Abstract

The irreversible behavior of polarization properties that appears when random unitary transformations are applied to three-dimensional (3D) random optical fields is investigated. The ability of 3D degrees of polarization not to increase and to evolve independently of each other with such transformations is analyzed.

© 2012 Optical Society of America

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References

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  1. C. Brosseau, Fundamentals of Polarized Light—a Statistical Optics Approach (Wiley, 1998).
  2. R. Barakat, Opt. Acta 30, 1171 (1983).
    [CrossRef]
  3. T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
    [CrossRef]
  4. J. Ellis and A. Dogariu, Opt. Commun. 253, 257 (2005).
    [CrossRef]
  5. Ph. Réfrégier and F. Goudail, J. Opt. Soc. Am. A 23, 671 (2006).
    [CrossRef]
  6. Ph. Réfrégier, M. Roche, and F. Goudail, J. Opt. Soc. Am. A 23, 124 (2006).
    [CrossRef]
  7. T. Setälä, K. Lindfors, and A. T. Friberg, Opt. Lett. 34, 3394 (2009).
    [CrossRef]
  8. Ph. Réfrégier and A. Luis, J. Opt. Soc. Am. A 25, 2749 (2008).
    [CrossRef]
  9. Ph. Réfrégier, F. Goudail, P. Chavel, and A. T. Friberg, J. Opt. Soc. Am. A 21, 2124 (2004).
    [CrossRef]

2009 (1)

2008 (1)

2006 (2)

2005 (1)

J. Ellis and A. Dogariu, Opt. Commun. 253, 257 (2005).
[CrossRef]

2004 (1)

2002 (1)

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

1983 (1)

R. Barakat, Opt. Acta 30, 1171 (1983).
[CrossRef]

Barakat, R.

R. Barakat, Opt. Acta 30, 1171 (1983).
[CrossRef]

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light—a Statistical Optics Approach (Wiley, 1998).

Chavel, P.

Dogariu, A.

J. Ellis and A. Dogariu, Opt. Commun. 253, 257 (2005).
[CrossRef]

Ellis, J.

J. Ellis and A. Dogariu, Opt. Commun. 253, 257 (2005).
[CrossRef]

Friberg, A. T.

Goudail, F.

Kaivola, M.

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Lindfors, K.

Luis, A.

Réfrégier, Ph.

Roche, M.

Setälä, T.

T. Setälä, K. Lindfors, and A. T. Friberg, Opt. Lett. 34, 3394 (2009).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Shevchenko, A.

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Acta (1)

R. Barakat, Opt. Acta 30, 1171 (1983).
[CrossRef]

Opt. Commun. (1)

J. Ellis and A. Dogariu, Opt. Commun. 253, 257 (2005).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (1)

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[CrossRef]

Other (1)

C. Brosseau, Fundamentals of Polarized Light—a Statistical Optics Approach (Wiley, 1998).

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Figures (1)

Fig. 1.
Fig. 1.

Possible domain of evolution of the normalized eigenvalues μ 1 E and μ 3 E when random unitary transformations are applied to the field, schematically represented with arrows. Curves of constant values of the 3D DOP of Eqs. (4) and (5) are shown respectively with solid and dashed curves. The segments correspond to (a)  μ 1 = 1 2 μ 3 and (b) μ 3 = 1 2 μ 1 (that are the limit values of μ 1 and μ 3 discussed in the text).

Equations (12)

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[ S E ( ω ) ] i , j = E i * ( ω ) E j ( ω ) ,
A ( ω ) = U ( ω ) E ( ω ) ,
P μ 1 0 and P μ 3 0
P s 2 = 3 2 ( λ 1 2 + λ 2 2 + λ 3 2 ( λ 1 + λ 2 + λ 3 ) 2 1 3 ) .
P b 2 = 1 27 λ 1 λ 2 λ 3 ( λ 1 + λ 2 + λ 3 ) 3 .
P = λ 1 λ 2 λ 1 + λ 2 + λ 3
P g = 1 R = 1 3 λ 3 λ 1 + λ 2 + λ 3 .
P ˜ 1 = f 1 ( μ 1 ) and P ˜ 2 = f 2 ( μ 3 ) .
P ˜ 2 = 3 2 ( λ 1 λ 1 + λ 2 + λ 3 1 3 ) .
U 2 = [ u 1 u 2 u 3 u 4 ]
U 3 = [ u 1 u 2 0 u 3 u 4 0 0 0 1 ] , U 1 = [ 1 0 0 0 u 1 u 2 0 u 3 u 4 ] .
δ P μ 1 f ( μ 1 , μ 3 ) δ μ 1 + μ 3 f ( μ 1 , μ 3 ) δ μ 3 .

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