Abstract

The polarization plane of a laser beam is made to rotate at high frequency with the help of a special setup containing wave plates and an acoustooptic modulator. The application of this beam for ellipsometric measurements is investigated and a number of applications are proposed. We describe some novel approaches for the analysis of thin films and optical surfaces and for measurements on static and time-varying anisotropic phenomena such as the electrooptic effect, optical activity, and strain analysis using the photoelastic effect.

© 1986 Optical Society of America

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References

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  1. See, for example, J. M. Bennett, H. E. Bennett, “Polarization” in Handbook of Optics, W. G. Driscoll, Ed. (McGraw-Hill, New York, 1978);R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977);A. R. M. Zaghloul, R. M. A. Azzam, “Single-Element Rotating-Polarizer Ellipsometer for Film-Substrate Systems,” J. Opt. Soc. Am. 67, 1286 (1977).
    [Crossref]
  2. J. Shamir, Y. Fainman, “Rotating Linearly Polarized Light Source,” Appl. Opt. 21, 365 (1982).
    [Crossref]
  3. H. Rosen, J. Shamir, “Interferometric Determination of Ellipsometric Parameters,” J. Phys. E 11, 1 (1978).
    [Crossref]
  4. J. Shamir, “Interferometer with Rotating Linearly Polarized Light,” in Conference Digest, Optics in Modern Science and Technology, Sapporo, 20–24 Aug 1984, pp. 494 and 495.
  5. R. C. Jones, “A New Calculus for the Treatment of Optical Systems: I, II, III,” J. Opt. Soc. Am 31, 488 (1941);“A New Calculus for the Treatment of Optical Systems: IV,” 32, 486 (1942).
    [Crossref]

1982 (1)

1978 (1)

H. Rosen, J. Shamir, “Interferometric Determination of Ellipsometric Parameters,” J. Phys. E 11, 1 (1978).
[Crossref]

1941 (1)

R. C. Jones, “A New Calculus for the Treatment of Optical Systems: I, II, III,” J. Opt. Soc. Am 31, 488 (1941);“A New Calculus for the Treatment of Optical Systems: IV,” 32, 486 (1942).
[Crossref]

Bennett, H. E.

See, for example, J. M. Bennett, H. E. Bennett, “Polarization” in Handbook of Optics, W. G. Driscoll, Ed. (McGraw-Hill, New York, 1978);R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977);A. R. M. Zaghloul, R. M. A. Azzam, “Single-Element Rotating-Polarizer Ellipsometer for Film-Substrate Systems,” J. Opt. Soc. Am. 67, 1286 (1977).
[Crossref]

Bennett, J. M.

See, for example, J. M. Bennett, H. E. Bennett, “Polarization” in Handbook of Optics, W. G. Driscoll, Ed. (McGraw-Hill, New York, 1978);R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977);A. R. M. Zaghloul, R. M. A. Azzam, “Single-Element Rotating-Polarizer Ellipsometer for Film-Substrate Systems,” J. Opt. Soc. Am. 67, 1286 (1977).
[Crossref]

Fainman, Y.

Jones, R. C.

R. C. Jones, “A New Calculus for the Treatment of Optical Systems: I, II, III,” J. Opt. Soc. Am 31, 488 (1941);“A New Calculus for the Treatment of Optical Systems: IV,” 32, 486 (1942).
[Crossref]

Rosen, H.

H. Rosen, J. Shamir, “Interferometric Determination of Ellipsometric Parameters,” J. Phys. E 11, 1 (1978).
[Crossref]

Shamir, J.

J. Shamir, Y. Fainman, “Rotating Linearly Polarized Light Source,” Appl. Opt. 21, 365 (1982).
[Crossref]

H. Rosen, J. Shamir, “Interferometric Determination of Ellipsometric Parameters,” J. Phys. E 11, 1 (1978).
[Crossref]

J. Shamir, “Interferometer with Rotating Linearly Polarized Light,” in Conference Digest, Optics in Modern Science and Technology, Sapporo, 20–24 Aug 1984, pp. 494 and 495.

Appl. Opt. (1)

J. Opt. Soc. Am (1)

R. C. Jones, “A New Calculus for the Treatment of Optical Systems: I, II, III,” J. Opt. Soc. Am 31, 488 (1941);“A New Calculus for the Treatment of Optical Systems: IV,” 32, 486 (1942).
[Crossref]

J. Phys. E (1)

H. Rosen, J. Shamir, “Interferometric Determination of Ellipsometric Parameters,” J. Phys. E 11, 1 (1978).
[Crossref]

Other (2)

J. Shamir, “Interferometer with Rotating Linearly Polarized Light,” in Conference Digest, Optics in Modern Science and Technology, Sapporo, 20–24 Aug 1984, pp. 494 and 495.

See, for example, J. M. Bennett, H. E. Bennett, “Polarization” in Handbook of Optics, W. G. Driscoll, Ed. (McGraw-Hill, New York, 1978);R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977);A. R. M. Zaghloul, R. M. A. Azzam, “Single-Element Rotating-Polarizer Ellipsometer for Film-Substrate Systems,” J. Opt. Soc. Am. 67, 1286 (1977).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Diagram of the system for production of rotating plane-polarized light beams: L, laser; AO, acoustooptic modulator; M, mirrors; B, beam splitter, and corresponding wave plates. The measuring beam is usually E2 while the other beam may serve as a reference.

Fig. 2
Fig. 2

Configuration of the quarterwave plate and polarizer leading to Eq. (9).

Fig. 3
Fig. 3

Sample (S) positioning in the measuring beam: P is a polarizer; D is a detector for reflecting samples, while D′ is an alternative position for analyzing transparent samples.

Fig. 4
Fig. 4

Curves showing the variation of A as a function of γ with ψ and Δ as parameters: (a) ψ = 30°, (b) ψ = 45°, (c) ψ = 60°, and (d) ψ = 70°. For all curves Δ increases downward with the values 0°, 30°, 60°, and 90°.

Equations (24)

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E 1 = { exp j [ ( ω + Ω ) t + φ ] exp j [ ( ω Ω ) t φ ] } = exp j ω t [ exp j ( Ω t + φ ) exp j ( Ω t + φ ) ] ,
E 2 = W E 1 ,
W = 1 2 ( 1 j j 1 ) .
E 2 = 2 exp j ( ω π / 2 ) [ sin ( Ω t + φ π / 4 ) cos ( Ω t + φ π / 4 ) ] .
P y = ( 0 0 0 1 )
R ( γ ) = ( cos γ sin γ sin γ cos γ ) ,
E γ = P y R ( γ ) E 2 .
E γ = 2 exp j ( ω t π / 4 ) ( 0 cos ( Ω t π / 4 + φ + γ ) .
I γ = 2 cos 2 ( Ω t π / 4 + φ + γ ) = 1 + sin 2 ( Ω t + φ + γ ) .
S = ( r p 0 0 r s ) ,
E 3 = SE 2 .
E γ = P y R ( γ ) E 3 = P y R ( γ ) SE 2
E γ = 2 exp j ( ω t π / 4 ) × [ 0 r s cos γ cos ( Ω t + φ π / 4 ) r p sin γ sin ( Ω t + φ π / 4 ) ] .
I γ = | E γ | 2 = 2 [ | r s | 2 cos 2 γ cos 2 ( Ω t + φ π / 4 ) + | r p | 2 sin 2 γ sin 2 ( Ω t + φ π / 4 ) + ( r s * r p + r s r p * ) sin γ cos γ sin ( Ω t + φ π / 4 ) × cos ( Ω t + φ π / 4 ) ] .
r s r p tan ψ exp j Δ
I γ = | r p | 2 [ tan 2 ψ cos 2 γ + sin 2 γ + ( tan 2 ψ cos 2 γ sin 2 γ ) sin 2 ( Ω t + φ ) + tan ψ cos Δ sin 2 γ cos 2 ( Ω t + θ ) ] .
tan β = tan ψ sin 2 γ cos Δ tan 2 γ cos 2 γ sin 2 γ = 2 tan ψ tan γ cos Δ tan 2 ψ tan 2 γ
I γ = | r p | 2 [ tan 2 ψ cos 2 γ + sin 2 γ + ( tan 2 ψ cos 2 γ sin 2 γ ) 2 + ( tan ψ cos Δ sin 2 γ ) 2 × cos ( 2 Ω t + 2 φ + β ) ] .
β ( 0 ) = 0 , β ( π / 2 ) = π ,
β = π / 2 for γ = ψ .
tan β 45 = 2 tan ψ cos Δ tan 2 ψ 1 = tan 2 ψ cos Δ .
A ( γ ) = ( tan 2 ψ cos 2 γ sin 2 γ ) 2 + tan 2 ψ cos 2 Δ sin 2 2 γ
( tan 2 ψ cos 2 γ sin 2 γ ) ( tan 2 ψ + 1 ) × sin 2 γ 2 tan 2 ψ cos 2 Δ cos 2 γ sin 2 γ = 0 .
A ( π / 2 ) = 1 .

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