Abstract

A tridimensional pseudo-spectral time domain (3D-PSTD) algorithm, that solves the full-wave Maxwell’s equations by using Fourier transforms to calculate the spatial derivatives, has been applied to determine the time characteristics of the propagation of electromagnetic waves in inhomogeneous media. Since the 3D simulation gives access to the full-vector components of the electromagnetic fields, it allowed us to analyse the polarization state of the scattered light with respect to the characteristics of the scattering medium and the polarization state of the incident light. We show that, while the incident light is strongly depolarized on the whole, the light that reaches the output face of the scattering medium is much less depolarized. This fact is consistent with our recently reported experimental results, where a rotation of the polarization does not preclude the restoration of an image by phase conjugation.

© 2013 OSA

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References

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  1. F. Devaux and E. Lantz, “Real time suppression of turbidity of biological tissues in motion by three-wave mixing phase conjugation,” J. of Biomed. Opt.18, 111405 (2013).
    [CrossRef]
  2. X. Wang, L. V. Wang, C.W. Sun, and C.C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiements,” J. of Biomed. Opt.8, 608–617 (2003).
    [CrossRef]
  3. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Transactions on Antennas and Propagation14, 302–307 (1966).
    [CrossRef]
  4. Q. H. Liu, “The PSTD algorithm: a time-domain method requiring only two cells per wavelength,” Microw. Opt. Technol. Lett.15, 158–165 (1997).
    [CrossRef]
  5. Z. Tang and Q. H. Liu, “The 2.5D FDTD and Fourier PSTD methods and applications,” Microw. Opt. Technol. Lett.36, 430–436 (2003).
    [CrossRef]
  6. T. W. Lee and S. C. Hagness, “Pseudospectral time-domain methods for modeling optical wave propagation in second-order nonlinear materials,” J. Opt. Soc. Am. B21, 330–342 (2004).
    [CrossRef]
  7. X. Liu and Y. Chen, “Applications of transformed-space non-uniform PSTD (TSNU-PSTD) in scattering analysis with the use of the non-uniform FFT,” Microw. Opt. Technol. Lett.38, 16–21 (2003).
    [CrossRef]
  8. C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Transfer113, 1728–1740 (2012).
    [CrossRef]
  9. S. H. Tseng, A. Taflove, D. Maitland, and V. Backman, “Pseudospectral time simulations of mutiple light scattering in three-dimensional macroscopic random media,” Radio Science41, RS4009 (2006).
    [CrossRef]
  10. C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudospectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express20, 16763–16776 (2012).
    [CrossRef]
  11. S. H. Tseng and C. Yang, “2-D PSTD simulation of optical phase conjugation for turbidity suppression,” Opt. Express15, 1605–1616 (2007).
    [CrossRef]
  12. S. H. Tseng, “PSTD simulation of optical phase conjugation of light propagating long optical paths,” Opt. Express17, 5490–5495 (2009).
    [CrossRef] [PubMed]
  13. Q. H. liu and G. Zhao, “Review of PSTD methods for transient electromagnetics,” Int. J. Numer. Model.17, 299–323 (2004).
    [CrossRef]
  14. J. -P. Berenger, “A perfect matched layer for the absorption of electromagnetic waves,” J. Comput. Phys.114, 185–200 (1994).
    [CrossRef]
  15. W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations,” Microw. Opt. Technol. Lett.7, 599–604 (1994).
    [CrossRef]
  16. Z. Li, “The optimal spatially-smoothed source patterns for the pseudospectral time-domain method,” IEEE Transactions on Antennas and Propagation58, 227–229 (2010).
    [CrossRef]
  17. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983 Chap. 4, pp. 82–129).
  18. M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt.28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  19. L. H. Wang, S. L. Jacques, and L. Q. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Computer Methods and Programs in Biomedicine47, 131–146 (1995).
    [CrossRef]
  20. N. Curry, P. Bondareff, M. Leclerq, N. K. Van Hulst, R. Sapienza, S. Gigan, and S. Grésillon, “Direct determination of diffusion properties of random media from speckle contrast,” Opt. Lett.36, 3332–3334 (2011).
    [CrossRef] [PubMed]
  21. R. Landauer and M. Büttiker, “Diffusive traversal time: Effective area in magnetically induced interference,” Phys. Rev. B36, 6255–6210 (1987).
    [CrossRef]
  22. 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. E49, 1767–1770 (1994).
    [CrossRef]
  23. F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B40, 9342–9345 (1989).
    [CrossRef]
  24. M. Cui, E. J. McDowell, and C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett.95, 123702 (2009).
    [CrossRef] [PubMed]

2013 (1)

F. Devaux and E. Lantz, “Real time suppression of turbidity of biological tissues in motion by three-wave mixing phase conjugation,” J. of Biomed. Opt.18, 111405 (2013).
[CrossRef]

2012 (2)

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Transfer113, 1728–1740 (2012).
[CrossRef]

C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudospectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express20, 16763–16776 (2012).
[CrossRef]

2011 (1)

2010 (1)

Z. Li, “The optimal spatially-smoothed source patterns for the pseudospectral time-domain method,” IEEE Transactions on Antennas and Propagation58, 227–229 (2010).
[CrossRef]

2009 (2)

M. Cui, E. J. McDowell, and C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett.95, 123702 (2009).
[CrossRef] [PubMed]

S. H. Tseng, “PSTD simulation of optical phase conjugation of light propagating long optical paths,” Opt. Express17, 5490–5495 (2009).
[CrossRef] [PubMed]

2007 (1)

S. H. Tseng and C. Yang, “2-D PSTD simulation of optical phase conjugation for turbidity suppression,” Opt. Express15, 1605–1616 (2007).
[CrossRef]

2006 (1)

S. H. Tseng, A. Taflove, D. Maitland, and V. Backman, “Pseudospectral time simulations of mutiple light scattering in three-dimensional macroscopic random media,” Radio Science41, RS4009 (2006).
[CrossRef]

2004 (2)

2003 (3)

X. Wang, L. V. Wang, C.W. Sun, and C.C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiements,” J. of Biomed. Opt.8, 608–617 (2003).
[CrossRef]

Z. Tang and Q. H. Liu, “The 2.5D FDTD and Fourier PSTD methods and applications,” Microw. Opt. Technol. Lett.36, 430–436 (2003).
[CrossRef]

X. Liu and Y. Chen, “Applications of transformed-space non-uniform PSTD (TSNU-PSTD) in scattering analysis with the use of the non-uniform FFT,” Microw. Opt. Technol. Lett.38, 16–21 (2003).
[CrossRef]

1997 (1)

Q. H. Liu, “The PSTD algorithm: a time-domain method requiring only two cells per wavelength,” Microw. Opt. Technol. Lett.15, 158–165 (1997).
[CrossRef]

1995 (1)

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Computer Methods and Programs in Biomedicine47, 131–146 (1995).
[CrossRef]

1994 (3)

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. E49, 1767–1770 (1994).
[CrossRef]

J. -P. Berenger, “A perfect matched layer for the absorption of electromagnetic waves,” J. Comput. Phys.114, 185–200 (1994).
[CrossRef]

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations,” Microw. Opt. Technol. Lett.7, 599–604 (1994).
[CrossRef]

1989 (2)

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B40, 9342–9345 (1989).
[CrossRef]

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt.28, 2331–2336 (1989).
[CrossRef] [PubMed]

1987 (1)

R. Landauer and M. Büttiker, “Diffusive traversal time: Effective area in magnetically induced interference,” Phys. Rev. B36, 6255–6210 (1987).
[CrossRef]

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Transactions on Antennas and Propagation14, 302–307 (1966).
[CrossRef]

Backman, V.

S. H. Tseng, A. Taflove, D. Maitland, and V. Backman, “Pseudospectral time simulations of mutiple light scattering in three-dimensional macroscopic random media,” Radio Science41, RS4009 (2006).
[CrossRef]

Berenger, J. -P.

J. -P. Berenger, “A perfect matched layer for the absorption of electromagnetic waves,” J. Comput. Phys.114, 185–200 (1994).
[CrossRef]

Bi, L.

Bicout, D.

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. E49, 1767–1770 (1994).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983 Chap. 4, pp. 82–129).

Bondareff, P.

Brosseau, C.

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. E49, 1767–1770 (1994).
[CrossRef]

Büttiker, M.

R. Landauer and M. Büttiker, “Diffusive traversal time: Effective area in magnetically induced interference,” Phys. Rev. B36, 6255–6210 (1987).
[CrossRef]

Chance, B.

Chen, Y.

X. Liu and Y. Chen, “Applications of transformed-space non-uniform PSTD (TSNU-PSTD) in scattering analysis with the use of the non-uniform FFT,” Microw. Opt. Technol. Lett.38, 16–21 (2003).
[CrossRef]

Chew, W. C.

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations,” Microw. Opt. Technol. Lett.7, 599–604 (1994).
[CrossRef]

Cui, M.

M. Cui, E. J. McDowell, and C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett.95, 123702 (2009).
[CrossRef] [PubMed]

Curry, N.

Devaux, F.

F. Devaux and E. Lantz, “Real time suppression of turbidity of biological tissues in motion by three-wave mixing phase conjugation,” J. of Biomed. Opt.18, 111405 (2013).
[CrossRef]

Gigan, S.

Grésillon, S.

Hagness, S. C.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983 Chap. 4, pp. 82–129).

Jacques, S. L.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Computer Methods and Programs in Biomedicine47, 131–146 (1995).
[CrossRef]

Landauer, R.

R. Landauer and M. Büttiker, “Diffusive traversal time: Effective area in magnetically induced interference,” Phys. Rev. B36, 6255–6210 (1987).
[CrossRef]

Lantz, E.

F. Devaux and E. Lantz, “Real time suppression of turbidity of biological tissues in motion by three-wave mixing phase conjugation,” J. of Biomed. Opt.18, 111405 (2013).
[CrossRef]

Leclerq, M.

Lee, T. W.

Li, Z.

Z. Li, “The optimal spatially-smoothed source patterns for the pseudospectral time-domain method,” IEEE Transactions on Antennas and Propagation58, 227–229 (2010).
[CrossRef]

Liu, C.

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Transfer113, 1728–1740 (2012).
[CrossRef]

C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudospectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express20, 16763–16776 (2012).
[CrossRef]

liu, Q. H.

Q. H. liu and G. Zhao, “Review of PSTD methods for transient electromagnetics,” Int. J. Numer. Model.17, 299–323 (2004).
[CrossRef]

Z. Tang and Q. H. Liu, “The 2.5D FDTD and Fourier PSTD methods and applications,” Microw. Opt. Technol. Lett.36, 430–436 (2003).
[CrossRef]

Q. H. Liu, “The PSTD algorithm: a time-domain method requiring only two cells per wavelength,” Microw. Opt. Technol. Lett.15, 158–165 (1997).
[CrossRef]

Liu, X.

X. Liu and Y. Chen, “Applications of transformed-space non-uniform PSTD (TSNU-PSTD) in scattering analysis with the use of the non-uniform FFT,” Microw. Opt. Technol. Lett.38, 16–21 (2003).
[CrossRef]

MacKintosh, F. C.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B40, 9342–9345 (1989).
[CrossRef]

Maitland, D.

S. H. Tseng, A. Taflove, D. Maitland, and V. Backman, “Pseudospectral time simulations of mutiple light scattering in three-dimensional macroscopic random media,” Radio Science41, RS4009 (2006).
[CrossRef]

martinez, A. S.

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. E49, 1767–1770 (1994).
[CrossRef]

McDowell, E. J.

M. Cui, E. J. McDowell, and C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett.95, 123702 (2009).
[CrossRef] [PubMed]

Panetta, R. L.

C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudospectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express20, 16763–16776 (2012).
[CrossRef]

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Transfer113, 1728–1740 (2012).
[CrossRef]

Patterson, M. S.

Pine, D. J.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B40, 9342–9345 (1989).
[CrossRef]

Sapienza, R.

Schmitt, J. M.

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. E49, 1767–1770 (1994).
[CrossRef]

Sun, C.W.

X. Wang, L. V. Wang, C.W. Sun, and C.C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiements,” J. of Biomed. Opt.8, 608–617 (2003).
[CrossRef]

Taflove, A.

S. H. Tseng, A. Taflove, D. Maitland, and V. Backman, “Pseudospectral time simulations of mutiple light scattering in three-dimensional macroscopic random media,” Radio Science41, RS4009 (2006).
[CrossRef]

Tang, Z.

Z. Tang and Q. H. Liu, “The 2.5D FDTD and Fourier PSTD methods and applications,” Microw. Opt. Technol. Lett.36, 430–436 (2003).
[CrossRef]

Tseng, S. H.

S. H. Tseng, “PSTD simulation of optical phase conjugation of light propagating long optical paths,” Opt. Express17, 5490–5495 (2009).
[CrossRef] [PubMed]

S. H. Tseng and C. Yang, “2-D PSTD simulation of optical phase conjugation for turbidity suppression,” Opt. Express15, 1605–1616 (2007).
[CrossRef]

S. H. Tseng, A. Taflove, D. Maitland, and V. Backman, “Pseudospectral time simulations of mutiple light scattering in three-dimensional macroscopic random media,” Radio Science41, RS4009 (2006).
[CrossRef]

Van Hulst, N. K.

Wang, L. H.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Computer Methods and Programs in Biomedicine47, 131–146 (1995).
[CrossRef]

Wang, L. V.

X. Wang, L. V. Wang, C.W. Sun, and C.C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiements,” J. of Biomed. Opt.8, 608–617 (2003).
[CrossRef]

Wang, X.

X. Wang, L. V. Wang, C.W. Sun, and C.C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiements,” J. of Biomed. Opt.8, 608–617 (2003).
[CrossRef]

Weedon, W. H.

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations,” Microw. Opt. Technol. Lett.7, 599–604 (1994).
[CrossRef]

Weitz, D. A.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B40, 9342–9345 (1989).
[CrossRef]

Wilson, B. C.

Yang, C.

M. Cui, E. J. McDowell, and C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett.95, 123702 (2009).
[CrossRef] [PubMed]

S. H. Tseng and C. Yang, “2-D PSTD simulation of optical phase conjugation for turbidity suppression,” Opt. Express15, 1605–1616 (2007).
[CrossRef]

Yang, C.C.

X. Wang, L. V. Wang, C.W. Sun, and C.C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiements,” J. of Biomed. Opt.8, 608–617 (2003).
[CrossRef]

Yang, P.

C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudospectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express20, 16763–16776 (2012).
[CrossRef]

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Transfer113, 1728–1740 (2012).
[CrossRef]

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Transactions on Antennas and Propagation14, 302–307 (1966).
[CrossRef]

Yurkin, M. A.

Zhao, G.

Q. H. liu and G. Zhao, “Review of PSTD methods for transient electromagnetics,” Int. J. Numer. Model.17, 299–323 (2004).
[CrossRef]

Zheng, L. Q.

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Computer Methods and Programs in Biomedicine47, 131–146 (1995).
[CrossRef]

Zhu, J. X.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B40, 9342–9345 (1989).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Cui, E. J. McDowell, and C. Yang, “Observation of polarization-gate based reconstruction quality improvement during the process of turbidity suppression by optical phase conjugation,” Appl. Phys. Lett.95, 123702 (2009).
[CrossRef] [PubMed]

Computer Methods and Programs in Biomedicine (1)

L. H. Wang, S. L. Jacques, and L. Q. Zheng, “Monte Carlo modeling of photon transport in multi-layered tissues,” Computer Methods and Programs in Biomedicine47, 131–146 (1995).
[CrossRef]

IEEE Transactions on Antennas and Propagation (2)

Z. Li, “The optimal spatially-smoothed source patterns for the pseudospectral time-domain method,” IEEE Transactions on Antennas and Propagation58, 227–229 (2010).
[CrossRef]

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Transactions on Antennas and Propagation14, 302–307 (1966).
[CrossRef]

Int. J. Numer. Model. (1)

Q. H. liu and G. Zhao, “Review of PSTD methods for transient electromagnetics,” Int. J. Numer. Model.17, 299–323 (2004).
[CrossRef]

J. Comput. Phys. (1)

J. -P. Berenger, “A perfect matched layer for the absorption of electromagnetic waves,” J. Comput. Phys.114, 185–200 (1994).
[CrossRef]

J. of Biomed. Opt. (2)

F. Devaux and E. Lantz, “Real time suppression of turbidity of biological tissues in motion by three-wave mixing phase conjugation,” J. of Biomed. Opt.18, 111405 (2013).
[CrossRef]

X. Wang, L. V. Wang, C.W. Sun, and C.C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiements,” J. of Biomed. Opt.8, 608–617 (2003).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Quant. Spectrosc. Transfer (1)

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Transfer113, 1728–1740 (2012).
[CrossRef]

Microw. Opt. Technol. Lett. (4)

Q. H. Liu, “The PSTD algorithm: a time-domain method requiring only two cells per wavelength,” Microw. Opt. Technol. Lett.15, 158–165 (1997).
[CrossRef]

Z. Tang and Q. H. Liu, “The 2.5D FDTD and Fourier PSTD methods and applications,” Microw. Opt. Technol. Lett.36, 430–436 (2003).
[CrossRef]

X. Liu and Y. Chen, “Applications of transformed-space non-uniform PSTD (TSNU-PSTD) in scattering analysis with the use of the non-uniform FFT,” Microw. Opt. Technol. Lett.38, 16–21 (2003).
[CrossRef]

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations,” Microw. Opt. Technol. Lett.7, 599–604 (1994).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (2)

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, “Polarization memory of multiply scattered light,” Phys. Rev. B40, 9342–9345 (1989).
[CrossRef]

R. Landauer and M. Büttiker, “Diffusive traversal time: Effective area in magnetically induced interference,” Phys. Rev. B36, 6255–6210 (1987).
[CrossRef]

Phys. Rev. E (1)

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. E49, 1767–1770 (1994).
[CrossRef]

Radio Science (1)

S. H. Tseng, A. Taflove, D. Maitland, and V. Backman, “Pseudospectral time simulations of mutiple light scattering in three-dimensional macroscopic random media,” Radio Science41, RS4009 (2006).
[CrossRef]

Other (1)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983 Chap. 4, pp. 82–129).

Supplementary Material (1)

» Media 1: AVI (2679 KB)     

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Figures (9)

Fig. 1
Fig. 1

(a) Section along the xz plane of the sampled volume. (b) Example of a scattering medium modelized by dielectric spheres randomly embedded in a homogeneous dielectric medium.

Fig. 2
Fig. 2

(a)–(d) Single-frame excerpts from the video ( Media 1) recording, in the xz plane and at the times 0, 70, 120 and 170 fs, the propagation of the 27 fs pulse in a scattering medium with βs = 7%. (a) The white contours show the locations and the shapes of the particles in the considered xz plane of the medium. (b)–(d) The white dotted lines represent the boundaries of the scattering medium. (e) Corresponding profiles along the z axis of the pulse intensity integrated in the (x, y) transverse plane.

Fig. 3
Fig. 3

Comparison of the time-shapes of the transmitted pulse given by the PSTD algorithm (green curves), Monte-Carlo simulations (cyan curves) and analytical transmittance convolved by the input pulse shape (red curves) for different values of N s *. The x-axis is graduated in optical pathlength units. The blue curves represent the input pulse and the vertical dotted lines correspond to the optical length of the scattering medium.

Fig. 4
Fig. 4

Normalized intensity of the output speckle pattern obtained with a 3 l s * scattering medium. The contrast is C = 0.21.

Fig. 5
Fig. 5

Time-integrated components of the local Stokes vector and the local degree of polarization (DOP) of the light transmitted through a 2 l s * scattering medium. Stokes parameters are normalized by the peak intensity of the speckle pattern.

Fig. 6
Fig. 6

Histograms of the time-integrated local Stokes parameters and of the DOP for different values of N s *.

Fig. 7
Fig. 7

Time variation of the space-integrated components of the Stokes vector for the different media. x-axes are graduated in optical pathlength units.

Fig. 8
Fig. 8

(a) Time variation of the time and space integrated DOP for the different media. (b)–(d) Time integrated local DOP at different time for the 2 l s * medium. The vertical black dotted line represents the optical pathlength through the homogeneous medium.

Fig. 9
Fig. 9

Comparison of the time variations of the space integrated Stokes parameters (I, Q) or (I, V), respectively for linearly (blue lines) or circularly (red lines) polarized incident pulses for scattering media with volume concentrations (a) βs = 7% and (b) βs = 9%. (c) Time variation of the space integrated linear and circular degrees of polarization when the incident light is, respectively, linearly and circularly polarized with βs =7, 9, 10 and 12 %.

Tables (3)

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Table 1 Scattering coefficients with respect to the volume concentrations βs of the dielectric spheres.

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Table 2 Comparison of the contrasts of the speckle patterns calculated with different methods and for different values of N s *.

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Table 3 Average values and standard deviations of the space and time-integrated local Stokes parameter Q and DOP.

Equations (10)

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{ D x t = D x y t + D x z t = 1 μ 0 [ B z y B y z ] E x = D x ε B x t = B x y t + B x z t = E z y + E y z
{ A z y } j k l { F y 1 ( 2 i π ν y F y ( A z ) ) } j k l ,
{ D x | j k l n + 1 = D x y | j k l n + 1 2 + Δ t μ 0 F y 1 ( 2 i π ν y F y ( B z | j k l n ) ) 1 + Δ t γ y | j k l + D x z | j k l n + 1 2 Δ t μ 0 F z 1 ( 2 i π ν z F z ( B y | j k l n ) ) 1 + Δ t γ z | j k l E x | j k l n + 1 = D x | j k l n + 1 ɛ j k l B x | j k l n + 1 B x y | j k l n 1 2 Δ t F y 1 ( 2 i π ν y F y ( E z | j k l n ) ) 1 + Δ t γ y | j k l + B x z | j k l n + 1 2 + Δ t F z 1 ( 2 i π ν z F z ( E y | j k l n ) ) 1 + Δ t γ z | j k l
{ D x z | j k l n + 1 2 = D x z | j k l n + S x | j k l n D y z | j k l n + 1 2 = D y z | j k l n + S y | j k l n
{ S x | j k l n = S 0 | j k l cos ψ e i ( ω n Δ t + φ x ) e ( n Δ t t 0 ) 2 2 σ t 2 S y | j k l n = S 0 | j k l sin ψ e i ( ω n Δ t + φ y ) e ( n Δ t t 0 ) 2 2 σ t 2
{ B x z | j k l n + 1 2 = B x z | j k l n μ 0 ε j k l S y | j k l n B y z | j k l n + 1 2 = B x z | j k l n + μ 0 ε j k l S x | j k l n
T ( t ) = ( 4 π D ν ) 1 2 t 3 2 × e μ a v t × { ( d l s * ) e ( d l s * ) 2 4 D v t ( d + l s * ) e ( d + l s * ) 2 4 D v t + ( 3 d l s * ) e ( 3 d l s * ) 2 4 D v t ( 3 d + l s * ) e ( 3 d + l s * ) 2 4 D v t }
C ~ τ l τ s
I | j k n = E x | j k n E x * | j k n + E y | j k n E y * | j k n Q | j k n = E x | j k n E x * | j k n E y | j k n E y * | j k n U | j k n = E x | j k n E y * | j k n + E x * | j k n E y | j k n V | j k n = i ( E x | j k n E y * | j k n E x * | j k n E y | j k n )
D O P = Q 2 + U 2 + V 2 I

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