Abstract

Experimental results on light depolarization due to multimode scattering are reported. By means of polarization tomography, we characterize the depolarizing power and the polarization entropy of a broad class of optically scattering media and confirm the recently predicted universal behavior of these two quantities [Phys. Rev. Lett. 94, 090406 (2005) ].

© 2005 Optical Society of America

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References

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  1. A. Aiello and J. P. Woerdman, Phys. Rev. Lett. 94, 090406 (2005).
    [CrossRef]
  2. F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron. 21, 109 (1997).
    [CrossRef]
  3. D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).
  4. G. Puentes, D. Voigt, A. Aiello, and J. P. Woerdman, “Depolarizing power and polarization entropy of light scattering media:?experiment and theory,” arXiv:physics/0412096 (2004).
  5. D. G. M. Anderson and R. Barakat, J. Opt. Soc. Am. A 11, 2305 (1994).
    [CrossRef]
  6. C.-H. Lin, A. Ying-Guey Fuh, T.-S. Mo, and C.-Y. Huang, Jpn. J. Appl. Phys. 41, 7441 (2002).
    [CrossRef]
  7. T. Okamoto and T. Asakura, Wave Motion 3, 211 (1993).
  8. J. Zubia and J. Arrue, Opt. Fiber Technol. 7, 101 (2001).
    [CrossRef]
  9. C. Koeppen, R. F. Shi, W. D. Chen, and A. F. Garito, J. Opt. Soc. Am. B 15, 727 (1998).
    [CrossRef]
  10. C. Emslie, J. Mater. Sci. 23, 2281 (1988).
    [CrossRef]
  11. M. Legré, M. Wegmüller, and N. Gisin, Phys. Rev. Lett. 91, 167902 (2003).
    [CrossRef]

2005 (1)

A. Aiello and J. P. Woerdman, Phys. Rev. Lett. 94, 090406 (2005).
[CrossRef]

2003 (1)

M. Legré, M. Wegmüller, and N. Gisin, Phys. Rev. Lett. 91, 167902 (2003).
[CrossRef]

2002 (1)

C.-H. Lin, A. Ying-Guey Fuh, T.-S. Mo, and C.-Y. Huang, Jpn. J. Appl. Phys. 41, 7441 (2002).
[CrossRef]

2001 (1)

J. Zubia and J. Arrue, Opt. Fiber Technol. 7, 101 (2001).
[CrossRef]

1998 (1)

1997 (1)

F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron. 21, 109 (1997).
[CrossRef]

1994 (1)

1993 (1)

T. Okamoto and T. Asakura, Wave Motion 3, 211 (1993).

1988 (1)

C. Emslie, J. Mater. Sci. 23, 2281 (1988).
[CrossRef]

Aiello, A.

A. Aiello and J. P. Woerdman, Phys. Rev. Lett. 94, 090406 (2005).
[CrossRef]

Anderson, D. G. M.

Arrue, J.

J. Zubia and J. Arrue, Opt. Fiber Technol. 7, 101 (2001).
[CrossRef]

Asakura, T.

T. Okamoto and T. Asakura, Wave Motion 3, 211 (1993).

Barakat, R.

Chen, W. D.

Emslie, C.

C. Emslie, J. Mater. Sci. 23, 2281 (1988).
[CrossRef]

Fuh, A. Ying-Guey

C.-H. Lin, A. Ying-Guey Fuh, T.-S. Mo, and C.-Y. Huang, Jpn. J. Appl. Phys. 41, 7441 (2002).
[CrossRef]

Garito, A. F.

Gisin, N.

M. Legré, M. Wegmüller, and N. Gisin, Phys. Rev. Lett. 91, 167902 (2003).
[CrossRef]

Huang, C.-Y.

C.-H. Lin, A. Ying-Guey Fuh, T.-S. Mo, and C.-Y. Huang, Jpn. J. Appl. Phys. 41, 7441 (2002).
[CrossRef]

Kliger, D. S.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Koeppen, C.

Le Jeune, B.

F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron. 21, 109 (1997).
[CrossRef]

Le Roy-Brehonnet, F.

F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron. 21, 109 (1997).
[CrossRef]

Legré, M.

M. Legré, M. Wegmüller, and N. Gisin, Phys. Rev. Lett. 91, 167902 (2003).
[CrossRef]

Lewis, J. W.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Lin, C.-H.

C.-H. Lin, A. Ying-Guey Fuh, T.-S. Mo, and C.-Y. Huang, Jpn. J. Appl. Phys. 41, 7441 (2002).
[CrossRef]

Mo, T.-S.

C.-H. Lin, A. Ying-Guey Fuh, T.-S. Mo, and C.-Y. Huang, Jpn. J. Appl. Phys. 41, 7441 (2002).
[CrossRef]

Okamoto, T.

T. Okamoto and T. Asakura, Wave Motion 3, 211 (1993).

Randall, C. E.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

Shi, R. F.

Wegmüller, M.

M. Legré, M. Wegmüller, and N. Gisin, Phys. Rev. Lett. 91, 167902 (2003).
[CrossRef]

Woerdman, J. P.

A. Aiello and J. P. Woerdman, Phys. Rev. Lett. 94, 090406 (2005).
[CrossRef]

Zubia, J.

J. Zubia and J. Arrue, Opt. Fiber Technol. 7, 101 (2001).
[CrossRef]

J. Mater. Sci. (1)

C. Emslie, J. Mater. Sci. 23, 2281 (1988).
[CrossRef]

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

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

Jpn. J. Appl. Phys. (1)

C.-H. Lin, A. Ying-Guey Fuh, T.-S. Mo, and C.-Y. Huang, Jpn. J. Appl. Phys. 41, 7441 (2002).
[CrossRef]

Opt. Fiber Technol. (1)

J. Zubia and J. Arrue, Opt. Fiber Technol. 7, 101 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

M. Legré, M. Wegmüller, and N. Gisin, Phys. Rev. Lett. 91, 167902 (2003).
[CrossRef]

A. Aiello and J. P. Woerdman, Phys. Rev. Lett. 94, 090406 (2005).
[CrossRef]

Prog. Quantum Electron. (1)

F. Le Roy-Brehonnet and B. Le Jeune, Prog. Quantum Electron. 21, 109 (1997).
[CrossRef]

Wave Motion (1)

T. Okamoto and T. Asakura, Wave Motion 3, 211 (1993).

Other (2)

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, 1990).

G. Puentes, D. Voigt, A. Aiello, and J. P. Woerdman, “Depolarizing power and polarization entropy of light scattering media:?experiment and theory,” arXiv:physics/0412096 (2004).

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Figures (2)

Fig. 1
Fig. 1

Schematic of the polarization tomography setup. A polarizer unit (PU) consisting of a fixed polarizer (P1), a half-wave plate (H1), and a quarter-wave plate (Q1) prepares the polarization input state. A microscope objective (MO) couples the light into the sample. The scattered light is collimated by a photographic objective (PO). An adjustable diaphragm (D) defines the amount of transverse spatial average to be performed at the detector. The analyzer unit (AU) consists of a quarter-wave plate (Q2) and a polarizer (P2). A lens (L) focuses the light coming from P2 into a photodiode (PD).

Fig. 2
Fig. 2

Measured polarization entropy ( E M ) versus index of depolarization ( D M ) for all samples. The theoretically possible parameter range in the ( E M , D M ) plane is indicated by the gray area. Solid curves corresponds to analytical boundaries predicted by theory. Cusp points are A = ( 0 , 1 ) , B = ( 1 3 , log 4 3 ) , C = ( 1 3 , 1 2 ) , and D = ( 1 , 0 ) .[1] Details of samples: (a) Dynamic samples, polystyrene microspheres suspended in water ( 2 μ m diameter, Duke Scientific); milk diluted in water (fat particles 2 3 μ m , Ref. [7]); sugar in watery microspheres suspension; polymer-dispersed liquid crystal (column thicknesses 2 mm , 0.1 mm , and 10 μ m , nematic liquid crystal E7,[6] chiral dope CB15, Merck). (b) Static samples, polymer sheet diffusers ( 100 μ m thick, Zenith, SphereOptics Hoffman); holographic light-shaping diffusers (diffusing full angle α = 0.5 ° , 1°, 5°, and 10°, Physical Optics); Quartz-wedge/Lyot depolarizers[3] (Halbo Optics); step-index polymer optical fiber ( N.A. = 0.55 , core diameters 250, 500, and 750 μ m ESKA CK type, Mitsubishi Rayon); step-index glass optical fiber, ( N.A. = 0.48 , core diameters 200, 400, and 600 μ m FT-x-URT type, Thorlabs); step-index glass optical fiber ( N.A. = 0.22 , core diameter 50 μ m ASF50 type, Thorlabs); graded-index glass optical fiber ( N.A. = 0.27 , core diameter 62.5 μ m , GIF625 type, Thorlabs).

Equations (3)

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H = 1 4 μ , ν 0 , 3 M μ ν ( σ μ σ ν * ) ,
E M = ν = 0 3 λ ν log 4 ( λ ν ) , D M = [ 1 3 ( 4 ν = 0 3 λ ν 2 1 ) ] 1 2 .
M eff = j = 1 D A ( j ) M J ( j , 1 ) ,

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