Abstract

This work quantifies the polarization persistence and memory of circularly polarized light in forward-scattering and isotropic (Rayleigh regime) environments; and for the first time, details the evolution of both circularly and linearly polarized states through scattering environments. Circularly polarized light persists through a larger number of scattering events longer than linearly polarized light for all forward-scattering environments; but not for scattering in the Rayleigh regime. Circular polarization’s increased persistence occurs for both forward and backscattered light. The simulated environments model polystyrene microspheres in water with particle diameters of 0.1 μm, 2.0 μm, and 3.0 μm. The evolution of the polarization states as they scatter throughout the various environments are illustrated on the Poincaré sphere after one, two, and ten scattering events.

© 2015 Optical Society of America

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References

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  1. G. D. Gilbert and J. C. Pernicka, “Improvement of underwater visibility by reduction of backscatter with a circular polarization technique,” Appl. Opt. 6, 741–746 (1967).
    [Crossref] [PubMed]
  2. G. D. Gilbert, “The effects of particle size on contrast improvement by polarization discrimination for underwater targets,” Appl. Opt. 9, 421–428 (1970).
    [Crossref] [PubMed]
  3. G. D. Lewis, D. L. Jordan, and P. J. Roberts, “Backscattering target detection in a turbid medium by polarization discrimination,” Appl. Opt. 38, 3937–3944 (1999).
    [Crossref]
  4. J. G. Walker, P. C. Chang, and K. I. Hopcraft, “Visibility depth improvement in active polarization imaging in scattering media,” Appl. Opt. 39, 4933–4941 (2000).
    [Crossref]
  5. S. Kartazayeva, X. Ni, and R. Alfano, “Backscattering target detection in a turbid medium by use of circularly and linearly polarized light,” Opt. Lett. 30, 1168–1170 (2005).
    [Crossref] [PubMed]
  6. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
    [Crossref] [PubMed]
  7. J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Detection range enhancement using circularly polarized light in scattering environments for infrared wavelengths,” Appl. Opt. 54, 2266–2274 (2015).
    [Crossref] [PubMed]
  8. J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Range and contrast imaging improvements using circularly polarized light in scattering environments,” Proc. SPIE 8706, 87060R (2013).
    [Crossref]
  9. J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Increasing detection range and minimizing polarization mixing with circularly polarized light through scattering environments,” Proc. SPIE 9099, 909908 (2014).
    [Crossref]
  10. F. MacKintosh, J. Zhu, D. Pine, and D. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
    [Crossref]
  11. M. Xu and R. Alfano, “Circular polarization memory of light,” Phys. Rev. E 72, 065601 (2005).
    [Crossref]
  12. D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
    [Crossref]
  13. A. Ishimaru, S. Jaruwatanadilok, and Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40, 5495–5502 (2001).
    [Crossref]
  14. A. D. Kim and M. Moscoso, “Backscattering of circularly polarized pulses,” Opt. Lett. 27, 1589–1591 (2002).
    [Crossref]
  15. W. Cai, X. Ni, S. Gayen, and R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
    [Crossref]
  16. J. Sorrentini, M. Zerrad, G. Soriano, and C. Amra, “Enpolarization of light by scattering media,” Opt. Express 19, 21313–21320 (2011).
    [Crossref] [PubMed]
  17. G. Soriano, M. Zerrad, and C. Amra, “Enpolarization and depolarization of light scattered from chromatic complex media,” Opt. Express 22, 12603–12613 (2014).
    [Crossref] [PubMed]
  18. 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, 2787–2794 (2013).
    [Crossref] [PubMed]
  19. 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, 14594–14609 (2014).
    [Crossref] [PubMed]
  20. M. Zerrad, J. Sorrentini, G. Soriano, and C. Amra, “Gradual loss of polarization in light scattered from rough surfaces: Electromagnetic prediction,” Opt. Express 18, 15832–15843 (2010).
    [Crossref] [PubMed]
  21. M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
    [Crossref] [PubMed]
  22. 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, 21427–21440 (2014).
    [Crossref] [PubMed]
  23. J. D. van der Laan, D. A. Scrymgeour, J. B. Wright, S. A. Kemme, and E. L. Dereniak, “Increasing persistence through scattering environments by using circularly polarized light,” Proc. SPIE 9465, 94650U (2015).
    [Crossref]
  24. D. Goldstein, Polarized Light, Revised and Expanded (CRC, 2003).
    [Crossref]
  25. W. A. Shurcliff, Polarized Light (Harvard University, 1962).
    [Crossref]
  26. J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13, 10392–10405 (2005).
    [Crossref] [PubMed]
  27. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, Inc., 1983).
  28. H. G. Akarçay, A. Hohmann, A. Kienle, M. Frenz, and J. Rička, “Monte Carlo modeling of polarized light propagation: Stokes vs. Jones. Part I,” Appl. Opt. 53, 7576–7585 (2014).
    [Crossref]
  29. G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Camb. Phil. Soc. 9, 399–416 (1852).

2015 (3)

2014 (5)

2013 (2)

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Range and contrast imaging improvements using circularly polarized light in scattering environments,” Proc. SPIE 8706, 87060R (2013).
[Crossref]

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, 2787–2794 (2013).
[Crossref] [PubMed]

2011 (1)

2010 (1)

2006 (2)

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
[Crossref] [PubMed]

W. Cai, X. Ni, S. Gayen, and R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
[Crossref]

2005 (3)

2002 (1)

2001 (1)

2000 (1)

1999 (1)

1994 (1)

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[Crossref]

1989 (1)

F. MacKintosh, J. Zhu, D. Pine, and D. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[Crossref]

1970 (1)

1967 (1)

1852 (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Camb. Phil. Soc. 9, 399–416 (1852).

Akarçay, H. G.

Alfano, R.

W. Cai, X. Ni, S. Gayen, and R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
[Crossref]

M. Xu and R. Alfano, “Circular polarization memory of light,” Phys. Rev. E 72, 065601 (2005).
[Crossref]

S. Kartazayeva, X. Ni, and R. Alfano, “Backscattering target detection in a turbid medium by use of circularly and linearly polarized light,” Opt. Lett. 30, 1168–1170 (2005).
[Crossref] [PubMed]

Amra, C.

Bicout, D.

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[Crossref]

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, Inc., 1983).

Brosseau, C.

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[Crossref]

Cai, W.

W. Cai, X. Ni, S. Gayen, and R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
[Crossref]

Chang, P. C.

Chenault, D. B.

Dereniak, E. L.

J. D. van der Laan, D. A. Scrymgeour, J. B. Wright, S. A. Kemme, and E. L. Dereniak, “Increasing persistence through scattering environments by using circularly polarized light,” Proc. SPIE 9465, 94650U (2015).
[Crossref]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Detection range enhancement using circularly polarized light in scattering environments for infrared wavelengths,” Appl. Opt. 54, 2266–2274 (2015).
[Crossref] [PubMed]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Increasing detection range and minimizing polarization mixing with circularly polarized light through scattering environments,” Proc. SPIE 9099, 909908 (2014).
[Crossref]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Range and contrast imaging improvements using circularly polarized light in scattering environments,” Proc. SPIE 8706, 87060R (2013).
[Crossref]

Frenz, M.

Gayen, S.

W. Cai, X. Ni, S. Gayen, and R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
[Crossref]

Ghabbach, A.

Gilbert, G. D.

Goldstein, D.

D. Goldstein, Polarized Light, Revised and Expanded (CRC, 2003).
[Crossref]

Goldstein, D. L.

Hohmann, A.

Hopcraft, K. I.

Huffman, D.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, Inc., 1983).

Ishimaru, A.

Jacques, S. L.

Jaruwatanadilok, S.

Jordan, D. L.

Kartazayeva, S.

Kemme, S. A.

J. D. van der Laan, D. A. Scrymgeour, J. B. Wright, S. A. Kemme, and E. L. Dereniak, “Increasing persistence through scattering environments by using circularly polarized light,” Proc. SPIE 9465, 94650U (2015).
[Crossref]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Detection range enhancement using circularly polarized light in scattering environments for infrared wavelengths,” Appl. Opt. 54, 2266–2274 (2015).
[Crossref] [PubMed]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Increasing detection range and minimizing polarization mixing with circularly polarized light through scattering environments,” Proc. SPIE 9099, 909908 (2014).
[Crossref]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Range and contrast imaging improvements using circularly polarized light in scattering environments,” Proc. SPIE 8706, 87060R (2013).
[Crossref]

Kienle, A.

Kim, A. D.

Kuga, Y.

Lewis, G. D.

Liukaityte, S.

MacKintosh, F.

F. MacKintosh, J. Zhu, D. Pine, and D. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[Crossref]

Martinez, A.

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[Crossref]

Moscoso, M.

Ni, X.

W. Cai, X. Ni, S. Gayen, and R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
[Crossref]

S. Kartazayeva, X. Ni, and R. Alfano, “Backscattering target detection in a turbid medium by use of circularly and linearly polarized light,” Opt. Lett. 30, 1168–1170 (2005).
[Crossref] [PubMed]

Pernicka, J. C.

Pine, D.

F. MacKintosh, J. Zhu, D. Pine, and D. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[Crossref]

Prahl, S. A.

Ramella-Roman, J. C.

Ricka, J.

Roberts, P. J.

Schmitt, J.

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[Crossref]

Scrymgeour, D. A.

J. D. van der Laan, D. A. Scrymgeour, J. B. Wright, S. A. Kemme, and E. L. Dereniak, “Increasing persistence through scattering environments by using circularly polarized light,” Proc. SPIE 9465, 94650U (2015).
[Crossref]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Detection range enhancement using circularly polarized light in scattering environments for infrared wavelengths,” Appl. Opt. 54, 2266–2274 (2015).
[Crossref] [PubMed]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Increasing detection range and minimizing polarization mixing with circularly polarized light through scattering environments,” Proc. SPIE 9099, 909908 (2014).
[Crossref]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Range and contrast imaging improvements using circularly polarized light in scattering environments,” Proc. SPIE 8706, 87060R (2013).
[Crossref]

Shaw, J. A.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard University, 1962).
[Crossref]

Soriano, G.

Sorrentini, J.

Stokes, G. G.

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Camb. Phil. Soc. 9, 399–416 (1852).

Tortel, H.

Tyo, J. S.

van der Laan, J. D.

J. D. van der Laan, D. A. Scrymgeour, J. B. Wright, S. A. Kemme, and E. L. Dereniak, “Increasing persistence through scattering environments by using circularly polarized light,” Proc. SPIE 9465, 94650U (2015).
[Crossref]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Detection range enhancement using circularly polarized light in scattering environments for infrared wavelengths,” Appl. Opt. 54, 2266–2274 (2015).
[Crossref] [PubMed]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Increasing detection range and minimizing polarization mixing with circularly polarized light through scattering environments,” Proc. SPIE 9099, 909908 (2014).
[Crossref]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Range and contrast imaging improvements using circularly polarized light in scattering environments,” Proc. SPIE 8706, 87060R (2013).
[Crossref]

Walker, J. G.

Weitz, D.

F. MacKintosh, J. Zhu, D. Pine, and D. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[Crossref]

Wright, J. B.

J. D. van der Laan, D. A. Scrymgeour, J. B. Wright, S. A. Kemme, and E. L. Dereniak, “Increasing persistence through scattering environments by using circularly polarized light,” Proc. SPIE 9465, 94650U (2015).
[Crossref]

Xu, M.

M. Xu and R. Alfano, “Circular polarization memory of light,” Phys. Rev. E 72, 065601 (2005).
[Crossref]

Zerrad, M.

Zhu, J.

F. MacKintosh, J. Zhu, D. Pine, and D. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[Crossref]

Appl. Opt. (8)

G. D. Gilbert and J. C. Pernicka, “Improvement of underwater visibility by reduction of backscatter with a circular polarization technique,” Appl. Opt. 6, 741–746 (1967).
[Crossref] [PubMed]

G. D. Gilbert, “The effects of particle size on contrast improvement by polarization discrimination for underwater targets,” Appl. Opt. 9, 421–428 (1970).
[Crossref] [PubMed]

G. D. Lewis, D. L. Jordan, and P. J. Roberts, “Backscattering target detection in a turbid medium by polarization discrimination,” Appl. Opt. 38, 3937–3944 (1999).
[Crossref]

J. G. Walker, P. C. Chang, and K. I. Hopcraft, “Visibility depth improvement in active polarization imaging in scattering media,” Appl. Opt. 39, 4933–4941 (2000).
[Crossref]

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
[Crossref] [PubMed]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Detection range enhancement using circularly polarized light in scattering environments for infrared wavelengths,” Appl. Opt. 54, 2266–2274 (2015).
[Crossref] [PubMed]

A. Ishimaru, S. Jaruwatanadilok, and Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40, 5495–5502 (2001).
[Crossref]

H. G. Akarçay, A. Hohmann, A. Kienle, M. Frenz, and J. Rička, “Monte Carlo modeling of polarized light propagation: Stokes vs. Jones. Part I,” Appl. Opt. 53, 7576–7585 (2014).
[Crossref]

Opt. Express (8)

J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13, 10392–10405 (2005).
[Crossref] [PubMed]

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

G. Soriano, M. Zerrad, and C. Amra, “Enpolarization and depolarization of light scattered from chromatic complex media,” Opt. Express 22, 12603–12613 (2014).
[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, 2787–2794 (2013).
[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, 14594–14609 (2014).
[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, 15832–15843 (2010).
[Crossref] [PubMed]

M. Zerrad, H. Tortel, G. Soriano, A. Ghabbach, and C. Amra, “Spatial depolarization of light from the bulks: electromagnetic prediction,” Opt. Express 23, 8246–8260 (2015).
[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, 21427–21440 (2014).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. B (1)

F. MacKintosh, J. Zhu, D. Pine, and D. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B 40, 9342–9345 (1989).
[Crossref]

Phys. Rev. E (3)

M. Xu and R. Alfano, “Circular polarization memory of light,” Phys. Rev. E 72, 065601 (2005).
[Crossref]

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E 49, 1767–1770 (1994).
[Crossref]

W. Cai, X. Ni, S. Gayen, and R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
[Crossref]

Proc. SPIE (3)

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Range and contrast imaging improvements using circularly polarized light in scattering environments,” Proc. SPIE 8706, 87060R (2013).
[Crossref]

J. D. van der Laan, D. A. Scrymgeour, S. A. Kemme, and E. L. Dereniak, “Increasing detection range and minimizing polarization mixing with circularly polarized light through scattering environments,” Proc. SPIE 9099, 909908 (2014).
[Crossref]

J. D. van der Laan, D. A. Scrymgeour, J. B. Wright, S. A. Kemme, and E. L. Dereniak, “Increasing persistence through scattering environments by using circularly polarized light,” Proc. SPIE 9465, 94650U (2015).
[Crossref]

Trans. Camb. Phil. Soc. (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Camb. Phil. Soc. 9, 399–416 (1852).

Other (3)

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, Inc., 1983).

D. Goldstein, Polarized Light, Revised and Expanded (CRC, 2003).
[Crossref]

W. A. Shurcliff, Polarized Light (Harvard University, 1962).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 Poincaré Sphere representation of vertical linearly polarized incident light. (Orange sphere represents location.)
Fig. 2
Fig. 2 Scattering profiles for particle sizes of (a) 2.0 μm and (b) 3.0 μm. Perpendicular and parallel incident polarization states scattering are plotted as black and blue curves. For these forward-scattering particles, the blue and black curves are indistinguishable and the blue curves are not visible on the plots.
Fig. 3
Fig. 3 Scattered Stokes parameter values for incident linearly polarized light after (a) 1, (b) 2, and (c) 10 scattering events for a scattering environment consisting of particles with diameter 2.0 μm and an illuminating wavelength of 543.5 nm. This figure shows the first 100,000 photons’ resulting Stokes parameters after each scattering event; forward-scattered photons are shown in red and backscattered photons are shown in blue. The resulting cumulative Stokes state, for the forward or backscattered photons, is shown as large orange or purple spheres.
Fig. 4
Fig. 4 Scattered Stokes parameter values for incident linearly polarized light after (a) 1, (b) 2, and (c) 10 scattering events for a scattering environment consisting of particles with diameter 3.0 μm and an illuminating wavelength of 543.5 nm. This figure shows the first 100,000 photons’ resulting Stokes parameters after each scattering event; forward-scattered photons are shown in red and backscattered photons are shown in blue. The resulting cumulative Stokes state, for the forward or backscattered photons, is shown as large orange or purple spheres.
Fig. 5
Fig. 5 Scattering profile for a particle size of 0.1 μm. Perpendicular and parallel incident polarization states scattering are plotted as a solid black and dashed blue curves.
Fig. 6
Fig. 6 Scattered Stokes parameter values for incident linearly polarized light after (a) 1, (b) 2, and (c) 10 scattering events for a scattering environment consisting of particles with diameter 0.1 μm and an illuminating wavelength of 543.5 nm. This figure shows the first 100,000 photons’ resulting Stokes parameters after each scattering event; forward-scattered photons are shown in red and backscattered photons are shown in blue. The resulting cumulative Stokes state, for the forward or backscattered photons, is shown as large orange or purple spheres.
Fig. 7
Fig. 7 Poincaré sphere representation of right circularly polarized incident light. (Orange sphere represents location.)
Fig. 8
Fig. 8 Scattered Stokes parameter values for incident circularly polarized light after (a) 1, (b) 2, and (c) 10 scattering events for a scattering environment consisting of particles with diameter 0.1 μm and an illuminating wavelength of 543.5 nm. This figure shows the first 100,000 photons’ resulting Stokes parameters after each scattering event; forward-scattered photons are shown in red and backscattered photons are shown in blue. The resulting cumulative Stokes state, for the forward or backscattered photons, is shown as large orange or purple spheres.
Fig. 9
Fig. 9 Cumulative DoP, for forward (x’s) and backscattered (o’s) photons, from circularly (red) and linearly (black) polarized incident polarization states versus number of scattering events. Both linear and circular forward and backscattered photons depolarize rapidly as a function of scattering event. Circularly polarized light is completely depolarized after merely eight scattering events while linear polarization is completely depolarized after fourteen scattering events.
Fig. 10
Fig. 10 Scattered Stokes parameter values for incident circularly polarized light after (a) 1, (b) 2, and (c) 10 scattering events for a scattering environment consisting of particles with diameter 2.0 μm and an illuminating wavelength of 543.5 nm. This figure shows the first 100,000 photons’ resulting Stokes parameters after each scattering event; forward-scattered photons are shown in red and backscattered photons are shown in blue. The resulting cumulative Stokes state, for the forward or backscattered photons, is shown as large orange or purple spheres.
Fig. 11
Fig. 11 Scattered Stokes parameter values for incident circularly polarized light after (a) 1, (b) 2, and (c) 10 scattering events for a scattering environment consisting of particles with diameter 3.0 μm and an illuminating wavelength of 543.5 nm. This figure shows the first 100,000 photons’ resulting Stokes parameters after each scattering event; forward-scattered photons are shown in red and backscattered photons are shown in blue. The resulting cumulative Stokes state, for the forward or backscattered photons, is shown as large orange or purple spheres.
Fig. 12
Fig. 12 Cumulative DoP, for (a) backscattered and (b) forward-scattered photons, from circularly (red) and linearly (black) polarized incident polarization states versus number of scattering events. The two particle sizes are plotted as follows: 2.0 μm is plotted with stars and 3.0 μm is plotted with triangles. Forward and backscattered light from incident circularly polarized light for the forward-scattering environments maintains its DoP and therefore persists through a larger number of scattering events.

Equations (2)

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DoP = S 1 2 + S 2 2 + S 3 2 S 0 .
x = 2 π a n λ 0

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