OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 22 — Oct. 24, 2011
  • pp: 21313–21320
« Show journal navigation

Enpolarization of light by scattering media

J. Sorrentini, M. Zerrad, G. Soriano, and C. Amra  »View Author Affiliations


Optics Express, Vol. 19, Issue 22, pp. 21313-21320 (2011)
http://dx.doi.org/10.1364/OE.19.021313


View Full Text Article

Acrobat PDF (1084 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The polarization of a coherent depolarized incident light beam passing through a scattering medium is investigated at the speckle scale. The polarization of the scattered far field at each direction and the probability density function of the degree of polarization are calculated and show an excellent agreement with experimental data. It is demonstrated that complex media may confer high degree of local polarization (0.75 DOP average) to the incident unpolarized light.

© 2011 OSA

1. Introduction

The state of polarization is one of the main observable parameters of an optical field. Many practical situations exist that make the light polarization properties depend on the spatial location. Indeed the polarization state of a light beam [1

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

4

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

] will change by propagation in free-space [5

5. D. F. V. James, “Change of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A 11(5), 1641–1643 (1994). [CrossRef]

, 6

6. E. Wolf, “Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation,” Opt. Lett. 28(13), 1078–1080 (2003). [CrossRef] [PubMed]

], by propagation in turbulent atmosphere [7

7. O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004). [CrossRef]

, 8

8. X. Y. Du and D. M. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17(6), 4257–4262 (2009). [CrossRef] [PubMed]

], by beam combination [9

9. M. Mujat and A. Dogariu, “Polarimetric and spectral changes in random electromagnetic fields,” Opt. Lett. 28(22), 2153–2155 (2003). [CrossRef] [PubMed]

], after scattering by a rough surface [10

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]

15

15. I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett. 104(22), 223904 (2010). [CrossRef] [PubMed]

] or an inhomogeneous medium [16

16. D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(2), 1767–1770 (1994). [CrossRef] [PubMed]

20

20. A. C. Maggs and V. Rossetto, “Writhing photons and Berry phases in polarized multiple scattering,” Phys. Rev. Lett. 87(25), 253901 (2001). [CrossRef] [PubMed]

]. Most of these works are devoted to the loss of polarization that can take place on the incident light, considering a full polarization but different spatial and temporal coherence properties for the incident beam. Different formalisms were proposed including Mueller-Stokes [18

18. T. W. Nee, S. M. F. Nee, D. M. Yang, and A. Chiou, “Optical scattering depolarization in a biomedium with anisotropic biomolecules,” J. Opt. Soc. Am. A 26(5), 1101–1108 (2009). [CrossRef] [PubMed]

], cross spectral density matrices [8

8. X. Y. Du and D. M. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17(6), 4257–4262 (2009). [CrossRef] [PubMed]

] and electromagnetic theories. Such loss of polarization (or depolarization process) most often originates from a temporal average of uncorrelated polarization modes of the optical field [5

5. D. F. V. James, “Change of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A 11(5), 1641–1643 (1994). [CrossRef]

, 7

7. O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004). [CrossRef]

, 8

8. X. Y. Du and D. M. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17(6), 4257–4262 (2009). [CrossRef] [PubMed]

, 12

12. S. M. F. Nee and T. W. Nee, “Polarization of transmission scattering simulated by using a multiple-facets model,” J. Opt. Soc. Am. A 21(9), 1635–1644 (2004). [CrossRef] [PubMed]

, 16

16. D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(2), 1767–1770 (1994). [CrossRef] [PubMed]

, 18

18. T. W. Nee, S. M. F. Nee, D. M. Yang, and A. Chiou, “Optical scattering depolarization in a biomedium with anisotropic biomolecules,” J. Opt. Soc. Am. A 26(5), 1101–1108 (2009). [CrossRef] [PubMed]

, 19

19. L. F. Rojas-Ochoa, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A 21(9), 1799–1804 (2004). [CrossRef] [PubMed]

], though spatial average may also be responsible for depolarization of a fully polarized incident beam [10

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

11. L. H. Jin, M. Kasahara, B. Gelloz, and K. Takizawa, “Polarization properties of scattered light from macrorough surfaces,” Opt. Lett. 35(4), 595–597 (2010). [CrossRef] [PubMed]

, 13

13. 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]

, 14

14. 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]

, 17

17. B. J. DeBoo, J. M. Sasian, and R. A. Chipman, “Depolarization of diffusely reflecting man-made objects,” Appl. Opt. 44(26), 5434–5445 (2005). [CrossRef] [PubMed]

, 21

21. J. Broky and A. Dogariu, “Complex degree of mutual polarization in randomly scattered fields,” Opt. Express 18(19), 20105–20113 (2010). [CrossRef] [PubMed]

] when the state of polarization rapidly varies within the detection area.

Scattering by arbitrary inhomogeneous media is known to modify the polarization or depolarization properties of the illumination beam. Usually the incident polarization of a light beam is lost after scattering by a highly inhomogeneous medium, which reduces the interest of polarimetric techniques to probe complex media [14

14. 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]

]. However one can have the benefits of a reversible effect in the sense that the same media may allow to significantly increase the polarization degree of a fully depolarized incident light. This is the scope of this paper where it is shown that unpolarized light can be “ordered” by a scattering process.

Repolarization of light has been observed by different authors; in particular Mujat and Dogariu [9

9. M. Mujat and A. Dogariu, “Polarimetric and spectral changes in random electromagnetic fields,” Opt. Lett. 28(22), 2153–2155 (2003). [CrossRef] [PubMed]

] used beam combination inside an interferometer and emphasized a procedure to produce partial polarization at the system output, though the input was unpolarized light. In this work similar results are obtained with light scattering in the far field, though the scattering process is strongly different from that of specular beams. A phenomenological approach is first used to calculate the spatial repartition of the local degree of polarization (dop) of incident unpolarized light after transmission in the far field by a disordered medium. The average value and the probability density function (pdf) of the dop are investigated and an excellent agreement is obtained between numerical and experimental results. The high average polarization degree of light (≈75%) compared with the incident one (<4%) allows considering that light has been locally ordered when passing through the disordered medium.

Emphasis must be given to the fact that this scattered-induced repolarization process is a local effect (ie. at one space location) which is here calculated and measured at the speckle scale in the far field. In other words, the polarization degree (dop) that we address is connected with a local temporal average of the scattered field and can be spatially distributed. The modification of polarization is demonstrated at each position of space, and we then study its spatial distribution. Hence such effect would not be confused with another global DOP which describes the average polarization that can be measured when a great number of speckle grains are collected within the detector aperture. This last phenomenon includes an additional spatial average and was previously investigated through a multiscale approach [14

14. 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]

] to take account of the detector aperture. Its value can be deduced from speckle histograms [13

13. 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]

]. Therefore and contrary to the local dop, the global DOP remains equal to zero when the incident light is unpolarized. In other words, the spatial average of local dop is most often different from the global DOP.

2. Repolarization by a scattering process: principles

2.1 The incident unpolarized field

Let us consider a coherent and depolarized incident light beam characterized by the electric field E(r,t) illuminating a scattering medium whose Jones matrix is denoted M = (νuv), and r is the spatial coordinate. In the plane z = z0 (Fig. 1
Fig. 1 Schematic view of the experiment.
), this field is written as:
E(r,t)=I(r)(es(t)ep(t))
(1)
where I(r) and (es(t)ep(t)) describe spatial and temporal variations. The degree of polarization of E(r,t) is assumed to be zero whatever the r location. Therefore, at any point of the plane z = z0, no temporal correlation exists between the Transverse Electric (TE or s) and the Transverse Magnetic (TM or p) modes, so that the complex modes correlation follows:
μ=es(t)ep(t)¯|es(t)|2|eP(t)|2=es(t)ep(t)¯=0
(2a)
with bars denoting the complex conjugation. In this relation, eS (t) and eP (t) are normalized as:

<|eS(t)|2> = <|eP(t)|2>= 1
(2b)

The brackets <> stand for the temporal average. The spectral bandwidth Δω of E(r,t) is centered on the average frequency ω0 and matches the quasi-monochromatic condition: Δω/ω0<<1. Moreover this beam illuminates a scattering medium whose linear response is not frequency-dependent within the spectral domain, in order to preserve temporal coherence. In relation (2a) the correlation μ represents the non-diagonal term of the coherency matrix as defined in [22

22. J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).

]

2.2 The scattered field

Therefore, following the schematic view of Fig. 1, one can write the field Esc scattered in the far field at one direction at infinity as Esc ≈M E, that is:
Esc=(νsses(t)+νpsep(t)νspes(t)+νppep(t))=(ESSCEPSC)
(3)
where the scattering coefficients (νuv) of the Jones matrix M are for the v-polarized scattered waves resulting from a u-polarized illumination. Notice here that relation (3) is for the field scattered at a particular direction at infinity in the far field; that is, the scattering coefficients νUV and the Jones matrix M are direction dependent. Notice also in this relation the absence of wave packet to take into account the propagation from z1 to z2; indeed we know from the stationary phase theorem [4

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

] that in the far field at infinity, the wave packet (whose first-order approximation gives the Fresnel formalism) that describes the exact field at a particular direction can be reduced to a single Fourier component of the packet, here characterized by the (νuv) coefficients. In other words, the scattered field is described by a plane wave in the far field.

Notice also that these calculation methods take into account the whole illuminated area on the sample under study. Moreover, because the complex medium under study is perfectly identified, there is no need to average the electromagnetic calculation over multiple realizations; in other words, the sample has not to be translated or rotated, and the Jones matrix is perfectly identified and unique for one sample position. Indeed any motion of the sample would create a spatial average and cancel specific polarization signatures (the local dop would be turned into the global DOP). To summarize, the variation of scattering coefficients with direction or localization is deterministic and can be fully predicted with electromagnetism, whatever their derivatives.

2.3 Polarization parameters

The degree of polarization is defined from the coherence matrix in [[22

22. J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).

], Eq. (4), 3-36, p136]. It is connected with the time averages of the modes squares and to their cross-correlation. For the scattered light this quantity is local and varies with location or direction. Comparison of theory and experiment can be immediate when the speckle is resolved.

Let us now express this dopSC of the scattered field Esc as a function of the correlation μsc between its polarization modes:
dopsc=14β(1|μsc|2)/(1+β)2
(4)
with β the polarization ratio:
β=|νSSeS(t)+νPSeP(t)|2|νSPeS(t)+νPPeP(t)|2=|ESSC|2|EPSC|2
(5)
and the correlation:

μsc=(νSSeS(t)+νPSeP(t))(νSPeS(t)+νPPeP(t))¯|νSSeS(t)+νPSeP(t)|2|νSPeS(t)+νPPeP(t)|2=ESSC.EPSC¯|ESSC|2|EPSC|2
(6)

Provided that all media are static (the scattering coefficients are time constants), and taking into account relations (2a), (2b), relations (5) and (6) are turned into:
β=|νSS|2+|νPS|2|νSP|2+|νPP|2
(7)
and

μsc=νssν¯sp+νpsν¯pp(|νss|2+|νps|2)(|νsp|2+|νpp|2)
(8)

Therefore and because the (νuv) coefficients are independent in the general case of arbitrary scattering media, Eq. (8) ensures that the temporal correlationμsc will not be identically equal to zero, but will be distributed in modulus within the interval [0;1] depending on space location and sample microstructure. Extreme situations may occur when this correlation is zero or unity. The first situation (zero correlation) is that of slightly inhomogeneous samples (polished surfaces or transparent bulk substrates) that are known [28

28. K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media 11(1), 1–30 (2001). [CrossRef]

] to exhibit negligible cross-scattering coefficients (νUV ≈0) in the incidence plane; with these samples the temporal correlation remains zero (μSC = 0) and the scattered light remains unpolarized (dopSC = 0) if the polarization ratio is unity (β = 1). On the other hand, in the general case of arbitrary samples, the presence of cross-scattering coefficients will make the temporal correlation and the dopSC not to be zero. So, even though the illumination beam is perfectly unpolarized, relation (8) shows that the scattered light can be partially or totally polarized in the far field depending on the scattering samples and the space direction.

3. Comparison of experiment and numerical calculation

3.1 Numerical calculation

Numerical simulation has first been performed to illustrate this phenomenon. We did not use exact electromagnetic theory because time-consuming is prohibitive for 3D bulk calculation. Instead of that we used a fully developed model from Goodman [29

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

] where each speckle pattern (νuv) is obtained via the Fourier Transform of a random phasor matrix [29

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

]. Here, the non-zero domain is a square of 27 points length within a square of 210 points length. Figure 2(a)
Fig. 2 (a-b): Calculation (left figure- a) of the local DOP in the far field with a random phasor matrix. The resulting dop average is 0.75. Lg is the mean speckle size. Probability density function (right figure- b) of the local degree of polarization.
shows the spatial repartition of the local dopSC of the scattered far field at infinity in a plane perpendicular to propagation. Depending on the space location (or direction), the dop varies from 0 to 1. Therefore it is different from that of the incident light, which was zero at any location. Such result is in agreement with the prediction of relation (8) given in the preceding section.

One can also address statistical properties of the local dop of the scattered light. Taking all data of Fig. 2(a), we extracted the dop spatial histogram and plotted the resulting probability density function (see Fig. 2(b)). We notice that the pdf dop function follows a p(u) = 3u2 law, and the resulting spatial average of local dop is found to be:

01up(u)du=3/4
(9)

Such value emphasizes a significant increase of local polarization. Notice that the pdf function and the average are here deduced from numerical simulation and not by theoretical analysis of the statistical properties of the scattering process. Equation (9) indicates that light scattered by a highly inhomogeneous sample under unpolarized illumination will exhibit a 75% average of local polarization degree. In other terms, polarization modes have recovered partial order at the speckle size when passing through the disordered medium.

Notice again that these results would not be confused with the global DOP which is different from the spatial average of the local DOP; in our configuration the global DOP is close to zero, due to the spatial independence of the scattering coefficients, and to their quasi-identical spatial mean squares [14

14. 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]

].

3.2 Experiment

4. Conclusion

Calculation and measurements have shown excellent agreement to emphasize the process of light repolarization by scattering media at the speckle scale. An illustration was given with a highly inhomogeneous bulk and the result is a 0.75 average degree of local polarization and a 3u2 pdf probability local dop function.

One may wonder whether specific media could allow to confer full local polarization to the scattered light resulting from unpolarized illumination. Following relation (8), one can show that such media would exhibit scattering coefficients following the condition:

vssvpp=vspvps
(10)

Such condition cannot be fulfilled in the framework of first-order theories [29

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

], but could occur when multiple reflection dominates scattering. Because it cancels the determinant of the Jones matrix, relation (10) would allow different incident waves to create the same speckle pattern. However keeping the condition for all speckle grains does not appear realistic a priori. Relation (10) addresses inverse problems outside the scope of this paper.

It is also necessary to notice one key difference in the repolarization processes obtained by beam combination inside an interferometer [9

9. M. Mujat and A. Dogariu, “Polarimetric and spectral changes in random electromagnetic fields,” Opt. Lett. 28(22), 2153–2155 (2003). [CrossRef] [PubMed]

] and by light scattering. In the first situation and though the beams are combined, there is no mixing (S with P) of the polarization modes, which means that only the S modes (resp. P modes) are superimposed for each beam. Therefore the modes cross-correlation is not changed (remains equal to zero) and temporal disorder is not reduced: the repolarization process only results from the relative weight of energy carried on each axis, which was modified by the interferometer; to be complete, in such experiment repolarization of light is connected with the polarization ratio β and vanishes in the case β = 1, due to the relationship:

μ=0DOP=|1β|/|1+β|
(11)

On the other hand, light scattering allows a spontaneous mixing of the polarization modes (see relation (3)), due to the presence of cross-scattering coefficients. Such mixing of S and P modes describes a linear combination of random variables (the polarization modes) on each axis. Hence the resulting variables on each axis may exhibit new cross-correlation values, though the initial ones were totally uncorrelated: the temporal disorder can be reduced, which allows the repolarization process. This result is valid whatever the β value. Notice also that this scatter-induced repolarization process would vanish in the absence of cross-scattering coefficients, what can occur at low scattering levels predicted with perturbative theories [23

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

, 30

30. C. Amra, C. Grèzes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32(28), 5492–5503 (1993). [CrossRef] [PubMed]

] and characteristic of slightly inhomogeneous media.

Applications concern security and remote sensing, biophotonic and biomedical optics, lighting, microscopy and metrology.

References and links

1.

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

2.

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

3.

R. Barakat, “Polarization entropy transfer and relative polarization entropy,” Opt. Commun. 123(4-6), 443–448 (1996). [CrossRef]

4.

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

5.

D. F. V. James, “Change of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A 11(5), 1641–1643 (1994). [CrossRef]

6.

E. Wolf, “Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation,” Opt. Lett. 28(13), 1078–1080 (2003). [CrossRef] [PubMed]

7.

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4-6), 225–230 (2004). [CrossRef]

8.

X. Y. Du and D. M. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express 17(6), 4257–4262 (2009). [CrossRef] [PubMed]

9.

M. Mujat and A. Dogariu, “Polarimetric and spectral changes in random electromagnetic fields,” Opt. Lett. 28(22), 2153–2155 (2003). [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.

L. H. Jin, M. Kasahara, B. Gelloz, and K. Takizawa, “Polarization properties of scattered light from macrorough surfaces,” Opt. Lett. 35(4), 595–597 (2010). [CrossRef] [PubMed]

12.

S. M. F. Nee and T. W. Nee, “Polarization of transmission scattering simulated by using a multiple-facets model,” J. Opt. Soc. Am. A 21(9), 1635–1644 (2004). [CrossRef] [PubMed]

13.

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]

14.

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]

15.

I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett. 104(22), 223904 (2010). [CrossRef] [PubMed]

16.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(2), 1767–1770 (1994). [CrossRef] [PubMed]

17.

B. J. DeBoo, J. M. Sasian, and R. A. Chipman, “Depolarization of diffusely reflecting man-made objects,” Appl. Opt. 44(26), 5434–5445 (2005). [CrossRef] [PubMed]

18.

T. W. Nee, S. M. F. Nee, D. M. Yang, and A. Chiou, “Optical scattering depolarization in a biomedium with anisotropic biomolecules,” J. Opt. Soc. Am. A 26(5), 1101–1108 (2009). [CrossRef] [PubMed]

19.

L. F. Rojas-Ochoa, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A 21(9), 1799–1804 (2004). [CrossRef] [PubMed]

20.

A. C. Maggs and V. Rossetto, “Writhing photons and Berry phases in polarized multiple scattering,” Phys. Rev. Lett. 87(25), 253901 (2001). [CrossRef] [PubMed]

21.

J. Broky and A. Dogariu, “Complex degree of mutual polarization in randomly scattered fields,” Opt. Express 18(19), 20105–20113 (2010). [CrossRef] [PubMed]

22.

J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).

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.

L. Arnaud, G. Georges, J. Sorrentini, M. Zerrad, C. Deumié, and C. Amra, “An enhanced contrast to detect bulk objects under arbitrary rough surfaces,” Opt. Express 17(7), 5758–5773 (2009). [CrossRef] [PubMed]

25.

D. Colton and R. Kress, Integral Equations in Scattering Theory (Elsevier, 1983).

26.

C. Macaskill and B. J. Kachoyan, “Iterative approach for the numerical simulation of scattering from one- and two-dimensional rough surfaces,” Appl. Opt. 32(15), 2839–2847 (1993). [CrossRef] [PubMed]

27.

G. Soriano and M. Saillard, “Scattering of electromagnetic waves from two-dimensional rough surfaces with an impedance approximation,” J. Opt. Soc. Am. A 18(1), 124–133 (2001). [CrossRef] [PubMed]

28.

K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media 11(1), 1–30 (2001). [CrossRef]

29.

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

30.

C. Amra, C. Grèzes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32(28), 5492–5503 (1993). [CrossRef] [PubMed]

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics
(260.2130) Physical optics : Ellipsometry and polarimetry
(260.5430) Physical optics : Polarization
(290.5855) Scattering : Scattering, polarization

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: July 25, 2011
Revised Manuscript: September 10, 2011
Manuscript Accepted: September 19, 2011
Published: October 12, 2011

Citation
J. Sorrentini, M. Zerrad, G. Soriano, and C. Amra, "Enpolarization of light by scattering media," Opt. Express 19, 21313-21320 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-22-21313


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. E. Jakeman and K. D. Ridley, Modeling Fluctuations in Scattered Waves (Taylor and Francis Group, 2006).
  2. C. Brosseau, Fundamentals of Polarized Light—A Statistical Approach (Wiley, 1998).
  3. R. Barakat, “Polarization entropy transfer and relative polarization entropy,” Opt. Commun.123(4-6), 443–448 (1996). [CrossRef]
  4. E. Wolf and L. Mandel, Optical Coherence and Quantum Optics (C. Cambridge University Press, 1995).
  5. D. F. V. James, “Change of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A11(5), 1641–1643 (1994). [CrossRef]
  6. E. Wolf, “Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation,” Opt. Lett.28(13), 1078–1080 (2003). [CrossRef] [PubMed]
  7. O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun.233(4-6), 225–230 (2004). [CrossRef]
  8. X. Y. Du and D. M. Zhao, “Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere,” Opt. Express17(6), 4257–4262 (2009). [CrossRef] [PubMed]
  9. M. Mujat and A. Dogariu, “Polarimetric and spectral changes in random electromagnetic fields,” Opt. Lett.28(22), 2153–2155 (2003). [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. Express16(14), 10372–10383 (2008). [CrossRef] [PubMed]
  11. L. H. Jin, M. Kasahara, B. Gelloz, and K. Takizawa, “Polarization properties of scattered light from macrorough surfaces,” Opt. Lett.35(4), 595–597 (2010). [CrossRef] [PubMed]
  12. S. M. F. Nee and T. W. Nee, “Polarization of transmission scattering simulated by using a multiple-facets model,” J. Opt. Soc. Am. A21(9), 1635–1644 (2004). [CrossRef] [PubMed]
  13. 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]
  14. M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: electromagnetic prediction,” Opt. Express18(15), 15832–15843 (2010). [CrossRef] [PubMed]
  15. I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett.104(22), 223904 (2010). [CrossRef] [PubMed]
  16. D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics49(2), 1767–1770 (1994). [CrossRef] [PubMed]
  17. B. J. DeBoo, J. M. Sasian, and R. A. Chipman, “Depolarization of diffusely reflecting man-made objects,” Appl. Opt.44(26), 5434–5445 (2005). [CrossRef] [PubMed]
  18. T. W. Nee, S. M. F. Nee, D. M. Yang, and A. Chiou, “Optical scattering depolarization in a biomedium with anisotropic biomolecules,” J. Opt. Soc. Am. A26(5), 1101–1108 (2009). [CrossRef] [PubMed]
  19. L. F. Rojas-Ochoa, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A21(9), 1799–1804 (2004). [CrossRef] [PubMed]
  20. A. C. Maggs and V. Rossetto, “Writhing photons and Berry phases in polarized multiple scattering,” Phys. Rev. Lett.87(25), 253901 (2001). [CrossRef] [PubMed]
  21. J. Broky and A. Dogariu, “Complex degree of mutual polarization in randomly scattered fields,” Opt. Express18(19), 20105–20113 (2010). [CrossRef] [PubMed]
  22. J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).
  23. C. Amra, “First-order vector theory of bulk scattering in optical multilayers,” J. Opt. Soc. Am. A10(2), 365–374 (1993). [CrossRef]
  24. L. Arnaud, G. Georges, J. Sorrentini, M. Zerrad, C. Deumié, and C. Amra, “An enhanced contrast to detect bulk objects under arbitrary rough surfaces,” Opt. Express17(7), 5758–5773 (2009). [CrossRef] [PubMed]
  25. D. Colton and R. Kress, Integral Equations in Scattering Theory (Elsevier, 1983).
  26. C. Macaskill and B. J. Kachoyan, “Iterative approach for the numerical simulation of scattering from one- and two-dimensional rough surfaces,” Appl. Opt.32(15), 2839–2847 (1993). [CrossRef] [PubMed]
  27. G. Soriano and M. Saillard, “Scattering of electromagnetic waves from two-dimensional rough surfaces with an impedance approximation,” J. Opt. Soc. Am. A18(1), 124–133 (2001). [CrossRef] [PubMed]
  28. K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media11(1), 1–30 (2001). [CrossRef]
  29. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).
  30. C. Amra, C. Grèzes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt.32(28), 5492–5503 (1993). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited