Abstract

We propose a simple and accurate method for measuring the refractive index and the absorption coefficient of an absorbing parallel plate. The method is essentially based on transmittance measurement with minimum reflectance at the Brewster angle for p-polarized light, which enables us to measure a low absorption loss of the order of 0.1dBcm for a typical plate thickness of 1mm. The error that is due to the approximation used is practically negligible, and the accuracy of measured results depends mainly on the variations in the flatness and parallelism of the two surfaces of the sample and on instrumental errors.

© 2006 Optical Society of America

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References

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2005

2004

2001

C. Cali, M. Mosca, and G. Targia, Opt. Commun. 191, 295 (2001).
[CrossRef]

2000

T. Uchino, K. Nakaguchi, Y. Nagashima, and T. Kondo, J. Non-Cryst. Solids 261, 72 (2000).
[CrossRef]

1999

1995

D. B. Kushev and N. N. Zheleva, J. Phys. D 28, 1239 (1995).
[CrossRef]

1992

M. Akimoto and Y. Gekka, Jpn. J. Appl. Phys. Part 1 31, 120 (1992).
[CrossRef]

1983

1982

1977

Akimoto, M.

M. Akimoto and Y. Gekka, Jpn. J. Appl. Phys. Part 1 31, 120 (1992).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and T. F. Thonn, Appl. Opt. 22, 4155 (1983).
[CrossRef] [PubMed]

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Beaglehole, D.

Buckley, R. G.

Cali, C.

C. Cali, M. Mosca, and G. Targia, Opt. Commun. 191, 295 (2001).
[CrossRef]

Chiu, M.-H.

Gekka, Y.

M. Akimoto and Y. Gekka, Jpn. J. Appl. Phys. Part 1 31, 120 (1992).
[CrossRef]

Hunter, W. R.

Kitao, M.

Kondo, T.

T. Uchino, K. Nakaguchi, Y. Nagashima, and T. Kondo, J. Non-Cryst. Solids 261, 72 (2000).
[CrossRef]

Kushev, D. B.

D. B. Kushev and N. N. Zheleva, J. Phys. D 28, 1239 (1995).
[CrossRef]

Lee, J.-Y.

Maeda, S.

Minakata, M.

Minikata, M.

Mosca, M.

C. Cali, M. Mosca, and G. Targia, Opt. Commun. 191, 295 (2001).
[CrossRef]

Nagashima, Y.

T. Uchino, K. Nakaguchi, Y. Nagashima, and T. Kondo, J. Non-Cryst. Solids 261, 72 (2000).
[CrossRef]

Nakaguchi, K.

T. Uchino, K. Nakaguchi, Y. Nagashima, and T. Kondo, J. Non-Cryst. Solids 261, 72 (2000).
[CrossRef]

Ogusu, K.

Palik, E. D.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985), pp. 566, 760.

Su, D.-C.

Suzuki, K.

Swanepoel, R.

R. Swanepoel, J. Phys. E 16, 1214 (1983).
[CrossRef]

Targia, G.

C. Cali, M. Mosca, and G. Targia, Opt. Commun. 191, 295 (2001).
[CrossRef]

Thonn, T. F.

Uchino, T.

T. Uchino, K. Nakaguchi, Y. Nagashima, and T. Kondo, J. Non-Cryst. Solids 261, 72 (2000).
[CrossRef]

Yamasaki, J.

Zheleva, N. N.

D. B. Kushev and N. N. Zheleva, J. Phys. D 28, 1239 (1995).
[CrossRef]

Appl. Opt.

J. Non-Cryst. Solids

T. Uchino, K. Nakaguchi, Y. Nagashima, and T. Kondo, J. Non-Cryst. Solids 261, 72 (2000).
[CrossRef]

J. Phys. D

D. B. Kushev and N. N. Zheleva, J. Phys. D 28, 1239 (1995).
[CrossRef]

J. Phys. E

R. Swanepoel, J. Phys. E 16, 1214 (1983).
[CrossRef]

Jpn. J. Appl. Phys. Part 1

M. Akimoto and Y. Gekka, Jpn. J. Appl. Phys. Part 1 31, 120 (1992).
[CrossRef]

Opt. Commun.

C. Cali, M. Mosca, and G. Targia, Opt. Commun. 191, 295 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Other

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985), pp. 566, 760.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

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Figures (4)

Fig. 1
Fig. 1

Two methods for measuring absorption coefficient α of an absorbing plate in air: (a) conventional method (normal incidence), (b) proposed method (oblique incidence at the Brewster angle). (c) Multiple reflection and transmission of a plane wave incident obliquely onto the absorbing plate.

Fig. 2
Fig. 2

Dependence of minimum reflectance R min and relative errors of n and k , n n n and k k k , on extinction coefficient k for λ = 1 μ m , n = 2 , and d = 1 mm .

Fig. 3
Fig. 3

Measured reflectance R as a function of angle of incidence θ 1 for a fused-silica plate with a thickness of 1.0 mm .

Fig. 4
Fig. 4

Measured reflectance R as a function of angle of incidence θ 1 for Si and As 2 Se 3 plates at λ = 1.047 μ m .

Equations (6)

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R = R 0 + ( 1 R 0 ) 2 R 0 exp ( 2 α d cos θ 2 ) 1 R 0 2 exp ( 2 α d cos θ 2 ) ,
T = ( 1 R 0 ) 2 exp ( α d cos θ 2 ) 1 R 0 2 exp ( 2 α d cos θ 2 ) ,
n = tan θ B ,
R = R 0 [ 1 + exp ( 2 α d cos θ 2 B ) ] R 0 , α d 1 ,
2 R 0 , α d 1 ,
T = ( 1 R 0 ) 2 exp ( α d cos θ 2 B ) ,

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