Abstract

The purpose of this Communication is to derive a generalized trace condition for a Mueller–Jones polarization matrix that is based on the Brosseau–Barakat [ Opt. Commun. 84, 127 ( 1991)] analysis of the effects of fluctuations in a linear scattering medium on a polarized wave field. The expression developed contains the previously known trace condition for a deterministic optical system as a special case.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. D. Abhyankar, A. L. Fymat, “Relations between the elements of the phase matrix for scattering,”J. Math. Phys. 10, 1935–1938 (1969).
    [CrossRef]
  2. E. Fry, G. Kattawar, “Relationships between elements of the Stokes matrix,” Appl. Opt. 20, 2811–2814 (1981).
    [CrossRef] [PubMed]
  3. R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller–Jones transfer matrix of polarization optics,” Opt. Commun. 38, 159–161 (1981).
    [CrossRef]
  4. R. Simon, “Mueller matrices and depolarization criteria,” J. Mod. Opt. 34, 569–575 (1987). See also R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
    [CrossRef]
  5. J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 15, 301–310 (1986).
  6. J. Gil, E. Bernabeu, “A depolarization criterion in Mueller matrices,” Opt. Acta 32, 259–261 (1985).
    [CrossRef]
  7. K. Kim, L. Mandel, E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. A 4, 433–437 (1987).
    [CrossRef]
  8. A. B. Kostinski, C. R. Givens, J. M. Kwiatkowski, “Constraints on Mueller matrices of polarization optics,” Appl. Opt. 32, 1646–1651 (1993).
    [CrossRef] [PubMed]
  9. C. Brosseau, “Analysis of experimental data for Mueller polarization matrices,” Optik 85, 83–86 (1990). See also C. Brosseau, “Polarization transfer in non-depolarizing optical linear media,” Optik 85, 190–193 (1990).
  10. R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990). This paper is concerned with the important fact that the class of linear optical devices that cannot decrease the degree of polarization of the light that has passed through these systems is not the same as the class of systems derivable from Jones matrices.
    [CrossRef]
  11. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).
  12. R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987).
    [CrossRef]
  13. C. Brosseau, R. Barakat, “Jones and Mueller matrices for random media,” Opt. Commun. 84, 127–132 (1991).
    [CrossRef]
  14. C. Brosseau, “Distribution of Stokes parameters in a random linear scattering,” J. Mod. Opt. 39, 1167–1171 (1992).
    [CrossRef]
  15. A. B. Kostinski, “Depolarization criterion for incoherent scattering,” Appl. Opt. 31, 3506–3508 (1992).
    [CrossRef] [PubMed]
  16. D. Bicout, C. Brosseau, “Multiply scattered waves through a spatially random medium: entropy production and depolarization,”J. Phys. I (Paris) 2, 2047–2063 (1992).

1993 (1)

1992 (3)

A. B. Kostinski, “Depolarization criterion for incoherent scattering,” Appl. Opt. 31, 3506–3508 (1992).
[CrossRef] [PubMed]

D. Bicout, C. Brosseau, “Multiply scattered waves through a spatially random medium: entropy production and depolarization,”J. Phys. I (Paris) 2, 2047–2063 (1992).

C. Brosseau, “Distribution of Stokes parameters in a random linear scattering,” J. Mod. Opt. 39, 1167–1171 (1992).
[CrossRef]

1991 (1)

C. Brosseau, R. Barakat, “Jones and Mueller matrices for random media,” Opt. Commun. 84, 127–132 (1991).
[CrossRef]

1990 (2)

C. Brosseau, “Analysis of experimental data for Mueller polarization matrices,” Optik 85, 83–86 (1990). See also C. Brosseau, “Polarization transfer in non-depolarizing optical linear media,” Optik 85, 190–193 (1990).

R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990). This paper is concerned with the important fact that the class of linear optical devices that cannot decrease the degree of polarization of the light that has passed through these systems is not the same as the class of systems derivable from Jones matrices.
[CrossRef]

1987 (3)

R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987).
[CrossRef]

R. Simon, “Mueller matrices and depolarization criteria,” J. Mod. Opt. 34, 569–575 (1987). See also R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
[CrossRef]

K. Kim, L. Mandel, E. Wolf, “Relationship between Jones and Mueller matrices for random media,” J. Opt. Soc. Am. A 4, 433–437 (1987).
[CrossRef]

1986 (1)

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 15, 301–310 (1986).

1985 (1)

J. Gil, E. Bernabeu, “A depolarization criterion in Mueller matrices,” Opt. Acta 32, 259–261 (1985).
[CrossRef]

1981 (2)

R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller–Jones transfer matrix of polarization optics,” Opt. Commun. 38, 159–161 (1981).
[CrossRef]

E. Fry, G. Kattawar, “Relationships between elements of the Stokes matrix,” Appl. Opt. 20, 2811–2814 (1981).
[CrossRef] [PubMed]

1969 (1)

K. D. Abhyankar, A. L. Fymat, “Relations between the elements of the phase matrix for scattering,”J. Math. Phys. 10, 1935–1938 (1969).
[CrossRef]

Abhyankar, K. D.

K. D. Abhyankar, A. L. Fymat, “Relations between the elements of the phase matrix for scattering,”J. Math. Phys. 10, 1935–1938 (1969).
[CrossRef]

Barakat, R.

C. Brosseau, R. Barakat, “Jones and Mueller matrices for random media,” Opt. Commun. 84, 127–132 (1991).
[CrossRef]

R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987).
[CrossRef]

R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller–Jones transfer matrix of polarization optics,” Opt. Commun. 38, 159–161 (1981).
[CrossRef]

Bernabeu, E.

J. Gil, E. Bernabeu, “A depolarization criterion in Mueller matrices,” Opt. Acta 32, 259–261 (1985).
[CrossRef]

Bicout, D.

D. Bicout, C. Brosseau, “Multiply scattered waves through a spatially random medium: entropy production and depolarization,”J. Phys. I (Paris) 2, 2047–2063 (1992).

Brosseau, C.

D. Bicout, C. Brosseau, “Multiply scattered waves through a spatially random medium: entropy production and depolarization,”J. Phys. I (Paris) 2, 2047–2063 (1992).

C. Brosseau, “Distribution of Stokes parameters in a random linear scattering,” J. Mod. Opt. 39, 1167–1171 (1992).
[CrossRef]

C. Brosseau, R. Barakat, “Jones and Mueller matrices for random media,” Opt. Commun. 84, 127–132 (1991).
[CrossRef]

C. Brosseau, “Analysis of experimental data for Mueller polarization matrices,” Optik 85, 83–86 (1990). See also C. Brosseau, “Polarization transfer in non-depolarizing optical linear media,” Optik 85, 190–193 (1990).

Fry, E.

Fymat, A. L.

K. D. Abhyankar, A. L. Fymat, “Relations between the elements of the phase matrix for scattering,”J. Math. Phys. 10, 1935–1938 (1969).
[CrossRef]

Gil, J.

J. Gil, E. Bernabeu, “A depolarization criterion in Mueller matrices,” Opt. Acta 32, 259–261 (1985).
[CrossRef]

Givens, C. R.

Hovenier, J. W.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 15, 301–310 (1986).

Kattawar, G.

Kim, K.

Kostinski, A. B.

Kwiatkowski, J. M.

Mandel, L.

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).

Simon, R.

R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990). This paper is concerned with the important fact that the class of linear optical devices that cannot decrease the degree of polarization of the light that has passed through these systems is not the same as the class of systems derivable from Jones matrices.
[CrossRef]

R. Simon, “Mueller matrices and depolarization criteria,” J. Mod. Opt. 34, 569–575 (1987). See also R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
[CrossRef]

van de Hulst, H. C.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 15, 301–310 (1986).

van der Mee, C. V. M.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 15, 301–310 (1986).

Wolf, E.

Appl. Opt. (3)

Astron. Astrophys. (1)

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, “Conditions for the elements of the scattering matrix,” Astron. Astrophys. 15, 301–310 (1986).

J. Math. Phys. (1)

K. D. Abhyankar, A. L. Fymat, “Relations between the elements of the phase matrix for scattering,”J. Math. Phys. 10, 1935–1938 (1969).
[CrossRef]

J. Mod. Opt. (3)

R. Simon, “Mueller matrices and depolarization criteria,” J. Mod. Opt. 34, 569–575 (1987). See also R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42, 293–297 (1982).
[CrossRef]

C. Brosseau, “Distribution of Stokes parameters in a random linear scattering,” J. Mod. Opt. 39, 1167–1171 (1992).
[CrossRef]

R. Barakat, “Conditions for the physical realizability of polarization matrices characterizing passive systems,” J. Mod. Opt. 34, 1535–1544 (1987).
[CrossRef]

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

J. Phys. I (Paris) (1)

D. Bicout, C. Brosseau, “Multiply scattered waves through a spatially random medium: entropy production and depolarization,”J. Phys. I (Paris) 2, 2047–2063 (1992).

Opt. Acta (1)

J. Gil, E. Bernabeu, “A depolarization criterion in Mueller matrices,” Opt. Acta 32, 259–261 (1985).
[CrossRef]

Opt. Commun. (3)

R. Barakat, “Bilinear constraints between elements of the 4 × 4 Mueller–Jones transfer matrix of polarization optics,” Opt. Commun. 38, 159–161 (1981).
[CrossRef]

C. Brosseau, R. Barakat, “Jones and Mueller matrices for random media,” Opt. Commun. 84, 127–132 (1991).
[CrossRef]

R. Simon, “Nondepolarizing systems and degree of polarization,” Opt. Commun. 77, 349–354 (1990). This paper is concerned with the important fact that the class of linear optical devices that cannot decrease the degree of polarization of the light that has passed through these systems is not the same as the class of systems derivable from Jones matrices.
[CrossRef]

Optik (1)

C. Brosseau, “Analysis of experimental data for Mueller polarization matrices,” Optik 85, 83–86 (1990). See also C. Brosseau, “Polarization transfer in non-depolarizing optical linear media,” Optik 85, 190–193 (1990).

Other (1)

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (34)

Equations on this page are rendered with MathJax. Learn more.

M J = A ( J × J * ) A - 1 ,
A = [ 1 0 0 1 1 0 0 - 1 0 1 1 0 0 - i i 0 ] .
( M J ) k l = ½ tr ( σ k J σ l J + ) = m k l ,
tr ( M J T M J ) = [ tr ( J + J ) ] 2 ,
tr ( M J T M J ) = 4 m 00 2 ,
I ( t ) = I D ( t ) + I R ( t ) .
I R ( t ) = 0 ,
I ( t ) = I D ( t ) .
E o ( t ; T ) = - [ I D ( t - t ) + I R ( t - t ) ] E i ( t ; T ) d t ,
E o ( ω ; T ) = J D ( ω ) E i ( ω ; T ) + J R ( ω ) E i ( ω ; T ) = J ( ω ) E i ( ω ; T ) .
S o ( ω ) = M J ( ω ) S i ( ω ) ,
S o ( ω ) = M J ( ω ) S i ( ω ) = M J ( ω ) S i ( ω ) .
M J = A ( J D × J D * ) A - 1 + A ( J R × J R * ) A - 1 + A ( J D × J R * ) A - 1 + A ( J R × J D * ) A - 1 .
M J = A ( J D × J D * ) A - 1 + A J R × J R * A - 1 M J ( D ) + M J ( R ) .
M J = Θ D + Θ R + Θ 3 + Θ 4 ,
Θ D = A ( J D × J D * ) A - 1 ,
Θ R = A ( J R × J R * ) A - 1 ,
Θ 3 = A ( J D × J R * ) A - 1 ,
Θ 4 = A ( J R × J D * ) A - 1 .
M J T M J = Θ D + Θ D + Θ R + Θ R + Θ 3 + Θ 3 + Θ 4 + Θ 4 + Θ D + Θ R + Θ R + Θ D + Θ D + Θ 3 + Θ 3 + Θ D + Θ D + Θ 4 + Θ 4 + Θ D + Θ R + Θ 3 + Θ 3 + Θ R + Θ R + Θ 4 + Θ 4 + Θ R + Θ 3 + Θ 4 + Θ 4 + Θ 3 .
Θ R + Θ R = A [ J R + J R × ( J R + J R ) * ] A - 1 = A [ Ω R × ( Ω R ) * ] A - 1 ,
Θ 3 + Θ 3 = A [ Ω D × ( Ω R ) * ] A - 1 ,
Θ 4 + Θ 4 = A [ Ω R × ( Ω D ) * ] A - 1 ,
Θ D + Θ R + Θ R + Θ D = A [ Ω D R × ( Ω D R ) * + Ω D R + × ( Ω D R + ) * ] A - 1 ,
Θ 3 + Θ 4 + Θ 4 + Θ 3 = A [ Ω D R × ( Ω D R + ) * + Ω D R + × ( Ω D R ) * ] A - 1 ,
Ω D J D + J D ,
Ω R J R + J R ,
Ω D R J D + J R = Ω R D + .
tr M J T M J = tr ( Ω D × Ω D * ) + tr Ω R × Ω R * + tr Ω D × Ω R * + tr Ω R × Ω D * + tr Ω D R × ( Ω D R ) * + Ω D R + × ( Ω D R + ) * + tr Ω D R × ( Ω D R + ) * + Ω D R + × Ω D R * .
tr M J T M J = 4 m 00 2 = [ tr ( J D + J D ) ] 2 + [ tr ( J R + J R ) ] 2 + 4 { Re [ tr ( J D + J R ) ] } 2 + 2 tr ( J D + J D ) tr ( J R + J R )
tr ( M J T M J ) = [ tr ( J D + J D ) ] 2 + 2 tr ( J D + J R ) 2 + tr ( J R × J R * + J R × J R * ) .
tr ( M J T M J ) = tr ( Ω D ) 2 = [ tr ( J D + J D ) ] 2 .
tr ( M J T M J ) [ tr ( J D + J D ) ] 2 = tr [ ( M J ( D ) ) T M J ( D ) ] .
J D [ 1 0 0 1 ]

Metrics