Abstract

Analytical expressions for the reflection and transmission of a plane light wave falling upon an anisotropic and absorbing interface are deduced. The reflectance and transmittance of an anisotropic and absorbing film is calculated, and a method for determining optical constants of an anisotropic absorbing film is developed.

© 1994 Optical Society of America

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  1. D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. V. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Opt. 23, 3571–3596 (1984).
    [CrossRef] [PubMed]
  2. F. Abelès, “Methods for determining optical parameters of thin films,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. II, pp. 251–288.
  3. P. Rouard, P. Bousquet, “Optical constants of thin films,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. IV, pp. 147–197.
  4. J. M. Bennett, M. J. Booty, “Computational method for determining n and k for a thin film from the measured reflectance, transmittance, and film thickness,” Appl. Opt. 5, 41–43 (1966).
    [CrossRef] [PubMed]
  5. P. O. Nilsson, “Determination of optical constants from intensity measurements at normal incidence,” Appl. Opt. 7, 435–442 (1968).
    [CrossRef] [PubMed]
  6. R. 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, 847–863 (1972).
    [CrossRef]
  7. R. E. Nestell, R. W. Christy, “Derivation of optical constants of metals from thin-film measurements at oblique incidence,” Appl. Opt. 11, 643–651 (1972).
    [CrossRef] [PubMed]
  8. A. Hjortsberg, “Determination of optical constants of absorbing materials using transmission and reflection of thin films on partially metallized substrates: analysis of the new (T, Rm) technique,” Appl. Opt. 20, 1254–1263 (1981).
    [CrossRef] [PubMed]
  9. J. P. Borgogno, B. Lazarides, E. Pelletier, “Automatic determination of the optical constants of inhomogeneous thin films,” Appl. Opt. 21, 4020–4029 (1982).
    [CrossRef] [PubMed]
  10. W. E. Case, “Algebraic method for extracting thin-film optical parameters from spectrophotometer measurements,” Appl. Opt. 22, 1832–1836 (1983).
    [CrossRef] [PubMed]
  11. J. A. Dobrowolski, F. C. Ho, A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Opt. 22, 3191–3200 (1983).
    [CrossRef] [PubMed]
  12. R. C. McPhedran, L. C. Botten, D. R. McKenzie, R. P. Netterfield, “Unambiguous determination of optical constants of absorbing films by reflectance and transmittance measurements,” Appl. Opt. 23, 1197–1205 (1984).
    [CrossRef] [PubMed]
  13. J. P. Borgogno, F. Flory, P. Roche, B. Schmitt, G. Albrand, E. Pelletier, H. A. Macleod, “Refractive index and inhomogeneity of thin films,” Appl. Opt. 23, 3567–3570 (1984).
    [CrossRef] [PubMed]
  14. I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. I. Wharton, “Measurement of the principal refractive indices of thin films deposited at oblique incidence,” J. Opt. Soc. Am. A 2, 1693–1697 (1985).
    [CrossRef]
  15. B. Bovard, F. J. van Milligen, M. J. Messerly, S. G. Saxe, H. A. Macleod, “Optical constants derivation for an inhomogeneous thin film from in situtransmission measurements,” Appl. Opt. 24, 1803–1807 (1985).
    [CrossRef] [PubMed]
  16. C. K. Carniglia, “Effects of dispersion on the determination of optical constants of thin films,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.652, 158–165 (1986).
    [CrossRef]
  17. M. C. Gupta, “Optical constant determination of thin films,” Appl. Opt. 27, 954–956 (1988).
    [CrossRef] [PubMed]
  18. D. M. Spink, C. B. Thomas, “Optical constants determination of thin films: an analytical solution,” Appl. Opt. 27, 4362 (1988).
    [CrossRef] [PubMed]
  19. D. A. Minkov, “Method for determining the optical constants of a thin film on a transparent substrate,” J. Phys. D 22, 199–205 (1989).
    [CrossRef]
  20. J.-P. Borgogno, E. Pelletier, “Determination of the extinction coefficient of dielectric thin films from spectrophotometric measurements,” Appl. Opt. 28, 2895–2901 (1989).
    [CrossRef] [PubMed]
  21. T. Kihara, K. Yokomori, “Simultaneous measurement of refractive index and thickness of thin film by polarized reflectances,” Appl. Opt. 29, 5069–5073 (1990).
    [CrossRef] [PubMed]
  22. B. J. Stagg, T. T. Charalampopoulos, “Method to minimize the effects of polarizer leakage on reflectivity measurements,” Appl. Opt. 29, 4638–4645 (1990).
    [CrossRef] [PubMed]
  23. D. A. Minkov, “Computation of the optical constants of a thin dielectric layer on a transmitting substrate from the reflection spectrum at inclined incidence of light,” J. Opt. Soc. Am. A 8, 306–310 (1991).
    [CrossRef]
  24. R. Brendel, R. Zeigler, R. Hezel, “A method for the measurement of thin film optical constants with a spectral photometer from 230 nm to 850 nm and its applications to plasma silicon (OXY) nitride,” Thin Solid Films 200, 219–228 (1991).
    [CrossRef]
  25. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k, and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1991).
    [CrossRef]
  26. V. Panayotov, I. Konstantinov, “Determination of thin film optical parameters from photometric measurements: an algebraic solution for the (T, Rf, Rb) method,” Appl. Opt. 30, 2795–2800 (1991).
    [CrossRef] [PubMed]
  27. M. Yanagihara, J. Cao, M. Yamamoto, A. Arai, S. Nakayama, T. Mizuide, T. Namioka, “Optical constants of very thin gold films in the soft x-ray region,” Appl. Opt. 30, 2807–2814 (1991).
    [CrossRef] [PubMed]
  28. Z. Yinping, Z. Chuang, G. Xinshi, L. Xingang, “A precise and simple method, the relative transmission fringe depth method, of determining the optical constants and thickness of thin semitransparent films,” J. Phys. D 25, 1004–1009 (1992).
    [CrossRef]
  29. J. L. Hernández-Rojas, M. L. Lucía, I. Mártil, G. González-Díaz, J. Santamaría, F. Sánchez-Quesada, “Optical analysis of absorbing thin films: application to ternary chalcopyrite semiconductors,” Appl. Opt. 31, 1606–1611 (1992).
    [CrossRef] [PubMed]
  30. M. Saito, S. Nakamura, M. Miyagi, “Measurement of the refractive index and thickness for infrared optical films deposited on rough substrates,” Appl. Opt. 31, 6139–6144 (1992).
    [CrossRef] [PubMed]
  31. E. E. Khawaja, F. Bouamrane, “Determination of the optical constants (n, k) of thin dielectric films,” Appl. Opt. 32, 1168–1172 (1993).
    [CrossRef] [PubMed]
  32. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).
  33. R. Ulrich, R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908 (1973).
    [CrossRef] [PubMed]
  34. G. Zhang, K. Sasaki, “Measuring anisotropic refractive indices and film thicknesses of thin organic crystals using the prism coupling method,” Appl. Opt. 27, 1358–1362 (1988).
    [CrossRef] [PubMed]
  35. H. Wang, “Determination of refractive indices and thickness of absorbing crystalline thin films by using prism coupler,” Fiber Integr. Opt. 13, 293–308 (1994).
    [CrossRef]
  36. T.-N. Ding, E. Garmire, “Measuring refractive index and thickness of thin films: a new technique,” Appl. Opt. 22, 3177–3181 (1983).
    [CrossRef] [PubMed]
  37. D. J. de Smet, “Reflection from an oriented biaxial surface,” Appl. Opt. 26, 995–998 (1987).
    [CrossRef] [PubMed]
  38. F. Brèhat, B. Wyncke, “Reflectivity, transmissivity and optical constants of anisotropic absorbing crystals,” J. Phys. D 24, 2055–2066 (1991).
    [CrossRef]
  39. W. E. Martin, “Refractive index profile measurements of diffused optical waveguides,” Appl. Opt. 13, 2112–2116 (1974).
    [CrossRef] [PubMed]
  40. J. Shamir, “Interferometric methods for the determination of thin-film parameters,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Boston, Mass., 1985), Vol. 1, Chap. 6, pp. 113–133.
  41. B. Hillevich, E. Weidel, D. Gruchmaan, “Automatic measurements of refractive index profile of slab waveguides by interference fringe processing,” in Integrated Optical Circuit Engineering III, R. T. Kersten, ed., Proc. Soc. Photo-Opt. Instrum. Eng.651, 252–258 (1986).
    [CrossRef]
  42. N. F. Foster, “Piezoelectric and piezoresistive properties of films,” in Handbook of Thin Film Technology, L. I. Maisell, R. Glang, eds. (McGraw-Hill, New York, 1970), Chap. 15, pp. 15-11–15-15.

1994

H. Wang, “Determination of refractive indices and thickness of absorbing crystalline thin films by using prism coupler,” Fiber Integr. Opt. 13, 293–308 (1994).
[CrossRef]

1993

1992

1991

D. A. Minkov, “Computation of the optical constants of a thin dielectric layer on a transmitting substrate from the reflection spectrum at inclined incidence of light,” J. Opt. Soc. Am. A 8, 306–310 (1991).
[CrossRef]

R. Brendel, R. Zeigler, R. Hezel, “A method for the measurement of thin film optical constants with a spectral photometer from 230 nm to 850 nm and its applications to plasma silicon (OXY) nitride,” Thin Solid Films 200, 219–228 (1991).
[CrossRef]

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k, and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1991).
[CrossRef]

V. Panayotov, I. Konstantinov, “Determination of thin film optical parameters from photometric measurements: an algebraic solution for the (T, Rf, Rb) method,” Appl. Opt. 30, 2795–2800 (1991).
[CrossRef] [PubMed]

M. Yanagihara, J. Cao, M. Yamamoto, A. Arai, S. Nakayama, T. Mizuide, T. Namioka, “Optical constants of very thin gold films in the soft x-ray region,” Appl. Opt. 30, 2807–2814 (1991).
[CrossRef] [PubMed]

F. Brèhat, B. Wyncke, “Reflectivity, transmissivity and optical constants of anisotropic absorbing crystals,” J. Phys. D 24, 2055–2066 (1991).
[CrossRef]

1990

1989

D. A. Minkov, “Method for determining the optical constants of a thin film on a transparent substrate,” J. Phys. D 22, 199–205 (1989).
[CrossRef]

J.-P. Borgogno, E. Pelletier, “Determination of the extinction coefficient of dielectric thin films from spectrophotometric measurements,” Appl. Opt. 28, 2895–2901 (1989).
[CrossRef] [PubMed]

1988

1987

1985

1984

1983

1982

1981

1974

1973

1972

R. 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, 847–863 (1972).
[CrossRef]

R. E. Nestell, R. W. Christy, “Derivation of optical constants of metals from thin-film measurements at oblique incidence,” Appl. Opt. 11, 643–651 (1972).
[CrossRef] [PubMed]

1968

1966

Abelès, F.

F. Abelès, “Methods for determining optical parameters of thin films,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. II, pp. 251–288.

Albrand, G.

Arai, A.

Arndt, D. P.

Azzam, R. M. A.

Bennett, J. M.

Booty, M. J.

Borgogno, J. P.

Borgogno, J.-P.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Botten, L. C.

Bouamrane, F.

Bousquet, P.

P. Rouard, P. Bousquet, “Optical constants of thin films,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. IV, pp. 147–197.

Bovard, B.

Brèhat, F.

F. Brèhat, B. Wyncke, “Reflectivity, transmissivity and optical constants of anisotropic absorbing crystals,” J. Phys. D 24, 2055–2066 (1991).
[CrossRef]

Brendel, R.

R. Brendel, R. Zeigler, R. Hezel, “A method for the measurement of thin film optical constants with a spectral photometer from 230 nm to 850 nm and its applications to plasma silicon (OXY) nitride,” Thin Solid Films 200, 219–228 (1991).
[CrossRef]

Campbell, R. D.

R. 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, 847–863 (1972).
[CrossRef]

Cao, J.

Carniglia, C. K.

Case, W. E.

Charalampopoulos, T. T.

Christy, R. W.

Chuang, Z.

Z. Yinping, Z. Chuang, G. Xinshi, L. Xingang, “A precise and simple method, the relative transmission fringe depth method, of determining the optical constants and thickness of thin semitransparent films,” J. Phys. D 25, 1004–1009 (1992).
[CrossRef]

de Smet, D. J.

Denton, R. E.

R. 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, 847–863 (1972).
[CrossRef]

Ding, T.-N.

Dobrowolski, J. A.

Fillard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k, and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1991).
[CrossRef]

Flory, F.

Foster, N. F.

N. F. Foster, “Piezoelectric and piezoresistive properties of films,” in Handbook of Thin Film Technology, L. I. Maisell, R. Glang, eds. (McGraw-Hill, New York, 1970), Chap. 15, pp. 15-11–15-15.

Garmire, E.

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k, and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1991).
[CrossRef]

Gibson, U. J.

González-Díaz, G.

Gruchmaan, D.

B. Hillevich, E. Weidel, D. Gruchmaan, “Automatic measurements of refractive index profile of slab waveguides by interference fringe processing,” in Integrated Optical Circuit Engineering III, R. T. Kersten, ed., Proc. Soc. Photo-Opt. Instrum. Eng.651, 252–258 (1986).
[CrossRef]

Gupta, M. C.

Hernández-Rojas, J. L.

Hezel, R.

R. Brendel, R. Zeigler, R. Hezel, “A method for the measurement of thin film optical constants with a spectral photometer from 230 nm to 850 nm and its applications to plasma silicon (OXY) nitride,” Thin Solid Films 200, 219–228 (1991).
[CrossRef]

Hillevich, B.

B. Hillevich, E. Weidel, D. Gruchmaan, “Automatic measurements of refractive index profile of slab waveguides by interference fringe processing,” in Integrated Optical Circuit Engineering III, R. T. Kersten, ed., Proc. Soc. Photo-Opt. Instrum. Eng.651, 252–258 (1986).
[CrossRef]

Hjortsberg, A.

Ho, F. C.

Hodgkin, V. V.

Hodgkinson, I. J.

Horowitz, F.

Khawaja, E. E.

Kihara, T.

Klapp, W. P.

Konstantinov, I.

Lazarides, B.

Lucía, M. L.

Macleod, H. A.

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k, and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1991).
[CrossRef]

Mártil, I.

Martin, W. E.

McKenzie, D. R.

McPhedran, R. C.

Messerly, M. J.

Minkov, D. A.

Miyagi, M.

Mizuide, T.

Nakamura, S.

Nakayama, S.

Namioka, T.

Nestell, R. E.

Netterfield, R. P.

Nilsson, P. O.

Panayotov, V.

Pelletier, E.

Purvis, M. K.

Quinn, D. M.

Roche, P.

Rouard, P.

P. Rouard, P. Bousquet, “Optical constants of thin films,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. IV, pp. 147–197.

Saito, M.

Sánchez-Quesada, F.

Santamaría, J.

Sasaki, K.

Saxe, S. G.

Schmitt, B.

Shamir, J.

J. Shamir, “Interferometric methods for the determination of thin-film parameters,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Boston, Mass., 1985), Vol. 1, Chap. 6, pp. 113–133.

Sikkens, M.

Spink, D. M.

Stagg, B. J.

Strome, D. H.

Swenson, R.

Temple, P. A.

Thomas, C. B.

Thonn, T. F.

Tomlin, S. G.

R. 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, 847–863 (1972).
[CrossRef]

Torge, R.

Tuttle Hart, T.

Ulrich, R.

van Milligen, F. J.

Waldorf, A.

Wang, H.

H. Wang, “Determination of refractive indices and thickness of absorbing crystalline thin films by using prism coupler,” Fiber Integr. Opt. 13, 293–308 (1994).
[CrossRef]

Weidel, E.

B. Hillevich, E. Weidel, D. Gruchmaan, “Automatic measurements of refractive index profile of slab waveguides by interference fringe processing,” in Integrated Optical Circuit Engineering III, R. T. Kersten, ed., Proc. Soc. Photo-Opt. Instrum. Eng.651, 252–258 (1986).
[CrossRef]

Wharton, J. I.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Wyncke, B.

F. Brèhat, B. Wyncke, “Reflectivity, transmissivity and optical constants of anisotropic absorbing crystals,” J. Phys. D 24, 2055–2066 (1991).
[CrossRef]

Xingang, L.

Z. Yinping, Z. Chuang, G. Xinshi, L. Xingang, “A precise and simple method, the relative transmission fringe depth method, of determining the optical constants and thickness of thin semitransparent films,” J. Phys. D 25, 1004–1009 (1992).
[CrossRef]

Xinshi, G.

Z. Yinping, Z. Chuang, G. Xinshi, L. Xingang, “A precise and simple method, the relative transmission fringe depth method, of determining the optical constants and thickness of thin semitransparent films,” J. Phys. D 25, 1004–1009 (1992).
[CrossRef]

Yamamoto, M.

Yanagihara, M.

Yinping, Z.

Z. Yinping, Z. Chuang, G. Xinshi, L. Xingang, “A precise and simple method, the relative transmission fringe depth method, of determining the optical constants and thickness of thin semitransparent films,” J. Phys. D 25, 1004–1009 (1992).
[CrossRef]

Yokomori, K.

Zeigler, R.

R. Brendel, R. Zeigler, R. Hezel, “A method for the measurement of thin film optical constants with a spectral photometer from 230 nm to 850 nm and its applications to plasma silicon (OXY) nitride,” Thin Solid Films 200, 219–228 (1991).
[CrossRef]

Zhang, G.

Appl. Opt.

R. E. Nestell, R. W. Christy, “Derivation of optical constants of metals from thin-film measurements at oblique incidence,” Appl. Opt. 11, 643–651 (1972).
[CrossRef] [PubMed]

A. Hjortsberg, “Determination of optical constants of absorbing materials using transmission and reflection of thin films on partially metallized substrates: analysis of the new (T, Rm) technique,” Appl. Opt. 20, 1254–1263 (1981).
[CrossRef] [PubMed]

J. P. Borgogno, B. Lazarides, E. Pelletier, “Automatic determination of the optical constants of inhomogeneous thin films,” Appl. Opt. 21, 4020–4029 (1982).
[CrossRef] [PubMed]

W. E. Case, “Algebraic method for extracting thin-film optical parameters from spectrophotometer measurements,” Appl. Opt. 22, 1832–1836 (1983).
[CrossRef] [PubMed]

J. A. Dobrowolski, F. C. Ho, A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Opt. 22, 3191–3200 (1983).
[CrossRef] [PubMed]

R. C. McPhedran, L. C. Botten, D. R. McKenzie, R. P. Netterfield, “Unambiguous determination of optical constants of absorbing films by reflectance and transmittance measurements,” Appl. Opt. 23, 1197–1205 (1984).
[CrossRef] [PubMed]

J. P. Borgogno, F. Flory, P. Roche, B. Schmitt, G. Albrand, E. Pelletier, H. A. Macleod, “Refractive index and inhomogeneity of thin films,” Appl. Opt. 23, 3567–3570 (1984).
[CrossRef] [PubMed]

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. V. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Opt. 23, 3571–3596 (1984).
[CrossRef] [PubMed]

J. M. Bennett, M. J. Booty, “Computational method for determining n and k for a thin film from the measured reflectance, transmittance, and film thickness,” Appl. Opt. 5, 41–43 (1966).
[CrossRef] [PubMed]

P. O. Nilsson, “Determination of optical constants from intensity measurements at normal incidence,” Appl. Opt. 7, 435–442 (1968).
[CrossRef] [PubMed]

B. Bovard, F. J. van Milligen, M. J. Messerly, S. G. Saxe, H. A. Macleod, “Optical constants derivation for an inhomogeneous thin film from in situtransmission measurements,” Appl. Opt. 24, 1803–1807 (1985).
[CrossRef] [PubMed]

M. C. Gupta, “Optical constant determination of thin films,” Appl. Opt. 27, 954–956 (1988).
[CrossRef] [PubMed]

D. M. Spink, C. B. Thomas, “Optical constants determination of thin films: an analytical solution,” Appl. Opt. 27, 4362 (1988).
[CrossRef] [PubMed]

J.-P. Borgogno, E. Pelletier, “Determination of the extinction coefficient of dielectric thin films from spectrophotometric measurements,” Appl. Opt. 28, 2895–2901 (1989).
[CrossRef] [PubMed]

T. Kihara, K. Yokomori, “Simultaneous measurement of refractive index and thickness of thin film by polarized reflectances,” Appl. Opt. 29, 5069–5073 (1990).
[CrossRef] [PubMed]

B. J. Stagg, T. T. Charalampopoulos, “Method to minimize the effects of polarizer leakage on reflectivity measurements,” Appl. Opt. 29, 4638–4645 (1990).
[CrossRef] [PubMed]

J. L. Hernández-Rojas, M. L. Lucía, I. Mártil, G. González-Díaz, J. Santamaría, F. Sánchez-Quesada, “Optical analysis of absorbing thin films: application to ternary chalcopyrite semiconductors,” Appl. Opt. 31, 1606–1611 (1992).
[CrossRef] [PubMed]

M. Saito, S. Nakamura, M. Miyagi, “Measurement of the refractive index and thickness for infrared optical films deposited on rough substrates,” Appl. Opt. 31, 6139–6144 (1992).
[CrossRef] [PubMed]

E. E. Khawaja, F. Bouamrane, “Determination of the optical constants (n, k) of thin dielectric films,” Appl. Opt. 32, 1168–1172 (1993).
[CrossRef] [PubMed]

V. Panayotov, I. Konstantinov, “Determination of thin film optical parameters from photometric measurements: an algebraic solution for the (T, Rf, Rb) method,” Appl. Opt. 30, 2795–2800 (1991).
[CrossRef] [PubMed]

M. Yanagihara, J. Cao, M. Yamamoto, A. Arai, S. Nakayama, T. Mizuide, T. Namioka, “Optical constants of very thin gold films in the soft x-ray region,” Appl. Opt. 30, 2807–2814 (1991).
[CrossRef] [PubMed]

R. Ulrich, R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908 (1973).
[CrossRef] [PubMed]

G. Zhang, K. Sasaki, “Measuring anisotropic refractive indices and film thicknesses of thin organic crystals using the prism coupling method,” Appl. Opt. 27, 1358–1362 (1988).
[CrossRef] [PubMed]

W. E. Martin, “Refractive index profile measurements of diffused optical waveguides,” Appl. Opt. 13, 2112–2116 (1974).
[CrossRef] [PubMed]

T.-N. Ding, E. Garmire, “Measuring refractive index and thickness of thin films: a new technique,” Appl. Opt. 22, 3177–3181 (1983).
[CrossRef] [PubMed]

D. J. de Smet, “Reflection from an oriented biaxial surface,” Appl. Opt. 26, 995–998 (1987).
[CrossRef] [PubMed]

Fiber Integr. Opt.

H. Wang, “Determination of refractive indices and thickness of absorbing crystalline thin films by using prism coupler,” Fiber Integr. Opt. 13, 293–308 (1994).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. D

D. A. Minkov, “Method for determining the optical constants of a thin film on a transparent substrate,” J. Phys. D 22, 199–205 (1989).
[CrossRef]

R. 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, 847–863 (1972).
[CrossRef]

Z. Yinping, Z. Chuang, G. Xinshi, L. Xingang, “A precise and simple method, the relative transmission fringe depth method, of determining the optical constants and thickness of thin semitransparent films,” J. Phys. D 25, 1004–1009 (1992).
[CrossRef]

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[CrossRef]

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[CrossRef]

Thin Solid Films

R. Brendel, R. Zeigler, R. Hezel, “A method for the measurement of thin film optical constants with a spectral photometer from 230 nm to 850 nm and its applications to plasma silicon (OXY) nitride,” Thin Solid Films 200, 219–228 (1991).
[CrossRef]

Other

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B. Hillevich, E. Weidel, D. Gruchmaan, “Automatic measurements of refractive index profile of slab waveguides by interference fringe processing,” in Integrated Optical Circuit Engineering III, R. T. Kersten, ed., Proc. Soc. Photo-Opt. Instrum. Eng.651, 252–258 (1986).
[CrossRef]

N. F. Foster, “Piezoelectric and piezoresistive properties of films,” in Handbook of Thin Film Technology, L. I. Maisell, R. Glang, eds. (McGraw-Hill, New York, 1970), Chap. 15, pp. 15-11–15-15.

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[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Illustration of the reflection and transmission of a plane wave at a thin film.

Fig. 2
Fig. 2

Layout of the experimental system for measuring reflectance and transmittance as functions of incident angle. L’s, lens; A’s, aperture; P’s, polarizers; Pre-Amp, preamplifier.

Fig. 3
Fig. 3

Reflectance Rs and transmittance Ts of a TE-mode plane wave versus incident angle θi for the s-polarization state; the plane wave impinges upon a CdS film with n = 2.437, k = 0.016, n = 2.418, k = 0.089, and thickness d = 170 nm, and is deposited onto a substrate of fused silica with n = 1.461.

Fig. 4
Fig. 4

Reflectance Rp and transmittance Tp of a TM-mode plane wave versus incident angle θi at the same film–substrate system as shown in Fig. 3, for the p-polarization state.

Tables (2)

Tables Icon

Table 1 Optical Constants (at λ = 632.8 nm) and Thickness of the CdS Film, Fitted from the Measured Data of Reflectance and Transmittance versus Incident Angles

Tables Icon

Table 2 Residual Errora of the Least-Squares Fit for the Optical Constants (at λ = 632.8 nm) and Thickness Shown in Table 1

Equations (39)

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r ̂ ( s ) = ( n ̂ x 1 2 N 2 ) 1 / 2 ( n ̂ x 2 2 N 2 ) 1 / 2 ( n ̂ x 1 2 N 2 ) 1 / 2 + ( n ̂ x 2 2 N 2 ) 1 / 2 , t ̂ ( s ) = 2 ( n ̂ x 1 2 N 2 ) 1 / 2 ( n ̂ x 1 2 N 2 ) 1 / 2 + ( n ̂ x 2 2 N 2 ) 1 / 2 ,
r ̂ ( p ) = n ̂ y 2 n ̂ z 2 ( n ̂ z 1 2 N 2 ) 1 / 2 n ̂ y 1 n ̂ z 1 ( n ̂ z 2 2 N 2 ) 1 / 2 n ̂ y 2 n ̂ z 2 ( n ̂ z 1 2 N 2 ) 1 / 2 + n ̂ y 1 n ̂ z 1 ( n ̂ z 2 2 N 2 ) 1 / 2 , Ô t ( p ) = n ̂ z 1 n ̂ z 2 [ n ̂ z 2 4 + ( n ̂ y 2 2 n ̂ z 2 2 ) N 2 ] 1 / 2 [ n ̂ z 1 4 + ( n ̂ y 1 2 n ̂ z 1 2 ) N 2 ] 1 / 2 × 2 n ̂ y 1 n ̂ z 1 ( n ̂ z 1 2 N 2 ) 1 / 2 n ̂ y 2 n ̂ z 2 ( n ̂ z 1 2 N 2 ) 1 / 2 + n ̂ y 1 n ̂ z 1 ( n ̂ z 2 2 N 2 ) 1 / 2 ,
q ̂ = ( n ̂ x 2 N 2 ) 1 / 2 = q exp ( i δ 2 ) = q ( R ) + i q ( I ) , q = [ ( n x 2 k x 2 N 2 ) 2 + 4 n x 2 k x 2 ] 1 / 4 , tan δ = 2 n x k x n x 2 k x 2 N 2 , q ( R ) = q cos δ 2 , q ( I ) = q sin δ 2 .
r ̂ 12 ( s ) = q ̂ 1 q ̂ 2 q ̂ 1 + q ̂ 2 = ρ 12 ( s ) exp [ i 2 ϕ 12 ( s ) ] = r 12 ( s R ) + i r 12 ( s I ) , t ̂ 12 ( s ) = 2 q ̂ 1 q ̂ 1 + q ̂ 2 = τ 12 ( s ) exp [ i 2 χ 12 ( s ) ] = t 12 ( s R ) + i t 12 ( s I ) ,
G c = cos δ 1 δ 2 2 , G s = sin δ 1 δ 2 2 .
ρ 12 ( s ) = [ ( q 1 2 q 2 2 ) 2 + 4 q 1 2 q 2 2 G s 2 ] 1 / 2 q 1 2 + q 2 2 + 2 q 1 q 2 G c , tan [ 2 ϕ 12 ( s ) ] = 2 q 1 q 2 G s q 1 2 q 2 2 , τ 12 ( s ) = 2 q 1 ( q 1 2 + q 2 2 + 2 q 1 q 2 G c ) 1 / 2 , tan [ 2 χ 12 ( s ) ] = q 2 G s q 1 + q 2 G c ,
r 12 ( s R ) = q 1 2 q 2 2 q 1 2 + q 2 2 + 2 F ( R ) , r 12 ( s I ) = 2 F ( I ) q 1 2 + q 2 2 + 2 F ( R ) , t 12 ( s R ) = 2 ( q 1 2 + F ( R ) ) q 1 2 + q 2 2 + 2 F ( R ) , t 12 ( S I ) = r 12 ( S I ) ,
F ̂ = q ̂ 1 q ̂ 2 * , F ( R ) = q 1 ( R ) q 2 ( R ) + q 1 ( I ) q 2 ( I ) , F ( I ) = q 1 ( I ) q 2 ( R ) q 1 ( R ) q 2 ( I ) .
G c = sin δ 1 2 , G s = cos δ 1 2 , F ( R ) = q 1 ( I ) q 2 ( I ) , F ( I ) = q 1 ( R ) q 2 ( I ) .
r ̂ 12 ( p ) = p ̂ 2 q ̂ 1 p ̂ 1 q ̂ 2 p ̂ 2 q ̂ 1 + p ̂ 1 q ̂ 2 = ρ 12 ( p ) exp [ i 2 ϕ 12 ( p ) ] = r 12 ( p R ) + i r 12 ( p I ) , t ̂ 12 ( p ) = n ̂ z 1 n ̂ z 2 υ ̂ 2 υ ̂ 1 2 p ̂ 1 q ̂ 1 p ̂ 2 q ̂ 1 + p ̂ 1 q ̂ 2 = τ 12 ( p ) tan [ 2 χ 12 ( p ) ] = t 12 ( p R ) + i t 12 ( p I ) ,
ρ 12 ( p ) = [ ( p 2 2 q 1 2 p 1 2 q 2 2 ) 2 + 4 p 1 2 p 2 2 q 1 2 q 2 2 G s 2 ] 1 / 2 p 2 2 q 1 2 + p 1 2 q 2 2 + 2 p 1 p 2 q 1 q 2 G c , tan [ 2 ϕ 12 ( p ) ] = 2 p 1 p 2 q 1 q 2 G c p 2 2 q 1 2 p 1 2 q 2 2 , τ 12 ( p ) = u 1 u 2 υ 2 υ 1 2 p 1 q 1 ( p 2 2 q 1 2 + p 1 2 q 2 2 + 2 p 1 p 2 q 1 q 2 G c ) 1 / 2 , 2 χ 12 ( p ) = ξ 1 ξ 2 η 1 + η 2 + γ 1 γ 2 2 arctan ( p 1 q 2 G s p 2 q 1 + p 1 q 2 G c ) ,
G c = cos δ 1 δ 2 γ 1 + γ 2 2 , G c = sin δ 1 δ 2 γ 1 + γ 2 2 ,
p ̂ = n ̂ y n ̂ z = p exp ( i γ 2 ) = p ( R ) + i p ( I ) , p = [ ( n y n z k y k z ) 2 + ( n y k z + n z k y ) 2 ] 1 / 2 , tan ( γ 2 ) = n y k z + n z k y n y n z k y k z , p ( R ) = p cos γ 2 , p ( I ) = p sin γ 2 ,
n ̂ z = u exp ( i ξ 2 ) , u = ( n z 2 + k z 2 ) 1 / 2 , tan ( ξ 2 ) = k z n z ,
υ ̂ = [ n ̂ z 4 + ( n ̂ y 2 n ̂ z 2 ) N 2 ] 1 / 2 = υ exp ( i η 2 ) , υ = { [ n z 2 k z 2 ) 2 4 n z 2 k z 2 + N 2 ( n y 2 n z 2 k y 2 + k z 2 ) ] 2 + 4 [ n z k z ( n z 2 k z 2 ) + ( n y k y n z k z ) N 2 ] 2 } 1 / 4 , tan η = 2 [ n z k z ( n z 2 k z 2 ) + ( n y k y n z k z ) N 2 ] ( n z 2 k z 2 ) 2 4 n z 2 k z 2 + N 2 ( n y 2 n z 2 k y 2 + k z 2 ) , υ p ( R ) = υ cos η 2 , υ p ( I ) = υ sin η 2 ,
r 12 ( p R ) = p 2 2 q 1 2 p 1 2 q 2 2 p 2 2 q 1 2 + p 1 2 q 2 2 + 2 F ( R ) , r 12 ( p I ) = 2 F ( I ) p 2 2 q 1 2 + p 1 2 q 2 2 + 2 F ( R ) ,
P ̂ = p ̂ 1 * p ̂ 2 , P ( R ) = p 1 ( R ) p 2 ( R ) + p 1 ( I ) p 2 ( I ) , P ( I ) = p 1 ( R ) p 2 ( I ) p 1 ( I ) p 2 ( R ) , Q ̂ = q ̂ 1 q ̂ 2 * , Q ( R ) = q 1 ( R ) q 2 ( R ) + q 1 ( I ) q 2 ( I ) , Q ( I ) = q 1 ( R ) q 2 ( I ) p 1 ( R ) q 2 ( R ) , F ̂ = P ̂ Q ̂ , F ( R ) = P ( R ) Q ( R ) P ( I ) Q ( I ) , F ( I ) = P ( I ) Q ( R ) + P ( R ) Q ( I ) .
G c = sin δ 1 γ 1 2 , G s = cos δ 1 γ 1 2 ,
Û = n ̂ z 1 n ̂ z 2 , U ( R ) = n z 1 n z 2 + k z 1 k z 2 n z 2 2 + k z 2 2 , U ( I ) = n z 2 k z 1 n z 1 k z 2 n z 2 2 + k z 2 2 . V ̂ = υ ̂ 2 υ ̂ 1 , V ( R ) = υ 1 ( R ) υ 2 ( R ) + υ 1 ( I ) υ 2 ( R ) [ υ 1 ( R ) ] 2 + [ υ 1 ( I ) ] 2 , V ( I ) = υ 1 ( R ) υ 2 ( I ) υ 1 ( I ) υ 2 ( R ) [ υ 1 ( R ) ] 2 + [ υ 1 ( I ) ] 2 , Ŵ = Û V ̂ , W ( R ) = U ( R ) V ( R ) U ( I ) V ( I ) , W ( I ) = U ( R ) V ( I ) + U ( I ) V ( R )
Ĥ = 2 ( q 1 2 P ̂ + p 1 2 Q ̂ ) p 2 2 q 1 2 + p 1 2 q 2 2 + 2 F ( R ) , H ( R ) = 2 [ q 1 2 P ( R ) + p 1 2 Q ( R ) ] p 2 2 q 1 2 + p 1 2 q 2 2 + 2 F ( R ) , H ( I ) = 2 [ q 1 2 P ( I ) + p 1 2 Q ( I ) ] p 2 2 q 1 2 + p 1 2 q 2 2 + 2 F ( R ) .
t 12 ( p R ) = W ( R ) H ( R ) W ( I ) H ( I ) , t 12 ( p I ) = W ( R ) H ( I ) + W ( I ) H ( R ) .
r ̂ 13 = r ̂ 12 + r ̂ 23 exp ( i 2 Δ 2 ) 1 + r ̂ 12 r ̂ 23 exp ( i 2 Δ 2 ) , t ̂ 13 = t ̂ 12 t ̂ 23 exp ( i Δ 2 ) 1 + r ̂ 12 r ̂ 23 exp ( i Δ 2 ) ,
exp ( i Δ 2 ) = exp ( i 2 π λ d 2 n ̂ 2 cos θ 2 ) , Γ ̂ 2 = n ̂ 2 cos θ 2 = Γ 2 ( R ) + i Γ 2 ( I )
Γ 2 ( R ) = q 2 cos δ 2 2 , Γ 2 ( I ) = q 2 sin δ 2 2 ,
Γ 2 ( R ) = p 2 2 q 2 [ p 2 2 cos δ 2 2 + w 2 2 cos ( γ 2 + δ 2 2 ζ 2 ) ] p 2 4 + w 2 4 + 2 p 2 2 + w 2 2 cos ( γ 2 ζ 2 ) , Γ 2 ( I ) = p 2 2 q 2 [ p 2 2 sin δ 2 2 + w 2 2 sin ( γ 2 + δ 2 2 ζ 2 ) ] p 2 4 + w 2 4 + 2 p 2 2 w 2 2 cos ( γ 2 ζ 2 ) ,
N 2 ( n ̂ z 2 2 n ̂ y 2 2 ) = w 2 2 exp ( i ζ 2 ) , w 2 2 = { [ n z 2 2 n y 2 2 ( k z 2 2 k y 2 2 ) ] 2 + 4 ( n z 2 k z 2 n y 2 k y 2 ) 2 } 1 / 2 , tan ζ 2 = 2 ( n z 2 k z 2 n y 2 k y 2 ) n z 2 2 n y 2 2 ( k z 2 2 k y 2 2 ) ·
r ̂ 13 = ρ 13 exp ( i 2 ϕ 13 ) = r 13 ( R ) + i r 13 ( I ) , t ̂ 13 = τ 13 exp ( i 2 χ 13 ) = t 13 ( R ) + i t 13 ( I ) ,
ρ 13 = { ρ 12 2 + ρ 23 2 a 2 4 + 2 ρ 12 ρ 23 a 2 2 cos [ 2 ( ϕ 12 ϕ 23 + σ 2 ) ] 1 + ρ 12 2 + ρ 23 2 a 2 4 + 2 ρ 12 ρ 23 a 2 2 cos [ 2 ( ϕ 12 + ϕ 23 σ 2 ) ] } 1 / 2 , tan ( 2 ϕ 13 ) = ρ 12 ( 1 ρ 23 2 a 2 4 ) sin 2 ϕ 12 + ρ 23 a 2 2 ( 1 ρ 12 2 ) sin 2 ( ϕ 23 σ 2 ) ρ 12 ( 1 + ρ 23 2 a 2 4 ) cos 2 ϕ 12 + ρ 23 a 2 2 ( 1 + ρ 12 2 ) cos 2 ( ϕ 23 σ 2 ) ,
τ 13 = τ 12 τ 13 a 2 [ 1 + ρ 12 2 ρ 23 2 a 2 4 + 2 ρ 12 ρ 23 a 2 2 cos 2 ( ϕ 12 + ϕ 23 σ 2 ) ] 1 / 2 , 2 χ 13 = ( χ 12 + χ 23 ) + σ 2 arctan ρ 12 ρ 23 a 2 2 sin 2 ( ϕ 12 + ϕ 23 ) + sin 2 σ 2 ρ 12 ρ 23 a 2 2 cos 2 ( ϕ 12 + ϕ 23 ) + cos 2 σ 2 ,
a 2 = exp ( 2 π λ d 2 Γ 2 ( I ) ) , σ 2 = 2 π λ d 2 Γ 2 ( R ) ,
r 13 ( R ) = h 13 ( R ) ( r 12 ( R ) + g 23 ( R ) ) + h 13 ( I ) ( r 12 ( I ) + g 23 ( I ) ) h 13 2 , r 13 ( I ) = h 13 ( R ) ( r 12 ( I ) + g 23 ( I ) ) h 13 ( I ) ( r 12 ( R ) + g 23 ( R ) ) h 13 2 , t 13 ( R ) = h 13 ( R ) f 12 ( R ) + h 13 ( I ) f 13 ( I ) h 13 2 , t 13 ( I ) = h 13 ( R ) f 13 ( I ) h 13 ( I ) f 13 ( R ) h 13 2 ,
â 2 = a 2 exp ( i σ 2 ) , a 2 ( R ) = a 2 cos σ 2 , a 2 ( I ) = a 2 sin 2 σ 2 , b ̂ 2 = a 2 2 exp ( i 2 σ 2 ) , b 2 ( R ) = a 2 2 cos σ 2 , b 2 ( I ) = a 2 2 sin 2 σ 2 ,
ĝ 23 = r ̂ 23 exp ( i 2 Δ 2 ) , g 23 ( R ) = b 2 ( R ) r 23 ( R ) b 2 ( I ) r 23 ( I ) , g 23 ( I ) = b 2 ( I ) r 23 ( R ) + b 2 ( R ) r 23 ( I ) ,
ĥ 13 = 1 + r ̂ 12 r ̂ 13 exp ( i 2 Δ 2 ) , h 13 2 = ρ 12 2 ρ 23 2 a 2 4 + 2 h 13 ( R ) 1 , h 13 ( R ) = 1 + r 12 ( R ) g 23 ( R ) r 12 ( I ) g 23 ( I ) , h 13 ( I ) = r 12 ( R ) g 23 ( R ) + r 12 ( I ) g 23 ( I ) ,
ê 23 = t ̂ 23 exp ( i Δ 2 ) , e 23 ( R ) = a 2 ( R ) t 23 ( R ) a 2 ( I ) t 23 ( I ) , e 23 ( I ) = a 2 ( I ) t 23 ( R ) + a 2 ( R ) t 23 ( I ) ,
f ̂ 13 = t ̂ 12 t ̂ 23 exp ( i Δ 2 ) , f 13 ( R ) = t 12 ( R ) e 23 ( R ) t 12 ( I ) e 23 ( I ) , f 23 ( I ) = t 12 ( I ) e 23 ( R ) + t 12 ( R ) e 23 ( I ) .
ρ system = ( ρ 13 2 + ρ 31 2 a 3 4 1 + ρ 13 2 + ρ 31 2 a 3 4 ) 1 / 2 , τ system = τ 13 τ 31 a 3 ( 1 + ρ 13 2 + ρ 31 2 a 3 4 ) 1 / 2 ·
| R ( calc ) ( n ) R ( meas ) ( n ) | R ( meas ) ( n ) × 100 % n = 1 , 2 , , N , | T ( calc ) ( n ) T ( meas ) ( n ) | T ( meas ) ( n ) × 100 % n = 1 , 2 , , N
δ ( % ) = 100 % N n = 1 N [ 1 R ( calc ) ( n ) R ( meas ) ( n ) ] 2 , δ ( % ) = 100 % N n = 1 N [ 1 T ( calc ) ( n ) T ( meas ) ( n ) ] 2

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