Abstract

Mueller and Jones matrices have been thoroughly studied as mathematical tools to describe the manipulation of the polarization state of classical light. In particular, the most general physical transformation on the polarization state has been represented as an ensemble of Jones matrices, as iViΦVi. But this has generally been directly assumed without proof by most authors. In this Letter, we derive this expression from simple physical principles and the matrix theory of positive maps.

© 2011 Optical Society of America

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References

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  1. G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).
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  5. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge, 2007).
  6. H. Mueller, J. Opt. Soc. Am. A 38, 661 (A) (1948).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).
  15. M. Born and E. Wolf, Principles of Optics (Cambridge, 1959).
  16. R. Boyd, Nonlinear Optics (Academic, 2003).
  17. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge, 2000).

2010 (1)

B. N. Simon, S. Simon, F. Gori, M. Santasiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901(2010).
[CrossRef] [PubMed]

2000 (1)

1987 (1)

1982 (1)

R. Simon, Opt. Commun. 42, 293 (1982).
[CrossRef]

1980 (1)

M. Choi, J. Oper. Theory 271 (1980).

1975 (1)

M. Choi, Linear Algebra Appl. 10, 285 (1975).
[CrossRef]

1954 (1)

E. Wolf, Nuovo Cimento 12, 884 (1954).
[CrossRef]

1948 (1)

H. Mueller, J. Opt. Soc. Am. A 38, 661 (A) (1948).

1941 (1)

1930 (1)

N. Wiener, Acta Math. 55, 117 (1930).
[CrossRef]

1852 (1)

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).

Borghi, R.

B. N. Simon, S. Simon, F. Gori, M. Santasiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901(2010).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge, 1959).

Boyd, R.

R. Boyd, Nonlinear Optics (Academic, 2003).

Brosseau, C.

C. Brosseau, Fundamentals of Polarized light: a Statistical Optics Approach (Wiley-Interscience, 1998).

Choi, M.

M. Choi, J. Oper. Theory 271 (1980).

M. Choi, Linear Algebra Appl. 10, 285 (1975).
[CrossRef]

Chuang, I.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge, 2000).

Gil, J. J.

Gori, F.

B. N. Simon, S. Simon, F. Gori, M. Santasiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901(2010).
[CrossRef] [PubMed]

Jones, R. C.

Kim, K.

Mandel, L.

K. Kim, L. Mandel, and E. Wolf, J. Opt. Soc. Am. A 4, 433(1987).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).

Mueller, H.

H. Mueller, J. Opt. Soc. Am. A 38, 661 (A) (1948).

Mukunda, N.

B. N. Simon, S. Simon, F. Gori, M. Santasiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901(2010).
[CrossRef] [PubMed]

Nielsen, M.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge, 2000).

Santasiero, M.

B. N. Simon, S. Simon, F. Gori, M. Santasiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901(2010).
[CrossRef] [PubMed]

Simon, B. N.

B. N. Simon, S. Simon, F. Gori, M. Santasiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901(2010).
[CrossRef] [PubMed]

Simon, R.

B. N. Simon, S. Simon, F. Gori, M. Santasiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901(2010).
[CrossRef] [PubMed]

R. Simon, Opt. Commun. 42, 293 (1982).
[CrossRef]

Simon, S.

B. N. Simon, S. Simon, F. Gori, M. Santasiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901(2010).
[CrossRef] [PubMed]

Stokes, G. G.

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).

Wiener, N.

N. Wiener, Acta Math. 55, 117 (1930).
[CrossRef]

Wolf, E.

K. Kim, L. Mandel, and E. Wolf, J. Opt. Soc. Am. A 4, 433(1987).
[CrossRef]

E. Wolf, Nuovo Cimento 12, 884 (1954).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Cambridge, 1959).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge, 2007).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).

Acta Math. (1)

N. Wiener, Acta Math. 55, 117 (1930).
[CrossRef]

J. Oper. Theory (1)

M. Choi, J. Oper. Theory 271 (1980).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Linear Algebra Appl. (1)

M. Choi, Linear Algebra Appl. 10, 285 (1975).
[CrossRef]

Nuovo Cimento (1)

E. Wolf, Nuovo Cimento 12, 884 (1954).
[CrossRef]

Opt. Commun. (1)

R. Simon, Opt. Commun. 42, 293 (1982).
[CrossRef]

Phys. Rev. Lett. (1)

B. N. Simon, S. Simon, F. Gori, M. Santasiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901(2010).
[CrossRef] [PubMed]

Trans. Cambridge Philos. Soc. (1)

G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).

Other (6)

C. Brosseau, Fundamentals of Polarized light: a Statistical Optics Approach (Wiley-Interscience, 1998).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge, 2007).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).

M. Born and E. Wolf, Principles of Optics (Cambridge, 1959).

R. Boyd, Nonlinear Optics (Academic, 2003).

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge, 2000).

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Equations (14)

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

Φ i j = E i E j * , i = 1 , 2 ,
S μ = T r [ Φ σ μ ] = Φ i j σ j i μ ,
Φ = 1 2 S μ σ μ ,
E i = T i j E j .
Φ = T Φ T .
S μ = M μ ν S ν ,
M μ ν = 1 2 T r [ σ μ T σ ν T ] ,
= A ( T T * ) A 1 = 1 2 A ( T T * ) A ,
A = [ 1 0 0 1 1 0 0 1 0 1 1 0 0 i i 0 ] .
Φ = e p e T e Φ T e ,
M μ ν = e p e 1 2 T r [ σ μ T e σ ν T e ] = e p e M μ ν ( e ) ,
E j ( t ) = { E ˜ j ( ω ) e i ω t d ω t 0 E j ( t ) t > 0 .
F ( Φ ) = i V i Φ V i + j W j Φ t W j ,
F ( Φ ) = i V i Φ V i .

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