Abstract

We formulate a framework to extend the idea of Berry’s topological phase to multiple light scattering, and in particular to backscattering of linearly polarized light. We show that the randomization of the geometric Berry’s phases in the medium leads to a loss of the polarization degree of the light, i.e., to a depolarization. We use Monte Carlo simulations in which Berry’s phase is calculated for each photon path. Then we average over the distribution of the geometric phases to calculate the form of the patterns, which we compare with experimental patterns formed by backscattered light between crossed or parallel polarizers.

© 2004 Optical Society of America

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References

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  1. M. Dogariu and T. Asakura, Opt. Eng. 35, 2234 (1996).
    [CrossRef]
  2. S. Bartel and A. Hielscher, Appl. Opt. 39, 1580 (2000).
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  3. M. J. Rakovic, G. W. Kattawar, M. Mehrubeoglu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cot, Appl. Opt. 38, 3399 (1999).
    [CrossRef]
  4. M. V. Berry, Nature 326, 277 (1987).
    [CrossRef]
  5. A. Tomita and R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
    [CrossRef] [PubMed]
  6. R. Bhandari, Phys. Rep. 281, 1 (1997).
    [CrossRef]
  7. V. Rossetto and A. C. Maggs, Eur. Phys. J. B 29, 323 (2002).
    [CrossRef]
  8. I. Freund and E. Barkai, J. Opt. Soc. Am. A 8, 1559 (1991).
    [CrossRef]
  9. E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. France 49, 77 (1988).
    [CrossRef]
  10. L. F. Rojas, D. Lacoste, P. Schurtenberger, R. Lenke, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A (to be published).
  11. D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, Phys. Rev. E 49, 1767 (1994).
    [CrossRef]
  12. A. D. Kim and J. B. Keller, J. Opt. Soc. Am. A 20, 92 (2003).
    [CrossRef]
  13. S. M. Rytov, C. R. Acad. Sci. 18, 263 (1938).
  14. J. P. Bouchaud, J. Phys. I 7, 985 (1991).

2003 (1)

2002 (1)

V. Rossetto and A. C. Maggs, Eur. Phys. J. B 29, 323 (2002).
[CrossRef]

2000 (1)

1999 (1)

1997 (1)

R. Bhandari, Phys. Rep. 281, 1 (1997).
[CrossRef]

1996 (1)

M. Dogariu and T. Asakura, Opt. Eng. 35, 2234 (1996).
[CrossRef]

1994 (1)

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, Phys. Rev. E 49, 1767 (1994).
[CrossRef]

1991 (2)

1988 (1)

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. France 49, 77 (1988).
[CrossRef]

1987 (1)

M. V. Berry, Nature 326, 277 (1987).
[CrossRef]

1986 (1)

A. Tomita and R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[CrossRef] [PubMed]

1938 (1)

S. M. Rytov, C. R. Acad. Sci. 18, 263 (1938).

Akkermans, E.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. France 49, 77 (1988).
[CrossRef]

Asakura, T.

M. Dogariu and T. Asakura, Opt. Eng. 35, 2234 (1996).
[CrossRef]

Barkai, E.

Bartel, S.

Berry, M. V.

M. V. Berry, Nature 326, 277 (1987).
[CrossRef]

Bhandari, R.

R. Bhandari, Phys. Rep. 281, 1 (1997).
[CrossRef]

Bicout, D.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, Phys. Rev. E 49, 1767 (1994).
[CrossRef]

Bouchaud, J. P.

J. P. Bouchaud, J. Phys. I 7, 985 (1991).

Brosseau, C.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, Phys. Rev. E 49, 1767 (1994).
[CrossRef]

Cameron, B. D.

Chiao, R. Y.

A. Tomita and R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[CrossRef] [PubMed]

Cot, G. L.

Dogariu, M.

M. Dogariu and T. Asakura, Opt. Eng. 35, 2234 (1996).
[CrossRef]

Freund, I.

Hielscher, A.

Kattawar, G. W.

Keller, J. B.

Kim, A. D.

Lacoste, D.

L. F. Rojas, D. Lacoste, P. Schurtenberger, R. Lenke, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A (to be published).

Lenke, R.

L. F. Rojas, D. Lacoste, P. Schurtenberger, R. Lenke, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A (to be published).

Maggs, A. C.

V. Rossetto and A. C. Maggs, Eur. Phys. J. B 29, 323 (2002).
[CrossRef]

Maret, G.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. France 49, 77 (1988).
[CrossRef]

Martinez, A. S.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, Phys. Rev. E 49, 1767 (1994).
[CrossRef]

Maynard, R.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. France 49, 77 (1988).
[CrossRef]

Mehrubeoglu, M.

Rakovic, M. J.

Rastegar, S.

Rojas, L. F.

L. F. Rojas, D. Lacoste, P. Schurtenberger, R. Lenke, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A (to be published).

Rossetto, V.

V. Rossetto and A. C. Maggs, Eur. Phys. J. B 29, 323 (2002).
[CrossRef]

Rytov, S. M.

S. M. Rytov, C. R. Acad. Sci. 18, 263 (1938).

Scheffold, F.

L. F. Rojas, D. Lacoste, P. Schurtenberger, R. Lenke, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A (to be published).

Schmitt, J. M.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, Phys. Rev. E 49, 1767 (1994).
[CrossRef]

Schurtenberger, P.

L. F. Rojas, D. Lacoste, P. Schurtenberger, R. Lenke, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A (to be published).

Tomita, A.

A. Tomita and R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[CrossRef] [PubMed]

Wang, L. V.

Wolf, P. E.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. France 49, 77 (1988).
[CrossRef]

Appl. Opt. (2)

C. R. Acad. Sci. (1)

S. M. Rytov, C. R. Acad. Sci. 18, 263 (1938).

Eur. Phys. J. B (1)

V. Rossetto and A. C. Maggs, Eur. Phys. J. B 29, 323 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. France (1)

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. France 49, 77 (1988).
[CrossRef]

J. Phys. I (1)

J. P. Bouchaud, J. Phys. I 7, 985 (1991).

Nature (1)

M. V. Berry, Nature 326, 277 (1987).
[CrossRef]

Opt. Eng. (1)

M. Dogariu and T. Asakura, Opt. Eng. 35, 2234 (1996).
[CrossRef]

Phys. Rep. (1)

R. Bhandari, Phys. Rep. 281, 1 (1997).
[CrossRef]

Phys. Rev. E (1)

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, Phys. Rev. E 49, 1767 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

A. Tomita and R. Y. Chiao, Phys. Rev. Lett. 57, 937 (1986).
[CrossRef] [PubMed]

Other (1)

L. F. Rojas, D. Lacoste, P. Schurtenberger, R. Lenke, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A (to be published).

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Figures (3)

Fig. 1
Fig. 1

Representation of a typical path in a semi-infinite random medium in backscattering. The Frénet frame consists of tangent u, normal n, and binormal b vectors. R denotes the distance between end points, ϕ is the initial angle between polarization vector E and normal n, and Ω is the geometric phase.

Fig. 2
Fig. 2

Distribution of geometric phase Ω for different values of path length s and in the inset variance of the distribution as a function of s/l*.

Fig. 3
Fig. 3

Contrast as a function of R: the crosses were obtained from Monte Carlo simulations by use of Eq. (8), and the squares are experimental values, obtained from an analysis of Stokes parameter Q.

Equations (8)

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I=142S11+S33-S22-14S22+S33cos 4ϕ,
I=142S11-S33+S22-S12×cos 2ϕ+14S22+S33cos 4ϕ,
I=12I01-C cos 4ϕ,
I=12I01+C cos 4ϕ,
Et=c1tnt+c2tbt,
Et=s=-cosϕ+Ωsns+sinϕ+Ωsbs,
IR=Ps,Rdssin22ϕ+Ωs,
CR=1I0RPs,Rdscos2Ωs.

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