Abstract

The elliptical birefringence of a quartz phase-retardation plate was precisely measured and discussed. A polarized optical heterodyne interferometer with a common path configuration was proposed and set up. It was used to measure the linear phase retardation of λ/4 quartz wave plate, taking the elliptical birefringence into consideration. The ratio of the amplitude of the heterodyned P and S waves versus the azimuth angle of the quartz plate was more sensitive to elliptical birefringence than was the phase retardation. The experimental data, which were well fitted to the theoretical curve, showed evidence of the existence of small elliptical birefringence in the tested λ/4 quartz wave plate. However, the results of the experiment confirm the general belief that the phase difference of the wave plate is not sensitive to the elliptical birefringence effect.

© 1997 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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1995 (2)

S. De Nicola, P. Ferraro, G. Pierattini, “Wavelength dependence of the phase retardation of a quarter-wave plate,” Appl. Phys. B 60, 405–407 (1995).
[Crossref]

K. Pietraszkiewicz, W. A. Wozniak, P. Kurzynowski, “Effect of multiple reflections in retardation plates with elliptical birefringence,” J. Opt. Soc. Am. A 12, 420–424 (1995).
[Crossref]

1994 (2)

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]

G. C. Nechev, “Analytical phase-measuring technique for retardation measurements,” Appl. Opt. 33, 6621–6625 (1994).
[Crossref] [PubMed]

1993 (2)

1991 (1)

1990 (2)

1988 (1)

1984 (1)

I. Scierski, F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik 68, 121–125 (1984).

1966 (1)

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarised Light (North-Holland, Amsterdam, 1979), pp. 84–85.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarised Light (North-Holland, Amsterdam, 1979), pp. 84–85.

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, K. S.

Chen, C. L.

Chidester, S. D.

Chou, C.

De Nicola, S.

S. De Nicola, P. Ferraro, G. Pierattini, “Wavelength dependence of the phase retardation of a quarter-wave plate,” Appl. Phys. B 60, 405–407 (1995).
[Crossref]

Ferraro, P.

S. De Nicola, P. Ferraro, G. Pierattini, “Wavelength dependence of the phase retardation of a quarter-wave plate,” Appl. Phys. B 60, 405–407 (1995).
[Crossref]

Grunstra, B. R.

Harvey, J. W.

Huang, Y. C.

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]

Hubbard, R. P.

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]

Kurzynowski, P.

Lin, C. H.

Lu, S. T.

Nakadate, S.

Nechev, G. C.

Perkins, H. B.

Pierattini, G.

S. De Nicola, P. Ferraro, G. Pierattini, “Wavelength dependence of the phase retardation of a quarter-wave plate,” Appl. Phys. B 60, 405–407 (1995).
[Crossref]

Pietraszkiewicz, K.

Ratajczyk, F.

I. Scierski, F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik 68, 121–125 (1984).

Runwen, W.

Scierski, I.

I. Scierski, F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik 68, 121–125 (1984).

Shyu, L. H.

Su, D. C.

Wozniak, W. A.

Yao, L.

Zhiyao, Z.

Appl. Opt. (6)

Appl. Phys. B (1)

S. De Nicola, P. Ferraro, G. Pierattini, “Wavelength dependence of the phase retardation of a quarter-wave plate,” Appl. Phys. B 60, 405–407 (1995).
[Crossref]

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

Opt. Commun. (1)

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]

Opt. Lett. (2)

Optik (1)

I. Scierski, F. Ratajczyk, “The Jones matrix of the real dichroic elliptic object,” Optik 68, 121–125 (1984).

Other (1)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarised Light (North-Holland, Amsterdam, 1979), pp. 84–85.

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Figures (4)

Fig. 1
Fig. 1

Orientation of the wave plate. The optical axis of the wave plate intersects at an angle α with the y axis.

Fig. 2
Fig. 2

Schematic diagram of the optical Mach–Zehnder heterodyne interferometer. BS1 and BS2, beam splitters; PBS, polarized beam splitter; M1 and M2, mirrors; P1, and P2, polarizers; AO1, and AO2, acousto-optic modulators; D1 and D2, drivers; Dp, Ds, and Dr, photodetectors; S, sample (λ/4 wave plate) mounted onto a precision stepping rotator; PC, personal computer; BF, bandpass filter; C, controller.

Fig. 3
Fig. 3

Phase difference of P and S waves versus azimuth angle of a λ/4 quartz wave plate. The theoretical data are represented by the solid curve (δf=2°) and the dashed curve (δf=30°). The experimental data are represented by large dots, where δ(0)(0) =86.22°, δ(0)(π/2)=-86.53° and δ(0)(π)=85.82°, δ(0)(3π/2)=-85.83°.

Fig. 4
Fig. 4

(a) Amplitude ratio of P and S waves versus azimuth angle of a λ/4 quartz wave plate. The theoretical and the experimental values are represented by the solid curve and the filled dots, respectively, where the theoretical curve is under the assumption of δf =0°, δ=86.1°. (b) Theoretical curve with the best fit of experimental data under the assumption of δf=2°, δ=86.1°.

Equations (8)

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J=T11T21T12T22=cos2 θ+sin2 θ exp(-iδ)sin θ cos θ[1-exp(-iδ)]exp(iδf)sin θ cos θ[1-exp(-iδ)]exp(-iδf)sin2 θ+cos2 θ exp(-iδ).
Ex(0)Ey(0)=cos δ2+i sin δ2 cos(2θ)i sin δ2 sin(2θ)exp(iδf)i sin δ2 sin(2θ)exp(-iδf)cos δ2-i sin δ2 cos(2θ)×Ex(i)Ey(i),
X(0)=T22X(i)+T21T12X(i)+T11,
|X(0)(θ, δ, δf)|=cos δ2-sin δ2 sin(2θ)sin δf2+sin2 δ2 [cos δf sin(2θ)-cos(2θ)]2cos δ2+sin δ2 sin(2θ)sin δf2+sin2 δ2 [cos δf sin(2θ)+cos(2θ)]21/2,
δ(0)(θ, δ, δf)=tan-1sin δ cos(2θ)-sin2 δ2 sin2(2θ)sin(2δf)cos2 δ2-sin2 δ2 cos2(2θ)+sin2 δ2 sin2(2θ)cos(2δf).
I p=Ip1+Ip2+2Ip1Ip2 cos(Δωt+δ p),
I s=Is1+Is2+2Is1Is2 cos(Δωt+δ s),
|X(0)|=Ip1Ip2Is1Is2,δ(0)=δp(0)-δs(0),

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