Abstract

The spatial depolarization of light emitted by heterogeneous bulks is predicted with exact electromagnetic theories. The sample microstructure and geometry is connected with partial polarization.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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  1. O. V. Angelsky, S. G. Hanson, C. Y. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “On polarization metrology (estimation) of the degree of coherence of optical waves,” Opt. Express 17(18), 15623–15634 (2009).
    [Crossref] [PubMed]
  2. C. Brosseau, Fundamentals of Polarized Light - A Statistical Approach (Wiley, 1998).
  3. E. Wolf, Theory of coherence and polarization of light (Cambridge University Press, 2007).
  4. E. Wolf and L. Mandel, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  5. R. Martnez-Herrero, P. M. Mejas, and G. Piquero, Characterization of Partially Polarized Light Fields (Springer, 2009).
  6. E. Jakeman and K. D. Ridley, Modeling Fluctuations in Scattered Waves (Taylor and Francis Group, 2006).
  7. I. Mokhun, “Introduction to linear singular optics,” in Optical Correlation Techniques and Applications, O. V. Angelsky, ed. (SPIE press, USA, 2007).
  8. E. Wolf, “Unified theory of Coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
    [Crossref]
  9. P. Réfrégier and F. Goudail, “Invariant degrees of coherence of partially polarized light,” Opt. Express 13(16), 6051–6060 (2005).
    [Crossref] [PubMed]
  10. C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces or bulks,” Opt. Express 16(14), 10372–10383 (2008).
    [Crossref] [PubMed]
  11. M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: Electromagnetic prediction,” Opt. Express 18(15), 15832–15843 (2010).
    [Crossref] [PubMed]
  12. J. Broky and A. Dogariu, “Correlations of polarization in random electro-magnetic fields,” Opt. Express 19(17), 15711–15719 (2011).
    [Crossref] [PubMed]
  13. G. Soriano, M. Zerrad, and C. Amra, “Enpolarization and depolarization of light scattered from chromatic complex media,” Opt. Express 22(10), 12603–12613 (2014).
    [Crossref] [PubMed]
  14. J. Sorrentini, M. Zerrad, G. Soriano, and C. Amra, “Enpolarization of light by scattering media,” Opt. Express 19(22), 21313–21320 (2011).
    [Crossref] [PubMed]
  15. M. Zerrad, G. Soriano, A. Ghabbach, and C. Amra, “Light enpolarization by disordered media under partial polarized illumination: The role of cross-scattering coefficients,” Opt. Express 21(3), 2787–2794 (2013).
    [Crossref] [PubMed]
  16. J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
    [Crossref] [PubMed]
  17. A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22(12), 14594–14609 (2014).
    [Crossref] [PubMed]
  18. A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22(18), 21427–21440 (2014).
    [Crossref] [PubMed]
  19. J. Sorrentini, M. Zerrad, and C. Amra, “Statistical signatures of random media and their correlation to polarization properties,” Opt. Lett. 34(16), 2429–2431 (2009).
    [Crossref] [PubMed]
  20. J. M. Elson and J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69(1), 31–47 (1979).
    [Crossref]
  21. C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11(1), 197–210 (1994).
    [Crossref]
  22. C. Amra, “Light scattering from multilayer optics. II. Application to experiment,” J. Opt. Soc. Am. A 11(1), 211–226 (1994).
    [Crossref]
  23. C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10(2), 365–374 (1993).
    [Crossref]
  24. M. Zerrad, M. Lequime, S. Liukaityte, and C. Amra, “Spatially-resolved surface topography retrieved from far-field intensity scattering measurements,” in Optical Interference Coatings, M. a. R. D. Tilsch, ed. (Optical Society of America, 2013), p. ThC.9.
  25. R. Brandel, A. Mokhun, I. Mokhun, and J. Viktorovskaya, “Fine structure of heterogeneous vector field and his space averaged polarization characteristics.,” (Opt. Appl., 2006), pp. 79–95.
  26. M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Multiscale spatial depolarization of light: electromagnetism and statistical optics,” in Physical Optics, D. G. Smith, F. Wyrowski, and Andreas Erdmann, eds. (Proceedings of SPIE, 2011).
  27. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).
  28. L. Mandel and E. Wolf, eds., Optical Coherence and Quantum Optics (Cambridge University Press 1995).
  29. G. Soriano, M. Zerrad, and C. Amra, “Mapping the coherence time of far-field speckle scattered by disordered media,” Opt. Express 21(20), 24191–24200 (2013).
    [Crossref] [PubMed]
  30. L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of electromagnetic waves: numerical simulations (Wiley-Interscience, 2001).
  31. I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
    [Crossref] [PubMed]
  32. O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
    [Crossref]
  33. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
    [Crossref]
  34. O. Cmielewski, H. Tortel, A. Litman, and M. Saillard, “A two step procedure for obstacle characterization under a rough surface,” IEEE Trans. Geosci. Rem. Sens. 45, 2850–2858 (2007).
    [Crossref]
  35. A. F. Peterson, L. R. Scott, and R. Mittra, Computational Method for Electromagnetics (Wiley-IEEE Press Oxford Univeristy Press, 1998).
  36. J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, Inc, 2002).
  37. P. Godard, “Optique électromagnétique non-linéaire polyharmonique: théorie et modélisation numérique,” in PhD thesis (Université de Provence, Marseille, France, 2009).
  38. C. Geuzaine and J. F. Remacle, “GMSH A three dimensional finite element mesh generator with built-in pre- and post-processing facilities,” Int. J. Numer. Methods Eng. 79, 1309–1331 (2009).
    [Crossref]

2014 (3)

2013 (2)

2012 (2)

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

2011 (2)

2010 (1)

2009 (3)

2008 (1)

2007 (1)

O. Cmielewski, H. Tortel, A. Litman, and M. Saillard, “A two step procedure for obstacle characterization under a rough surface,” IEEE Trans. Geosci. Rem. Sens. 45, 2850–2858 (2007).
[Crossref]

2005 (1)

2003 (1)

E. Wolf, “Unified theory of Coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[Crossref]

2002 (1)

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
[Crossref] [PubMed]

1994 (2)

1993 (1)

1988 (1)

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

1979 (1)

Amra, C.

G. Soriano, M. Zerrad, and C. Amra, “Enpolarization and depolarization of light scattered from chromatic complex media,” Opt. Express 22(10), 12603–12613 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22(12), 14594–14609 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22(18), 21427–21440 (2014).
[Crossref] [PubMed]

G. Soriano, M. Zerrad, and C. Amra, “Mapping the coherence time of far-field speckle scattered by disordered media,” Opt. Express 21(20), 24191–24200 (2013).
[Crossref] [PubMed]

M. Zerrad, G. Soriano, A. Ghabbach, and C. Amra, “Light enpolarization by disordered media under partial polarized illumination: The role of cross-scattering coefficients,” Opt. Express 21(3), 2787–2794 (2013).
[Crossref] [PubMed]

J. Sorrentini, M. Zerrad, G. Soriano, and C. Amra, “Enpolarization of light by scattering media,” Opt. Express 19(22), 21313–21320 (2011).
[Crossref] [PubMed]

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: Electromagnetic prediction,” Opt. Express 18(15), 15832–15843 (2010).
[Crossref] [PubMed]

J. Sorrentini, M. Zerrad, and C. Amra, “Statistical signatures of random media and their correlation to polarization properties,” Opt. Lett. 34(16), 2429–2431 (2009).
[Crossref] [PubMed]

C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces or bulks,” Opt. Express 16(14), 10372–10383 (2008).
[Crossref] [PubMed]

C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11(1), 197–210 (1994).
[Crossref]

C. Amra, “Light scattering from multilayer optics. II. Application to experiment,” J. Opt. Soc. Am. A 11(1), 211–226 (1994).
[Crossref]

C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A 10(2), 365–374 (1993).
[Crossref]

Angelsky, O. V.

Bennett, J. M.

Broky, J.

Cmielewski, O.

O. Cmielewski, H. Tortel, A. Litman, and M. Saillard, “A two step procedure for obstacle characterization under a rough surface,” IEEE Trans. Geosci. Rem. Sens. 45, 2850–2858 (2007).
[Crossref]

Deumié, C.

Dogariu, A.

Elson, J. M.

Feng, S.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Fink, M.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

Freund, I.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Georges, G.

Geuzaine, C.

C. Geuzaine and J. F. Remacle, “GMSH A three dimensional finite element mesh generator with built-in pre- and post-processing facilities,” Int. J. Numer. Methods Eng. 79, 1309–1331 (2009).
[Crossref]

Ghabbach, A.

Gorodyns’ka, N. V.

Gorsky, M. P.

Goudail, F.

Hanson, S. G.

Katz, O.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

Li, J.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
[Crossref] [PubMed]

Litman, A.

O. Cmielewski, H. Tortel, A. Litman, and M. Saillard, “A two step procedure for obstacle characterization under a rough surface,” IEEE Trans. Geosci. Rem. Sens. 45, 2850–2858 (2007).
[Crossref]

Liukaityte, S.

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

Réfrégier, P.

Remacle, J. F.

C. Geuzaine and J. F. Remacle, “GMSH A three dimensional finite element mesh generator with built-in pre- and post-processing facilities,” Int. J. Numer. Methods Eng. 79, 1309–1331 (2009).
[Crossref]

Rosenbluh, M.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Saillard, M.

O. Cmielewski, H. Tortel, A. Litman, and M. Saillard, “A two step procedure for obstacle characterization under a rough surface,” IEEE Trans. Geosci. Rem. Sens. 45, 2850–2858 (2007).
[Crossref]

Silberberg, Y.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Siozade, L.

Small, E.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Soriano, G.

Sorrentini, J.

Tortel, H.

O. Cmielewski, H. Tortel, A. Litman, and M. Saillard, “A two step procedure for obstacle characterization under a rough surface,” IEEE Trans. Geosci. Rem. Sens. 45, 2850–2858 (2007).
[Crossref]

Wang, L. V.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
[Crossref] [PubMed]

Wolf, E.

E. Wolf, “Unified theory of Coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[Crossref]

Yao, G.

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
[Crossref] [PubMed]

Zenkova, C. Y.

Zerrad, M.

G. Soriano, M. Zerrad, and C. Amra, “Enpolarization and depolarization of light scattered from chromatic complex media,” Opt. Express 22(10), 12603–12613 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22(12), 14594–14609 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22(18), 21427–21440 (2014).
[Crossref] [PubMed]

G. Soriano, M. Zerrad, and C. Amra, “Mapping the coherence time of far-field speckle scattered by disordered media,” Opt. Express 21(20), 24191–24200 (2013).
[Crossref] [PubMed]

M. Zerrad, G. Soriano, A. Ghabbach, and C. Amra, “Light enpolarization by disordered media under partial polarized illumination: The role of cross-scattering coefficients,” Opt. Express 21(3), 2787–2794 (2013).
[Crossref] [PubMed]

J. Sorrentini, M. Zerrad, G. Soriano, and C. Amra, “Enpolarization of light by scattering media,” Opt. Express 19(22), 21313–21320 (2011).
[Crossref] [PubMed]

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: Electromagnetic prediction,” Opt. Express 18(15), 15832–15843 (2010).
[Crossref] [PubMed]

J. Sorrentini, M. Zerrad, and C. Amra, “Statistical signatures of random media and their correlation to polarization properties,” Opt. Lett. 34(16), 2429–2431 (2009).
[Crossref] [PubMed]

C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces or bulks,” Opt. Express 16(14), 10372–10383 (2008).
[Crossref] [PubMed]

IEEE Trans. Geosci. Rem. Sens. (1)

O. Cmielewski, H. Tortel, A. Litman, and M. Saillard, “A two step procedure for obstacle characterization under a rough surface,” IEEE Trans. Geosci. Rem. Sens. 45, 2850–2858 (2007).
[Crossref]

Int. J. Numer. Methods Eng. (1)

C. Geuzaine and J. F. Remacle, “GMSH A three dimensional finite element mesh generator with built-in pre- and post-processing facilities,” Int. J. Numer. Methods Eng. 79, 1309–1331 (2009).
[Crossref]

J. Biomed. Opt. (1)

J. Li, G. Yao, and L. V. Wang, “Degree of polarization in laser speckles from turbid media: implications in tissue optics,” J. Biomed. Opt. 7(3), 307–312 (2002).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Nat. Photonics (2)

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

Opt. Express (11)

P. Réfrégier and F. Goudail, “Invariant degrees of coherence of partially polarized light,” Opt. Express 13(16), 6051–6060 (2005).
[Crossref] [PubMed]

C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces or bulks,” Opt. Express 16(14), 10372–10383 (2008).
[Crossref] [PubMed]

O. V. Angelsky, S. G. Hanson, C. Y. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, “On polarization metrology (estimation) of the degree of coherence of optical waves,” Opt. Express 17(18), 15623–15634 (2009).
[Crossref] [PubMed]

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: Electromagnetic prediction,” Opt. Express 18(15), 15832–15843 (2010).
[Crossref] [PubMed]

J. Broky and A. Dogariu, “Correlations of polarization in random electro-magnetic fields,” Opt. Express 19(17), 15711–15719 (2011).
[Crossref] [PubMed]

J. Sorrentini, M. Zerrad, G. Soriano, and C. Amra, “Enpolarization of light by scattering media,” Opt. Express 19(22), 21313–21320 (2011).
[Crossref] [PubMed]

M. Zerrad, G. Soriano, A. Ghabbach, and C. Amra, “Light enpolarization by disordered media under partial polarized illumination: The role of cross-scattering coefficients,” Opt. Express 21(3), 2787–2794 (2013).
[Crossref] [PubMed]

G. Soriano, M. Zerrad, and C. Amra, “Mapping the coherence time of far-field speckle scattered by disordered media,” Opt. Express 21(20), 24191–24200 (2013).
[Crossref] [PubMed]

G. Soriano, M. Zerrad, and C. Amra, “Enpolarization and depolarization of light scattered from chromatic complex media,” Opt. Express 22(10), 12603–12613 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, and C. Amra, “Accurate metrology of polarization curves measured at the speckle size of visible light scattering,” Opt. Express 22(12), 14594–14609 (2014).
[Crossref] [PubMed]

A. Ghabbach, M. Zerrad, G. Soriano, S. Liukaityte, and C. Amra, “Depolarization and enpolarization DOP histograms measured for surface and bulk speckle patterns,” Opt. Express 22(18), 21427–21440 (2014).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Lett. A (1)

E. Wolf, “Unified theory of Coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[Crossref]

Phys. Rev. Lett. (1)

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Other (15)

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of electromagnetic waves: numerical simulations (Wiley-Interscience, 2001).

C. Brosseau, Fundamentals of Polarized Light - A Statistical Approach (Wiley, 1998).

E. Wolf, Theory of coherence and polarization of light (Cambridge University Press, 2007).

E. Wolf and L. Mandel, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

R. Martnez-Herrero, P. M. Mejas, and G. Piquero, Characterization of Partially Polarized Light Fields (Springer, 2009).

E. Jakeman and K. D. Ridley, Modeling Fluctuations in Scattered Waves (Taylor and Francis Group, 2006).

I. Mokhun, “Introduction to linear singular optics,” in Optical Correlation Techniques and Applications, O. V. Angelsky, ed. (SPIE press, USA, 2007).

M. Zerrad, M. Lequime, S. Liukaityte, and C. Amra, “Spatially-resolved surface topography retrieved from far-field intensity scattering measurements,” in Optical Interference Coatings, M. a. R. D. Tilsch, ed. (Optical Society of America, 2013), p. ThC.9.

R. Brandel, A. Mokhun, I. Mokhun, and J. Viktorovskaya, “Fine structure of heterogeneous vector field and his space averaged polarization characteristics.,” (Opt. Appl., 2006), pp. 79–95.

M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Multiscale spatial depolarization of light: electromagnetism and statistical optics,” in Physical Optics, D. G. Smith, F. Wyrowski, and Andreas Erdmann, eds. (Proceedings of SPIE, 2011).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).

L. Mandel and E. Wolf, eds., Optical Coherence and Quantum Optics (Cambridge University Press 1995).

A. F. Peterson, L. R. Scott, and R. Mittra, Computational Method for Electromagnetics (Wiley-IEEE Press Oxford Univeristy Press, 1998).

J. Jin, The Finite Element Method in Electromagnetics (John Wiley & Sons, Inc, 2002).

P. Godard, “Optique électromagnétique non-linéaire polyharmonique: théorie et modélisation numérique,” in PhD thesis (Université de Provence, Marseille, France, 2009).

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Figures (15)

Fig. 1
Fig. 1 Dispersion of polarization state within a spatially depolarizing speckle pattern- Schematic view
Fig. 2
Fig. 2 Example of inhomogeneous bulk ( δ n /n = 10−2, 5.10−1 and 10−1)
Fig. 3
Fig. 3 Mean value of the Total Integrated Scattering in the reflected half-space calculated over 10 realizations and plotted vs the bulk thickness for each index dispersion / mean free path
Fig. 4
Fig. 4 Polarization ratio for δ n /n = 5.10−2 and d = 5λ (left) and d = 40λ (right)
Fig. 5
Fig. 5 :Polarimetric phase for δ n /n = 5.10−2 and d = 5 λ (left) and d = 40 λ (right)
Fig. 6
Fig. 6 Polarization ratio for δ n /n = 10−1 and d =5 λ (left) and d = 40 λ (right)
Fig. 7
Fig. 7 Polarimetric phase for δ n /n = 10−1 and d = 5 λ (left) and d = 40 λ (right)
Fig. 8
Fig. 8 Dispersion of the polarization states taken by the scattered field on an angular aperture covering 10 speckle areas d = 5 λ and δ n /n = 5.10−2 (top spheres) and 10−1 (bottom spheres). Black & green crosses are respectively for L + 45° and L-45° polarization states.
Fig. 9
Fig. 9 Dispersion of the polarization states taken by the scattered field on an angular aperture covering 10 speckle areas d = 40λ and δ n /n = 5.10−3 (top) and 10−1 (bottom). Black & green crosses are respectively for L + 45° an L-45° polarization states.
Fig. 10
Fig. 10 Continuous variation of the polarization state versus the scattering angle ( δ n /n =5.10-2 and d=25λ ). (Media 1).
Fig. 11
Fig. 11 MDOP (ΔΩ) for δ n /n = 5. 10−2 (left) and 10−2(right) for thickness d=5λ and 40λ .
Fig. 12
Fig. 12 Normalized Standard deviation of the polarization ratio β versus the relative index inhomogeneity δ n /n and the thickness d.
Fig. 13
Fig. 13 Standard deviation of the polarimetric phase difference δ normalized by π and expressed versus the relative index inhomogeneity δ n /n and the thickness d.
Fig. 14
Fig. 14 Macroscopic degree of polarization after integration of 4 speckle areas versus the relative index inhomogeneity δ n /n and the thickness d.
Fig. 15
Fig. 15 Zoom- macroscopic degree of polarization and linear approximation after integration of 4 speckle areas versus the relative index inhomogeneity δ n /n and the thickness d.

Equations (24)

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µ 0 (ρ)= 1 α 0 E S 0 ( ρ,t ) E P 0 * ( ρ,t ) t
α 0 ( ρ ) 2 = | E S 0 ( ρ,t ) | 2 t | E P 0 ( ρ,t ) | 2 t
( E S E P )( ρ,t )=( ν SS ( ρ ) ν PS ( ρ ) ν SP ( ρ ) ν PP ( ρ ) )( E S 0 E P 0 )( ρ,t )
µ(ρ)= 1 α E S ( ρ,t ) E P * ( ρ,t ) t
α 2 = | E S ( ρ,t ) | 2 t | E P ( ρ,t ) | 2 t
µ(ρ)= E S ( ρ ) E P * ( ρ ) | E S ( ρ ) | 2 | E P ( ρ ) | 2 | μ |=1
µ(ρ,ΔΩ)= E S ( ρ ) E P * ( ρ ) ΔΩ α(ΔΩ)
α 2 (ΔΩ)= | E S ( ρ,ΔΩ ) | 2 ΔΩ | E P ( ρ,ΔΩ ) | 2 ΔΩ
MDOP(ρ,ΔΩ)= 14 det{ J( ρ,ΔΩ ) } [ tr{ J( ρ,ΔΩ ) } ] 2
J(ρ,ΔΩ)=( ( E S ) * E S ΔΩ ( E S ) * E P ΔΩ ( E P ) * E S ΔΩ ( E P ) * E P ΔΩ )
div( ξgrad( u t ) )+ ω 0 2 ε 0 μ 0 χ u t =0
{ ξ= 1 μ( x,z ) = 1 μ 0 χ=ε( x,z ) u=E( x,z )
{ ξ= 1 ε( x,z ) χ=μ( x,z )= μ 0 u=H( x,y )
div( ξgrad( u i ) )+ ω 0 2 ε 0 μ 0 χ u i =0
χ 0 =1& ξ 0 =1
u t = u S + u i
u t = u S + u ref
div( ξgrad( u S ) )+ ω 0 2 ε 0 μ 0 χ u S =div{ ( ξ ref ξ ).grad( u S ) }+ ω 0 2 ε 0 μ 0 ( χ ref χ ). u ref
div( ξgrad( u t ) )+ ω 0 2 ε 0 μ 0 χ u i =j ω 0 μ 0 j Γ δ Γ inΩ
j Γ = 1 i ω 0 μ 0 [ u pec n ] Γ
δ n | n ¯ | = | Δn n ¯ | 2 x,z = 1 d x d z x,z | Δn( x,z ) n ¯ | 2 dxdz
A S = I S e j δ S A P = I P e j δ P δ= δ P δ S
σ X X = 1 X 1 N k=& N ( X X ) 2 withX=β,δ
DO P inf 1| 2100. δ n | n ¯ | | n ¯ e 50

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