Abstract

Phase retardation between two orthogonal circularly polarized light waves that propagate in an optical active medium is proportional to its optical activity. The measurement of optical activity of a quartz depolarizer in terms of the phase difference of two orthogonal circularly polarized waves is proposed. A circularly polarized optical heterodyne interferometer with a Zeeman laser to measure the optical activity of a quartz crystal is demonstrated experimentally. The accuracy of the measurement is discussed. In addition, the effect of elliptical polarization and nonorthogonality of linearly polarized light waves of a Zeeman laser on the optical activity measurement is analyzed.

© 2003 Optical Society of America

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References

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  1. T. W. Lowry, Optical Rotation Power (Dover, New York, 1964), Chap. 1, p. 9.
  2. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 4, p. 96.
  3. H. J. King, C. Chou, S. T. Lu, “Optical heterodyne polarimeter for measuring the chiral parameter and the circular refraction indices of optical activity,” Opt. Lett. 18, 1970–1972 (1993).
    [CrossRef] [PubMed]
  4. C. Chou, Y. C. Huang, M. Chang, “Precise optical activity measurement of quartz plate by using a true phase-sensitive technique,” Appl. Opt. 36, 3604–3609 (1997).
    [CrossRef] [PubMed]
  5. H. J. King, C. Chou, H. Chang, Y. C. Huang, “Concentration measurements in chiral media using optical heterodyne polarimeter,” Opt. Commun. 110, 259–262 (1994).
    [CrossRef]
  6. S. C. Cohen, “Heterodyne detection: phase front alignment, beam spot size, and detector uniformity,” Appl. Opt. 14, 1953–1958 (1975).
    [CrossRef] [PubMed]
  7. P. L. Polavarapu, “Optical rotation: recent advances in determining the absolute configuration,” Chirality 14, 768–781 (2002).
    [CrossRef] [PubMed]
  8. C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, C. Chou, “A true phase sensitive optical heterodyne polarimeter on glucose concentration measurement,” Opt. Commun. 141, 314–321 (1997).
    [CrossRef]
  9. T. Müller, K. B. Wiberg, P. H. Vaccaro, J. R. Cheeseman, M. J. Frisch, “Cavity ring-down polarimetry (CRDP): theoretical and experimental characterization,” J. Opt. Soc. Am. B 19, 125–141 (2002).
    [CrossRef]
  10. P. T. Beyersdorf, M. M. Fejer, R. L. Byer, “Polarization Sagnac interferometer with a common-path local oscillator for heterodyne detection,” J. Opt. Soc. Am. B 16, 1354–1358 (1999).
    [CrossRef]
  11. Y. C. Huang, C. Chou, M. Chang, “Direct measurement of refractive indices (ne, no) of a linear birefringent retardation plate,” Opt. Commun. 133, 11–16 (1997).
    [CrossRef]
  12. C. Chou, Y. C. Huang, M. Chang, “Effect of elliptical birefringence on the measurement of the phase retardation of a quartz wave plate by an optical heterodyne polarimeter,” J. Opt. Soc. Am. A 14, 1367–1372 (1997).
    [CrossRef]
  13. C. Chou, L. G. Peng, Y. H. Chou, Y. H. Tang, C. Y. Han, C. W. Lyu, “Polarized optical coherence imaging in turbid media by use of a Zeeman laser,” Opt. Lett. 25, 1517–1519 (2000).
    [CrossRef]

2002

2000

1999

1997

C. Chou, Y. C. Huang, M. Chang, “Precise optical activity measurement of quartz plate by using a true phase-sensitive technique,” Appl. Opt. 36, 3604–3609 (1997).
[CrossRef] [PubMed]

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

Y. C. Huang, C. Chou, M. Chang, “Direct measurement of refractive indices (ne, no) of a linear birefringent retardation plate,” Opt. Commun. 133, 11–16 (1997).
[CrossRef]

C. Chou, Y. C. Huang, M. Chang, “Effect of elliptical birefringence on the measurement of the phase retardation of a quartz wave plate by an optical heterodyne polarimeter,” J. Opt. Soc. Am. A 14, 1367–1372 (1997).
[CrossRef]

1994

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

1993

1975

Beyersdorf, P. T.

Byer, R. L.

Chang, H.

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

Chang, J. G.

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

Chang, M.

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

C. Chou, Y. C. Huang, M. Chang, “Precise optical activity measurement of quartz plate by using a true phase-sensitive technique,” Appl. Opt. 36, 3604–3609 (1997).
[CrossRef] [PubMed]

C. Chou, Y. C. Huang, M. Chang, “Effect of elliptical birefringence on the measurement of the phase retardation of a quartz wave plate by an optical heterodyne polarimeter,” J. Opt. Soc. Am. A 14, 1367–1372 (1997).
[CrossRef]

Y. C. Huang, C. Chou, M. Chang, “Direct measurement of refractive indices (ne, no) of a linear birefringent retardation plate,” Opt. Commun. 133, 11–16 (1997).
[CrossRef]

Cheeseman, J. R.

Chou, C.

Chou, Y. H.

Cohen, S. C.

Fejer, M. M.

Feng, C. M.

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

Frisch, M. J.

Han, C. Y.

Huang, Y. C.

Y. C. Huang, C. Chou, M. Chang, “Direct measurement of refractive indices (ne, no) of a linear birefringent retardation plate,” Opt. Commun. 133, 11–16 (1997).
[CrossRef]

C. Chou, Y. C. Huang, M. Chang, “Effect of elliptical birefringence on the measurement of the phase retardation of a quartz wave plate by an optical heterodyne polarimeter,” J. Opt. Soc. Am. A 14, 1367–1372 (1997).
[CrossRef]

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

C. Chou, Y. C. Huang, M. Chang, “Precise optical activity measurement of quartz plate by using a true phase-sensitive technique,” Appl. Opt. 36, 3604–3609 (1997).
[CrossRef] [PubMed]

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

King, H. J.

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

H. J. King, C. Chou, S. T. Lu, “Optical heterodyne polarimeter for measuring the chiral parameter and the circular refraction indices of optical activity,” Opt. Lett. 18, 1970–1972 (1993).
[CrossRef] [PubMed]

Lowry, T. W.

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

Lu, S. T.

Lyu, C. W.

Müller, T.

Peng, L. G.

Polavarapu, P. L.

P. L. Polavarapu, “Optical rotation: recent advances in determining the absolute configuration,” Chirality 14, 768–781 (2002).
[CrossRef] [PubMed]

Tang, Y. H.

Vaccaro, P. H.

Wiberg, K. B.

Yariv, A.

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

Yeh, P.

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

Appl. Opt.

Chirality

P. L. Polavarapu, “Optical rotation: recent advances in determining the absolute configuration,” Chirality 14, 768–781 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

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

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

Y. C. Huang, C. Chou, M. Chang, “Direct measurement of refractive indices (ne, no) of a linear birefringent retardation plate,” Opt. Commun. 133, 11–16 (1997).
[CrossRef]

Opt. Lett.

Other

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

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

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Figures (3)

Fig. 1
Fig. 1

Geometry of the QD.

Fig. 2
Fig. 2

Schematic diagram of a circularly polarized optical heterodyne interferometer: ZL, Zeeman laser; QD, quartz depolarizer; PBS, polarized beam splitter; T, translation state; D p , D r , detectors; A r , analyzer; BPF, bandpass filters; LIA, lock-in amplifier; T, translation stage; PC, personal computer.

Fig. 3
Fig. 3

Experimental result of the measured phase difference.

Equations (25)

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12 Ap expiωpt1-i,
12 As expiωst1i,
J=expikrd00expikld,
kr=2πλ nr,
kl=2πλ nl,
expikrd1expiωpt1-i,
expikld1expiωst1i,
12 Ap expiωptexpikrd1expikld21-i,
12 As expiωstexpikld1expikrd21i.
Ioutpt=12 Ap expiωptexpikrd1+kld2+12 As expiωstexpikld1+krd22=12Ap2+As2+ApAs cosΔω+Δϕ,
Δϕ=kr-kld1-d2
IrΔωt=12Ap2+As2+ApAs cosΔωt.
δΔϕ=kr-kld1-d1+d2-d2=2kr-klΔh.
Δn=δΔϕ4πΔh λ0,
δΔn=δnr-nl=λ04πδδΔϕΔh2+δΔϕδΔhΔh221/2λ04πδΔϕΔhδδΔϕδΔϕ=λ04πδΔϕΔh1SNRδΔϕ,
SNR|δΔϕ=δΔϕδδΔϕ8
Exp expiδxpEyp expiδypexpiωpt, Exp  EypExs expiδxsEys expiδysexpiωst, Eys  Exs.
1/2Exp expiδxp1-i+1/2Eyp expiδyp1iexpiωpt,
1/2Exs expiδxs1-i+1/2Eys expiδys1iexpiωst.
1/2Exp expiδxpexpikrd1+kld21-i+1/2Eyp expiδypexpikld1+krd21i×expiωpt,
1/2Exs expiδxsexpikrd1+kld21-i+1/2Eys expiδysexpikld1+krd21i×expiωst.
1/2Exp expiδxpexpikrd1+kld2expiωpt+Eys expiδysexpikld1+krd2expiωst+Eyp expiδypexpikld1+krd2expiωpt+Exs expiδxsexpikrd1+kld2expiωst.
ExpEys cosΔωt+kr-kld1-d2+δxp-δys+ExsEyp cosΔωt+kl-krd1-d2+δyp-δxs.
Δϕkr-kld1-d2+δxp-δys,
δΔϕ=kr-klδd1-d2=2kr-klΔh.

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