Abstract

We analyze an apparent disagreement between simulational and experimental results in a recent work of Puentes et al. [Opt. Lett., 30(23):3216, 2005] on the universality in depolarized light scattering. We show that the distribution of experimental points in the allowed region of the index of depolarization versus entropy diagram is ultimately determined by the statistics on the Mueller matrices, rather than on the eigenvalues of an associated Hermitian matrix. We propose a reasonable criterion that distinguishes the class of physically admissible from the physically realizable scattering media. This strategy yields further insight into the depolarization properties of media.

© 2008 Optical Society of America

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References

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  1. D. P. Cubián, L. A. José, R. Diego, and Rentmeesters, “Characterization of depolarizing optical media by means of the entropy factor: application to biological tissues”, Appl. Opt. 44, 358–365 (2005).
    [Crossref]
  2. A. Aiello, G. Puentes, and J. P. Woerdman, “Linear optics and quantum maps”, Phys. Rev. A 76, 032323 (2007).
    [Crossref]
  3. J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system”, J. Mod. Opt. 33, 185–189 (1986).
  4. F. Le Roy-Brehonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties”, Prog. Quantum Electron. 21, 109–151 (1997).
    [Crossref]
  5. G. Puentes, D. Voigt, A. Aiello, and J. P. Woerdman, “Experimental observation of universality in depolarized light scattering”, Opt. Lett. 30, 3216–3218 (2005).
    [Crossref] [PubMed]
  6. A. Aiello and J. P. Woerdman, “Physical bounds to the entropy-depolarization relation in random light scattering”, Phys. Rev. Lett. 94, 090406 (2005).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2007 (1)

A. Aiello, G. Puentes, and J. P. Woerdman, “Linear optics and quantum maps”, Phys. Rev. A 76, 032323 (2007).
[Crossref]

2005 (3)

2002 (1)

A. A. Kokhanovsky and A. R. Jones, “The cross-polarization of light by large non-spherical particles”, J. Phys. D: Appl. Phys. 35, 1903–1906 (2002).
[Crossref]

1999 (1)

J. B. A. Card and A. R. Jones, “An investigation of the potential of polarized light scattering for the characterization of irregular particles”, J. Phys. D: Appl. Phys. 32, 2467–2474 (1999).
[Crossref]

1998 (1)

M. Pozniak, K. Zyczkowski, and M. Kus, “Composed ensembles of random unitary matrices”, J. Phys. A 31, 1059–1071 (1998).
[Crossref]

1997 (1)

F. Le Roy-Brehonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties”, Prog. Quantum Electron. 21, 109–151 (1997).
[Crossref]

1996 (1)

1995 (1)

1994 (1)

1993 (3)

1989 (1)

1986 (2)

J. W. Hovenier, H. C. van de Hulst, and C. V. M. van der Mee, “Conditions for the elements of the scattering matrix”, Astron. Astrophys. 157, 301–310 (1986).

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system”, J. Mod. Opt. 33, 185–189 (1986).

1981 (1)

1942 (1)

F. Perrin, “Polarization of light scattered by opalescent media”, J. Chem. Phys. 10, 415–427 (1942).
[Crossref]

1938 (1)

R. S. Krishnan, “The reciprocity theorem in colloid optics and its generalization”, Proc. Indian Acad. Sci.  fA,21–35 (1938).

1935 (1)

R. S. Krishnan, “Reciprocity theorem in colloid optics”, Proc. Indian Acad. Sci. fA, 782–789 (1935).

1934 (1)

R. S. Krishnan, “Optical evidence for molecular clustering in fluids”, Proc. Indian Acad. Sci. fA, 211–216 (1934).

Aiello, A.

A. Aiello, G. Puentes, and J. P. Woerdman, “Linear optics and quantum maps”, Phys. Rev. A 76, 032323 (2007).
[Crossref]

A. Aiello and J. P. Woerdman, “Physical bounds to the entropy-depolarization relation in random light scattering”, Phys. Rev. Lett. 94, 090406 (2005).
[Crossref] [PubMed]

G. Puentes, D. Voigt, A. Aiello, and J. P. Woerdman, “Experimental observation of universality in depolarized light scattering”, Opt. Lett. 30, 3216–3218 (2005).
[Crossref] [PubMed]

Anderson, D. G. M.

Barakat, R.

Bernabeu, E.

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system”, J. Mod. Opt. 33, 185–189 (1986).

Brosseau, C.

Card, J. B. A.

J. B. A. Card and A. R. Jones, “An investigation of the potential of polarized light scattering for the characterization of irregular particles”, J. Phys. D: Appl. Phys. 32, 2467–2474 (1999).
[Crossref]

Chipman, R. A.

Cubián, D. P.

Diego, R.

Fry, E. S.

Gil, J. J.

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system”, J. Mod. Opt. 33, 185–189 (1986).

Givens, C. R.

Glatter, O.

Hofer, M.

Hovenier, J. W.

J. W. Hovenier, H. C. van de Hulst, and C. V. M. van der Mee, “Conditions for the elements of the scattering matrix”, Astron. Astrophys. 157, 301–310 (1986).

Jones, A. R.

A. A. Kokhanovsky and A. R. Jones, “The cross-polarization of light by large non-spherical particles”, J. Phys. D: Appl. Phys. 35, 1903–1906 (2002).
[Crossref]

J. B. A. Card and A. R. Jones, “An investigation of the potential of polarized light scattering for the characterization of irregular particles”, J. Phys. D: Appl. Phys. 32, 2467–2474 (1999).
[Crossref]

José, L. A.

Kattawar, G. W.

Kokhanovsky, A. A.

A. A. Kokhanovsky and A. R. Jones, “The cross-polarization of light by large non-spherical particles”, J. Phys. D: Appl. Phys. 35, 1903–1906 (2002).
[Crossref]

Kotinski, A. B.

Krishnan, R. S.

R. S. Krishnan, “The reciprocity theorem in colloid optics and its generalization”, Proc. Indian Acad. Sci.  fA,21–35 (1938).

R. S. Krishnan, “Reciprocity theorem in colloid optics”, Proc. Indian Acad. Sci. fA, 782–789 (1935).

R. S. Krishnan, “Optical evidence for molecular clustering in fluids”, Proc. Indian Acad. Sci. fA, 211–216 (1934).

Kus, M.

M. Pozniak, K. Zyczkowski, and M. Kus, “Composed ensembles of random unitary matrices”, J. Phys. A 31, 1059–1071 (1998).
[Crossref]

Le Jeune, B.

F. Le Roy-Brehonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties”, Prog. Quantum Electron. 21, 109–151 (1997).
[Crossref]

Le Roy-Brehonnet, F.

F. Le Roy-Brehonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties”, Prog. Quantum Electron. 21, 109–151 (1997).
[Crossref]

Lu, S.

Luna, R. E.

Macke, A.

McClain, W. M.

A. Shi and W. M. McClain, “Closed-form Mueller scattering matrix for a random ensemble of long, thin cylinders”, J. Chem. Phys. 98, 1695–1711 (1993).
[Crossref]

Méndez, E. R.

Navarrette, A. G.

Perrin, F.

F. Perrin, “Polarization of light scattered by opalescent media”, J. Chem. Phys. 10, 415–427 (1942).
[Crossref]

Pozniak, M.

M. Pozniak, K. Zyczkowski, and M. Kus, “Composed ensembles of random unitary matrices”, J. Phys. A 31, 1059–1071 (1998).
[Crossref]

Puentes, G.

Rentmeesters,

Shi, A.

A. Shi and W. M. McClain, “Closed-form Mueller scattering matrix for a random ensemble of long, thin cylinders”, J. Chem. Phys. 98, 1695–1711 (1993).
[Crossref]

van de Hulst, H. C.

J. W. Hovenier, H. C. van de Hulst, and C. V. M. van der Mee, “Conditions for the elements of the scattering matrix”, Astron. Astrophys. 157, 301–310 (1986).

van der Mee, C. V. M.

J. W. Hovenier, H. C. van de Hulst, and C. V. M. van der Mee, “Conditions for the elements of the scattering matrix”, Astron. Astrophys. 157, 301–310 (1986).

Voigt, D.

Woerdman, J. P.

A. Aiello, G. Puentes, and J. P. Woerdman, “Linear optics and quantum maps”, Phys. Rev. A 76, 032323 (2007).
[Crossref]

A. Aiello and J. P. Woerdman, “Physical bounds to the entropy-depolarization relation in random light scattering”, Phys. Rev. Lett. 94, 090406 (2005).
[Crossref] [PubMed]

G. Puentes, D. Voigt, A. Aiello, and J. P. Woerdman, “Experimental observation of universality in depolarized light scattering”, Opt. Lett. 30, 3216–3218 (2005).
[Crossref] [PubMed]

Zyczkowski, K.

M. Pozniak, K. Zyczkowski, and M. Kus, “Composed ensembles of random unitary matrices”, J. Phys. A 31, 1059–1071 (1998).
[Crossref]

Appl. Opt. (4)

Astron. Astrophys. (1)

J. W. Hovenier, H. C. van de Hulst, and C. V. M. van der Mee, “Conditions for the elements of the scattering matrix”, Astron. Astrophys. 157, 301–310 (1986).

J. Chem. Phys. (2)

F. Perrin, “Polarization of light scattered by opalescent media”, J. Chem. Phys. 10, 415–427 (1942).
[Crossref]

A. Shi and W. M. McClain, “Closed-form Mueller scattering matrix for a random ensemble of long, thin cylinders”, J. Chem. Phys. 98, 1695–1711 (1993).
[Crossref]

J. Mod. Opt. (1)

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system”, J. Mod. Opt. 33, 185–189 (1986).

J. Opt. Soc. Am. A (4)

J. Phys. A (1)

M. Pozniak, K. Zyczkowski, and M. Kus, “Composed ensembles of random unitary matrices”, J. Phys. A 31, 1059–1071 (1998).
[Crossref]

J. Phys. D: Appl. Phys. (2)

J. B. A. Card and A. R. Jones, “An investigation of the potential of polarized light scattering for the characterization of irregular particles”, J. Phys. D: Appl. Phys. 32, 2467–2474 (1999).
[Crossref]

A. A. Kokhanovsky and A. R. Jones, “The cross-polarization of light by large non-spherical particles”, J. Phys. D: Appl. Phys. 35, 1903–1906 (2002).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (1)

A. Aiello, G. Puentes, and J. P. Woerdman, “Linear optics and quantum maps”, Phys. Rev. A 76, 032323 (2007).
[Crossref]

Phys. Rev. Lett. (1)

A. Aiello and J. P. Woerdman, “Physical bounds to the entropy-depolarization relation in random light scattering”, Phys. Rev. Lett. 94, 090406 (2005).
[Crossref] [PubMed]

Proc. Indian Acad. Sci. (3)

R. S. Krishnan, “The reciprocity theorem in colloid optics and its generalization”, Proc. Indian Acad. Sci.  fA,21–35 (1938).

R. S. Krishnan, “Optical evidence for molecular clustering in fluids”, Proc. Indian Acad. Sci. fA, 211–216 (1934).

R. S. Krishnan, “Reciprocity theorem in colloid optics”, Proc. Indian Acad. Sci. fA, 782–789 (1935).

Prog. Quantum Electron. (1)

F. Le Roy-Brehonnet and B. Le Jeune, “Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties”, Prog. Quantum Electron. 21, 109–151 (1997).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1.

(a) Numerical simulation of the physically accessible region in the plane D M ×E M . The points were obtained from an ensemble of uniformly distributed eigenvalues λ. The analytical expressions for the boundaries curves can be be found in [6]. (b) Experimental results obtained by G. Puentes et al. in Opt. Lett. 30, 3216 (2005) for the depolarization properties of a broad class of optically scattering media.

Fig. 2.
Fig. 2.

Scattering geometry. A monochromatic light beam propagating along the z axis is scattered by a medium located in its path. The observed scattering direction and the z axis define the scattering plane. The scattered “horizontal” and “vertical” polarization directions H and V are defined as the directions perpendicular and parallel to the scattering plane, respectively, both perpendicular to the scattering direction.

Fig. 3.
Fig. 3.

Depolarization properties of an ensemble of randomly oriented non-spherical microscopic particles. D M is the index of depolarization of the medium and E M the entropy of the medium. After obtaining a set of physically acceptable Mueller matrices we post select the results according to (a) physically realizable matrices as specified by the cross-polarization ratio criterion; both ρ h ≤1 and ρ v ≤1. (b) Matrices for media with “anomalous depolarization”, that is, ρ h >1 and ρ v >1.

Fig. 4.
Fig. 4.

Numerical simulations of the depolarization properties of random Mueller matrices obtained according to the polar decomposition criterion (see text). (a) Singular values of the submatrix mΔ are all equal, a=b=c, and nonnegative. We impose further restrictions: (b) modulus of the polarizance vector |p|≤0.1, (c) diattenuation vector|d|≤0.1 and (d) diattenuation vector |d|≥0.9.

Equations (14)

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H = 1 4 i , j = 0 3 M ij ( σ i σ j * ) ,
E M = i = 0 3 λ i log 4 ( λ i ) ,
D M = [ ( 4 i = 0 4 λ i 2 1 ) 3 ] 1 2 .
S 0 = M 00 S 0 + M 01 S 1 + M 02 S 2 + M 03 S 3 ,
S 1 = M 10 S 0 + M 11 S 1 + M 12 S 2 + M 13 S 3 ,
S 2 = M 20 S 0 + M 21 S 1 + M 22 S 2 + M 23 S 3 ,
S 3 = M 30 S 0 + M 31 S 1 + M 32 S 2 + M 33 S 3 ,
M = [ M 00 M 01 0 0 M 01 M 11 0 0 0 0 M 22 M 23 0 0 M 23 M 33 ] .
ρ h = V h H h and ρ v = H v V v
ρ h = 1 m 11 1 + 2 m 01 + m 11 and ρ v = 1 m 11 1 2 m 01 + m 11 .
M = ( 1 d T p m ) ,
M R = ( 1 0 T 0 m R ) , M D = ( 1 d T d m d ) and M Δ = ( 1 0 T p m Δ ) .
M = M R M Δ diag M R T M R M D ,
= M R M Δ diag M R M D .

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