Abstract

A systematic method has been proposed to evaluate the complex refractive indices and thicknesses of dispersive polymer thin films in both visible and infrared regions. The curve-fitting method has been applied to the measurement of the film thicknesses and complex refractive indices in the visible and near-infrared regions. The accuracy of the evaluated film thickness is of the order of ±0.5%. The presented method is useful for characterizing the optical properties of polymers whose refractive indices are near to those of substrates.

© 1997 Optical Society of America

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  1. Y. Kato, M. Osawa, M. Miyagi, S. Abe, M. Aizawa, S. Onodera, “Loss characteristics of polyimide-coated silver hollow glass waveguides for the infrared,” Electron. Lett. 31, 31–32 (1995).
    [CrossRef]
  2. Y. Kato, M. Osawa, M. Miyagi, M. Aizawa, S. Abe, S. Onodera, “Transmission characteristics of polyimide-coated silver hollow glass-waveguides for medical applications,” in Biomedical Optoelectronic Devices and Systems II, R. Pratesi, J. M. Wolfrum, N. I. Croitoru, eds., Proc. SPIE2328, 16–21 (1994).
  3. M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
    [CrossRef]
  4. Y. Matsuura, M. Miyagi, “Er:YAG, CO, and CO2 laser delivery by ZnS-coated Ag hollow waveguides,” Appl. Opt. 32, 6598–6601 (1993).
    [CrossRef] [PubMed]
  5. N. Croitoru, J. Dror, I. Gannot, “Characterization of hollow fibers for the transmission of infrared radiation,” Appl. Opt. 29, 1805–1809 (1990).
    [CrossRef] [PubMed]
  6. Y. Matsuura, T. Abel, J. A. Harrington, “Optical properties of small-bore hollow waveguides,” Appl. Opt. 34, 6842–6847 (1995).
    [CrossRef] [PubMed]
  7. P. O. Nilsson, “Determination of optical constants from intensity measurements at normal incidence,” Appl. Opt. 7, 435–442 (1968).
    [CrossRef] [PubMed]
  8. 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]
  9. M. Saito, S. Nakamura, M. Miyagi, “Measurement of the refractive index and thickness for infrared optical films deposited on rough substrate,” Appl. Opt. 31, 6139–6144 (1992).
    [CrossRef] [PubMed]
  10. W. J. Moore, “Errors in film refractive-index determinations from interference fringes,” Appl. Opt. 33, 4164–4166 (1994).
    [CrossRef] [PubMed]
  11. S. Gosse, D. Labrie, P. Chylek, “Refractive index of ice in the 1.4–7.8-µm spectral range,” Appl. Opt. 34, 6582–6586 (1995).
    [CrossRef] [PubMed]
  12. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, κ and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004, (1976).
    [CrossRef]
  13. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
    [CrossRef]
  14. D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).
    [CrossRef]
  15. M. Saito, T. Gojo, Y. Kato, M. Miyagi, “Optical constants of polymer coatings in the infrared,” Infrared Phys. Technol. 36, 1125–1129 (1995).
    [CrossRef]
  16. E. D. Palik, Handbook of Optical Constants of Solids, 1st ed. (Academic, Orlando, Fla., 1985), Chap. 4, pp. 81–87.
  17. M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 2, pp. 94–98.

1995 (4)

Y. Kato, M. Osawa, M. Miyagi, S. Abe, M. Aizawa, S. Onodera, “Loss characteristics of polyimide-coated silver hollow glass waveguides for the infrared,” Electron. Lett. 31, 31–32 (1995).
[CrossRef]

Y. Matsuura, T. Abel, J. A. Harrington, “Optical properties of small-bore hollow waveguides,” Appl. Opt. 34, 6842–6847 (1995).
[CrossRef] [PubMed]

S. Gosse, D. Labrie, P. Chylek, “Refractive index of ice in the 1.4–7.8-µm spectral range,” Appl. Opt. 34, 6582–6586 (1995).
[CrossRef] [PubMed]

M. Saito, T. Gojo, Y. Kato, M. Miyagi, “Optical constants of polymer coatings in the infrared,” Infrared Phys. Technol. 36, 1125–1129 (1995).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1990 (1)

1989 (1)

D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).
[CrossRef]

1984 (1)

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

1983 (1)

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[CrossRef]

1982 (1)

1976 (1)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, κ and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004, (1976).
[CrossRef]

1968 (1)

Abe, S.

Y. Kato, M. Osawa, M. Miyagi, S. Abe, M. Aizawa, S. Onodera, “Loss characteristics of polyimide-coated silver hollow glass waveguides for the infrared,” Electron. Lett. 31, 31–32 (1995).
[CrossRef]

Y. Kato, M. Osawa, M. Miyagi, M. Aizawa, S. Abe, S. Onodera, “Transmission characteristics of polyimide-coated silver hollow glass-waveguides for medical applications,” in Biomedical Optoelectronic Devices and Systems II, R. Pratesi, J. M. Wolfrum, N. I. Croitoru, eds., Proc. SPIE2328, 16–21 (1994).

Abel, T.

Aizawa, M.

Y. Kato, M. Osawa, M. Miyagi, S. Abe, M. Aizawa, S. Onodera, “Loss characteristics of polyimide-coated silver hollow glass waveguides for the infrared,” Electron. Lett. 31, 31–32 (1995).
[CrossRef]

Y. Kato, M. Osawa, M. Miyagi, M. Aizawa, S. Abe, S. Onodera, “Transmission characteristics of polyimide-coated silver hollow glass-waveguides for medical applications,” in Biomedical Optoelectronic Devices and Systems II, R. Pratesi, J. M. Wolfrum, N. I. Croitoru, eds., Proc. SPIE2328, 16–21 (1994).

Borgogno, J. P.

Born, M.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 2, pp. 94–98.

Chenault, D. B.

D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).
[CrossRef]

Chipman, R. A.

D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).
[CrossRef]

Chylek, P.

Croitoru, N.

Dror, J.

Fillard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, κ and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004, (1976).
[CrossRef]

Gannot, I.

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, κ and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004, (1976).
[CrossRef]

Gojo, T.

M. Saito, T. Gojo, Y. Kato, M. Miyagi, “Optical constants of polymer coatings in the infrared,” Infrared Phys. Technol. 36, 1125–1129 (1995).
[CrossRef]

Goldstein, D. H.

D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).
[CrossRef]

Gosse, S.

Harrington, J. A.

Kato, Y.

Y. Kato, M. Osawa, M. Miyagi, S. Abe, M. Aizawa, S. Onodera, “Loss characteristics of polyimide-coated silver hollow glass waveguides for the infrared,” Electron. Lett. 31, 31–32 (1995).
[CrossRef]

M. Saito, T. Gojo, Y. Kato, M. Miyagi, “Optical constants of polymer coatings in the infrared,” Infrared Phys. Technol. 36, 1125–1129 (1995).
[CrossRef]

Y. Kato, M. Osawa, M. Miyagi, M. Aizawa, S. Abe, S. Onodera, “Transmission characteristics of polyimide-coated silver hollow glass-waveguides for medical applications,” in Biomedical Optoelectronic Devices and Systems II, R. Pratesi, J. M. Wolfrum, N. I. Croitoru, eds., Proc. SPIE2328, 16–21 (1994).

Kawakami, S.

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

Labrie, D.

Lazarides, B.

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, κ and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004, (1976).
[CrossRef]

Matsuura, Y.

Miyagi, M.

Y. Kato, M. Osawa, M. Miyagi, S. Abe, M. Aizawa, S. Onodera, “Loss characteristics of polyimide-coated silver hollow glass waveguides for the infrared,” Electron. Lett. 31, 31–32 (1995).
[CrossRef]

M. Saito, T. Gojo, Y. Kato, M. Miyagi, “Optical constants of polymer coatings in the infrared,” Infrared Phys. Technol. 36, 1125–1129 (1995).
[CrossRef]

Y. Matsuura, M. Miyagi, “Er:YAG, CO, and CO2 laser delivery by ZnS-coated Ag hollow waveguides,” Appl. Opt. 32, 6598–6601 (1993).
[CrossRef] [PubMed]

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

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

Y. Kato, M. Osawa, M. Miyagi, M. Aizawa, S. Abe, S. Onodera, “Transmission characteristics of polyimide-coated silver hollow glass-waveguides for medical applications,” in Biomedical Optoelectronic Devices and Systems II, R. Pratesi, J. M. Wolfrum, N. I. Croitoru, eds., Proc. SPIE2328, 16–21 (1994).

Moore, W. J.

Nakamura, S.

Nilsson, P. O.

Onodera, S.

Y. Kato, M. Osawa, M. Miyagi, S. Abe, M. Aizawa, S. Onodera, “Loss characteristics of polyimide-coated silver hollow glass waveguides for the infrared,” Electron. Lett. 31, 31–32 (1995).
[CrossRef]

Y. Kato, M. Osawa, M. Miyagi, M. Aizawa, S. Abe, S. Onodera, “Transmission characteristics of polyimide-coated silver hollow glass-waveguides for medical applications,” in Biomedical Optoelectronic Devices and Systems II, R. Pratesi, J. M. Wolfrum, N. I. Croitoru, eds., Proc. SPIE2328, 16–21 (1994).

Osawa, M.

Y. Kato, M. Osawa, M. Miyagi, S. Abe, M. Aizawa, S. Onodera, “Loss characteristics of polyimide-coated silver hollow glass waveguides for the infrared,” Electron. Lett. 31, 31–32 (1995).
[CrossRef]

Y. Kato, M. Osawa, M. Miyagi, M. Aizawa, S. Abe, S. Onodera, “Transmission characteristics of polyimide-coated silver hollow glass-waveguides for medical applications,” in Biomedical Optoelectronic Devices and Systems II, R. Pratesi, J. M. Wolfrum, N. I. Croitoru, eds., Proc. SPIE2328, 16–21 (1994).

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids, 1st ed. (Academic, Orlando, Fla., 1985), Chap. 4, pp. 81–87.

Pelletier, E.

Saito, M.

M. Saito, T. Gojo, Y. Kato, M. Miyagi, “Optical constants of polymer coatings in the infrared,” Infrared Phys. Technol. 36, 1125–1129 (1995).
[CrossRef]

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

Swanepoel, R.

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 2, pp. 94–98.

Appl. Opt. (8)

Electron. Lett. (1)

Y. Kato, M. Osawa, M. Miyagi, S. Abe, M. Aizawa, S. Onodera, “Loss characteristics of polyimide-coated silver hollow glass waveguides for the infrared,” Electron. Lett. 31, 31–32 (1995).
[CrossRef]

Infrared Phys. Technol. (1)

M. Saito, T. Gojo, Y. Kato, M. Miyagi, “Optical constants of polymer coatings in the infrared,” Infrared Phys. Technol. 36, 1125–1129 (1995).
[CrossRef]

J. Lightwave Technol. (1)

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

J. Phys. E (2)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, κ and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004, (1976).
[CrossRef]

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[CrossRef]

Opt. Eng. (1)

D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).
[CrossRef]

Other (3)

E. D. Palik, Handbook of Optical Constants of Solids, 1st ed. (Academic, Orlando, Fla., 1985), Chap. 4, pp. 81–87.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Chap. 2, pp. 94–98.

Y. Kato, M. Osawa, M. Miyagi, M. Aizawa, S. Abe, S. Onodera, “Transmission characteristics of polyimide-coated silver hollow glass-waveguides for medical applications,” in Biomedical Optoelectronic Devices and Systems II, R. Pratesi, J. M. Wolfrum, N. I. Croitoru, eds., Proc. SPIE2328, 16–21 (1994).

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Figures (11)

Fig. 1
Fig. 1

Light transmitting through a single thin film on a substrate.

Fig. 2
Fig. 2

Process of determination of (a) exact peak order m and (b) thickness and complex refractive index.

Fig. 3
Fig. 3

Evaluation of the film thickness and extinction coefficient: (a) determination of d (2) around a peak, where theoretical results are obtained by changing the thickness of the film for κ = 0; (b) determination of κ(2) evaluated by fitting the measured transmittance with a theoretical curve.

Fig. 4
Fig. 4

Extinction coefficients κ s of a BaF2 substrate. (Δκ s is the evaluation error of κ s , found by taking the measurement errors of the thickness and transmittance of BaF2 sheets into account.)

Fig. 5
Fig. 5

Transmittance spectrum in the visible and near-infrared regions of polyester with a thickness of 1.16 µm on a BaF2 substrate with a thickness of 1.58 mm. The measured and theoretical results predicted by using the evaluated optical constants cannot be distinguished from each other.

Fig. 6
Fig. 6

Measured refractive index and extinction coefficient of polyester (Kemit R-248) in the visible and near-infrared regions. Solid curves are least-squares-fitting curves, described by Eqs. (19) and (20), respectively.

Fig. 7
Fig. 7

Extinction coefficient κ of polyester (Kemit R-248) for (a) thin film and (b) thick film in the middle-infrared; Δκ is an error predicted by Eq. (21).

Fig. 8
Fig. 8

Extinction coefficient κ of polyester (Kemit R-248) in the middle-infrared region.

Fig. 9
Fig. 9

Comparison of measured (dotted curve) and theoretical (solid curve) transmittances of sample B of polyester (Kemit R-248) with a thickness of 1.16 µm on a BaF2 substrate with a thickness of 1.58 mm in the middle-infrared region.

Fig. 10
Fig. 10

Variation of the relative error of n (1) with the relative error of transmittance for various n (1) - n s ; λ is 0.841 µm between two adjacent maxima and minima from the transmission spectrum of sample B.

Fig. 11
Fig. 11

Extinction coefficient of polyester (Kemit R-248) calculated directly by using Eqs. (24)–(26) in visible and near-infrared regions.

Tables (2)

Tables Icon

Table 1 Conditions for T to Take the Maximum or Minimum at Particular Wavelengthsa

Tables Icon

Table 2 Evaluation Process of the Thickness and Refractive Index for Sample B

Equations (31)

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T02=nsn0t01t12 exp-jβd1-r12r10 exp-2jβd2,
β=2πλn-jκ,
R21=r21+r10 exp-2jβd1+r21r10 exp-2jβd2
T=T02T20 exp-4πκsds/λ1-R20R21 exp-8πκsds/λ,
T20=4n0nsns2+κs2ns+n02+κs2,
R20=ns-n02+κs2ns+n02+κs2.
TT02T201-R20R21.
n1=A+A2-ns21/2,
A=ns2+12+2ns1Tmax-1Tmin× 1,ns > n-1,ns < n.
d1=λipλi+1p2λipni+1p-λi+1pnip.
m=2nipd1λip,
TT02T20 exp-4πκsdsλt01t122nsn0T20 exp-4πλκsds+κd,
ln T=C+-4πλ κd,
Ts=2nsns2+1
ns=1Ts+1Ts2-11/2.
ns=1.419+7.7×10-3λ-2-3.1×10-4λ-4.
nglass-n < ns-n.
n>ns.
n=1.526+2.4×10-3λ-2+8.9×10-4λ-4.
κ=7.9×10-4λ exp-7.8×10-2λ2.
Δκ=κmax-κmin.
Δnsns=-1nsTs1+11-Ts2ΔTsTs.
Δn2=m2dΔλip-mλ2d2Δd.
κ=λ4πdlnn-13ns2-nB+B2+n2-13ns4-n21/2,
B=-8nsn2Tmax+n2-ns2n2-1× 1,ns > n-1,ns > n.
B=-8nsn2Tmin-n2-ns2n2-1× 1,ns > n-1,ns > n.
Δn1=12A+A2-ns2-1/2Q+AQ-ns×A2-ns2-1/2Δns+12PA+A2-ns2-1/2×1+AA2-ns2-1/2ΔT,
A=ns2+12+2nsg1Tmax-1Tmin,
P=2nsg-1Tmax2+1Tmin2,
Q=2g1Tmax-1Tmin+ns,
g= 1,ns > n-1,ns < n.

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