Abstract

The mechanical rotation of an optical element around the axis of a beam of polarized light can be easily simulated by using the phenomenon of optical rotation. Because optical rotation can be magnetically or electrically induced, virtually any kind of mechanical rotation can be mimicked. This interesting principle is applied to the design of a new Fourier photopolarimeter that uses an oscillating-azimuth retarder (OAR). The OAR consists of a quarter-wave plate surrounded by two ac-excited Faraday cells that produce equal and opposite sinusoidal optical rotations. Analysis of the operation of this polarimeter of no moving parts proves its ability to measure all four Stokes parameters of incident partially polarized radiation.

© 1978 Optical Society of America

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Corrections

R. M. A. Azzam, "Errata: Simulation of mechanical rotation by optical rotation: Application to the design of a new Fourier photopolarimeter," J. Opt. Soc. Am. 68, 1292-1292 (1978)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-68-9-1292

References

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  1. G. E. Sommargren, “Up/down frequency shifter for optical hetrodyne interferometry,” J. Opt. Soc. Am. 65, 960–961 (1975).
    [Crossref]
  2. K. Serkowski, “Polarimeters for optical astronomy,” in Planets, Stars and Nebulae Studied by Photopolarimetry, edited by T. Gehrels (University of Arizona Press, Tuscon, 1974). pp. 135–174.
  3. D. L. Coffeen, “Optical polarimeters in space,” in Ref. 2, pp. 189–217.
  4. R. H. Muller, “Present status of automatic ellipsometers,” Surf. Sci. 56, 19–36 (1976); also in Proceedings of the Third International Conference on Ellipsometry, edited by N. M. Bashara and R. M. A. Azzam (North-Holland, Amsterdam, 1976).
    [Crossref]
  5. D. E. Aspnes and P. S. Hauge, “Rotating-compensator/analyzer fixed analyzer ellipsometer: Analysis and comparison to other automatic ellipsometers,” J. Opt. Soc. Am. 66, 949–954 (1976).
    [Crossref]
  6. P. S. Hauge, “Survey of methods for the complete determination of a state of polarization,” in Polarized Light: Instruments, Devices, and Applications, edited by W. L. Hyde and R. M. A. Azzam; also in Proc. Soc. Photo-Opt. Instrum., Eng.,  88, pp. 3–10 (1976).
  7. B. H. Billings, “The electro-optic effect in uniaxial crystals of the dihydrogen phosphate type,” J. Opt. Soc. Am. 42, 12–20 (1952).
    [Crossref]
  8. J. C. Kemp, “Piezo-optical birefringence modulators: New use for a long-known effect,” J. Opt. Soc. Am. 59, 950–954 (1969).
  9. R. M. A. Azzam, “Oscillating-analyzer ellipsometer,” Rev. Sci. Instrum. 47, 624–628 (1976).
    [Crossref]
  10. See, for example, D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971), p. 124.
  11. Handbook of Mathematical Functions, edited by M. Abramowitz and J. A. Stegun (Dover, New York, 1965), p. 361.
  12. Z. Sekera, “Light scattering in the atmosphere and the polarization of sky light,” J. Opt. Soc. Am. 47, 484–490 (1957); P. S. Hauge and F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–434 (1975).
    [Crossref]

1976 (3)

R. H. Muller, “Present status of automatic ellipsometers,” Surf. Sci. 56, 19–36 (1976); also in Proceedings of the Third International Conference on Ellipsometry, edited by N. M. Bashara and R. M. A. Azzam (North-Holland, Amsterdam, 1976).
[Crossref]

D. E. Aspnes and P. S. Hauge, “Rotating-compensator/analyzer fixed analyzer ellipsometer: Analysis and comparison to other automatic ellipsometers,” J. Opt. Soc. Am. 66, 949–954 (1976).
[Crossref]

R. M. A. Azzam, “Oscillating-analyzer ellipsometer,” Rev. Sci. Instrum. 47, 624–628 (1976).
[Crossref]

1975 (1)

1969 (1)

1957 (1)

1952 (1)

Aspnes, D. E.

Azzam, R. M. A.

R. M. A. Azzam, “Oscillating-analyzer ellipsometer,” Rev. Sci. Instrum. 47, 624–628 (1976).
[Crossref]

Billings, B. H.

Clarke, D.

See, for example, D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971), p. 124.

Coffeen, D. L.

D. L. Coffeen, “Optical polarimeters in space,” in Ref. 2, pp. 189–217.

Grainger, J. F.

See, for example, D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971), p. 124.

Hauge, P. S.

D. E. Aspnes and P. S. Hauge, “Rotating-compensator/analyzer fixed analyzer ellipsometer: Analysis and comparison to other automatic ellipsometers,” J. Opt. Soc. Am. 66, 949–954 (1976).
[Crossref]

P. S. Hauge, “Survey of methods for the complete determination of a state of polarization,” in Polarized Light: Instruments, Devices, and Applications, edited by W. L. Hyde and R. M. A. Azzam; also in Proc. Soc. Photo-Opt. Instrum., Eng.,  88, pp. 3–10 (1976).

Kemp, J. C.

Muller, R. H.

R. H. Muller, “Present status of automatic ellipsometers,” Surf. Sci. 56, 19–36 (1976); also in Proceedings of the Third International Conference on Ellipsometry, edited by N. M. Bashara and R. M. A. Azzam (North-Holland, Amsterdam, 1976).
[Crossref]

Sekera, Z.

Serkowski, K.

K. Serkowski, “Polarimeters for optical astronomy,” in Planets, Stars and Nebulae Studied by Photopolarimetry, edited by T. Gehrels (University of Arizona Press, Tuscon, 1974). pp. 135–174.

Sommargren, G. E.

J. Opt. Soc. Am. (5)

Rev. Sci. Instrum. (1)

R. M. A. Azzam, “Oscillating-analyzer ellipsometer,” Rev. Sci. Instrum. 47, 624–628 (1976).
[Crossref]

Surf. Sci. (1)

R. H. Muller, “Present status of automatic ellipsometers,” Surf. Sci. 56, 19–36 (1976); also in Proceedings of the Third International Conference on Ellipsometry, edited by N. M. Bashara and R. M. A. Azzam (North-Holland, Amsterdam, 1976).
[Crossref]

Other (5)

See, for example, D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971), p. 124.

Handbook of Mathematical Functions, edited by M. Abramowitz and J. A. Stegun (Dover, New York, 1965), p. 361.

P. S. Hauge, “Survey of methods for the complete determination of a state of polarization,” in Polarized Light: Instruments, Devices, and Applications, edited by W. L. Hyde and R. M. A. Azzam; also in Proc. Soc. Photo-Opt. Instrum., Eng.,  88, pp. 3–10 (1976).

K. Serkowski, “Polarimeters for optical astronomy,” in Planets, Stars and Nebulae Studied by Photopolarimetry, edited by T. Gehrels (University of Arizona Press, Tuscon, 1974). pp. 135–174.

D. L. Coffeen, “Optical polarimeters in space,” in Ref. 2, pp. 189–217.

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Figures (3)

FIG. 1
FIG. 1

Optical element E of azimuth θ which is surrounded by two optical rotators OR1 and OR2 with equal and opposite rotations +α and −α is equivalent to itself in a new azimuth position θ + α.

FIG. 2
FIG. 2

(a) If the optical rotation α (in Fig. 1) varies as a saw-tooth function of time, the equivalent element E will be synchronously rotating. (b) If the optical rotation α varies sinusoidally with time, the equivalent element E will execute a pendulumlike oscillation.

FIG. 3
FIG. 3

New Fourier photopolarimeter using an oscillating-azimuth retarder (OAR). The OAR consists of a fixed quarter-square plate (QWP) surrounded by two identical ac-excited Faraday cells FC1 and FC2 that produce equal and opposite sinusoidal optical rotations. (Additonal dc excitation of the Faraday cells may be utilized to control the bias azimuth C0.) A is a fixed linear analyzer and D is a linear photodetector. Fourier analysis of the output signal i of D gives the Stokes vector S of the light incident on the polarimeter. The azimuthal orientations A of the transmission axis t of the analyzer and C0 of the fast axis f of the QWP are indicated (right).

Equations (21)

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T E x , y = R ( - θ ) T E x , y R ( θ ) ,
T OR 1 + E + OR 2 x , y = R ( - α ) T E x , y R ( α ) ,
T OR 1 + E + OR 2 x , y = R ( - α ) R ( - θ ) T E x , y R ( θ ) R ( α ) = R [ - ( θ + α ) ] T E x , y R [ + ( θ + α ) ] ,
R ( x ) R ( v ) = R ( x + y ) .
α = ω ( t - n T ) ,             ( n - 1 2 ) T t ( n + 1 2 ) T , n = 0 , ± 1 , ± 2 , ,             ω T = 2 π
α = α ˆ sin ω t
2 S 0 = S 0 + S 1 [ cos 2 C cos ( 2 A - 2 C ) - sin 2 C sin ( 2 A - 2 C ) cos δ ] + S 2 [ sin 2 C cos ( 2 A - 2 C ) + cos 2 C sin ( 2 A - 2 C ) cos δ ] + S 3 [ sin ( 2 A - 2 C ) sin δ ] .
k i = ( S 0 + 1 2 S 1 ) + 1 2 S 1 cos 4 C + 1 2 S 2 sin 4 C - S 3 sin 2 C ,
k i = β 0 + β 1 cos 4 C + β 2 sin 4 C + β 3 sin 2 C ,
β 0 = S 0 + 1 2 S 1 ,             β 1 = 1 2 S 1 ,             β 2 = 1 2 S 2 ,             β 3 = - S 3 ,
C = C 0 + ĉ sin ω t ,
k î 3 ω = β 1 [ - 2 sin 4 C 0 J 3 ( 4 ĉ ) ] + β 2 [ 2 cos 4 C 0 J 3 ( 4 ĉ ) ] + β 3 [ 2 cos 2 C 0 J 3 ( 2 ĉ ) ] .
k î = C β ,
î = ( î ω î 2 ω î 3 ω ) ,             β = ( β 1 β 2 β 3 ) ,
C = ( - 2 sin 4 C 0 J 1 ( 4 ĉ ) 2 cos 4 C 0 J 1 ( 4 ĉ ) 2 cos 2 C 0 J 1 ( 2 ĉ ) 2 cos 4 C 0 J 2 ( 4 ĉ ) 2 sin 4 C 0 J 2 ( 4 ĉ ) 2 sin 2 C 0 J 2 ( 2 ĉ ) - 2 sin 4 C 0 J 3 ( 4 ĉ ) 2 cos 4 C 0 J 3 ( 4 ĉ ) 2 cos 2 C 0 J 3 ( 2 ĉ ) ) .
β = k C - 1 î ,
cos ( x sin ω t ) = J 0 ( x ) + 2 n = 1 J 2 n ( x ) cos 2 n ω t , sin ( x sin ω t ) = 2 n = 0 J 2 n + 1 ( x ) sin [ ( 2 n + 1 ) ω t ] ,
k i d c = β 0 + β 1 [ cos 4 C 0 J 0 ( 4 ĉ ) ] + β 2 [ sin 4 C 0 J 0 ( 4 ĉ ) ] + β 3 [ sin 2 C 0 J 0 ( 2 ĉ ) ] ,
k î ω = β 1 [ - 2 sin 4 C 0 J 1 ( 4 ĉ ) ] + β 2 [ 2 cos 4 C 0 J 1 ( 4 ĉ ) ] + β 3 [ 2 cos 2 C 0 J 1 ( 2 ĉ ) ] ,
k î 2 ω = β 1 [ 2 cos 4 C 0 J 2 ( 4 ĉ ) ] + β 2 [ 2 sin 4 C 0 J 2 ( 4 ĉ ) ] + β 3 [ 2 sin 2 C 0 J 2 ( 2 ĉ ) ] ,
C c 0 = 0 , ± π / 2 = ( 0 2 J 1 ( 4 ĉ ) ± 2 J 1 ( 2 ĉ ) 2 J 2 ( 4 ĉ ) 0 0 0 2 J 3 ( 4 ĉ ) ± 2 J 3 ( 2 ĉ ) ) ,