Abstract

What we believe to be a novel amplitude sensitive optical heterodyne polarimeter in which a Zeeman laser is associated with balanced detector detection was set up. The aim was to measure the optical activity of a quartz crystal with a Cornu depolarizer at high accuracy. The features of this novel polarimeter, which include the use of a two-frequency laser that ensures the accuracy of the measurement, are discussed. Furthermore, the detection sensitivity of the optical activity of a quartz crystal was measured as 8.5×1010. To our knowledge, this is the highest sensitivity obtained for optical activity measurement of a quartz crystal when the error of the measurement is also analyzed.

© 2006 Optical Society of America

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References

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  1. T. W. Lowry, Optical Rotation Power (Dover, 1964), Chap. 1, p. 9.
  2. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), Chap. 4, p. 96.
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  5. C. Chou, H. M. Tsai, K. Y. Liao, and L. D. Chou, "Balanced detection optical heterodyne polarimeter for optical activity measurement of a quartz crystal," in Second Asian and Pacific Rim Symposium on Biophotonics, Taipei, Taiwan, 15-17 December 2004, pp. 203-204.
  6. C. Chou, L. G. Peng, Y. H. Chou, Y. H. Tang, C. Y. Han, and C. W. Lyu, "Polarized optical coherence imaging in turbid media by use of a Zeeman laser," Opt. Lett. 25, 1517-1519 (2000).
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  8. C. Chou, C. Y. Han, W. C. Kuo, Y. C. Huang, C. M. Feng, and J. C. Shyu "Noninvasive glucose monitors in vivo with an optical heterodyne polarimeter," Appl. Opt. 37, 3553-3557 (1998).
    [PubMed]
  9. C. Chou, Y. C. Huang, and M. Chang, "Precise optical activity measurement of quartz plate by using a true phase-sensitive technique," Appl. Opt. 36, 3604-3609 (1997).
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  10. C. Chou, W. C. Kuo, T. S. Hsieh, and H. K. Teng, "A phase sensitive optical rotation measurement in a scattered chiral medium using a Zeeman laser," Opt. Commun. 230, 259-266 (2004).
    [CrossRef]
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  13. T. Müller, K. B. Wiberg, P. H. Vaccaro, J. R. Cheeseman, and M. J. Frisch, "Cavity ring-down polarimetry (CRDP): theoretical and experimental characterization," J. Opt. Soc. Am. B 19, 125-141 (2002).
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  15. Cornu Pseudodepolarizer, www.MellesGriot.com
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2004 (1)

C. Chou, W. C. Kuo, T. S. Hsieh, and H. K. Teng, "A phase sensitive optical rotation measurement in a scattered chiral medium using a Zeeman laser," Opt. Commun. 230, 259-266 (2004).
[CrossRef]

2003 (3)

2002 (1)

2000 (1)

1999 (1)

1997 (2)

1995 (1)

1992 (1)

Beyersdorf, P. T.

Byer, R. L.

Chang, M.

Cheeseman, J. R.

Chou, C.

Chou, L. D.

C. Chou, H. M. Tsai, K. Y. Liao, and L. D. Chou, "Balanced detection optical heterodyne polarimeter for optical activity measurement of a quartz crystal," in Second Asian and Pacific Rim Symposium on Biophotonics, Taipei, Taiwan, 15-17 December 2004, pp. 203-204.

Chou, Y. H.

Diettrich, G.

Fejer, M. M.

Feng, C. M.

Frisch, M. J.

Han, C. Y.

Han, C.-Y.

Hsieh, T. S.

C. Chou, W. C. Kuo, T. S. Hsieh, and H. K. Teng, "A phase sensitive optical rotation measurement in a scattered chiral medium using a Zeeman laser," Opt. Commun. 230, 259-266 (2004).
[CrossRef]

Huang, Y. C.

Kuo, W. C.

C. Chou, W. C. Kuo, T. S. Hsieh, and H. K. Teng, "A phase sensitive optical rotation measurement in a scattered chiral medium using a Zeeman laser," Opt. Commun. 230, 259-266 (2004).
[CrossRef]

C. Chou, C. Y. Han, W. C. Kuo, Y. C. Huang, C. M. Feng, and J. C. Shyu "Noninvasive glucose monitors in vivo with an optical heterodyne polarimeter," Appl. Opt. 37, 3553-3557 (1998).
[PubMed]

Kuo, W.-C.

Kurzynowski, P.

Liao, K. Y.

C. Chou, H. M. Tsai, K. Y. Liao, and L. D. Chou, "Balanced detection optical heterodyne polarimeter for optical activity measurement of a quartz crystal," in Second Asian and Pacific Rim Symposium on Biophotonics, Taipei, Taiwan, 15-17 December 2004, pp. 203-204.

Lowry, T. W.

T. W. Lowry, Optical Rotation Power (Dover, 1964), Chap. 1, p. 9.

Lyu, C. W.

Mitrofanov, O.

Müller, T.

Peng, L. G.

Pietraszkiewicz, K.

Riedling, K.

K. Riedling, Ellipsometry for Industrial Publications (Springer, 1988), p. 7.

Shyu, J. C.

Tang, Y. H.

Teng, H. K.

C. Chou, W. C. Kuo, T. S. Hsieh, and H. K. Teng, "A phase sensitive optical rotation measurement in a scattered chiral medium using a Zeeman laser," Opt. Commun. 230, 259-266 (2004).
[CrossRef]

Tsai, H. M.

C. Chou, H. M. Tsai, K. Y. Liao, and L. D. Chou, "Balanced detection optical heterodyne polarimeter for optical activity measurement of a quartz crystal," in Second Asian and Pacific Rim Symposium on Biophotonics, Taipei, Taiwan, 15-17 December 2004, pp. 203-204.

Vaccaro, P. H.

Van Leeuwen, N. J.

Wiberg, K. B.

Wilson, A. C.

Wozniak, W. A.

Wu, Y. Z.

Xie, Y.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), Chap. 4, p. 96.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), Chap. 4, p. 96.

Appl. Opt. (6)

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

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

Opt. Commun. (1)

C. Chou, W. C. Kuo, T. S. Hsieh, and H. K. Teng, "A phase sensitive optical rotation measurement in a scattered chiral medium using a Zeeman laser," Opt. Commun. 230, 259-266 (2004).
[CrossRef]

Opt. Lett. (1)

Other (5)

K. Riedling, Ellipsometry for Industrial Publications (Springer, 1988), p. 7.

C. Chou, H. M. Tsai, K. Y. Liao, and L. D. Chou, "Balanced detection optical heterodyne polarimeter for optical activity measurement of a quartz crystal," in Second Asian and Pacific Rim Symposium on Biophotonics, Taipei, Taiwan, 15-17 December 2004, pp. 203-204.

T. W. Lowry, Optical Rotation Power (Dover, 1964), Chap. 1, p. 9.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), Chap. 4, p. 96.

Cornu Pseudodepolarizer, www.MellesGriot.com

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Figures (4)

Fig. 1
Fig. 1

Optical setup of the balanced detection optical heterodyne polarimeter: ZL, Zeeman laser; λ∕2, half-wave plate; PBS, polarized beam splitter; D1, D2, photodetectors; DA, differential amplifier; DVM, digital voltmeter; PC, personal computer.

Fig. 2
Fig. 2

Schematic diagram of a QCD.

Fig. 3
Fig. 3

Experimental result of output voltage versus rotation angle. The inset is a detailed response of measurement at 2Δθ ≅ 45°.

Fig. 4
Fig. 4

Detection sensitivity of optical activity versus optical rotation angle of QCD in this polarimeter.

Equations (34)

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A p exp ( i ω p t ) ( 1 0 ) = 1 2 A p exp ( i ω p t ) ( 1 i ) + 1 2 A p exp ( i ω p t ) ( 1 i ) .
A s exp ( i ω s t ) ( 0 1 ) = 1 2 i A s exp ( i ω s t ) ( 1 i ) 1 2 i A s exp ( i ω s t ) ( 1 i ) ,
J = [ exp ( i k r d ) 0 0 exp ( i k l d ) ] ,
E p = 1 2 A p { exp [ i ( k r d 1 + k l d 2 ) ] ( 1 i ) + exp [ i ( k l d 1 + k r d 2 ) ] ( 1 i ) } exp [ i ( ω p t + ϕ p ) ] .
E s = 1 2 i A s { exp [ i ( k l d 1 + k r d 2 ) ] ( 1 i ) exp [ i ( k r d 1 + k l d 2 ) ] ( 1 i ) } exp [ i ( ω s t + ϕ s ) ] ,
I P ( Δ ω t ) = A p     2 2 + A p     2 2 cos ( Δ k Δ d ) + A s     2 2 A s     2 2 cos ( Δ k Δ d ) A p A s sin ( Δ k Δ d ) cos ( Δ ω t + Δ ϕ ) ,
I S ( Δ ω t ) = A p     2 2 A p     2 2 cos ( Δ k Δ d ) + A s     2 2 + A s     2 2 cos ( Δ k Δ d ) + A p A s sin ( Δ k Δ d ) cos ( Δ ω t + Δ ϕ ) .
I P ( Δ ω t ) A 2 [ 1 sin ( Δ k Δ d ) cos ( Δ ω t ) ] ,
I S ( Δ ω t ) A 2 [ 1 + sin ( Δ k Δ d ) cos ( Δ ω t ) ] ,
Δ I ( Δ ω t ) = | I P I S | = 2 A 2 | sin ( Δ k Δ d ) | cos ( Δ ω t ) .
| Δ I | = 2 A 2 | sin ( Δ k Δ d ) | .
Δ θ = π λ ( n r n l ) Δ d .
| n r n l | = λ 2 π sin 1 ( | Δ I | 2 A 2 ) 1 Δ d .
| n r n l | = λ 4 π sin 1 ( | Δ I | 2 A 2 ) 1 Δ h .
| n r n l | = λ | Δ I | 8 π A 2 Δ h .
A 2 = | Δ I | max 2 .
| n r n l | = λ 4 π sin 1 ( | Δ I | | Δ I | max ) 1 Δ h .
δ ( n r n l ) = λ π δ ( Δ θ Δ d )
= λ π [ ( Δ θ Δ d ) 2 ( δ ( Δ d ) Δ d ) 2 + ( Δ θ Δ d ) 2 ( δ ( Δ θ ) Δ θ ) 2 ] 1 / 2
λ π ( δ ( Δ θ ) Δ θ ) ( Δ θ Δ d ) ,
δ | Δ I | = 4 A 2 cos ( 2 Δ θ ) δ ( Δ θ ) ,
δ | Δ I | | Δ I | = 2 cot ( 2 Δ θ ) δ ( Δ θ ) ,
δ ( Δ θ ) Δ θ = 1 2 δ | Δ I | | Δ I | tan ( 2 Δ θ ) 1 Δ θ .
δ ( n r n l ) = λ 2 π δ | Δ I | | Δ I | tan ( 2 Δ θ ) ( Δ θ Δ d ) 1 Δ θ .
p ˜ = [ A x     p exp ( i δ x     p ) A y     p exp ( i δ y     p ) ] exp ( i ω p t ) , A x     p A y     p ,
s ˜ = [ A x     s exp ( i δ x     s ) A y     s exp ( i δ y     s ) ] exp ( i ω s t ) ,     A y     s A x     s .
p ˜ = [ 1 2 A x     p ( 1 i ) + 1 2 A x     p ( 1 i ) ] exp [ i ( ω p t + δ x     p ) ] + [ 1 2 i A y     p ( 1 i ) 1 2 i A y     p ( 1 i ) ] exp [ i ( ω p t + δ y     p ) ] ,
s ˜ = [ 1 2 A x     s ( 1 i ) + 1 2 A x       s ( 1 i ) ] exp [ i ( ω s t + δ x       s ) ] + [ 1 2 i A y       s ( 1 i ) 1 2 i A y     s ( 1 i ) ] exp [ i ( ω s t + δ y     s ) ] .
E p ˜ = 1 2 A x p { exp [ i ( k r d 1 k l d 2 ) ] ( 1 i ) + exp [ i ( k l d 1 k r d 2 ) ] ( 1 i ) } exp [ i ( ω p t + δ x     p + ϕ p ) ] + 1 2 i A y p { exp [ i ( k l d 1 k r d 2 ) ] ( 1 i ) + exp [ i ( k r d 1 k l d 2 ) ] ( 1 i ) } exp [ i ( ω p t + δ y     p + ϕ p ) ] ,
E s ˜ = 1 2 A x s { exp [ i ( k r d 1 k l d 2 ) ] ( 1 - i ) + exp [ i ( k l d 1 k r d 2 ) ] ( 1 i ) } exp [ i ( ω s t + δ x     s + ϕ s ) ] + 1 2 i A y s { exp [ i ( k l d 1 k r d 2 ) ] ( 1 i ) + exp [ i ( k r d 1 k l d 2 ) ] ( 1 - i ) } exp [ i ( ω s t + δ y     s + ϕ s ) ] ,
I x ( Δ ω t ) = | A x     p 2 { exp [ i ( k r d 1 + k l d 2 ) ] + exp [ i ( k l d 1 + k r d 2 ) ] exp [ i ( ω p t + δ x     p ) ] + A y     p 2 i { exp [ i ( k l d 1 + k r d 2 ) ] + exp [ i ( k r d 1 + k l d 2 ) ] } exp [ i ( ω p t + δ y     p ) ] + A x     s 2 i { exp [ i ( k r d 1 + k l d 2 ) ] + exp [ i ( k l d 1 + k r d 2 ) ] } exp [ i ( ω s t + δ x     s ) ] + A y     s 2 i { exp [ i ( k l d 1 + k r d 2 ) ] + exp [ i ( k r d 1 + k l d 2 ) ] } exp [ i ( ω s t + δ y     s ) ] | 2
= [ A x     p 2 2 + A x     s 2 2 + A x     p A x     s cos ( δ x     p δ x     s + Δ ω t ) ] [ 1 + cos ( Δ k Δ d ) ] + [ A y     p 2 2 + A y     s 2 2 + A y     p A y     s cos ( δ y     p δ y     s + Δ ω t ) ] [ 1 cos ( Δ k Δ d ) ] [ A x     p A y     p cos ( δ x     p δ y     p ) + A x     s A y     p cos ( δ x     s δ y     p Δ ω t ) + A x     p A y     s cos ( δ y     p δ y     s + Δ ω t ) + A x     s A y     s cos ( δ x     s δ y     s ) ] sin ( Δ k Δ d ) .
I y ( Δ ω t ) = [ A x     p 2 2 + A x     s 2 2 + A x     p A x     s cos ( δ x     p δ x     s + Δ ω t ) ] [ 1 cos ( Δ k Δ d ) ] + [ A y     p 2 2 + A y     s 2 2 + A y     p A y     s cos ( δ y     p δ y     s + Δ ω t ) ] [ 1 + cos ( Δ k Δ d ) ] + [ A x     p A y     p cos ( δ x     p δ y     p ) + A x     s A y     p cos ( δ x     s δ y     p Δ ω t ) + A x     p A y     s cos ( δ x     p δ y     s + Δ ω t ) + A x     s A y     s cos ( δ x     s δ y     s ) ] sin ( Δ k Δ d ) .
Δ I = | I x I y | 2 A 2 | sin ( Δ k Δ d ) | cos ( Δ ω t + δ x     p δ y     s ) .

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