Abstract

In this Letter we demonstrate a polarization controller capable of changing any state of polarization of light from one arbitrary state to another. The controller consists of a stack of three homogeneous nematic liquid-crystal cells. The polarization state is controlled by proper adjustment of the voltages applied across each of the cells. The mathematical algorithm and principles of this polarization controller are developed in the framework of the Stokes parameters, allowing easy visualization by use of a Poincaré sphere representation. The transformation functions are given for conversion of an arbitrary input state to any output state. Experiments are carried out to demonstrate arbitrary polarization transformation.

© 1999 Optical Society of America

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References

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  1. C. D. Poole and J. Nagel, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 114–162.
    [CrossRef]
  2. N. G. Walker and G. R. Walker, J. Lightwave Technol. 8, 438 (1990).
    [CrossRef]
  3. J. Slaz, AT&T Tech. J. 64, 2153 (1985).
    [CrossRef]
  4. T. Okoshi, Y. H. Cheng, and K. Kikuchi, Electron. Lett. 21, 787 (1985).
    [CrossRef]
  5. T. Okoshi, J. Lightwave Technol. 3, 1232 (1985).
    [CrossRef]
  6. T. Imai, K. Nosu, and H. Yamaguchi, Electron. Lett. 21, 52 (1985).
    [CrossRef]
  7. S. H. Rumbaugh, M. D. Jones, and L. W. Casperson, J. Lightwave Technol. 8, 459 (1990).
    [CrossRef]
  8. G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 309 (1852).
  9. H. Poincaré, in Theorie Mathematique de la Lumiere II, G. Carré, ed. (Gauthier-Villars, Paris, 1892), p. 275.
  10. J. E. Bieglow and R. A. Kashnow, Appl. Opt. 16, 2090 (1977).
    [CrossRef]
  11. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, New York, 1988), p. 94.

1990 (2)

N. G. Walker and G. R. Walker, J. Lightwave Technol. 8, 438 (1990).
[CrossRef]

S. H. Rumbaugh, M. D. Jones, and L. W. Casperson, J. Lightwave Technol. 8, 459 (1990).
[CrossRef]

1985 (4)

J. Slaz, AT&T Tech. J. 64, 2153 (1985).
[CrossRef]

T. Okoshi, Y. H. Cheng, and K. Kikuchi, Electron. Lett. 21, 787 (1985).
[CrossRef]

T. Okoshi, J. Lightwave Technol. 3, 1232 (1985).
[CrossRef]

T. Imai, K. Nosu, and H. Yamaguchi, Electron. Lett. 21, 52 (1985).
[CrossRef]

1977 (1)

1852 (1)

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 309 (1852).

Bieglow, J. E.

Casperson, L. W.

S. H. Rumbaugh, M. D. Jones, and L. W. Casperson, J. Lightwave Technol. 8, 459 (1990).
[CrossRef]

Cheng, Y. H.

T. Okoshi, Y. H. Cheng, and K. Kikuchi, Electron. Lett. 21, 787 (1985).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, New York, 1988), p. 94.

Imai, T.

T. Imai, K. Nosu, and H. Yamaguchi, Electron. Lett. 21, 52 (1985).
[CrossRef]

Jones, M. D.

S. H. Rumbaugh, M. D. Jones, and L. W. Casperson, J. Lightwave Technol. 8, 459 (1990).
[CrossRef]

Kashnow, R. A.

Kikuchi, K.

T. Okoshi, Y. H. Cheng, and K. Kikuchi, Electron. Lett. 21, 787 (1985).
[CrossRef]

Nagel, J.

C. D. Poole and J. Nagel, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 114–162.
[CrossRef]

Nosu, K.

T. Imai, K. Nosu, and H. Yamaguchi, Electron. Lett. 21, 52 (1985).
[CrossRef]

Okoshi, T.

T. Okoshi, J. Lightwave Technol. 3, 1232 (1985).
[CrossRef]

T. Okoshi, Y. H. Cheng, and K. Kikuchi, Electron. Lett. 21, 787 (1985).
[CrossRef]

Poincaré, H.

H. Poincaré, in Theorie Mathematique de la Lumiere II, G. Carré, ed. (Gauthier-Villars, Paris, 1892), p. 275.

Poole, C. D.

C. D. Poole and J. Nagel, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 114–162.
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, New York, 1988), p. 94.

Rumbaugh, S. H.

S. H. Rumbaugh, M. D. Jones, and L. W. Casperson, J. Lightwave Technol. 8, 459 (1990).
[CrossRef]

Slaz, J.

J. Slaz, AT&T Tech. J. 64, 2153 (1985).
[CrossRef]

Stokes, G. G.

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 309 (1852).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, New York, 1988), p. 94.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, New York, 1988), p. 94.

Walker, G. R.

N. G. Walker and G. R. Walker, J. Lightwave Technol. 8, 438 (1990).
[CrossRef]

Walker, N. G.

N. G. Walker and G. R. Walker, J. Lightwave Technol. 8, 438 (1990).
[CrossRef]

Yamaguchi, H.

T. Imai, K. Nosu, and H. Yamaguchi, Electron. Lett. 21, 52 (1985).
[CrossRef]

Appl. Opt. (1)

AT&T Tech. J. (1)

J. Slaz, AT&T Tech. J. 64, 2153 (1985).
[CrossRef]

Electron. Lett. (2)

T. Okoshi, Y. H. Cheng, and K. Kikuchi, Electron. Lett. 21, 787 (1985).
[CrossRef]

T. Imai, K. Nosu, and H. Yamaguchi, Electron. Lett. 21, 52 (1985).
[CrossRef]

J. Lightwave Technol. (3)

S. H. Rumbaugh, M. D. Jones, and L. W. Casperson, J. Lightwave Technol. 8, 459 (1990).
[CrossRef]

T. Okoshi, J. Lightwave Technol. 3, 1232 (1985).
[CrossRef]

N. G. Walker and G. R. Walker, J. Lightwave Technol. 8, 438 (1990).
[CrossRef]

Trans. Cambridge Philos. Soc. (1)

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 309 (1852).

Other (3)

H. Poincaré, in Theorie Mathematique de la Lumiere II, G. Carré, ed. (Gauthier-Villars, Paris, 1892), p. 275.

C. D. Poole and J. Nagel, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), pp. 114–162.
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University, New York, 1988), p. 94.

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Figures (4)

Fig. 1
Fig. 1

Configuration of the arbitrary SOP controller.

Fig. 2
Fig. 2

Arbitrary–arbitrary SOP mapping algorithms on a Poincaré sphere. V, vertical linear; H, horizontal linear; P, +45° linear; Q, -45° linear; L, left-handed circular; R, right-handed circular.

Fig. 3
Fig. 3

Measured relationship between the applied voltages and the birefringence of the liquid-crystal cell. Filled circles, measured data; solid curve, result from the cubic spline interpolation. For clarity, only one tenth of the measured data are shown.

Fig. 4
Fig. 4

Experimental results of arbitrary polarization transformation. The initial polarization state is arbitrarily chosen as Si=-0.61,0.11,-0.71. The final states are chosen to be two circles: (a) S3°=0, (b) S2°=0.866. The results are shown in (a) the S1S2 and (b) the S1S3 planes.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ExiEyi=cosαsinαexpiδ.
S1i=ExiExi*-EyiEyi*=cos2α,S2i=ExiEyi*+EyiExi*=sin2αcosδ,S3i=iExiEyi*-EyiExi*=sin2αsinδ.
ExoEyo=JB3R-π/4JB2Rπ/4JB1ExiEyi,
S1o=cosB2cos2α+sinB2sinB1-δsin2α,S2o=sinB3sinB2cos2α+cosB3sin2αcosB1-δ-sinB3cosB2sinB1-δsin2α,S3o=cosB3sinB2cos2α-sinB3sin2αcosB1-δ-cosB3cosB2sinB1-δsin2α.
B1-δ=π/2,
S1o=cosB2-2α,S2o=sinB3sinB2-2α,S3o=cosB3sinB2-2α.
B1=π/2+ tan-1S3i/S2i+mπ,B2= cos-1S1i+ cos-1S1o,B3=  tan-1S2o/S3o+nπ,

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