Abstract

Based on the phenomena of Brewster's angle and the principles of common-path heterodyne interferometry, we present an optical method for measuring the optical rotation angle and the refractive index of a chiral solution simultaneously in one optical configuration. A heterodyne light beam and a circularly polarized heterodyne light beam are separately guided to project onto the interface of a semicircle glass and a chiral solution. One of the beams is transmitted through the solution, and the other is reflected near Brewster's angle at the interface. Then the two beams pass through polarization components respectively for interference. The phase differences of the two interference signals used to determine the rotation angle and the refractive index become very high with the proper azimuth angles of some polarization components, hence achieving an accurate rotational angle and a refractive index. The feasibility of the measuring method was demonstrated by our experimental results. This method should bear the merits of high accuracy, short sample medium length, and simpler operational endeavor.

© 2007 Optical Society of America

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References

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  1. I. J. Lalov and A. I. Miteva, "Optically active Fabry-Perot etalon," J. Mod. Opt. 38, 395-411 (1991).
    [CrossRef]
  2. J. Lalov and E. M. Georgieva, "Optically active absorptive Fabry-Perot etalon," J. Mod. Opt. 42, 1713-1723 (1995).
    [CrossRef]
  3. R. J. McNicols and G. L. Cote, "Optical glucose sensing in biological fluids: an overview," J. Biomed. Opt. 5, 1-12 (2000).
  4. P. K. Yang and J. Y. Huang "Sum-frequency generation from an isotropic chiral medium," J. Opt. Soc. Am. B 15, 1698-1706 (1998).
    [CrossRef]
  5. M. P. Silverman, N. Ritchie, G. M. Cushman, and B. Fisher, "Experiment configurations using optical phase modulation to measure chiral asymmetries in light specularly reflected from a naturally gyotropic medium," J. Opt. Soc. Am. A 5, 1852-1862 (1988).
    [CrossRef]
  6. T. Asahi and J. Kobayashi, "Polarimeter for anisotropic optically active materials," in Introduction to Complex Mediums for Optics and Electromagnetics, W. S. Weighlhofer and A. Lakhtakia, eds. (SPIE, 2003).
    [CrossRef]
  7. H. Meeks and A. Janner, "The high-accuracy universal polarimeter," J. Phys. D: Appl. Phys. 24, 1851-1868 (1991).
  8. H. J. King, C. Chou, H. Chang, and Y. C. Huang, "Concentration measurements in chiral media using optical heterodyne polarimeter," Opt. Commun. 110, 259-262 (1994).
    [CrossRef]
  9. T. W. King, G. L. Cote, R. McNichols, and M. J. Goetz, Jr., "Multispectral polarimetric glucose detection using a single Pockels cell," Opt. Eng. 33, 2746-2753 (1994).
    [CrossRef]
  10. C. Chou, Y. C. Huang, C. M. Feng, and M. Chang, "Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid," Jpn. J. Appl. Phys. 36, 356-359 (1997).
    [CrossRef]
  11. G. L. Cote, M. D. Fox, and R. B. Northrop, "Noninvasive optical polarimetric glucose sensing using a true phase measurement technique," IEEE Trans. Biomed. Eng. 39, 752-756 (1992).
    [CrossRef] [PubMed]
  12. C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, "A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement," Opt. Commun. 141, 314-321 (1997).
    [CrossRef]
  13. M. H. Chiu, J. Y. Lee, and D. C. Su, "Refractive-index measurement based on the effects of total internal reflection and the uses of heterodyne interferometry," Appl. Opt. 36, 2936-2939 (1997).
    [CrossRef] [PubMed]
  14. C. C. Hsu, K. H. Chen, and D. C. Su, "Normal incidence refractometer," Opt. Commun. 218, 205-211 (2003).
    [CrossRef]
  15. Kun-Huang Chen, Jing-Heng Chen, and Jiun-You Lin, "Comparison of Kretschmann-Raether configuration angular and thickness regimes with phase-difference shift for measuring changes in refractive index," Opt. Eng. 2, 023803 (2006).
    [CrossRef]
  16. R. C. Weast, ed., Handbook of Chemistry and Physics, 61st ed. (CRC Press, 1981), pp. D227-270 and E-418.
  17. N. Berova, K. Nakanishi, and R. W. Woody, Circular Dichroism: Principles and Applications, 2nd ed. (Wiley, 2002), pp. 30-31.
  18. M. H. Chiu, J. Y. Lee, and D. C. Su, "Complex refractive-index measurement based on Fresnel's equations and the uses of heterodyne interferometry," Appl. Opt. 19, 4047-4052 (1999).
    [CrossRef]

2006 (1)

Kun-Huang Chen, Jing-Heng Chen, and Jiun-You Lin, "Comparison of Kretschmann-Raether configuration angular and thickness regimes with phase-difference shift for measuring changes in refractive index," Opt. Eng. 2, 023803 (2006).
[CrossRef]

2003 (1)

C. C. Hsu, K. H. Chen, and D. C. Su, "Normal incidence refractometer," Opt. Commun. 218, 205-211 (2003).
[CrossRef]

2000 (1)

R. J. McNicols and G. L. Cote, "Optical glucose sensing in biological fluids: an overview," J. Biomed. Opt. 5, 1-12 (2000).

1999 (1)

M. H. Chiu, J. Y. Lee, and D. C. Su, "Complex refractive-index measurement based on Fresnel's equations and the uses of heterodyne interferometry," Appl. Opt. 19, 4047-4052 (1999).
[CrossRef]

1998 (1)

1997 (3)

C. Chou, Y. C. Huang, C. M. Feng, and M. Chang, "Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid," Jpn. J. Appl. Phys. 36, 356-359 (1997).
[CrossRef]

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, "A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement," Opt. Commun. 141, 314-321 (1997).
[CrossRef]

M. H. Chiu, J. Y. Lee, and D. C. Su, "Refractive-index measurement based on the effects of total internal reflection and the uses of heterodyne interferometry," Appl. Opt. 36, 2936-2939 (1997).
[CrossRef] [PubMed]

1995 (1)

J. Lalov and E. M. Georgieva, "Optically active absorptive Fabry-Perot etalon," J. Mod. Opt. 42, 1713-1723 (1995).
[CrossRef]

1994 (2)

H. J. King, C. Chou, H. Chang, and Y. C. Huang, "Concentration measurements in chiral media using optical heterodyne polarimeter," Opt. Commun. 110, 259-262 (1994).
[CrossRef]

T. W. King, G. L. Cote, R. McNichols, and M. J. Goetz, Jr., "Multispectral polarimetric glucose detection using a single Pockels cell," Opt. Eng. 33, 2746-2753 (1994).
[CrossRef]

1992 (1)

G. L. Cote, M. D. Fox, and R. B. Northrop, "Noninvasive optical polarimetric glucose sensing using a true phase measurement technique," IEEE Trans. Biomed. Eng. 39, 752-756 (1992).
[CrossRef] [PubMed]

1991 (2)

I. J. Lalov and A. I. Miteva, "Optically active Fabry-Perot etalon," J. Mod. Opt. 38, 395-411 (1991).
[CrossRef]

H. Meeks and A. Janner, "The high-accuracy universal polarimeter," J. Phys. D: Appl. Phys. 24, 1851-1868 (1991).

1988 (1)

Appl. Opt. (2)

M. H. Chiu, J. Y. Lee, and D. C. Su, "Refractive-index measurement based on the effects of total internal reflection and the uses of heterodyne interferometry," Appl. Opt. 36, 2936-2939 (1997).
[CrossRef] [PubMed]

M. H. Chiu, J. Y. Lee, and D. C. Su, "Complex refractive-index measurement based on Fresnel's equations and the uses of heterodyne interferometry," Appl. Opt. 19, 4047-4052 (1999).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

G. L. Cote, M. D. Fox, and R. B. Northrop, "Noninvasive optical polarimetric glucose sensing using a true phase measurement technique," IEEE Trans. Biomed. Eng. 39, 752-756 (1992).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

R. J. McNicols and G. L. Cote, "Optical glucose sensing in biological fluids: an overview," J. Biomed. Opt. 5, 1-12 (2000).

J. Mod. Opt. (2)

I. J. Lalov and A. I. Miteva, "Optically active Fabry-Perot etalon," J. Mod. Opt. 38, 395-411 (1991).
[CrossRef]

J. Lalov and E. M. Georgieva, "Optically active absorptive Fabry-Perot etalon," J. Mod. Opt. 42, 1713-1723 (1995).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

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

H. Meeks and A. Janner, "The high-accuracy universal polarimeter," J. Phys. D: Appl. Phys. 24, 1851-1868 (1991).

Jpn. J. Appl. Phys. (1)

C. Chou, Y. C. Huang, C. M. Feng, and M. Chang, "Amplitude sensitive optical heterodyne and phase lock-in technique on small optical rotation angle detection of chiral liquid," Jpn. J. Appl. Phys. 36, 356-359 (1997).
[CrossRef]

Opt. Commun. (3)

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, "A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement," Opt. Commun. 141, 314-321 (1997).
[CrossRef]

C. C. Hsu, K. H. Chen, and D. C. Su, "Normal incidence refractometer," Opt. Commun. 218, 205-211 (2003).
[CrossRef]

H. J. King, C. Chou, H. Chang, and Y. C. Huang, "Concentration measurements in chiral media using optical heterodyne polarimeter," Opt. Commun. 110, 259-262 (1994).
[CrossRef]

Opt. Eng. (2)

T. W. King, G. L. Cote, R. McNichols, and M. J. Goetz, Jr., "Multispectral polarimetric glucose detection using a single Pockels cell," Opt. Eng. 33, 2746-2753 (1994).
[CrossRef]

Kun-Huang Chen, Jing-Heng Chen, and Jiun-You Lin, "Comparison of Kretschmann-Raether configuration angular and thickness regimes with phase-difference shift for measuring changes in refractive index," Opt. Eng. 2, 023803 (2006).
[CrossRef]

Other (3)

R. C. Weast, ed., Handbook of Chemistry and Physics, 61st ed. (CRC Press, 1981), pp. D227-270 and E-418.

N. Berova, K. Nakanishi, and R. W. Woody, Circular Dichroism: Principles and Applications, 2nd ed. (Wiley, 2002), pp. 30-31.

T. Asahi and J. Kobayashi, "Polarimeter for anisotropic optically active materials," in Introduction to Complex Mediums for Optics and Electromagnetics, W. S. Weighlhofer and A. Lakhtakia, eds. (SPIE, 2003).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Schematic diagram for measuring the refractive index and rotational angle of a chiral solution: H, half-wave plate; Q, quarter-wave plate; EO, electro-optic modulator; G, semicircle glass; AN, analyzer; D, photodetector.

Tables (1)

Tables Icon

Table 1 Experimental Results and the Corresponding Reference Data a

Equations (33)

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E i = ( cos   α sin   α ) .
E i = ( exp ( i ω t / 2 ) 0 0 exp ( i ω t / 2 ) ) ( cos   α sin   α ) = ( cos   α   exp ( i ω t / 2 ) sin   α   exp ( i ω t / 2 ) ) .
E r = 1 2 ( 1 1 1 1 ) 1 2 ( 1 0 0 e i ϕ B S 1 ) ( cos   α   exp ( i ω t / 2 ) sin   α   exp ( i ω t / 2 ) ) = 1 2 2 [ cos   α   exp ( i ω t / 2 ) + sin   α × exp ( i ω t / 2 + i ϕ B S 1 ) ] ( 1 1 ) ,
I r = 1 4 [ 1 + sin   2 α   cos ( ω t ϕ BS 1 ) ] ,
E t 1 = ( cos 2 β 1 sin   β 1   cos   β 1 sin   β 1   cos   β 1 sin 2 β 1 ) ( 1 0 0 i ) 1 2 ( cos   α   cos   θ   exp ( i ω t / 2 ) sin   α   sin   θ   exp ( i ω t / 2 + i ϕ B S 2 + i ϕ M ) cos   α   sin   θ   exp ( i ω t / 2 ) + sin   α   cos   θ exp ( i ω t / 2 + i ϕ B S 2 + i ϕ M ) ) = 1 2 [ A   exp ( i ω t / 2 + i ϕ a ) + B   exp ( i ω t / 2 + i ϕ b + i ϕ B S 2 + i ϕ M + i π / 2 ) ] ( cos   β 1 sin   β 1 ) ,
A = cos   α ( cos 2 β 1 cos 2 θ + sin 2 β 1 sin 2 θ ) 1 / 2 ,
B = sin   α ( cos 2 β 1 sin 2 θ + sin 2 β 1 cos 2 θ ) 1 / 2 ,
ϕ a = tan 1 ( tan   β 1   tan   θ ) ,
ϕ b = tan 1 ( cot   β 1   tan   θ ) .
I t 1 = | E t 1 | 2 = 1 4 [ A 2 + B 2 + 2 A B   cos ( ω t + ψ 1 ) ] ,
ψ 1 = ϕ 1 ϕ BS 2 ϕ M π / 2 ,
ϕ 1 = ϕ a ϕ b = tan 1 [ ( tan   β 1 cot   β 1 ) tan   θ sec 2 θ ] .
E i = 1 2 ( 1 i i 1 ) ( 1 0 0 i ) ( r spr , p 0 0 r spr , s ) × 1 2 ( cos   α   exp ( i ω t / 2 ) sin   α   exp ( i ω t / 2 ) ) = 1 2 2 [ r spr , p   cos   α ( 1 i ) exp ( i ω t / 2 ) + r spr , s   sin   α ( 1 i ) × exp ( i ω t / 2 ) ] ,
r spr , q = r 12 q + r 23 q   exp ( i 2 k z 2 d 2 ) 1 + r 12 q r 23 q   exp ( i 2 k z 2 d 2 ) = | r spr , q | exp ( i ϕ spr , q )
q = p , s ,
r i j q = X i q X j q X i q + X j q ,
X i q = { n i 2 / k z i q = p , k z i q = s ,
k z i = k 0 ( n i 2 n 1 2 sin 2 θ ) 1 / 2 .
E t 2 = ( cos 2 β 2 sin   β 2   cos   β 2 sin   β 2   cos   β 2 sin 2 β 2 ) ( r p 0 0 r s ) × 1 2 2 [ r spr , p   cos   α ( 1 i ) exp ( i ω t / 2 ) + r spr , s   sin   α ( 1 i )   exp ( i ω t / 2 ) ] = 1 2 2 [ C  exp ( i ω t / 2 + i ϕ c ) + D  exp ( i ω t / 2 + i ϕ d ) ] × ( cos   β 2 sin   β 2 ) ,
C = | r spr , p | cos   α [ ( r p   cos   β 2 ) 2 + ( r s   sin   β 2 ) 2 ] 1 / 2 ,
D = | r spr , s | sin   α [ ( r p   cos   β 2 ) 2 + ( r s   sin   β 2 ) 2 ] 1 / 2 ,
r p = n 2   cos   θ i ( n 2 sin 2 θ i ) 1 / 2 n 2   cos   θ i + ( n 2 sin 2 θ i ) 1 / 2 ,
r s = cos   θ i ( n 2 sin 2 θ i ) 1 / 2 cos   θ i + ( n 2 sin 2 θ i ) 1 / 2 ,
I t 2 = | E t 2 | 2 = 1 8 [ C 2 + D 2 + 2 C D   cos ( ω t + ψ 2 ) ] ,
             ψ 2 = ϕ c ϕ d , = ϕ 2 + ϕ spr = tan 1 [ sin   2 β 2 × r p r s r p 2 cos 2 β 2 r s 2 sin 2 β 2 ] + ϕ spr ,
ϕ 2 = tan 1 [ ( sin 2 θ i n 2 × cos 2 θ i ) × sin   2 β 2 ( 2 sin 4 θ i sin 2 θ i + n 2 × cos 2 θ i ) × cos   2 β 2 2 sin 2 θ i   cos   θ i ( n 2 sin 2 θ i ) 1 / 2 ] = f ( n ) .
ψ 1 = ψ 1 + ϕ BS 1
= ϕ 1 ϕ BS 2 ϕ M π / 2 + ϕ BS 1 ,
ψ 2 = ϕ 2 + ϕ spr + ϕ BS 1
θ = 1 2 sin 1 ( 2   tan   ϕ 1 tan   β 1 cot   β 1 ) ,
n = f 1 ( ϕ 2 ) .
Δ θ = | sec 2 ϕ 1 ( tan   β 1 cot   β 1 ) cos   2 θ Δ ϕ 1 | ,
Δ n = | 1 f ( n ) Δ ϕ 2 | ,

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