectrometer (grating with 600 lines/mm); DA, silicon diode array detection system (Tracor DARSS) connected to the microcomputer. The inset shows the sample region in more detail.

Fig. 5
Fig. 5

(a) Refractive indices and extinction coefficients vs wavelength for 0.4-mol/liter rhodamine 6G in methanol. Temperature 21°C. The dashed curve represents the refractive index of the solvent methanol, (b) Absorption cross section vs wavelength for rhodamine 6G in methanol. Dashed curve, concentration 10−5 mol/liter; solid curve, concentration 0.4 mol/liter.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

E r E i = n 2 μ cos ϕ ( n 2 sin 2 ϕ ) 1 / 2 n 2 μ cos ϕ + ( n 2 sin 2 ϕ ) 1 / 2 ,
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 ( λ , ϕ ) = R ref ( λ , ϕ ) S ( λ , ϕ ) / S F S ref ( λ , ϕ ) / S F , ref ,

Metrics