Abstract

Influence of the variations of the scattering properties of a disordered medium with respect to frequency on the polarization of scattered light is investigated. We focus on the strongly scattering regime with the sum of random phasors scattering model that is extended to chromatic media and made frequency-sensitive. It is numerically shown how the scattered polarization depends on the incident polarization and the incident light bandwidth to scattering coefficients chromatic length ratio. Under the presented approach, both phenomena of depolarization and enpolarization of light appear unified.

© 2014 Optical Society of America

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  1. R. Martnez-Herrero, P. M. Mejas, G. Piquero, Characterization of partially polarized light fields (Springer, 2009), vol. 147.
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. G. Soriano, M. Zerrad, C. Amra, “Mapping the coherence time of far-field speckle scattered by disordered media,” Opt. Express 21, 24191–24200 (2013).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  18. J. Broky, A. Dogariu, “Correlations of polarization in random electro-magnetic fields,” Opt. Express 19, 15711–15719 (2011).
    [CrossRef] [PubMed]
  19. M. Zerrad, J. Sorrentini, G. Soriano, C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: Electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  25. A. G. Voronovich, Wave scattering from rough surfaces (Springer-Verlag, 1994).
    [CrossRef]
  26. J. Goodman, Speckle phenomena in optics: theory and applications (Roberts & Co, 2007).
  27. W. H. Press, Numerical recipes in Fortran 77: the art of scientific computing (Cambridge University, 1992), vol. 1.
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    [CrossRef]

2013

2012

2011

2010

2009

2004

1939

J. Stratton, L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56, 99–107 (1939).
[CrossRef]

Alouini, M.

Amra, C.

Angelsky, O.

Antonelli, M.-R.

Benali, A.

Bénière, A.

Broky, J.

Brosseau, C.

C. Brosseau, Fundamentals of polarized light: a statistical optics approach (Wiley-Blackwell, 1998).

Cai, Y.

Chen, X.

Cheng, C.

Chipman, R.

Chu, L.

J. Stratton, L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56, 99–107 (1939).
[CrossRef]

De Martino, A.

DeBoo, B.

Ding, C.

Dogariu, A.

Ellis, J.

Fade, J.

Gayet, B.

Gbur, G.

G. Gbur, T. Visser, “The structure of partially coherent fields,” Prog. Opt. 55, 285 (2011).
[CrossRef]

Ghabbach, A.

M. Zerrad, G. Soriano, A. Ghabbach, C. Amra, “Light enpolarization by disordered media under partial polarized illumination: The role of cross-scattering coefficients,” Opt. Express 21, 2787–2794 (2013).
[CrossRef] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering: surface signatures,” submitted to Opt. Express.

Goodman, J.

J. Goodman, Speckle phenomena in optics: theory and applications (Roberts & Co, 2007).

Gorodynska, N.

Gorsky, M.

Goudail, F.

Hamel, C.

Hanson, S. G.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media, an IEEE OUP classic reissue (Wiley, 1999).

Korotkova, O.

Z. Tong, O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A 82, 033836 (2010).
[CrossRef]

Li, Z.

Liang, G.

Mandel, L.

L. Mandel, E. Wolf, Optical coherence and quantum optics (Cambridge University, 1995).
[CrossRef]

Martnez-Herrero, R.

R. Martnez-Herrero, P. M. Mejas, G. Piquero, Characterization of partially polarized light fields (Springer, 2009), vol. 147.
[CrossRef]

Mejas, P. M.

R. Martnez-Herrero, P. M. Mejas, G. Piquero, Characterization of partially polarized light fields (Springer, 2009), vol. 147.
[CrossRef]

Novikova, T.

Pan, L.

Pierangelo, A.

Piquero, G.

R. Martnez-Herrero, P. M. Mejas, G. Piquero, Characterization of partially polarized light fields (Springer, 2009), vol. 147.
[CrossRef]

Ponomarenko, S.

Pouget, L.

Press, W. H.

W. H. Press, Numerical recipes in Fortran 77: the art of scientific computing (Cambridge University, 1992), vol. 1.

Réfrégier, P.

Sasian, J.

Soriano, G.

Sorrentini, J.

Stratton, J.

J. Stratton, L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56, 99–107 (1939).
[CrossRef]

Teng, S.

Tong, Z.

Z. Tong, O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A 82, 033836 (2010).
[CrossRef]

Validire, P.

Van Bladel, J.

J. Van Bladel, Electromagnetic fields (Wiley-IEEE Press, 2007), vol. 19.
[CrossRef]

Visser, T.

G. Gbur, T. Visser, “The structure of partially coherent fields,” Prog. Opt. 55, 285 (2011).
[CrossRef]

Voronovich, A. G.

A. G. Voronovich, Wave scattering from rough surfaces (Springer-Verlag, 1994).
[CrossRef]

Wang, S.

Wolf, E.

J. Ellis, A. Dogariu, S. Ponomarenko, E. Wolf, “Correlation matrix of a completely polarized, statistically stationary electromagnetic field,” Opt. Lett. 29, 1536–1538 (2004).
[CrossRef] [PubMed]

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

L. Mandel, E. Wolf, Optical coherence and quantum optics (Cambridge University, 1995).
[CrossRef]

Zenkova, C. Y.

Zerrad, M.

Zhang, M.

Zhang, Y.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Express

M. Zerrad, G. Soriano, A. Ghabbach, C. Amra, “Light enpolarization by disordered media under partial polarized illumination: The role of cross-scattering coefficients,” Opt. Express 21, 2787–2794 (2013).
[CrossRef] [PubMed]

M. Zhang, Z. Li, X. Chen, G. Liang, S. Wang, S. Teng, C. Cheng, “Evolutions of speckles on rough glass/silver surfaces with film thickness,” Opt. Express 21, 8831–8842 (2013).
[CrossRef] [PubMed]

G. Soriano, M. Zerrad, C. Amra, “Mapping the coherence time of far-field speckle scattered by disordered media,” Opt. Express 21, 24191–24200 (2013).
[CrossRef] [PubMed]

M. Zerrad, J. Sorrentini, G. Soriano, C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: Electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
[CrossRef] [PubMed]

J. Broky, A. Dogariu, “Complex degree of mutual polarization in randomly scattered fields,” Opt. Express 18, 20105–20113 (2010).
[CrossRef] [PubMed]

A. Pierangelo, A. Benali, M.-R. Antonelli, T. Novikova, P. Validire, B. Gayet, A. De Martino, “Ex-vivo characterization of human colon cancer by mueller polarimetric imaging,” Opt. Express 19, 1582–1593 (2011).
[CrossRef] [PubMed]

J. Broky, A. Dogariu, “Correlations of polarization in random electro-magnetic fields,” Opt. Express 19, 15711–15719 (2011).
[CrossRef] [PubMed]

J. Sorrentini, M. Zerrad, G. Soriano, C. Amra, “Enpolarization of light by scattering media,” Opt. Express 19, 21313–21320 (2011).
[CrossRef] [PubMed]

B. DeBoo, J. Sasian, R. Chipman, “Degree of polarization surfaces and maps for analysis of depolarization,” Opt. Express 12, 4941–4958 (2004).
[CrossRef] [PubMed]

O. Angelsky, S. G. Hanson, C. Y. Zenkova, M. Gorsky, N. Gorodynska, “On polarization metrology (estimation) of the degree of coherence of optical waves,” Opt. Express 17, 15623–15634 (2009).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev.

J. Stratton, L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56, 99–107 (1939).
[CrossRef]

Phys. Rev. A

Z. Tong, O. Korotkova, “Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media,” Phys. Rev. A 82, 033836 (2010).
[CrossRef]

Prog. Opt.

G. Gbur, T. Visser, “The structure of partially coherent fields,” Prog. Opt. 55, 285 (2011).
[CrossRef]

Other

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

A. Ghabbach, M. Zerrad, G. Soriano, C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering: surface signatures,” submitted to Opt. Express.

R. Martnez-Herrero, P. M. Mejas, G. Piquero, Characterization of partially polarized light fields (Springer, 2009), vol. 147.
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media, an IEEE OUP classic reissue (Wiley, 1999).

J. Van Bladel, Electromagnetic fields (Wiley-IEEE Press, 2007), vol. 19.
[CrossRef]

A. G. Voronovich, Wave scattering from rough surfaces (Springer-Verlag, 1994).
[CrossRef]

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, 1992), vol. 1.

C. Brosseau, Fundamentals of polarized light: a statistical optics approach (Wiley-Blackwell, 1998).

L. Mandel, E. Wolf, Optical coherence and quantum optics (Cambridge University, 1995).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Map of the square modulus of one scattering coefficient (arbitrary unit) generated by the sum of random phasors method.

Fig. 2
Fig. 2

Square modulus of the four scattering coefficients (arbitrary unit) generated by the spectral version of the sum of random phasors method in a given scattering direction against frequency (same unit as ΔνΣ).

Fig. 3
Fig. 3

Scattered DoP densities for unpolarized incident light and five different values of the incident bandwidth to scattering coefficients correlation length ratio R (solid lines) and the 3 P s 2 density (dashed line).

Fig. 4
Fig. 4

Mean scattered DoP against the incident bandwidth to scattering coefficients correlation length ratio R for five different values of the incident DoP Pi.

Fig. 5
Fig. 5

Scattered DoP densities for fully polarized incident light and different values of the incident bandwidth to scattering coefficients chromatic length ratio R.

Fig. 6
Fig. 6

Mean scattered DoP against the incident bandwidth to scattering coefficients chromatic length ratio R for different values of the incident DoP Pi.

Fig. 7
Fig. 7

RL against u = tanh 1 ( 1 2 P i 2 ) with Pi the incident DoP for numerical data in the Gaussian correlation case (blue symbols), for model (13) with parameters a = 0.7 and b = 0.0 (blue line), for numerical data in the exponential correlation case (red symbols) and for model (13) with a = 1.0 and b = −0.3 (red line).

Fig. 8
Fig. 8

Mean scattered DoP against the incident bandwidth to scattering coefficients chromatic length ratio R for different values of the incident DoP Pi in the case of a Lorentzian dependency to frequency.

Equations (13)

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

¯ i ( ν ) = [ i x ( ν ) i y ( ν ) ] ¯ s ( ν ) = [ s x ( ν ) s y ( ν ) ]
¯ s ( ν ) = Σ ¯ ¯ ( ν ) ¯ i ( ν )
Σ ¯ ¯ ( ν ) = [ Σ x x ( ν ) Σ x y ( ν ) Σ y x ( ν ) Σ y y ( ν ) ]
{ k x = ( ω 0 / c ) sin θ cos φ k y = ( ω 0 / c ) sin θ sin φ .
Δ ν Σ = 1 n t δ t
¯ * ( ν 1 ) ¯ T ( ν 2 ) = W ¯ ¯ ( ν 2 ) δ ( ν 2 ν 1 )
W ¯ ¯ s ( ν ) = Σ ¯ ¯ * ( ν ) W ¯ ¯ i ( ν ) Σ ¯ ¯ T ( ν )
J ¯ ¯ = 0 W ¯ ¯ ( ν ) d ν = I 2 [ 1 + P cos 2 χ cos 2 ψ P ( cos 2 χ sin 2 ψ + i sin 2 χ ) P ( cos 2 χ sin 2 ψ i sin 2 χ ) 1 P cos 2 χ cos 2 ψ ]
W ¯ ¯ i ( ν ) = I i [ 1 0 0 1 ] e 2 π ( ( ν ν c ) / Δ ν i ) 2 2 Δ ν i
R = Δ ν i Δ ν Σ
W ¯ ¯ i ( ν ) = J i ¯ ¯ ( P i , χ i , ψ i ) e 2 π ( ( ν ν c ) / Δ ν i ) 2 2 Δ ν i
lim P i 0 R L = + lim P i 1 R L = 0
R L = a u + b u = tanh 1 ( 1 2 P i 2 )

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