Abstract

Shadowing causes form birefringence in optical thin films that are deposited at oblique incidence. For light incident in the plane containing the direction of deposition and the substrate normal, the TE and TM polarizations in the film are decoupled, and field transfer can be described using 2×2 matrices. The three principal indices of birefringent films are deduced from measurements made on narrow-band interference filters. In one example refractive indices of 2.688, 2.429, and 2.452 were computed for TiO2 deposited at 27° to the substrate normal. Both TiO2 and ZrO2 behave as positive biaxial media.

© 1985 Optical Society of America

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References

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1984 (2)

1983 (1)

C. C. Lee, M. Sikkens, I. J. Hodgkinson, H. A. Macleod, R. H. Potoff, R. Sprague, M. R. Jacobson, “Anisotropic moisture-penetration in optical coatings,” J. Opt. Soc. Am. 73, 1871 (1983).

1981 (1)

R. J. King, S. P. Talim, “A comparison of thin film measurements by guided waves, ellipsometry and reflectometry,” Opt. Acta 28, 1107–1123(1981).
[CrossRef]

1979 (1)

1977 (1)

A. G. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–233 (1977).
[CrossRef]

1972 (1)

1966 (3)

1950 (1)

Berreman, D. W.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Chilwell, J. T.

Dirks, A. G.

A. G. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–233 (1977).
[CrossRef]

Feucht, D. L.

Haanstra, H. B.

J. M. Nieuwenhuizen, H. B. Haanstra, “Microfractography of thin films,” Philips Tech. Rev. 27, 87–91 (1966).

Henvis, B. W.

Hodgkinson, I. J.

J. T. Chilwell, I. J. Hodgkinson, “Thin films field transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A 1, 742–753 (1984).
[CrossRef]

C. C. Lee, M. Sikkens, I. J. Hodgkinson, H. A. Macleod, R. H. Potoff, R. Sprague, M. R. Jacobson, “Anisotropic moisture-penetration in optical coatings,” J. Opt. Soc. Am. 73, 1871 (1983).

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Structural effects in thin film coatings,” in Digest of the Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984).

Holmes, D. A.

Horowitz, F.

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Structural effects in thin film coatings,” in Digest of the Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984).

Jacobson, M. R.

C. C. Lee, M. Sikkens, I. J. Hodgkinson, H. A. Macleod, R. H. Potoff, R. Sprague, M. R. Jacobson, “Anisotropic moisture-penetration in optical coatings,” J. Opt. Soc. Am. 73, 1871 (1983).

King, R. J.

R. J. King, S. P. Talim, “A comparison of thin film measurements by guided waves, ellipsometry and reflectometry,” Opt. Acta 28, 1107–1123(1981).
[CrossRef]

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970).

Leamy, H. J.

A. G. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–233 (1977).
[CrossRef]

Lee, C. C.

C. C. Lee, M. Sikkens, I. J. Hodgkinson, H. A. Macleod, R. H. Potoff, R. Sprague, M. R. Jacobson, “Anisotropic moisture-penetration in optical coatings,” J. Opt. Soc. Am. 73, 1871 (1983).

Lin-Chung, P. J.

Macleod, H. A.

C. C. Lee, M. Sikkens, I. J. Hodgkinson, H. A. Macleod, R. H. Potoff, R. Sprague, M. R. Jacobson, “Anisotropic moisture-penetration in optical coatings,” J. Opt. Soc. Am. 73, 1871 (1983).

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Structural effects in thin film coatings,” in Digest of the Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984).

Nieuwenhuizen, J. M.

J. M. Nieuwenhuizen, H. B. Haanstra, “Microfractography of thin films,” Philips Tech. Rev. 27, 87–91 (1966).

Potoff, R. H.

C. C. Lee, M. Sikkens, I. J. Hodgkinson, H. A. Macleod, R. H. Potoff, R. Sprague, M. R. Jacobson, “Anisotropic moisture-penetration in optical coatings,” J. Opt. Soc. Am. 73, 1871 (1983).

Scott, G. D.

Sennett, R. S.

Sikkens, M.

C. C. Lee, M. Sikkens, I. J. Hodgkinson, H. A. Macleod, R. H. Potoff, R. Sprague, M. R. Jacobson, “Anisotropic moisture-penetration in optical coatings,” J. Opt. Soc. Am. 73, 1871 (1983).

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Structural effects in thin film coatings,” in Digest of the Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984).

Sprague, R.

C. C. Lee, M. Sikkens, I. J. Hodgkinson, H. A. Macleod, R. H. Potoff, R. Sprague, M. R. Jacobson, “Anisotropic moisture-penetration in optical coatings,” J. Opt. Soc. Am. 73, 1871 (1983).

Talim, S. P.

R. J. King, S. P. Talim, “A comparison of thin film measurements by guided waves, ellipsometry and reflectometry,” Opt. Acta 28, 1107–1123(1981).
[CrossRef]

Teitler, S.

Wharton, J. J.

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Structural effects in thin film coatings,” in Digest of the Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Yeh, P.

J. Opt. Soc. Am. (6)

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

Opt. Acta (1)

R. J. King, S. P. Talim, “A comparison of thin film measurements by guided waves, ellipsometry and reflectometry,” Opt. Acta 28, 1107–1123(1981).
[CrossRef]

Philips Tech. Rev. (1)

J. M. Nieuwenhuizen, H. B. Haanstra, “Microfractography of thin films,” Philips Tech. Rev. 27, 87–91 (1966).

Thin Solid Films (1)

A. G. Dirks, H. J. Leamy, “Columnar microstructure in vapor-deposited thin films,” Thin Solid Films 47, 219–233 (1977).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Structural effects in thin film coatings,” in Digest of the Topical Meeting on Optical Interference Coatings (Optical Society of America, Washington, D.C., 1984).

M. V. Klein, Optics (Wiley, New York, 1970).

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Figures (3)

Fig. 1
Fig. 1

Location of the principal axes in a biaxial thin film model. The film surfaces are parallel to the y-z plane. Principal-axis 1 is parallel to the columns that form the microstructure. Axis 3 is parallel to the plane of the film and parallel to the z axis.

Fig. 2
Fig. 2

An incident plane wave causes four plane waves to propagate in the anisotropic film. Each wave has the same value of β = n sin θ.

Fig. 3
Fig. 3

Measured values of the wavelengths of transmission peaks are used for the realization of the principal indices of the anisotropic layers.

Tables (1)

Tables Icon

Table 1 Refractive Indices of Zirconium Oxide and Titanium Oxide

Equations (12)

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tan ψ = ½ tan δ ,
f = ( E z H y H z E y ) ,
( c 11 2 n 1 2 + c 12 2 n 2 2 + c 13 2 n 3 2 ) α 4 + 2 β ( c 11 c 21 n 1 2 + c 12 c 22 n 2 2 + c 13 c 23 n 3 2 ) α 3 + { β 2 [ ( c 11 2 + c 21 2 ) n 1 2 + ( c 12 2 + c 22 2 ) n 2 2 + ( c 13 2 + c 23 2 ) n 3 2 ] + ( c 11 2 1 ) n 2 2 n 3 2 + ( c 12 2 1 ) n 3 2 n 1 2 + ( c 13 2 1 ) n 1 2 n 2 2 } α 2 + { 2 β 3 ( c 11 c 21 n 1 2 + c 12 c 22 n 2 2 + c 13 c 23 n 3 2 ) + 2 β ( c 11 c 21 n 2 2 n 3 2 + c 12 c 22 n 3 2 n 1 2 + c 13 c 23 n 1 2 c 2 2 ) } α + β 4 ( c 21 2 n 1 2 + c 22 2 n 2 2 + c 23 2 n 3 2 ) + β 2 [ ( c 21 2 1 ) n 2 2 n 3 2 + ( c 22 2 1 ) n 3 2 n 1 2 + ( c 23 2 1 ) n 1 2 n 2 2 ] + n 1 2 n 2 2 n 3 2 = 0 .
E z = c 31 ( c 11 α + c 21 β ) α 2 + β 2 n 1 2 + c 32 ( c 12 α + c 22 β ) α 2 + β 2 n 2 2 + c 33 ( c 13 α + c 23 β ) α 2 + β 2 n 3 2 , H y = α E z , H z = ( c 21 α c 11 β ) ( c 11 α + c 21 β ) α 2 + β 2 n 1 2 + ( c 22 α c 12 β ) ( c 12 α + c 22 β ) α 2 + β 2 n 2 2 + ( c 23 α c 13 β ) ( c 13 α + c 23 β ) α 2 + β 2 n 3 2 E y = c 21 ( c 11 α + c 21 β ) α 2 + β 2 n 1 2 + c 22 ( c 12 α + c 22 β ) α 2 + β 2 n 2 2 + c 23 ( c 13 α + c 23 β ) α 2 + β 2 n 3 2 .
T F F Φ ,
Φ = ( e i ϕ ( 1 ) 0 0 0 0 e i ϕ ( 2 ) 0 0 0 0 e i ϕ ( 3 ) 0 0 0 0 e i ϕ ( 4 ) ) ,
T = F Φ F 1 .
[ ( n 1 2 cos 2 ψ + n 2 2 sin 2 ψ ) α 2 2 β cos ψ sin ψ ( n 1 2 n 2 2 ) α + β 2 ( n 1 2 sin 2 ψ n 2 2 cos 2 ψ ) n 1 2 n 2 2 ] × ( α 2 + β 2 n 3 2 ) = 0 .
F = ( 1 1 0 0 γ ( 1 ) γ ( 2 ) 0 0 0 0 1 1 0 0 γ ( 3 ) γ ( 4 ) ) ,
( U j 1 V j 1 ) = M ( U j V j ) .
M = ( cos ϕ i / γ sin ϕ i γ sin ϕ cos ϕ ) .
N = ( sin 2 ψ / n 1 2 + cos 2 ψ / n 2 2 ) 1 / 2 .

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