Abstract

The polarization and temporal coherence properties of light are altered by scattering events. In this paper, we follow a far-field approach, modelizing the scattering from disordered media with the scattering matrix formalism. The degree of polarization and coherence time of the scattered light are expressed with respect to the characteristics of the incident field.

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. J. Goodman, Speckle Phenomena in Optics: Theory and Applications(Roberts & Co, 2007).
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2013 (1)

2012 (2)

2011 (3)

2010 (3)

2009 (1)

2007 (2)

P. Réfrégier and A. Roueff, “Intrinsic coherence: a new concept in polarization and coherence theory,” Optics and photonics news18, 30–35 (2007).
[CrossRef]

W. Huang, S. Ponomarenko, M. Cada, and G. P. Agrawal, “Polarization changes of partially coherent pulses propagating in optical fibers,” J. Opt. Soc. Am. A24, 3063–3068 (2007).
[CrossRef]

2006 (1)

2005 (2)

2004 (4)

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves in Random Media14, 513–523 (2004).
[CrossRef]

J. Tervo, T. Setälä, and A. T. Friberg, “Theory of partially coherent electromagnetic fields in the space–frequency domain,” J. Opt. Soc. Am. A21, 2205–2215 (2004).
[CrossRef]

P. Vahimaa and J. Tervo, “Unified measures for optical fields: degree of polarization and effective degree of coherence,” Journal of Optics A: Pure and Applied Optics6, S41 (2004).
[CrossRef]

J. Ellis and A. Dogariu, “Complex degree of mutual polarization,” Opt. Lett.29, 536–538 (2004).
[CrossRef] [PubMed]

1975 (1)

J. Dainty, A. Ennos, M. Françon, J. Goodman, T. McKechnie, G. Parry, and J. Goodman, “Statistical properties of laser speckle patterns,” Topics in Applied Physics9, 9–75 (1975).
[CrossRef]

Agrawal, G. P.

Amra, C.

Andrés, P.

Cada, M.

Cai, Y.

Dainty, J.

J. Dainty, A. Ennos, M. Françon, J. Goodman, T. McKechnie, G. Parry, and J. Goodman, “Statistical properties of laser speckle patterns,” Topics in Applied Physics9, 9–75 (1975).
[CrossRef]

Ding, C.

Dogariu, A.

J. Ellis and A. Dogariu, “Complex degree of mutual polarization,” Opt. Lett.29, 536–538 (2004).
[CrossRef] [PubMed]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves in Random Media14, 513–523 (2004).
[CrossRef]

Ellis, J.

Ennos, A.

J. Dainty, A. Ennos, M. Françon, J. Goodman, T. McKechnie, G. Parry, and J. Goodman, “Statistical properties of laser speckle patterns,” Topics in Applied Physics9, 9–75 (1975).
[CrossRef]

Françon, M.

J. Dainty, A. Ennos, M. Françon, J. Goodman, T. McKechnie, G. Parry, and J. Goodman, “Statistical properties of laser speckle patterns,” Topics in Applied Physics9, 9–75 (1975).
[CrossRef]

Friberg, A. T.

Gbur, G.

G. Gbur and T. Visser, “The structure of partially coherent fields,” Progress in optics55, 285 (2011).
[CrossRef]

Ghabbach, A.

Goodman, J.

J. Dainty, A. Ennos, M. Françon, J. Goodman, T. McKechnie, G. Parry, and J. Goodman, “Statistical properties of laser speckle patterns,” Topics in Applied Physics9, 9–75 (1975).
[CrossRef]

J. Dainty, A. Ennos, M. Françon, J. Goodman, T. McKechnie, G. Parry, and J. Goodman, “Statistical properties of laser speckle patterns,” Topics in Applied Physics9, 9–75 (1975).
[CrossRef]

J. Goodman, Speckle Phenomena in Optics: Theory and Applications(Roberts & Co, 2007).

J. Goodman, Statistical Optics (Wiley-Interscience, 1985).

Goudail, F.

Huang, W.

Korotkova, O.

C. Ding, Y. Cai, O. Korotkova, Y. Zhang, and L. Pan, “Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse,” Opt. Lett.36, 517–519 (2011).
[CrossRef] [PubMed]

Z. Tong and O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A82, 033836 (2010).
[CrossRef]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves in Random Media14, 513–523 (2004).
[CrossRef]

Lancis, J.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University press, 1995).
[CrossRef]

McKechnie, T.

J. Dainty, A. Ennos, M. Françon, J. Goodman, T. McKechnie, G. Parry, and J. Goodman, “Statistical properties of laser speckle patterns,” Topics in Applied Physics9, 9–75 (1975).
[CrossRef]

Pan, L.

Parry, G.

J. Dainty, A. Ennos, M. Françon, J. Goodman, T. McKechnie, G. Parry, and J. Goodman, “Statistical properties of laser speckle patterns,” Topics in Applied Physics9, 9–75 (1975).
[CrossRef]

Ponomarenko, S.

Press, W. H.

W. H. Press, Numerical Recipes in Fortran 77: the Art of Scientific Computing, (Cambridge University Press, 1992).

Réfrégier, P.

Roueff, A.

P. Réfrégier and A. Roueff, “Intrinsic coherence: a new concept in polarization and coherence theory,” Optics and photonics news18, 30–35 (2007).
[CrossRef]

Roychowdhury, H.

Salem, M.

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves in Random Media14, 513–523 (2004).
[CrossRef]

Setälä, T.

Silvestre, E.

Soriano, G.

Sorrentini, J.

Tervo, J.

P. Vahimaa and J. Tervo, “Unified measures for optical fields: degree of polarization and effective degree of coherence,” Journal of Optics A: Pure and Applied Optics6, S41 (2004).
[CrossRef]

J. Tervo, T. Setälä, and A. T. Friberg, “Theory of partially coherent electromagnetic fields in the space–frequency domain,” J. Opt. Soc. Am. A21, 2205–2215 (2004).
[CrossRef]

Tong, Z.

Z. Tong and O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A82, 033836 (2010).
[CrossRef]

Torres-Company, V.

Vahimaa, P.

P. Vahimaa and J. Tervo, “Unified measures for optical fields: degree of polarization and effective degree of coherence,” Journal of Optics A: Pure and Applied Optics6, S41 (2004).
[CrossRef]

Van Bladel, J. G.

J. G. Van Bladel, Electromagnetic Fields (Wiley-IEEE Press, 2007).
[CrossRef]

Visser, T.

G. Gbur and T. Visser, “The structure of partially coherent fields,” Progress in optics55, 285 (2011).
[CrossRef]

Voronovich, A. G.

A. G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, 1994).
[CrossRef]

Wang, T.

Wolf, E.

H. Roychowdhury, G. P. Agrawal, and E. Wolf, “Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber,” J. Opt. Soc. Am. A23, 940–948 (2006).
[CrossRef]

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves in Random Media14, 513–523 (2004).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University press, 1995).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).

Zerrad, M.

Zhang, Y.

Zhao, D.

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

Journal of Optics A: Pure and Applied Optics (1)

P. Vahimaa and J. Tervo, “Unified measures for optical fields: degree of polarization and effective degree of coherence,” Journal of Optics A: Pure and Applied Optics6, S41 (2004).
[CrossRef]

Opt. Express (4)

Opt. Lett. (6)

Optics and photonics news (1)

P. Réfrégier and A. Roueff, “Intrinsic coherence: a new concept in polarization and coherence theory,” Optics and photonics news18, 30–35 (2007).
[CrossRef]

Phys. Rev. A (1)

Z. Tong and O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A82, 033836 (2010).
[CrossRef]

Progress in optics (1)

G. Gbur and T. Visser, “The structure of partially coherent fields,” Progress in optics55, 285 (2011).
[CrossRef]

Topics in Applied Physics (1)

J. Dainty, A. Ennos, M. Françon, J. Goodman, T. McKechnie, G. Parry, and J. Goodman, “Statistical properties of laser speckle patterns,” Topics in Applied Physics9, 9–75 (1975).
[CrossRef]

Waves in Random Media (1)

M. Salem, O. Korotkova, A. Dogariu, and E. Wolf, “Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere,” Waves in Random Media14, 513–523 (2004).
[CrossRef]

Other (7)

J. Goodman, Statistical Optics (Wiley-Interscience, 1985).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University press, 1995).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).

J. Goodman, Speckle Phenomena in Optics: Theory and Applications(Roberts & Co, 2007).

W. H. Press, Numerical Recipes in Fortran 77: the Art of Scientific Computing, (Cambridge University Press, 1992).

J. G. Van Bladel, Electromagnetic Fields (Wiley-IEEE Press, 2007).
[CrossRef]

A. G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, 1994).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Maps (left column) and densities (right column) of the scattered normalized intensity (top line), degree of polarization (middle line) and coherence time (bottom line) for parameters β = 1, μi = 1/2, θ = π/8 and r ≃ 1.8.

Fig. 2
Fig. 2

Densities of the degree of polarization (left) and coherence time (right) for parameters μi = 1/2, θ = π/8, r ≃ 1.8 and three values of parameter βi.

Fig. 3
Fig. 3

The coherence time coefficient of variation and the mean DOP against the cross-correlation coefficient (left) and densities of the coherence time for several values of the cross-correlation coefficient (right) for parameters βi = 1 and θ = π 4 μ i.

Equations (35)

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E ¯ ( t ) = [ E x ( t ) E y ( t ) ]
Γ ¯ ¯ ( τ ) = E ¯ * ( t ) E ¯ T ( t + τ ) = 0 W ¯ ¯ ( ν ) e 2 i π ν τ d ν
T = Γ x x + Γ y y
D = Γ x x Γ y y Γ x y Γ y x
P = 1 4 D ( 0 ) T ( 0 ) 2
Δ τ = 1 T ( 0 ) 2 + | T ( τ ) | 2 d τ = 0 T ˜ ( ν ) 2 d ν ( 0 T ˜ ( ν ) d ν ) 2
τ 2 | T ( τ ) | 2 d τ / | T ( τ ) | 2 d τ
¯ s ( ν ) = Σ ¯ ¯ ( ν ) ¯ i ( ν )
Σ ¯ ¯ = [ Σ x x Σ x y Σ y x Σ y y ]
¯ * ( ν 1 ) ¯ T ( ν 2 ) = W ¯ ¯ ( ν 2 ) δ ( ν 2 ν 1 )
W ¯ ¯ s ( ν ) = Σ ¯ ¯ * ( ν ) W ¯ ¯ i ( ν ) Σ ¯ ¯ T ( ν )
Γ ¯ ¯ s ( τ ) = Σ ¯ ¯ * ( ν 0 ) Γ ¯ ¯ i ( τ ) Σ ¯ ¯ T ( ν 0 )
D s ( τ ) = | D Σ ( ν 0 ) | 2 D i ( τ ) D Σ = Σ x x Σ y y Σ x y Σ y x
T s ( τ ) = Tr ( M ¯ ¯ ( ν 0 ) Γ ¯ ¯ i ( τ ) ) M ¯ ¯ = Σ ¯ ¯ * Σ ¯ ¯ T = [ | Σ x x | 2 + | Σ x y | 2 Σ x x * Σ y x + Σ x y * Σ y y ( Σ x x * Σ y x + Σ x y * Σ y y ) * | Σ y x | 2 + | Σ y y | 2 ]
Γ x x i ( τ ) = Γ 0 e 2 i π ν 0 τ g i ( τ ) W x x i ( ν ) = Γ 0 g ˜ i ( ν ν 0 ) Γ y y i ( τ ) = β i Γ 0 e 2 i π ν 0 τ g i ( τ ) W y y i ( ν ) = β i Γ 0 g ˜ i ( ν ν 0 )
Δ τ i = + | g i ( τ ) | 2 d τ = 0 g ˜ i 2 ( ν ν 0 ) d ν
W x y i ( ν ) = ( W y x i ) * ( ν ) = β i Γ 0 g ˜ i ( ν ν 0 ) w i ( ν ) | w i ( ν ) | 1
D i ( 0 ) = Γ 0 2 β i ( 1 | μ i | 2 ) μ i = Γ x y i ( 0 ) Γ x x i ( 0 ) Γ y y i ( 0 ) = 0 g ˜ i ( ν ν 0 ) w i ( ν ) d ν
P i = 1 4 β i ( 1 + β i ) 2 ( 1 | μ i | 2 )
T ˜ s ( ν ) = Γ 0 χ g ˜ i ( ν ν 0 ) ( 1 + e [ α w i ( ν ) ] )
χ = M x x ( ν 0 ) + β i M y y ( ν 0 ) > 0 α = 2 β i M y x ( ν 0 ) χ
T s ( 0 ) = 0 T ˜ s ( ν ) d ν = Γ 0 χ ( 1 + e [ α μ i ] )
P s = 1 | D Σ ( ν 0 ) | 2 χ 2 4 β i ( 1 | μ i | 2 ) ( 1 + e [ α μ i ] ) 2
Σ x x Σ y y = Σ x y Σ y x
0 T ˜ s 2 ( ν ) d ν = Γ 0 2 χ 2 ( Δ τ i + | α | 2 A + e [ 2 α B + α 2 2 C ] )
A = 0 g ˜ 2 ( ν ν 0 ) | w ( ν ) | 2 d ν
B = 0 g ˜ 2 ( ν ν 0 ) w ( ν ) d ν
C = 0 g ˜ 2 ( ν ν 0 ) w 2 ( ν ) d ν
Δ τ s = Δ τ i + | α | 2 2 A + e [ 2 α B + α 2 2 C ] ( 1 + e [ α μ i ] ) 2
g i ( τ ) = e π 2 ( τ Δ τ i ) 2 w ( ν + ν 0 ) = e i φ 0 e 2 π ( z ν ) 2
μ i = e i φ 0 1 + ( z Δ τ i ) 2 A = Δ τ i 1 + e [ ( z Δ τ i ) 2 ] B = Δ τ i e i φ 0 1 + 1 2 ( z Δ τ i ) 2 C = Δ τ i e 2 i φ 0 1 + ( z Δ τ i ) 2
{ k x = ( ω 0 / c ) sin θ cos φ k y = ( ω 0 / c ) sin θ sin φ .
| φ 0 arg μ i k π | 1 2 arccos ( | μ i | 2 )
μ i 0 r θ 0
θ = π 4 μ i

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