Abstract

We have studied the depolarization of light from nitrobenzene in a Kerr cell. We observed that absorption in nitrobenzene is electric-field dependent. For modeling a nitrobenzene device we formulated a Mueller matrix for the Kerr-cell assembly, and by operating it on a Stokes vector of the input light we obtained a corresponding Stokes vector for the output light. The first parameter of the output Stokes vector corresponds to the intensity transmittance. It was simulated and compared with the measured intensity transmittance for several orientations of the polarizer–analyzer pair with respect to the applied voltages. The measurement of all unknown coefficients in a Mueller matrix consisting of the superposition of nondepolarizing and depolarizing components predicts the depolarization, scattering, and absorption in the nitrobenzene electro-optic device. The output intensities of the orthogonally polarized and cross-coupled depolarizing coefficients are in good agreement for a semi-isotropic medium. The formulated Mueller matrix agrees with the experimentally measured transmittance.

© 2005 Optical Society of America

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References

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  1. R. E. Hebner, M. Misakian, “Temperature dependence of the electro-optic Kerr coefficient of nitrobenzene,” J. Appl. Phys. 50, 6016–6021 (1979).
    [CrossRef]
  2. P. H. White, R. H. Gobbett, B. R. Withey, “Measurement of the Kerr electro-optic effect,” J. Phys. D 20, 105–111 (1987).
    [CrossRef]
  3. J. L. Pezzaniti, S. C. McClain, R. A. Chipman, S. Y. Lu, “Depolarization in liquid-crystal televisions,” Opt. Lett. 18, 2071–2074 (1993).
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  4. J. J. Choi, D. Y. Kim, G. T. Park, H. E. Kim, “Electro-optic properties of PLZT thickfilm on glass substrate with embedded electrodes structure,” J. Korean Phys. Soc. 42, S1310–S1312 (2003).
  5. K. Kim, L. Mandel, E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. 4, 433–437 (1987).
    [CrossRef]
  6. J. S. Baba, J. R. Chung, A. H. D. Laughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
    [CrossRef] [PubMed]
  7. D. G. M. Anderson, R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” J. Opt. Soc. Am. A 11, 2305–2319 (1994).
    [CrossRef]
  8. E. Hecht, Optics (Adelph U. Press, Menlo Park, Calif., 1998), Chap. 7.
  9. R. Barakat, “Theory of the coherency matrix for light of arbitrary spectral bandwidth,” J. Opt. Soc. Am. 53, 317–323 (1963).
    [CrossRef]
  10. R. M. A. Azzam, N. M. Bashara, Ellipsometry and polarized light, 3rd ed. (Elsevier, North-Holland, Amsterdam, 1999), Chap. 2.
  11. C. Brosseau, Polarized Light: A Statistical Optics Approach (Wiley, New York, 1998).
  12. P. E. Shames, P. C. Sun, Y. Fainman, “Modeling of scattering and depolarizing electro-optic devices. I. Characterization of lanthanum-modified lead zirconate titanate,” Appl. Opt. 37, 3717–3725 (1998).
    [CrossRef]
  13. A. Peshkovsky, A. E. McDermott, “NMR spectroscopy in the presence of strong ac electric fields: degree of alignment of polar molecules,” J. Phys. Chem. A 103, 8604–8609 (1999).
    [CrossRef]

2003 (1)

J. J. Choi, D. Y. Kim, G. T. Park, H. E. Kim, “Electro-optic properties of PLZT thickfilm on glass substrate with embedded electrodes structure,” J. Korean Phys. Soc. 42, S1310–S1312 (2003).

2002 (1)

J. S. Baba, J. R. Chung, A. H. D. Laughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef] [PubMed]

1999 (1)

A. Peshkovsky, A. E. McDermott, “NMR spectroscopy in the presence of strong ac electric fields: degree of alignment of polar molecules,” J. Phys. Chem. A 103, 8604–8609 (1999).
[CrossRef]

1998 (1)

1994 (1)

1993 (1)

1987 (2)

K. Kim, L. Mandel, E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. 4, 433–437 (1987).
[CrossRef]

P. H. White, R. H. Gobbett, B. R. Withey, “Measurement of the Kerr electro-optic effect,” J. Phys. D 20, 105–111 (1987).
[CrossRef]

1979 (1)

R. E. Hebner, M. Misakian, “Temperature dependence of the electro-optic Kerr coefficient of nitrobenzene,” J. Appl. Phys. 50, 6016–6021 (1979).
[CrossRef]

1963 (1)

Anderson, D. G. M.

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and polarized light, 3rd ed. (Elsevier, North-Holland, Amsterdam, 1999), Chap. 2.

Baba, J. S.

J. S. Baba, J. R. Chung, A. H. D. Laughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef] [PubMed]

Barakat, R.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and polarized light, 3rd ed. (Elsevier, North-Holland, Amsterdam, 1999), Chap. 2.

Brosseau, C.

C. Brosseau, Polarized Light: A Statistical Optics Approach (Wiley, New York, 1998).

Cameron, B. D.

J. S. Baba, J. R. Chung, A. H. D. Laughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef] [PubMed]

Chipman, R. A.

Choi, J. J.

J. J. Choi, D. Y. Kim, G. T. Park, H. E. Kim, “Electro-optic properties of PLZT thickfilm on glass substrate with embedded electrodes structure,” J. Korean Phys. Soc. 42, S1310–S1312 (2003).

Chung, J. R.

J. S. Baba, J. R. Chung, A. H. D. Laughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef] [PubMed]

Coté, G. L.

J. S. Baba, J. R. Chung, A. H. D. Laughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef] [PubMed]

Fainman, Y.

Gobbett, R. H.

P. H. White, R. H. Gobbett, B. R. Withey, “Measurement of the Kerr electro-optic effect,” J. Phys. D 20, 105–111 (1987).
[CrossRef]

Hebner, R. E.

R. E. Hebner, M. Misakian, “Temperature dependence of the electro-optic Kerr coefficient of nitrobenzene,” J. Appl. Phys. 50, 6016–6021 (1979).
[CrossRef]

Hecht, E.

E. Hecht, Optics (Adelph U. Press, Menlo Park, Calif., 1998), Chap. 7.

Kim, D. Y.

J. J. Choi, D. Y. Kim, G. T. Park, H. E. Kim, “Electro-optic properties of PLZT thickfilm on glass substrate with embedded electrodes structure,” J. Korean Phys. Soc. 42, S1310–S1312 (2003).

Kim, H. E.

J. J. Choi, D. Y. Kim, G. T. Park, H. E. Kim, “Electro-optic properties of PLZT thickfilm on glass substrate with embedded electrodes structure,” J. Korean Phys. Soc. 42, S1310–S1312 (2003).

Kim, K.

K. Kim, L. Mandel, E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. 4, 433–437 (1987).
[CrossRef]

Laughter, A. H. D.

J. S. Baba, J. R. Chung, A. H. D. Laughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef] [PubMed]

Lu, S. Y.

Mandel, L.

K. Kim, L. Mandel, E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. 4, 433–437 (1987).
[CrossRef]

McClain, S. C.

McDermott, A. E.

A. Peshkovsky, A. E. McDermott, “NMR spectroscopy in the presence of strong ac electric fields: degree of alignment of polar molecules,” J. Phys. Chem. A 103, 8604–8609 (1999).
[CrossRef]

Misakian, M.

R. E. Hebner, M. Misakian, “Temperature dependence of the electro-optic Kerr coefficient of nitrobenzene,” J. Appl. Phys. 50, 6016–6021 (1979).
[CrossRef]

Park, G. T.

J. J. Choi, D. Y. Kim, G. T. Park, H. E. Kim, “Electro-optic properties of PLZT thickfilm on glass substrate with embedded electrodes structure,” J. Korean Phys. Soc. 42, S1310–S1312 (2003).

Peshkovsky, A.

A. Peshkovsky, A. E. McDermott, “NMR spectroscopy in the presence of strong ac electric fields: degree of alignment of polar molecules,” J. Phys. Chem. A 103, 8604–8609 (1999).
[CrossRef]

Pezzaniti, J. L.

Shames, P. E.

Sun, P. C.

White, P. H.

P. H. White, R. H. Gobbett, B. R. Withey, “Measurement of the Kerr electro-optic effect,” J. Phys. D 20, 105–111 (1987).
[CrossRef]

Withey, B. R.

P. H. White, R. H. Gobbett, B. R. Withey, “Measurement of the Kerr electro-optic effect,” J. Phys. D 20, 105–111 (1987).
[CrossRef]

Wolf, E.

K. Kim, L. Mandel, E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. 4, 433–437 (1987).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

R. E. Hebner, M. Misakian, “Temperature dependence of the electro-optic Kerr coefficient of nitrobenzene,” J. Appl. Phys. 50, 6016–6021 (1979).
[CrossRef]

J. Biomed. Opt. (1)

J. S. Baba, J. R. Chung, A. H. D. Laughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7, 341–349 (2002).
[CrossRef] [PubMed]

J. Korean Phys. Soc. (1)

J. J. Choi, D. Y. Kim, G. T. Park, H. E. Kim, “Electro-optic properties of PLZT thickfilm on glass substrate with embedded electrodes structure,” J. Korean Phys. Soc. 42, S1310–S1312 (2003).

J. Opt. Soc. Am. (2)

K. Kim, L. Mandel, E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. 4, 433–437 (1987).
[CrossRef]

R. Barakat, “Theory of the coherency matrix for light of arbitrary spectral bandwidth,” J. Opt. Soc. Am. 53, 317–323 (1963).
[CrossRef]

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

J. Phys. Chem. A (1)

A. Peshkovsky, A. E. McDermott, “NMR spectroscopy in the presence of strong ac electric fields: degree of alignment of polar molecules,” J. Phys. Chem. A 103, 8604–8609 (1999).
[CrossRef]

J. Phys. D (1)

P. H. White, R. H. Gobbett, B. R. Withey, “Measurement of the Kerr electro-optic effect,” J. Phys. D 20, 105–111 (1987).
[CrossRef]

Opt. Lett. (1)

Other (3)

E. Hecht, Optics (Adelph U. Press, Menlo Park, Calif., 1998), Chap. 7.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and polarized light, 3rd ed. (Elsevier, North-Holland, Amsterdam, 1999), Chap. 2.

C. Brosseau, Polarized Light: A Statistical Optics Approach (Wiley, New York, 1998).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for the measurement of transmitted light intensity through a nitrobenzene sample by use of a cross-polarizer setup at 45° relative to the direction of the applied field. In Cartesian coordinates (as shown) an optical axis is along the z direction and an applied electric field is along the x axis.

Fig. 2
Fig. 2

Normalized transmitted intensity measurements for six configurations of polarizers and analyzers.

Fig. 3
Fig. 3

Normalized absorbed intensity as a function of applied voltage.

Fig. 4
Fig. 4

Normalized absorbed intensity (filled diamonds) as a function of the orientation of the polarizer. Solid curve, sin2(2θi).

Fig. 5
Fig. 5

Curve fits for I, I||, MaxI45, 45, MinI45, 45, and IA for the calculation of unknown coefficients.

Fig. 6
Fig. 6

Simulation of the transmittance for θi = θo = π/4 (solid curve), θi = π/4 and θo = −π/4 (dashed curve), θi = θo = 0° (dotted curve), and θi = 0° and θo = π/2 (dashed–dotted curve).

Fig. 7
Fig. 7

Simulation of transmitted intensity for θi = 25° and θo = 115° (solid curve); the dots are experimental observed points.

Equations (46)

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Δ φ = 2 π K L V 2 d 2 ,
I = I 0 sin 2 ( ϕ / 2 ) .
Δ n = λ K V 2 d 2 .
[ S out ] = [ M system ] [ S in ] ,
[ M syst ] = [ A M ] [ M nit ] [ P M ] ,
[ M nit ] = [ 1 2 ( A + B + U 1 + U 2 + U 3 + U 4 ) 1 2 ( A - B + U 1 - U 2 - U 3 + U 4 ) 0 0 1 2 ( A - B + U 1 - U 2 + U 3 - U 4 ) 1 2 ( A + B + U 1 + U 2 - U 3 - U 4 ) 0 0 0 0 A B cos ( Δ ϕ ) A B sin ( Δ ϕ ) 0 0 - A B sin ( Δ ϕ ) A B cos ( Δ ϕ ) ] ,
[ S in ] = [ 1 0 0 1 ] .
I θ i , θ o = 1 8 [ ( A + B + U 1 + U 2 + U 3 + U 4 ) + ( A - B + U 1 - U 2 - U 3 + U 4 ) ( C 2 i ) + C 2 o { ( A - B + U 1 - U 2 + U 3 - U 4 ) + ( A + B + U 1 + U 2 - U 3 - U 4 ) ( C 2 i ) } + 2 A B S 2 o S 2 i cos ( Δ ϕ ) ] ,
I 45 , 45 = 1 8 [ A + B + U 1 + U 2 + U 3 + U 4 + 2 A B cos ( Δ ϕ ) ] ,
I 45 , - 45 = 1 8 [ A + B + U 1 + U 2 + U 3 + U 4 - 2 A B cos ( Δ ϕ ) ] ,
I 0 , 0 = 1 2 [ A + U 1 ] ,
I 90 , 90 = 1 2 [ B + U 2 ] ,
I 0 , 90 = 1 2 U 4 ,
I 90 , 0 = 1 2 U 3 .
Max I 45 , 45 = Max I 45 ,     - 45 = [ A + B + U 1 + U 2 + U 3 + U 4 + 2 A B ] .
Min I 45 , 45 = Min I 45 ,     - 45 = [ A + B + U 1 + U 2 + U 3 + U 4 - 2 A B ] .
Max I 45 , 45 + Min I 45 ,     - 45 = ¼ [ A + B + U 1 + U 2 + U 3 + U 4 ] .
Max I 45 , 45 + Min I 45 , 45 = ½ [ I 0 , 0 + I 90 , 90 + I 90 , 0 + I 0 , 90 ] .
I 0 , 0 I 90 , 90 = I ,             I 0 , 90 I 90 , 0 = I .
I = 1 2 ( A + U 1 ) = 1 2 ( B + U 2 ) ,
I = 1 2 U 4 = 1 2 U 3 .
A = B ,             U 1 = U 2 = U ,             U 4 = U 3 = U ,
I = 1 2 ( A + U ) ,
I = 1 2 U .
Max I 45 , 45 = 1 4 [ 2 A + U + U ] ,
Min I 45 , 45 = 1 4 [ U + U ] .
Max I 45 , 45 - Min I 45 , 45 = A / 2.
Max I 45 , 45 + Min I 45 , 45 = 1 2 [ A + U + U ] .
Max I 45 , 45 + Min I 45 , 45 = I + I .
Max I 45 , 45 + Min I 45 , 45 = I + I + I A f ( θ i ) .
I - [ Max I 45 , 45 - I A f ( θ i ) 2 ] - [ Min I 45 , 45 - I A f ( θ i ) 2 ] + I = 0 ,
I - I M - I m + I = 0 ,
Max I 45 , 45 = I A f ( θ i ) 2 + 1 4 [ U + U + 2 A ] ,
Min I 45 , 45 = I A f ( θ i ) 2 + 1 4 [ U + U ] ,
I 45 , 45 = I A f ( θ i ) 2 + 1 4 [ U + U + A { 1 + cos ( Δ ϕ ) } ] .
I θ i , θ o = 1 4 [ A + U + U + ( A + U - U ) C 2 i C 2 o + A S 2 o S 2 i cos ( Δ ϕ ) ] + I k c ,
I k c = 2 I A f ( θ i ) .
α = - 1 L ln [ 1 - 2 I A f ( θ i ) ] .
[ M A ] = [ 2 I A f ( θ i ) 0 0 0 0 2 I A f ( θ i ) 0 0 0 0 2 I A f ( θ i ) 0 0 0 0 2 I A f ( θ i ) ] .
[ M P ] = [ A + U + U + 2 I A f ( θ i ) 0 0 0 0 A + U - U + 2 I A f ( θ i ) 0 0 0 0 A cos ( Δ ϕ ) + 2 I A f ( θ i ) A sin ( Δ ϕ ) 0 0 - A sin ( Δ ϕ ) A cos ( Δ ϕ ) + 2 I A f ( θ i ) ] ,
I θ i , θ o = 2 I A f ( θ i ) + 1 4 [ A + U + U + ( A + U - U ) C 2 i C 2 o + A S 2 o S 2 i cos ( Δ ϕ ) ] .
I = 0.00289 + 1.24916 × 10 - 5 V - 5.90669 × 10 - 9 V 2 + 7.78655 × 10 - 13 V 3 ,
I = 0.9353 + 8.76251 × 10 - 5 V - 3.4633 × 10 - 8 V 2 + 1.97968 × 10 - 12 V 3 ,
Max I 45 , 45 = 0.98547 + 6.24724 × 10 - 5 V - 2.85453 × 10 - 8 V 2 + 1.48832 × 10 - 12 V 3 ,
Min I 45 , 45 = 0.03357 - 1.9448 × 10 - 4 V + 1.25109 × 10 - 7 V 2 - 1.2393 × 10 - 11 V 3 ,
I A = 0.08085 - 2.3212 × 10 - 4 V + 1.37103 × 10 - 7 V 2 - 1.3663 × 10 - 11 V 3 .

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