Abstract

A new method for measuring the refractive index is presented. First, the phase difference between s and p polarizations that is due to the total internal reflection is measured by heterodyne interferometry. Then, substituting this phase difference into the Fresnel equations, we can obtain the refractive index of the test medium.

© 1997 Optical Society of America

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References

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  1. P. R. Jarvis, G. H. Meeten, “Critical-angle measurement of refractive index of absorbing materials: an experimental study,” J. Phys. E 19, 296–298 (1986).
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  2. R. Ulrich, R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908 (1973).
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  3. H. Ringneault, F. Flory, S. Monneret, “Nonlinear totally reflecting prism coupler: thermomechanic effects and intensity-dependent refractive index of thin films,” Appl. Opt. 34, 4358–4369 (1995).
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  4. S. T. Kirsch, “Determining the refractive index and thickness of thin films from prism coupler measurements,” Appl. Opt. 20, 2085–2089 (1981).
    [CrossRef] [PubMed]
  5. M. Akimoto, Y. Gekka, “Brewster and pseudo-Brewster angle technique for determination of optical constants,” Jpn. J. Appl. Phys. 31, 120–122 (1992).
    [CrossRef]
  6. S. F. Noe, H. E. Bennett, “Accurate null polarimetry for measuring the refractive index of transparent materials,” J. Opt. Soc. Am. A 10, 2076–2083 (1993).
    [CrossRef]
  7. R. M. A. Azzam, “Maximum minimum reflectance of parallel-polarized light at interfaces between transparent and absorbing media,” J. Opt. Soc. Am. 73, 959–962 (1983).
    [CrossRef]
  8. H. Kitajima, H. Hieda, Y. Suematsu, “Use of a total absorption ATR method to measure complex refractive indices of metal-foils,” J. Opt. Soc. Am. 70, 1507–1513 (1980).
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  9. L. Lèvesque, B. E. Paton, S. H. Payne, “Precise thickness and refractive index determination of polyimide films using attenuated total reflection,” Appl. Opt. 33, 8036–8040 (1994).
    [CrossRef] [PubMed]
  10. H. Wang, “Determination of optical constants of absorbing crystalline thin films from reflectance and transmittance measurements with oblique incidence,” J. Opt. Soc. Am. A 11, 2331–2337 (1994).
    [CrossRef]
  11. U. Beak, G. Reiners, I. Urban, “Evaluation of optical properties of decorative coating by spectroscopic ellipsometry,” Thin Solid Films 220, 234–240 (1992).
    [CrossRef]
  12. R. M. A. Azzam, “Simple and direct determination of complex refractive index and thickness of unsupported or embedded thin films by combined reflection and transmission ellipsometry at 45° angle of incidence,” J. Opt. Soc. Am. 73, 1080–1082 (1983).
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  13. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 48–50.
  14. L. H. Shyu, C. L. Chen, D. C. Su, “Method for measuring the retardation of a wave plate,” Appl. Opt. 32, 4228–4230 (1993).
    [CrossRef] [PubMed]
  15. J. M. De Freitas, M. A. Player, “Importance of rotational beam alignment in the generation of second harmonic error in laser heterodyne interferometry,” Meas. Sci. Technol. 4, 1173–1176 (1993).
    [CrossRef]
  16. K. P. Birch, M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
    [CrossRef]

1995 (1)

1994 (2)

1993 (4)

S. F. Noe, H. E. Bennett, “Accurate null polarimetry for measuring the refractive index of transparent materials,” J. Opt. Soc. Am. A 10, 2076–2083 (1993).
[CrossRef]

J. M. De Freitas, M. A. Player, “Importance of rotational beam alignment in the generation of second harmonic error in laser heterodyne interferometry,” Meas. Sci. Technol. 4, 1173–1176 (1993).
[CrossRef]

K. P. Birch, M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

L. H. Shyu, C. L. Chen, D. C. Su, “Method for measuring the retardation of a wave plate,” Appl. Opt. 32, 4228–4230 (1993).
[CrossRef] [PubMed]

1992 (2)

M. Akimoto, Y. Gekka, “Brewster and pseudo-Brewster angle technique for determination of optical constants,” Jpn. J. Appl. Phys. 31, 120–122 (1992).
[CrossRef]

U. Beak, G. Reiners, I. Urban, “Evaluation of optical properties of decorative coating by spectroscopic ellipsometry,” Thin Solid Films 220, 234–240 (1992).
[CrossRef]

1986 (1)

P. R. Jarvis, G. H. Meeten, “Critical-angle measurement of refractive index of absorbing materials: an experimental study,” J. Phys. E 19, 296–298 (1986).
[CrossRef]

1983 (2)

1981 (1)

1980 (1)

1973 (1)

Akimoto, M.

M. Akimoto, Y. Gekka, “Brewster and pseudo-Brewster angle technique for determination of optical constants,” Jpn. J. Appl. Phys. 31, 120–122 (1992).
[CrossRef]

Azzam, R. M. A.

Beak, U.

U. Beak, G. Reiners, I. Urban, “Evaluation of optical properties of decorative coating by spectroscopic ellipsometry,” Thin Solid Films 220, 234–240 (1992).
[CrossRef]

Bennett, H. E.

Birch, K. P.

K. P. Birch, M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 48–50.

Chen, C. L.

De Freitas, J. M.

J. M. De Freitas, M. A. Player, “Importance of rotational beam alignment in the generation of second harmonic error in laser heterodyne interferometry,” Meas. Sci. Technol. 4, 1173–1176 (1993).
[CrossRef]

Downs, M. J.

K. P. Birch, M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

Flory, F.

Gekka, Y.

M. Akimoto, Y. Gekka, “Brewster and pseudo-Brewster angle technique for determination of optical constants,” Jpn. J. Appl. Phys. 31, 120–122 (1992).
[CrossRef]

Hieda, H.

Jarvis, P. R.

P. R. Jarvis, G. H. Meeten, “Critical-angle measurement of refractive index of absorbing materials: an experimental study,” J. Phys. E 19, 296–298 (1986).
[CrossRef]

Kirsch, S. T.

Kitajima, H.

Lèvesque, L.

Meeten, G. H.

P. R. Jarvis, G. H. Meeten, “Critical-angle measurement of refractive index of absorbing materials: an experimental study,” J. Phys. E 19, 296–298 (1986).
[CrossRef]

Monneret, S.

Noe, S. F.

Paton, B. E.

Payne, S. H.

Player, M. A.

J. M. De Freitas, M. A. Player, “Importance of rotational beam alignment in the generation of second harmonic error in laser heterodyne interferometry,” Meas. Sci. Technol. 4, 1173–1176 (1993).
[CrossRef]

Reiners, G.

U. Beak, G. Reiners, I. Urban, “Evaluation of optical properties of decorative coating by spectroscopic ellipsometry,” Thin Solid Films 220, 234–240 (1992).
[CrossRef]

Ringneault, H.

Shyu, L. H.

Su, D. C.

Suematsu, Y.

Torge, R.

Ulrich, R.

Urban, I.

U. Beak, G. Reiners, I. Urban, “Evaluation of optical properties of decorative coating by spectroscopic ellipsometry,” Thin Solid Films 220, 234–240 (1992).
[CrossRef]

Wang, H.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 48–50.

Appl. Opt. (5)

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

J. Phys. E (1)

P. R. Jarvis, G. H. Meeten, “Critical-angle measurement of refractive index of absorbing materials: an experimental study,” J. Phys. E 19, 296–298 (1986).
[CrossRef]

Jpn. J. Appl. Phys. (1)

M. Akimoto, Y. Gekka, “Brewster and pseudo-Brewster angle technique for determination of optical constants,” Jpn. J. Appl. Phys. 31, 120–122 (1992).
[CrossRef]

Meas. Sci. Technol. (1)

J. M. De Freitas, M. A. Player, “Importance of rotational beam alignment in the generation of second harmonic error in laser heterodyne interferometry,” Meas. Sci. Technol. 4, 1173–1176 (1993).
[CrossRef]

Metrologia (1)

K. P. Birch, M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

Thin Solid Films (1)

U. Beak, G. Reiners, I. Urban, “Evaluation of optical properties of decorative coating by spectroscopic ellipsometry,” Thin Solid Films 220, 234–240 (1992).
[CrossRef]

Other (1)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 48–50.

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Figures (5)

Fig. 1
Fig. 1

Total internal reflection at the boundary between a prism and a test medium.

Fig. 2
Fig. 2

Schematic diagrams for measuring the phase difference owing to (a) the total internal reflection and (b) the reflection at BS: EO, electro-optic modulator; BS, beam splitter; AN, analyzer; D, photodetector.

Fig. 3
Fig. 3

Theoretical and experimental curves of ϕ versus θ i for air, water, and index-matching oil.

Fig. 4
Fig. 4

Relation curves of ϕ versus θ i for several different n.

Fig. 5
Fig. 5

Relation curves of Δn versus n for several different θ R .

Equations (12)

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θ1=θp+sin-1sin θin1.
rs=cos θ1-isin2 θ1-n21/2cos θ1+isin2 θ1-n21/2=expiδs,
rp=-n2 cos θ1-isin2 θ1-n21/2n2 cos θ1+isin2 θ1-n21/2=expiδp,
ϕ=δs-δp=2 tan-1sin2 θ1-n21/2tan θ1 sin θ1.
ϕn, θi=2 tan-1sin2θp+sin-1sin θi/n1-n21/2tanθp+sin-1sin θi/n1sinθp+sin-1sin θi/n1,
n=sinθp+sin-1sin θi/n1×1-tan2ϕ2tan2θp+sin-1sin θi/n1½.
Ir=1/21+coswt+ϕr,
It=I021+coswt+ϕ,
ϕ=ϕ-ϕr,
Δndndϕ×Δϕ,
dndϕ=-121-tan2ϕ2tan2 θ11/2×tanϕ2sec2ϕ2sin θ1 tan2 θ1,
Δϕ=tan ϕsec 2θR-11+sec 2θR tan2 ϕ,

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