Abstract

A novel high speed interferometric ellipsometer (HSIE) is proposed and demonstrated. It is based on a novel differential-phase decoder which is able to convert the phase modulation into amplitude modulation in a polarized heterodyne interferometer. Not only high detection sensitivity but also fast response ability on ellipsometric parameters (EP) measurements based on amplitude-sensitive method is constructed whereas different amplitudes with respect to P and S polarized heterodyne signals in this phase to amplitude modulation conversion is discussed. The ability of HSIE was verified by testing a quarter wave plate while a real time differential-phase detection of a liquid crystal device versus applied voltage by using HSIE was demonstrated too. These results confirm that HSIE is able to characterize the optical property of specimen in terms of EP at high speed and high detection sensitivity experimentally.

© 2008 Optical Society of America

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References

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2007 (1)

2006 (1)

2004 (1)

2002 (1)

2001 (2)

2000 (1)

M. Sato, K. Seino, K. Onodera and N. Tanno, "Phase-drift suppression using harmonics in heterodyne detection and its application to optical coherence tomography," Opt. Commun.  184, 95-104 (2000).
[CrossRef]

1999 (2)

Y. Q. Li, D. Guzun, and M. Xiao, "Sub-shot-noise-limited optical heterodyne detection using an amplitude-squeezed local oscillator," Phys. Rev. Lett 82, 5225-5228 (1999).
[CrossRef]

T. E. Jenkins, "Multiple-angle-of-incidence ellipsometry," J. Phys. D. Appl. Phys. 32, R45-R56 (1999).
[CrossRef]

1997 (1)

1990 (1)

1985 (1)

Chang, K. S.

Chang, M.

Cheng, Y. Y.

Chou, C.

Dasari, R. R.

Feld, M. S.

Guzun, D.

Y. Q. Li, D. Guzun, and M. Xiao, "Sub-shot-noise-limited optical heterodyne detection using an amplitude-squeezed local oscillator," Phys. Rev. Lett 82, 5225-5228 (1999).
[CrossRef]

Hoogerland, M. D.

Hsieh, C. H.

Hsieh, J. C.

Huang, H. S.

Huang, Y. C.

Jenkins, T. E.

T. E. Jenkins, "Multiple-angle-of-incidence ellipsometry," J. Phys. D. Appl. Phys. 32, R45-R56 (1999).
[CrossRef]

Li, Y. Q.

Y. Q. Li, D. Guzun, and M. Xiao, "Sub-shot-noise-limited optical heterodyne detection using an amplitude-squeezed local oscillator," Phys. Rev. Lett 82, 5225-5228 (1999).
[CrossRef]

Lin, C. H.

Lyu, C. W.

Onodera, K.

M. Sato, K. Seino, K. Onodera and N. Tanno, "Phase-drift suppression using harmonics in heterodyne detection and its application to optical coherence tomography," Opt. Commun.  184, 95-104 (2000).
[CrossRef]

Peng, L. C.

Sato, M.

M. Sato, K. Seino, K. Onodera and N. Tanno, "Phase-drift suppression using harmonics in heterodyne detection and its application to optical coherence tomography," Opt. Commun.  184, 95-104 (2000).
[CrossRef]

Seino, K.

M. Sato, K. Seino, K. Onodera and N. Tanno, "Phase-drift suppression using harmonics in heterodyne detection and its application to optical coherence tomography," Opt. Commun.  184, 95-104 (2000).
[CrossRef]

Tanno, N.

M. Sato, K. Seino, K. Onodera and N. Tanno, "Phase-drift suppression using harmonics in heterodyne detection and its application to optical coherence tomography," Opt. Commun.  184, 95-104 (2000).
[CrossRef]

Teng, H. K.

Tsai, C. C.

Watkins, L. R.

Wax, A.

Wei, H. C.

Wyant, J. C.

Xiao, M.

Y. Q. Li, D. Guzun, and M. Xiao, "Sub-shot-noise-limited optical heterodyne detection using an amplitude-squeezed local oscillator," Phys. Rev. Lett 82, 5225-5228 (1999).
[CrossRef]

Yang, C.

Yu, C. R.

Yu, L. P.

Appl. Opt. (4)

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

J. Phys. D. Appl. Phys. (1)

T. E. Jenkins, "Multiple-angle-of-incidence ellipsometry," J. Phys. D. Appl. Phys. 32, R45-R56 (1999).
[CrossRef]

Opt. Commun. (1)

M. Sato, K. Seino, K. Onodera and N. Tanno, "Phase-drift suppression using harmonics in heterodyne detection and its application to optical coherence tomography," Opt. Commun.  184, 95-104 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett (1)

Y. Q. Li, D. Guzun, and M. Xiao, "Sub-shot-noise-limited optical heterodyne detection using an amplitude-squeezed local oscillator," Phys. Rev. Lett 82, 5225-5228 (1999).
[CrossRef]

Other (4)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

K. Riedling, Ellipsometry for Industrial Applications (Springer-Verlag, New York, 1988).
[CrossRef]

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, New York, 1999), Chap. 5.

[1] . R. E. Ziemer and W. H. Tranter, Principles of Communications (Wiley, New York, 1995), Chap. 6.

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Figures (7)

Fig. 1.
Fig. 1.

The optical setup: He-Ne: laser source, BS1 , BS2 : beam splitters, AOM1 , AOM2 : acousto-optic modulators, M1 , M2 : mirrors, Po1 , Po2 : polarizers, C: compensator, S: sample, PBS: polarization beam splitter, Dp , Ds : detectors, BPF: band-pass filter, DA: differential amplifier, FG: function generator, DAU: data acquisition unit, PC: personal computer

Fig. 2.
Fig. 2.

Experimental results of (a) the amplitudes of P polarized, S polarized heterodyne signals, and their difference, (b) the amplitude ratio of P and S heterodyne signals, (c) the parameter ψ, (d) the absolute value of phase retardation versus rotation angle of 180° dynamic range, (e) the recovered phase retardation with DC phase bias, (f) the phase retardation of zero DC phase bias is consistent with the experimental curve measured by LIA (solid line).

Fig. 3.
Fig. 3.

The molecular alignment of homogeneous LC at (a) parallel-aligned condition at offstate with initial orientation θpre, (b) the effective index ellipsoid model of homogeneous LC, (c) the side view of PALCD in order to find the relation between PALCD and the incident laser beam, (d) symmetrically tilted condition of molecules to the central surface (z=d/2) between two ITO films with applied voltage at on-state where the effective tilt angle is θet.

Fig. 4.
Fig. 4.

Experimental results of phase retardation versus AC square-wave voltage (1 KHz) on homogeneous PALCD by slowly increasing the voltage from 0 V to 12 V.

Fig. 5.
Fig. 5.

The rise time τrise and decay time τdecay of phase retardation of homogeneous PALC under the condition of applying 10 VAC square-wave voltage (1 KHz). In this experiment, τrise=186 ms and τdecay=213 ms were measured.

Fig. 6.
Fig. 6.

The repeatable phase retardation measurements of test1 and test2 at different time.

Fig. 7.
Fig. 7.

The error of Δ under the conditions of (δκP /κP )=0.01, (δκS /κS )=0.01, and (δκDiff /κDiff )=0.0025 when (a) the Δ is from 0° to 2°, (b) the Δ is from 178° to 180°, (c) the Δ is from 45° to 135°. The error of ψ from 0° to 90° is shown in (d).

Equations (18)

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I P ( δ ω t ) = A P 1 2 + A P 2 2 + 2 A P 1 A P 2 cos [ δ ω t + δ ϕ P ] ,
I S ( δ ω t ) = A S 1 2 + A S 2 2 + 2 A S 1 A S 2 cos [ δ ω t + δ ϕ S ] ,
I P ( δ ω t ) = 2 A P 1 A P 2 cos [ δ ω t + δ ϕ P ] ,
I S ( δ ω t ) = 2 A S 1 A S 2 cos [ δ ω t + δ ϕ S ] ,
I P ( δ ω t ) κ P cos [ α β ] ,
I S ( δ ω t ) κ S cos [ α + β ] ,
I Diff ( δ ω t ) = I S ( δ ω t ) I P ( δ ω t )
= ( κ S κ P ) cos β cos α ( κ S + κ P ) sin β sin α
= cos γ cos α sin γ sin α = κ S 2 + κ P 2 2 κ S κ P cos ( δ ϕ S δ ϕ P ) cos ( α + γ ) ,
= κ Diff cos ( α + γ )
Δ = cos 1 [ κ P 2 + κ S 2 κ Diff 2 2 κ P κ S ] ,
ψ = tan 1 ( κ S κ P ) .
δ Δ = [ ( Δ k P ) 2 ( δ k P ) 2 + ( Δ k S ) 2 ( δ k S ) 2 + ( Δ k Diff ) 2 ( δ k Diff ) 2 ] 1 2
= [ ( κ S κ P cos Δ ) 2 ( δ κ P κ P ) 2 + ( κ P κ S cos Δ ) 2 ( δ κ S κ S ) 2 + 2 ( κ S κ P + κ P κ S cos Δ ) 2 ( δ κ Diff κ Diff ) 2 2 ( 1 cos 2 Δ ) ] 1 2 .
= [ ( σ cos Δ ) 2 ( δ κ P κ P ) 2 + ( 1 σ cos Δ ) 2 ( δ κ S κ S ) 2 + 2 ( σ + 1 σ cos Δ ) 2 ( δ κ Diff κ Diff ) 2 2 ( 1 cos 2 Δ ) ] 1 2
δ ψ = [ ( ψ k P ) 2 ( δ k P ) 2 + ( ψ k S ) 2 ( δ k S ) 2 ] 1 2
= [ ( 1 k P k S + k S k P ) 2 ( ( δ k P k P ) 2 + ( δ k S k S ) 2 ) ] 1 2
= [ ( 1 1 tan 1 ψ + tan 1 ψ ) 2 ( ( δ k P k P ) 2 + ( δ k S k S ) 2 ) ] 1 2 .

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